Computational Fluid Dynamics Study of Perforated Monopiles

Computational Fluid Dynamics Study of Perforated Monopiles

Mary Kathryn Walker
Florida Institute of Technology, mwalker2022@my.fit.edu

Robert J. Weaver, Ph.D.
Associate Professor
Ocean Engineering and Marine Sciences
Major Advisor


Chungkuk Jin, Ph.D.
Assistant Professor
Ocean Engineering and Marine Sciences


Kelli Z. Hunsucker, Ph.D.
Assistant Professor
Ocean Engineering and Marine Sciences


Richard B. Aronson, Ph.D.
Professor and Department Head
Ocean Engineering and Marine Sciences

Abstract

모노파일은 해상 풍력 터빈 건설에 사용되며 일반적으로 설계 수명은 25~50년입니다. 모노파일은 수명 주기 동안 부식성 염수 환경에 노출되어 구조물을 빠르게 분해하는 전기화학적 산화 공정을 용이하게 합니다. 이 공정은 모노파일을 보호 장벽으로 코팅하고 음극 보호 기술을 구현하여 완화할 수 있습니다.

역사적으로 모노파일 설계자는 파일 내부가 완전히 밀봉되고 전기화학적 부식 공정이 결국 사용 가능한 모든 산소를 소모하여 반응을 중단시킬 것이라고 가정했습니다. 그러나 도관을 위해 파일 벽에 만든 관통부는 종종 누출되어 신선하고 산소화된 물이 내부 공간으로 유입되었습니다.

표준 부식 방지 기술을 보다 효과적으로 적용할 수 있는 산소화된 환경으로 내부 공간을 재고하는 새로운 모노파일 설계가 연구되고 있습니다. 이러한 새로운 모노파일은 간조대 또는 조간대 수준에서 벽에 천공이 있어 신선하고 산소화된 물이 구조물을 통해 흐를 수 있습니다.

이러한 천공은 또한 구조물의 파도 하중을 줄일 수 있습니다. 유체 역학적 하중 감소의 크기는 천공의 크기와 방향에 따라 달라집니다. 이 연구에서는 천공의 크기에 따른 모노파일의 힘 감소 분석에서 전산 유체 역학(CFD)의 적용 가능성을 연구하고 주어진 파도의 접근 각도 변화의 효과를 분석했습니다.

모노파일의 힘 감소를 결정하기 위해 이론적 3D 모델을 제작하여 FLOW-3D® HYDRO를 사용하여 테스트했으며, 천공되지 않은 모노파일을 제어로 사용했습니다. 이론적 데이터를 수집한 후, 동일한 종류의 천공이 있는 물리적 스케일 모델을 파도 탱크를 사용하여 테스트하여 이론적 모델의 타당성을 확인했습니다.

CFD 시뮬레이션은 물리적 모델의 10% 이내, 이전 연구의 5% 이내에 있는 것으로 나타났습니다. 물리적 모델과 시뮬레이션 모델을 검증한 후, 천공의 크기가 파도 하중 감소에 뚜렷한 영향을 미치고 주어진 파도의 접근 각도에 대한 테스트를 수행할 수 있음을 발견했습니다.

접근 각도의 변화는 모노파일을 15°씩 회전하여 시뮬레이션했습니다. 이 논문에 제시된 데이터는 모노파일의 방향이 통계적으로 유의하지 않으며 천공 모노파일의 설계 고려 사항이 되어서는 안 된다는 것을 시사합니다.

또한 파도 하중 감소와 구조적 안정성 사이의 균형을 찾기 위해 천공의 크기와 모양에 대한 연구를 계속하는 것이 좋습니다.

Monopiles are used in the construction of offshore wind turbines and typically have a design life of 25 to 50 years. Over their lifecycle, monopiles are exposed to a corrosive saltwater environment, facilitating a galvanic oxidation process that quickly degrades the structure. This process can be mitigated by coating the monopile in a protective barrier and implementing cathodic protection techniques. Historically, monopile designers assumed the interior of the pile would be completely sealed and the galvanic corrosion process would eventually consume all the available oxygen, halting the reaction. However, penetrations made in the pile wall for conduit often leaked and allowed fresh, oxygenated water to enter the interior space. New monopile designs are being researched that reconsider the interior space as an oxygenated environment where standard corrosion protection techniques can be more effectively applied. These new monopiles have perforations through the wall at intertidal or subtidal levels to allow fresh, oxygenated water to flow through the structure. These perforations can also reduce wave loads on the structure. The magnitude of the hydrodynamic load reduction depends on the size and orientation of the perforations. This research studied the applicability of computational fluid dynamics (CFD) in analysis of force reduction on monopiles in relation to size of a perforation and to analyze the effect of variation in approach angle of a given wave. To determine the force reduction on the monopile, theoretical 3D models were produced and tested using FLOW-3D® HYDRO with an unperforated monopile used as the control. After the theoretical data was collected, physical scale models with the same variety of perforations were tested using a wave tank to determine the validity of the theoretical models. The CFD simulations were found to be within 10% of the physical models and within 5% of previous research. After the physical and simulated models were validated, it was found that the size of the perforations has a distinct impact on the wave load reduction and testing for differing approach angles of a given wave could be conducted. The variation in approach angle was simulated by rotating the monopile in 15° increments. The data presented in this paper suggests that the orientation of the monopile is not statistically significant and should not be a design consideration for perforated monopiles. It is also suggested to continue the study on the size and shape of the perforations to find the balance between wave load reduction and structural stability.

Figure 1: Overview sketch of typical monopile (MP) foundation and transition piece (TP) design with an internal j-tube (Hilbert et al., 2011)
Figure 1: Overview sketch of typical monopile (MP) foundation and transition
piece (TP) design with an internal j-tube (Hilbert et al., 2011)

References
Andersen, J., Abrahamsen, R., Andersen, T., Andersen, M., Baun, T., & Neubauer,
J. (2020). Wave Load Mitigation by Perforation of Monopiles. Journal of
Marine Science and Engineering, 8(5), 352.
https://doi.org/10.3390/jmse8050352
Bakker A. (2008) Lectures on Applied Computational Fluid Dynamics.
www.bakker.org.
Bustamante, A., Vera-Tudela, L., & Kühn, M. (2015). Evaluation of wind farm
effects on fatigue loads of an individual wind turbine at the EnBW baltic 1
offshore wind farm. Journal of Physics: Conference Series, 625, 012020.
https://doi.org/10.1088/1742-6596/625/1/012020
Chakrabarti SK. Hydrodynamics of offshore structures. Springer Verlag;1987.
Christiansen, R. (2020). Living Docks: Structural Implications and Determination
of Force Coefficients of Oyster Mats on Dock Pilings in the Indian River
Lagoon [Master’s Thesis, Florida Institute of Technology].
Clauss, G. (1992). Offshore Structures, Volume 1, Conceptual Design and
Hydromechanics. Springer, London, UK.
COMSOL Multiphysics® v. 6.1. www.comsol.com. COMSOL AB, Stockholm,
Sweden.
Delwiche, A. & Tavares, I. (2017). Retrofit Strategy using Aluminum Anodes for
the Internal section of Windturbine Monopiles. NACE Internation
Corrosion Conference & Expo, Paper no. 8955.
Det Norske Veritas (2014) Fatigue design of offshore steel structures. Norway.
70
Det Norske Veritas (1989). Rules for the Classification of Fixed Offshore
Installations. Technical report, DNV, Hovik, Norway.
DNV. (2011). DNV-RP-C203 Fatigue Design of Offshore Steel Structures (tech.
rep.). http://www.dnv.com
Elger, D. F., LeBret, B. A., Crowe, C. T., & Roberson, J. A. (2022). Engineering
fluid mechanics. John Wiley & Sons, Inc.
FLOW-3D® Version 12.0 Users Manual (2018). FLOW-3D [Computer software].
Santa Fe, NM: Flow Science, Inc. https://www.flow3d.com
Gaertner, Evan, Jennifer Rinker, Latha Sethuraman, Frederik Zahle, Benjamin
Andersen, Garrett Barter, Nikhar Abbas, Fanzhong Meng, Pietro Bortolotti,
Witold Skrzypinski, George Scott, Roland Feil, Henrik Bredmose,
Katherine Dykes, Matt Shields, Christopher Allen, and Anthony Viselli.
(2020). Definition of the IEA 15-Megawatt Offshore Reference Wind.
Golden, CO: National Renewable Energy Laboratory. NREL/TP-5000-

  1. https://www.nrel.gov/docs/fy20osti/75698.pdf
    Goodisman, Jerry (2001). “Observations on Lemon Cells”. Journal of Chemical
    Education. 78 (4): 516–518. Bibcode:2001JChEd..78..516G.
    doi:10.1021/ed078p516. Goodisman notes that many chemistry textbooks
    use an incorrect model for a cell with zinc and copper electrodes in an
    acidic electrolyte
    Hilbert, L.R. & Black, Anders & Andersen, F. & Mathiesen, Troels. (2011).
    Inspection and monitoring of corrosion inside monopile foundations for
    offshore wind turbines. European Corrosion Congress 2011, EUROCORR
  2. 3. 2187-2201.
    H. J. Landau, “Sampling, data transmission, and the Nyquist rate,” in Proceedings
    of the IEEE, vol. 55, no. 10, pp. 1701-1706, Oct. 1967, doi:
    10.1109/PROC.1967.5962.
    71
    Journee, J. M., and W. W. Massie. Offshore Hydrodynamics, First Edition.
    Delft University of Technology, 2001.
    Keulegan, G. H., and L. H. Carpenter. “Forces on Cylinders and Plates in an
    Oscillating Fluid.” Journal of Research of the National Bureau of
    Standards, vol. 60, no. 5, 1958, pp. 423–40.
    Lahlou, O. (2019). Experimental and Numerical Analysis of the Drag Force on
    Surfboards with Different Shapes (thesis).
    L. H. Holthuijsen. Waves in Oceanic and Coastal Waters. Cam-bridge University
    Press, 2007. doi:10.1017/cbo9780511618536.
    MacCamy, R.C., Fuchs, R.A.: Wave Forces on Piles: a Diffraction Theory. Corps
    of Engineers Washington DC Beach Erosion Board (1954)
    M. M. Maher and G. Swain, “The Corrosion and Biofouling Characteristics of
    Sealed vs. Perforated Offshore Monopile Interiors Experiment Design
    Comparing Corrosion and Environment Inside Steel Pipe,” OCEANS 2018
    MTS/IEEE Charleston, Charleston, SC, USA, 2018, pp. 1-4, doi:
    10.1109/OCEANS.2018.8604522.
    Morison, J. R.; O’Brien, M. P.; Johnson, J. W.; Schaaf, S. A. (1950), “The force
    exerted by surface waves on piles”, Petroleum Transactions, American
    Institute of Mining Engineers, 189 (5): 149–154, doi:10.2118/950149-G
    Paluzzi, Alexander John, “Effects of Perforations on Internal Cathodic Protection
    and Recruitment of Marine Organisms to Steel Pipes” (2023). Theses and
    Dissertations. 1403. https://repository.fit.edu/etd/1403
    Ploeg, J.V.D. (2021). Perforation of monopiles to reduce hydrodynamic loads and
    enable use in deep waters [Master’s Thesis, Delft University of
    Technology] Institutional Repository at Delft University of Technology.
    http://resolver.tudelft.nl/uuid:91eada6f-4f2b-4ae6-be59-2b5ff0590c6f.
    72
    Shi, W., Zhang, S., Michailides, C., Zhang, L., Zhang, P., & Li, X. (2023).
    Experimental investigation of the hydrodynamic effects of breaking waves
    on monopiles in model scale. Journal of Marine Science and Technology,
    28(1), 314–325. https://doi.org/10.1007/s00773-023-00926-9
    Santamaria Gonzalez, G.A. (2023) Advantages and Challenges of Perforated
    Monopiles in Deep Water Sites [Master’s Thesis, Delft University of
    Technology] Institutional Repository at Delft University of Technology.
    http://resolver.tudelft.nl/uuid:490791b6-a912-4bac-a007-f77012c01107
    Sarpkaya, T. and Isaacson, M. (1981). Mechanics of Wave Forces on Offshore
    Structures. Number ISBN 0-442-25402-4. Van Nostrand Reinhold
    Company Inc., New York.
    Tang, Y., Shi, W., Ning, D., You, J., & Michailides, C. (2020). Effects of spilling
    and plunging type breaking waves acting on large monopile offshore wind
    turbines. Frontiers in Marine Science, 7.
    https://doi.org/10.3389/fmars.2020.00427
    Teja, R. (2021, June 25). Wheatstone bridge: Working, examples, applications.
    ElectronicsHub. https://www.electronicshub.org/wheatstone-bridge/
    The MathWorks Inc. (2022). MATLAB version: 9.13.0 (R2022b), Natick,
    Massachusetts: The MathWorks Inc. https://www.mathworks.com
    Wave gauges. Edinburgh Designs. (2016).
    http://www4.edesign.co.uk/product/wavegauges/
    Wilberts, F. (2017). MEASUREMENT DRIVEN FATIGUE ASSESSMENT OF
    OFFSHORE WIND TURBINE FOUNDATIONS (Master’s Thesis,
    Uppsala University).
Numerical Investigation of the Local Scour for Tripod Pile Foundation

Numerical Investigation of the Local Scour for Tripod Pile Foundation

Waqed H. Hassan Zahraa Mohammad Fadhe* Rifqa F. Thiab Karrar Mahdi
Civil Engineering Department, Faculty of Engineering, University of Warith Al-Anbiyaa, Kerbala 56001, Iraq
Civil Engineering Department, Faculty of Engineering, University of Kerbala, Kerbala 56001, Iraq
Corresponding Author Email: Waqed.hammed@uowa.edu.iq

OPEN ACCESS

Abstract: 

This work investigates numerically a local scour moves in irregular waves around tripods. It is constructed and proven to use the numerical model of the seabed-tripod-fluid with an RNG k turbulence model. The present numerical model then examines the flow velocity distribution and scour characteristics. After that, the suggested computational model Flow-3D is a useful tool for analyzing and forecasting the maximum scour development and the flow field in random waves around tripods. The scour values affecting the foundations of the tripod must be studied and calculated, as this phenomenon directly and negatively affects the structure of the structure and its design life. The lower diagonal braces and the main column act as blockages, increasing the flow accelerations underneath them.  This increases the number of particles that are moved, which in turn creates strong scouring in the area. The numerical model has a good agreement with the experimental model, with a maximum percentage of error of 10% between the experimental and numerical models. In addition, Based on dimensional analysis parameters, an empirical equation has been devised to forecast scour depth with flow depth, median size ratio, Keulegan-Carpenter (Kc), Froud number flow, and wave velocity that the results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50) and the scour depth attains its steady-current value for Vw < 0.75. As the Froude number rises, the maximum scour depth will be large.

Keywords: 

local scour, tripod foundation, Flow-3D​, waves

1. Introduction

New energy sources have been used by mankind since they become industrialized. The main energy sources have traditionally been timber, coal, oil, and gas, but advances in the science of new energies, such as nuclear energy, have emerged [1, 2]. Clean and renewable energy such as offshore wind has grown significantly during the past few decades. There are numerous different types of foundations regarding offshore wind turbines (OWTs), comprising the tripod, jacket, gravity foundation, suction anchor (or bucket), and monopile [3, 4]. When the water depth is less than 30 meters, Offshore wind farms usually employ the monopile type [4]. Engineers must deal with the wind’s scouring phenomenon turbine foundations when planning and designing wind turbines for an offshore environment [5]. Waves and currents generate scour, this is the erosion of soil near a submerged foundation and at its location [6]. To predict the regional scour depth at a bridge pier, Jalal et al. [7-10] developed an original gene expression algorithm using artificial neural networks. Three monopiles, one main column, and several diagonal braces connecting the monopiles to the main column make up the tripod foundation, which has more complicated shapes than a single pile. The design of the foundation may have an impact on scour depth and scour development since the foundation’s form affects the flow field [11, 12]. Stahlmann [4] conducted several field investigations. He discovered that the main column is where the greatest scour depth occurred. Under the main column is where the maximum scour depth occurs in all experiments. The estimated findings show that higher wave heights correspond to higher flow velocities, indicating that a deeper scour depth is correlated with finer silt granularity [13] recommends as the design value for a single pile. These findings support the assertion that a tripod may cause the seabed to scour more severely than a single pile. The geography of the scour is significantly more influenced by the KC value (Keulegan–Carpenter number)

The capability of computer hardware and software has made computational fluid dynamics (CFD) quite popular to predict the behavior of fluid flow in industrial and environmental applications has increased significantly in recent years [14].

Finding an acceptable piece of land for the turbine’s construction and designing the turbine pile precisely for the local conditions are the biggest challenges. Another concern related to working in a marine environment is the effect of sea waves and currents on turbine piles and foundations. The earth surrounding the turbine’s pile is scoured by the waves, which also render the pile unstable.

In this research, the main objective is to investigate numerically a local scour around tripods in random waves. It is constructed and proven to use the tripod numerical model. The present numerical model is then used to examine the flow velocity distribution and scour characteristics.

2. Numerical Model

To simulate the scouring process around the tripod foundation, the CFD code Flow-3D was employed. By using the fractional area/volume method, it may highlight the intricate boundaries of the solution domain (FAVOR).

This model was tested and validated utilizing data derived experimentally from Schendel et al. [15] and Sumer and Fredsøe [6]. 200 runs were performed at different values of parameters.

2.1 Momentum equations

The incompressible viscous fluid motion is described by the three RANS equations listed below [16]:

(1)

\frac{\partial u}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial u}{\partial x}+v{{A}_{y}}\frac{\partial u}{\partial y}+w{{A}_{z}}\frac{\partial u}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial x}+{{G}_{x}}+fx

(2)

\frac{\partial v}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial v}{\partial x}+v{{A}_{y}}\frac{\partial v}{\partial y}+w{{A}_{z}}\frac{\partial v}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial y}+{{G}_{y}}+\text{f}y

 (3)

\frac{\partial w}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial w}{\partial x}+v{{A}_{y}}\frac{\partial w}{\partial y}+w{{A}_{z}}\frac{\partial w}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial z}+{{G}_{z}}+\text{fz}

where, respectively, uv, and w represent the xy, and z flow velocity components; volume fraction (VF), area fraction (AiI=xyz), water density (f), viscous force (fi), and body force (Gi) are all used in the formula.

2.2 Model of turbulence

Several turbulence models would be combined to solve the momentum equations. A two-equation model of turbulence is the RNG k-model, which has a high efficiency and accuracy in computing the near-wall flow field. Therefore, the flow field surrounding tripods was captured using the RNG k-model.

2.3 Model of sediment scour

2.3.1 Induction and deposition

Eq. (4) can be used to determine the particle entrainment lift velocity [17].

(4)

{{u}_{lift,i}}={{\alpha }_{i}}{{n}_{s}}d_{*}^{0.3}{{\left( \theta -{{\theta }_{cr}} \right)}^{1.5}}\sqrt{\frac{\parallel g\parallel {{d}_{i}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{{{\rho }_{f}}}}

α𝛼  is the Induction parameter, ns the normal vector is parallel to the seafloor, and for the present numerical model, ns=(0,0,1), θ𝜃cr is the essential Shields variable, g is the accelerated by gravity, di is the size of the particles, ρi is species density in beds, and d The diameter of particles without dimensions; these values can be obtained in Eq. (5).

(5)

{{d}_{*}}={{d}_{i}}{{\left( \frac{\parallel g\parallel {{\rho }_{f}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{\mu _{f}^{2}} \right)}^{1/3}}

μ𝜇f is this equation a dynamic viscosity of the fluid. cr was determined from an equation based on Soulsby [18].

(6)

{{\theta }_{cr}}=\frac{0.3}{1+1.2{{d}_{*}}}+0.055\left[ 1-\text{exp}\left( -0.02{{d}_{*}} \right) \right]

The equation was used to determine how quickly sand particles set Eq. (7):

(7)

{{\mathbf{u}}_{\text{nsettling},i}}=\frac{{{v}_{f}}}{{{d}_{i}}}\left[ {{\left( {{10.36}^{2}}+1.049d_{*}^{3} \right)}^{0.5}}-10.36 \right]

vf  stands for fluid kinematic viscosity.

2.3.2 Transportation for bed loads

Van Rijn [19] states that the speed of bed load conveyance was determined as:

(8)

{{~}_{\text{bedload},i}}=\frac{{{q}_{b,i}}}{{{\delta }_{i}}{{c}_{b,i}}{{f}_{b}}}

fb  is the essential particle packing percentage, qbi is the bed load transportation rate, and cb, I the percentage of sand by volume i. These variables can be found in Eq. (9), Eq. (10), fbδ𝛿i the bed load thickness.

(9)

{{q}_{b,i}}=8{{\left[ \parallel g\parallel \left( \frac{{{\rho }_{i}}-{{\rho }_{f}}}{{{\rho }_{f}}} \right)d_{i}^{3} \right]}^{\frac{1}{2}}}

(10)

{{\delta }_{i}}=0.3d_{*}^{0.7}{{\left( \frac{\theta }{{{\theta }_{cr}}}-1 \right)}^{0.5}}{{d}_{i}}

In this paper, after the calibration of numerous trials, the selection of parameters for sediment scour is crucial. Maximum packing fraction is 0.64 with a shields number of 0.05, entrainment coefficient of 0.018, the mass density of 2650, bed load coefficient of 12, and entrainment coefficient of 0.01.

3. Model Setup

To investigate the scour characteristics near tripods in random waves, the seabed-tripod-fluid numerical model was created as shown in Figure 1. The tripod basis, a seabed, and fluid and porous medium were all components of the model. The seabed was 240 meters long, 40 meters wide, and three meters high. It had a median diameter of d50 and was composed of uniformly fine sand. The 2.5-meter main column diameter D. The base of the main column was three dimensions above the original seabed. The center of the seafloor was where the tripod was, 130 meters from the offshore and 110 meters from the onshore. To prevent wave reflection, the porous media were positioned above the seabed on the onshore side.

image013.png

Figure 1. An illustration of the numerical model for the seabed-tripod-fluid

3.1 Generation of meshes

Figure 2 displays the model’s mesh for the Flow-3D software grid. The current model made use of two different mesh types: global mesh grid and nested mesh grid. A mesh grid with the following measurements was created by the global hexahedra mesh grid: 240m length, 40m width, and 32m height. Around the tripod, a finer nested mesh grid was made, with dimensions of 0 to 32m on the z-axis, 10 to 30 m on the x-axis, and 25 to 15 m on the y-axis. This improved the calculation’s precision and mesh quality.

image014.png

Figure 2. The mesh block sketch

3.2 Conditional boundaries

To increase calculation efficiency, the top side, The model’s two x-z plane sides, as well as the symmetry boundaries, were all specified. For u, v, w=0, the bottom boundary wall was picked. The offshore end of the wave boundary was put upstream. For the wave border, random waves were generated using the wave spectrum from the Joint North Sea Wave Project (JONSWAP). Boundary conditions are shown in Figure 3.

image015.png

Figure 3. Boundary conditions of the typical problem

The wave spectrum peak enhancement factor (=3.3 for this work) and can be used to express the unidirectional JONSWAP frequency spectrum.

3.3 Mesh sensitivity

Before doing additional research into scour traits and scour depth forecasting, mesh sensitivity analysis is essential. Three different mesh grid sizes were selected for this section: Mesh 1 has a 0.45 by 0.45 nested fine mesh and a 0.6 by 0.6 global mesh size. Mesh 2 has a 0.4 global mesh size and a 0.35 nested fine mesh size, while Mesh 3 has a 0.25 global mesh size and a nested fine mesh size of 0.15. Comparing the relative fine mesh size (such as Mesh 2 or Mesh 3) to the relatively coarse mesh size (such as Mesh 1), a larger scour depth was seen; this shows that a finer mesh size can more precisely represent the scouring and flow field action around a tripod. Significantly, a lower mesh size necessitates a time commitment and a more difficult computer configuration. Depending on the sensitivity of the mesh guideline utilized by Pang et al., when Mesh 2 is applied, the findings converge and the mesh size is independent [20]. In the next sections, scouring the area surrounding the tripod was calculated using Mesh 2 to ensure accuracy and reduce computation time. The working segment generates a total of 14, 800,324 cells.

3.4 Model validation

Comparisons between the predicted outcomes from the current model and to confirm that the current numerical model is accurate and suitably modified, experimental data from Sumer and Fredsøe [6] and Schendel et al. [15] were used. For the experimental results of Run 05, Run 15, and Run 22 from Sumer and Fredsøe [6], the experimental A9, A13, A17, A25, A26, and A27 results from Schendel et al. [15], and the numerical results from the current model are shown in Figure 4. The present model had d50=0.051cm, the height of the water wave(h)=10m, and wave velocity=0.854 m.s-1.

image016.png

Figure 4. Cell size effect

image017.png

Figure 5. Comparison of the present study’s maximum scour depth with that authored by Sumer and Fredsøe [6] and Schendel et al. [15]

According to Figure 5, the highest discrepancy between the numerical results and experimental data is about 10%, showing that overall, there is good agreement between them. The ability of the current numerical model to accurately depict the scour process and forecast the maximum scour depth (S) near foundations is demonstrated by this. Errors in the simulation were reduced by using the calibrated values of the parameter. Considering these results, a suggested simulated scouring utilizing a Flow-3D numerical model is confirmed as a superior way for precisely forecasting the maximum scour depth near a tripod foundation in random waves.

3.5 Dimensional analysis

The variables found in this study as having the greatest impacts, variables related to flow, fluid, bed sediment, flume shape, and duration all had an impact on local scouring depth (t). Hence, scour depth (S) can be seen as a function of these factors, shown as:

(11)

S=f\left(\rho, v, V, h, g, \rho s, d_{50}, \sigma g, V_w, D, d, T_v, t\right)

With the aid of dimensional analysis, the 14-dimensional parameters in Eq. (11) were reduced to 6 dimensionless variables using Buckingham’s -theorem. D, V, and were therefore set as repetition parameters and others as constants, allowing for the ignoring of their influence. Eq. (12) thus illustrates the relationship between the effect of the non-dimensional components on the depth of scour surrounding a tripod base.

(12)

\frac{S}{D}=f\left(\frac{h}{D}, \frac{d 50}{D}, \frac{V}{V W}, F r, K c\right)

where, SD𝑆𝐷 are scoured depth ratio, VVw𝑉𝑉𝑤 is flow wave velocity, d50D𝑑50𝐷 median size ratio, $Fr representstheFroudnumber,and𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠𝑡ℎ𝑒𝐹𝑟𝑜𝑢𝑑𝑛𝑢𝑚𝑏𝑒𝑟,𝑎𝑛𝑑Kc$ is the Keulegan-Carpenter.

4. Result and Discussion

4.1 Development of scour

Similar to how the physical model was used, this numerical model was also used. The numerical model’s boundary conditions and other crucial variables that directly influence the outcomes were applied (flow depth, median particle size (d50), and wave velocity). After the initial 0-300 s, the scour rate reduced as the scour holes grew quickly. The scour depths steadied for about 1800 seconds before reaching an asymptotic value. The findings of scour depth with time are displayed in Figure 6.

4.2 Features of scour

Early on (t=400s), the scour hole began to appear beneath the main column and then began to extend along the diagonal bracing connecting to the wall-facing pile. Gradually, the geography of the scour; of these results is similar to the experimental observations of Stahlmann [4] and Aminoroayaie Yamini et al. [1]. As the waves reached the tripod, there was an enhanced flow acceleration underneath the main column and the lower diagonal braces as a result of the obstructing effects of the structural elements. More particles are mobilized and transported due to the enhanced near-bed flow velocity, it also increases bed shear stress, turbulence, and scour at the site. In comparison to a single pile, the main column and structural components of the tripod have a significant impact on the flow velocity distribution and, consequently, the scour process and morphology. The main column and seabed are separated by a gap, therefore the flow across the gap may aid in scouring. The scour hole first emerged beneath the main column and subsequently expanded along the lower structural components, both Aminoroayaie Yamini et al. [1] and Stahlmann [4] made this claim. Around the tripod, there are several different scour morphologies and the flow velocity distribution as shown in Figures 7 and 8.

image023.png

Figure 6. Results of scour depth with time

image024.png

image025.png

image026.png

image027.png

Figure 7. The sequence results of scour depth around tripod development (reached to steady state) simulation time

image028.png

image029.png

image030.png

image031.png

Figure 8. Random waves of flow velocity distribution around a tripod

4.3 Wave velocity’s (Vw) impact on scour depth

In this study’s section, we looked at how variations in wave current velocity affected the scouring depth. Bed scour pattern modification could result from an increase or decrease in waves. As a result, the backflow area produced within the pile would become stronger, which would increase the depth of the sediment scour. The quantity of current turbulence is the primary cause of the relationship between wave height and bed scour value. The current velocity has increased the extent to which the turbulence energy has changed and increased in strength now present. It should be mentioned that in this instance, the Jon swap spectrum random waves are chosen. The scour depth attains its steady-current value for Vw<0.75, Figure 9 (a) shows that effect. When (V) represents the mean velocity=0.5 m.s-1.

image032.png

(a)

image033.png

(b)

image034.png

(c)

image035.png

(d)

Figure 9Main effects on maximum scour depth (Smax) as a function of column diameter (D)

4.4 Impact of a median particle (d50) on scour depth

In this section of the study, we looked into how variations in particle size affected how the bed profile changed. The values of various particle diameters are defined in the numerical model for each run numerical modeling, and the conditions under which changes in particle diameter have an impact on the bed scour profile are derived. Based on Figure 9 (b), the findings of the numerical modeling show that as particle diameter increases the maximum scour depth caused by wave contact decreases. When (d50) is the diameter of Sediment (d50). The Shatt Al-Arab soil near Basra, Iraq, was used to produce a variety of varied diameters.

4.5 Impact of wave height and flow depth (h) on scour depth

One of the main elements affecting the scour profile brought on by the interaction of the wave and current with the piles of the wind turbines is the height of the wave surrounding the turbine pile causing more turbulence to develop there. The velocity towards the bottom and the bed both vary as the turbulence around the pile is increased, modifying the scour profile close to the pile. According to the results of the numerical modeling, the depth of scour will increase as water depth and wave height in random waves increase as shown in Figure 9 (c).

4.6 Froude number’s (Fr) impact on scour depth

No matter what the spacing ratio, the Figure 9 shows that the Froude number rises, and the maximum scour depth often rises as well increases in Figure 9 (d). Additionally, it is crucial to keep in mind that only a small portion of the findings regarding the spacing ratios with the smallest values. Due to the velocity acceleration in the presence of a larger Froude number, the range of edge scour downstream is greater than that of upstream. Moreover, the scouring phenomena occur in the region farthest from the tripod, perhaps as a result of the turbulence brought on by the collision of the tripod’s pile. Generally, as the Froude number rises, so does the deposition height and scour depth.

4.7 Keulegan-Carpenter (KC) number

The geography of the scour is significantly more influenced by the KC value. Greater KC causes a deeper equilibrium scour because an increase in KC lengthens the horseshoe vortex’s duration and intensifies it as shown in Figure 10.

The result can be attributed to the fact that wave superposition reduced the crucial KC for the initiation of the scour, particularly under small KC conditions. The primary variable in the equation used to calculate This is the depth of the scouring hole at the bed. The following expression is used to calculate the Keulegan-Carpenter number:

Kc=Vw∗TpD𝐾𝑐=𝑉𝑤∗𝑇𝑝𝐷                          (13)

where, the wave period is Tp and the wave velocity is shown by Vw.

image037.png

Figure 10. Relationship between the relative maximum scour depth and KC

5. Conclusion

(1) The existing seabed-tripod-fluid numerical model is capable of faithfully reproducing the scour process and the flow field around tripods, suggesting that it may be used to predict the scour around tripods in random waves.

(2) Their results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50).

(3) A diagonal brace and the main column act as blockages, increasing the flow accelerations underneath them. This raises the magnitude of the disturbance and the shear stress on the seafloor, which in turn causes a greater number of particles to be mobilized and conveyed, as a result, causes more severe scour at the location.

(4) The Froude number and the scouring process are closely related. In general, as the Froude number rises, so does the maximum scour depth and scour range. The highest maximum scour depth always coincides with the bigger Froude number with the shortest spacing ratio.

Since the issue is that there aren’t many experiments or studies that are relevant to this subject, therefore we had to rely on the monopile criteria. Therefore, to gain a deeper knowledge of the scouring effect surrounding the tripod in random waves, further numerical research exploring numerous soil, foundation, and construction elements as well as upcoming physical model tests will be beneficial.

Nomenclature

CFDComputational fluid dynamics
FAVORFractional Area/Volume Obstacle Representation
VOFVolume of Fluid
RNGRenormalized Group
OWTsOffshore wind turbines
Greek Symbols
ε, ωDissipation rate of the turbulent kinetic energy, m2s-3
Subscripts
d50Median particle size
VfVolume fraction
GTTurbulent energy of buoyancy
KTTurbulent velocity
PTKinetic energy of the turbulence
ΑiInduction parameter
nsInduction parameter
ΘΘcrThe essential Shields variable
DiDiameter of sediment
dThe diameter of particles without dimensions
µfDynamic viscosity of the fluid
qb,iThe bed load transportation rate
Cs,iSand particle’s concentration of mass
DDiameter of pile
DfDiffusivity
DDiameter of main column
FrFroud number
KcKeulegan–Carpenter number
GAcceleration of gravity g
HFlow depth
VwWave Velocity
VMean Velocity
TpWave Period
SScour depth

  References

[1] Aminoroayaie Yamini, O., Mousavi, S.H., Kavianpour, M.R., Movahedi, A. (2018). Numerical modeling of sediment scouring phenomenon around the offshore wind turbine pile in marine environment. Environmental Earth Sciences, 77: 1-15. https://doi.org/10.1007/s12665-018-7967-4

[2] Hassan, W.H., Hashim, F.S. (2020). The effect of climate change on the maximum temperature in Southwest Iraq using HadCM3 and CanESM2 modelling. SN Applied Sciences, 2(9): 1494. https://doi.org/10.1007/s42452-020-03302-z

[3] Fazeres-Ferradosa, T., Rosa-Santos, P., Taveira-Pinto, F., Pavlou, D., Gao, F.P., Carvalho, H., Oliveira-Pinto, S. (2020). Preface: Advanced research on offshore structures and foundation design part 2. In Proceedings of the Institution of Civil Engineers-Maritime Engineering. Thomas Telford Ltd, 173(4): 96-99. https://doi.org/10.1680/jmaen.2020.173.4.96

[4] Stahlmann, A. (2013). Numerical and experimental modeling of scour at foundation structures for offshore wind turbines. In ISOPE International Ocean and Polar Engineering Conference. ISOPE, pp. ISOPE-I.

[5] Petersen, T.U., Sumer, B.M., Fredsøe, J. (2014). Edge scour at scour protections around offshore wind turbine foundations. In 7th International Conference on Scour and Erosion. CRC Press, pp. 587-592.

[6] Sumer, B.M., Fredsøe, J. (2001). Scour around pile in combined waves and current. Journal of Hydraulic Engineering, 127(5): 403-411. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:5(403)

[7] Jalal, H.K., Hassan, W.H. (2020). Effect of bridge pier shape on depth of scour. In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 671(1): 012001. https://doi.org/10.1088/1757-899X/671/1/012001

[8] Hassan, W.H., Jalal, H.K. (2021). Prediction of the depth of local scouring at a bridge pier using a gene expression programming method. SN Applied Sciences, 3(2): 159. https://doi.org/10.1007/s42452-020-04124-9

[9] Jalal, H.K., Hassan, W.H. (2020). Three-dimensional numerical simulation of local scour around circular bridge pier using Flow-3D software. In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 745(1): 012150. https://doi.org/10.1088/1757-899X/745/1/012150

[10] Hassan, W.H., Attea, Z.H., Mohammed, S.S. (2020). Optimum layout design of sewer networks by hybrid genetic algorithm. Journal of Applied Water Engineering and Research, 8(2): 108-124. https://doi.org/10.1080/23249676.2020.1761897

[11] Hassan, W.H., Hussein, H.H., Alshammari, M.H., Jalal, H.K., Rasheed, S.E. (2022). Evaluation of gene expression programming and artificial neural networks in PyTorch for the prediction of local scour depth around a bridge pier. Results in Engineering, 13: 100353. https://doi.org/10.1016/j.rineng.2022.100353

[12] Hassan, W.H., Hh, H., Mohammed, S.S., Jalal, H.K., Nile, B.K. (2021). Evaluation of gene expression programming to predict the local scour depth around a bridge pier. Journal of Engineering Science and Technology, 16(2): 1232-1243. https://doi.org/10.1016/j.rineng.2022.100353

[13] Nerland, C. (2010). Offshore wind energy: Balancing risk and reward. In Proceedings of the Canadian Wind Energy Association’s 2010 Annual Conference and Exhibition, Canada, p. 2000. 

[14] Hassan, W.H., Nile, B.K., Mahdi, K., Wesseling, J., Ritsema, C. (2021). A feasibility assessment of potential artificial recharge for increasing agricultural areas in the kerbala desert in Iraq using numerical groundwater modeling. Water, 13(22): 3167. https://doi.org/10.3390/w13223167

[15] Schendel, A., Welzel, M., Schlurmann, T., Hsu, T.W. (2020). Scour around a monopile induced by directionally spread irregular waves in combination with oblique currents. Coastal Engineering, 161: 103751. https://doi.org/10.1016/j.coastaleng.2020.103751

[16] Yakhot, V., Orszag, S.A. (1986). Renormalization group analysis of turbulence. I. Basic theory. Journal of Scientific Computing, 1(1): 3-51. https://doi.org/10.1007/BF01061452

[17] Mastbergen, D.R., Van Den Berg, J.H. (2003). Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology, 50(4): 625-637. https://doi.org/10.1046/j.1365-3091.2003.00554.x

[18] Soulsby, R. (1997). Dynamics of marine sands. https://doi.org/10.1680/doms.25844

[19] Van Rijn, L.C. (1984). Sediment transport, part I: Bed load transport. Journal of Hydraulic Engineering, 110(10): 1431-1456. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:10(1431)

[20] Pang, A.L.J., Skote, M., Lim, S.Y., Gullman-Strand, J., Morgan, N. (2016). A numerical approach for determining equilibrium scour depth around a mono-pile due to steady currents. Applied Ocean Research, 57: 114-124. https://doi.org/10.1016/j.apor.2016.02.010

Fig 1. (a) The Location of the Bahman Shir dam (upstream), (b) Bahman Shir dam (downstream dam) and (c) Mared Dam. Note: The borders of the countries are not exact.

Initial Maintenance Notes about the First River Ship Lock in Iran

M.T. Mansouri Kia1,2, H.R. Sheibani 3, A. Hoback 4
1 Manager of Dam and Power Plant Construction, Khuzestan Water and Power Authority (KWPA), Ahwaz, Iran.
2 Ph.D., Department of Civil Engineering, Payame Noor University, Tehran, Iran.
3 Associate Professor of PNU University, Tehran, Iran.
4 Professor of Civil, Architectural & Environmental Engineering, University of Detroit Mercy Civil, Rome, Italy.

Abstract

Mared Dam in northern Abadan is under construction on the Karun River and it is the first ship lock in Iran. In this study, the ship’s lock was examined. Every vessel must pass through this lock in order to transport water from Arvand River to Karun and vice versa. The interior dimensions of the Mared Shipping Lock are 160 meters long, 25 meters wide and 8 meters deep. Several important times are calculated for lock operation. 𝑇is the first time the gates open, 𝑇15 the time the initial gates remain open until the height difference between the two sides reaches 150 mm, 𝑇filled is the duration between the start of the opening the gates till the difference between the two ends becomes zero after 𝑇15. Finally, T is the total time required for opening or closing the gates completely. The rotational speeds of the gates range from 5 to 35 radians per minute. Numerical modeling has been used to study fluid behavior and interaction between fluid and gates in flow 3D software. Different lock maintenance scenarios have been analyzed. Important parameters such as inlet and outlet flow rate changes from gates, water depth changes at different times, stress and strain fields, hydrodynamic forces acting on different points of the lock have been calculated. Based on this, the forces acting on hydraulic jacks and gates have been calculated. The minimum time required for the safe passage of the ship through the lock is calculated.

북부 아바단의 마레드 댐은 카룬 강에 건설 중이며 이란 최초의 선박 잠금 장치입니다. 본 연구에서는 선박의 자물쇠를 조사하였습니다. Arvand 강에서 Karun으로 또는 그 반대로 물을 운송하려면 모든 선박이 이 수문을 통과해야 합니다.

Mared Shipping Lock의 내부 치수는 길이 160m, 너비 25m, 깊이 8m입니다. 잠금 작동을 위해 몇 가지 중요한 시간이 계산됩니다. 𝑇은 게이트가 처음 열릴 때, 𝑇15는 양쪽의 높이 차이가 150mm에 도달할 때까지 초기 게이트가 열린 상태로 유지되는 시간, 𝑇filled는 게이트가 열리는 시작부터 이후 두 끝의 차이가 0이 될 때까지의 시간입니다.

𝑇15. 마지막으로 T는 게이트를 완전히 열거나 닫는 데 필요한 총 시간입니다. 게이트의 회전 속도는 분당 5~35라디안입니다. 수치 모델링은 유동 3D 소프트웨어에서 유체 거동과 유체와 게이트 사이의 상호 작용을 연구하는 데 사용되었습니다. 다양한 잠금 유지 관리 시나리오가 분석되었습니다.

게이트의 입구 및 출구 유속 변화, 다양한 시간에 따른 수심 변화, 응력 및 변형 필드, 수문의 다양한 지점에 작용하는 유체역학적 힘과 같은 중요한 매개변수가 계산되었습니다.

이를 바탕으로 유압잭과 게이트에 작용하는 힘을 계산하였습니다. 선박이 자물쇠를 안전하게 통과하는 데 필요한 최소 시간이 계산됩니다.

Fig 1. (a) The Location of the Bahman Shir dam (upstream), (b) Bahman Shir dam (downstream dam) and (c) Mared Dam. Note: The borders of the countries are not exact.
Fig 1. (a) The Location of the Bahman Shir dam (upstream), (b) Bahman Shir dam (downstream dam) and (c) Mared Dam. Note: The borders of the countries are not exact.

References

  • Ables, J.H., 1978. Filling and Emptying System, New Ship Lock, Mississippi River-Gulf Outlet, Louisiana: Hydraulic Model Investigation, 78. US Army Engineer Waterways Experiment Station.
  • Army, U., 1964. Corps of Engineers, 1965. National Inventory of Physical Resources. Agency for International Development, Costa Rica.
  • Belzner, F., Simons, F., Thorenz, C., 2018. An application-oriented model for lock filling processes, 34th PIANC-World Congress (Proceedings). Online verfügbar unter https://coms.events/piancpanama/data/full_pa pers/full_paper_183.pdf, zuletzt geprüft am, pp. 2018.
  • Brolsma, J., Roelse, K., 2011. Waterway guidelines 2011. ISBN 9789036900690. Dhanuka, A., Agrawal, S., Mehra, H., 2018. Hydraulic and Structural Design of Navigational Locks. J Civil Environ Eng, 8(297): 2.
  • Gao, Z., Fang, S.L., Shi, X.T., Gu, Z.H., 2013. Computation of Filling Time of a Ship Lock. Applied Mechanics and Materials, 256: 2509- 2513.
  • Hu, Q., Li, Y., Zhu, L., 2024. Effect of Parameters of Ditch Geometry on the Uniformity of Water Filling in Ship Lock Chambers. Journal of Marine Science and Engineering, 12(1): 86. Iranian sahel Omid Co., Engineer, L.C., 2015. Numerical Modeling of Flow in Lock Chamber, Abadan ship Lock Dam Project. 0920-4741.
  • Iuorio, L., 2024. Dams are fragile: the frenzy and legacy of modern infrastructures along the Klamath and Allegheny Rivers. Water History: 1-26.
  • Li, J., Hu, Y., Wang, X., Diao, M., 2023. Operation safety evaluation system of ship lock based on extension evaluation and combination weighting method. Journal of Hydroinformatics, 25(3): 755-781.
  • Liu, B., Yang, J., Huang, Y., Wang, L., 2022. Hydraulic Research on Filling and Emptying System of Water-Saving Ship Lock for Navigation-Power Junction in Mountainous River, Smart Rivers. Springer, pp. 1492-1501.
  • Mäck, A., Lorke, A., 2014. Ship‐lock–induced surges in an impounded river and their impact on subdaily flow velocity variation. River research and applications, 30(4): 494-507. Mahab., S., 1976. Final technical Report of Feasibility study. 25-96.
  • Mansouri Kia, M.T., 2022. Hydraulic design and optimization of navigation lock performance – A case study of Karun and Bahman Shir river locks. . PNU University. The Ph. D thesis (in Civil Engineering).
  • Mansouri Kia, M.T., Ansari, Z., 2008. Feasibility of Water Transport in Karun Waterway. 4th National Congress of Civil Engineering, Tehran University Iran: 1-8 (in Persian).
  • Mansouri Kia, M.T., Rajabi, E., Sheybani, H.R., 2022. Determining the Optimal Dimensions of River Transportation Channel in Iran. . Fourth International Conference of Civil, Architectural and sustainable green city, Hamedan, Iran. (in Persian): 298-309.
  • Moore, F.G., 1950. Three canal projects, Roman and Byzantine. American Journal of Archaeology, 54(2): 97-111.
  • Negi, P., Kromanis, R., Dorée, A.G., Wijnberg, K.M., 2024. Structural health monitoring of inland navigation structures and ports: a review on developments and challenges. Structural Health Monitoring, 23(1): 605-645.
  • Nogueira, H.I., Van Der Hout, A., O’Mahoney, T.S., Kortlever, W.C., 2024. The Impact of Density Differences on the Hydraulic Design of Leveling Systems: The Case of New Large Sea Locks in IJmuiden and Terneuzen. Journal of Waterway, Port, Coastal, and Ocean Engineering, 150(1): 05023002.
  • O’Mahoney, T., De Loor, A., 2015. Paper 55- Computational Fluid Dynamics simulations of the effects of density differences during the filling process in a sea lock. Scott_Wilson;, Piesold., 2005. Karun River, Interim report NO 6, Transportation component.
  • Wang, H.-z., Zou, Z.-j., 2014. Numerical prediction of hydrodynamic forces on a ship passing through a lock. China Ocean Engineering, 28(3): 421-432.
  • Yang, Z., Sun, Y., Lian, F., Feng, H., Li, G., 2024. Optimization of river container port-access transport based on the innovatively designed electric ship in the Yangtze River Delta. Ocean & Coastal Management, 248: 106976.

Figure 3 – Free surface views. Bottom left: k-ε RNG model. Bottom right: LES.

Physical Modeling and CFD Comparison: Case Study of a HydroCombined Power Station in Spillway Mode

물리적 모델링 및 CFD 비교: 방수로 모드의 HydroCombined 발전소 사례 연구

Gonzalo Duró, Mariano De Dios, Alfredo López, Sergio O. Liscia

ABSTRACT

This study presents comparisons between the results of a commercial CFD code and physical model measurements. The case study is a hydro-combined power station operating in spillway mode for a given scenario. Two turbulence models and two scales are implemented to identify the capabilities and limitations of each approach and to determine the selection criteria for CFD modeling for this kind of structure. The main flow characteristics are considered for analysis, but the focus is on a fluctuating frequency phenomenon for accurate quantitative comparisons. Acceptable representations of the general hydraulic functioning are found in all approaches, according to physical modeling. The k-ε RNG, and LES models give good representation of the discharge flow, mean water depths, and mean pressures for engineering purposes. The k-ε RNG is not able to characterize fluctuating phenomena at a model scale but does at a prototype scale. The LES is capable of identifying the dominant frequency at both prototype and model scales. A prototype-scale approach is recommended for the numerical modeling to obtain a better representation of fluctuating pressures for both turbulence models, with the complement of physical modeling for the ultimate design of the hydraulic structures.

본 연구에서는 상용 CFD 코드 결과와 물리적 모델 측정 결과를 비교합니다. 사례 연구는 주어진 시나리오에 대해 배수로 모드에서 작동하는 수력 복합 발전소입니다.

각 접근 방식의 기능과 한계를 식별하고 이러한 종류의 구조에 대한 CFD 모델링의 선택 기준을 결정하기 위해 두 개의 난류 모델과 두 개의 스케일이 구현되었습니다. 주요 흐름 특성을 고려하여 분석하지만 정확한 정량적 비교를 위해 변동하는 주파수 현상에 중점을 둡니다.

일반적인 수리학적 기능에 대한 허용 가능한 표현은 물리적 모델링에 따라 모든 접근 방식에서 발견됩니다. k-ε RNG 및 LES 모델은 엔지니어링 목적을 위한 배출 유량, 평균 수심 및 평균 압력을 잘 표현합니다.

k-ε RNG는 모델 규모에서는 변동 현상을 특성화할 수 없지만 프로토타입 규모에서는 특성을 파악합니다. LES는 프로토타입과 모델 규모 모두에서 주요 주파수를 식별할 수 있습니다.

수력학적 구조의 궁극적인 설계를 위한 물리적 모델링을 보완하여 두 난류 모델에 대한 변동하는 압력을 더 잘 표현하기 위해 수치 모델링에 프로토타입 규모 접근 방식이 권장됩니다.

Figure 1 – Physical scale model (left). Upstream flume and point gauge (right)
Figure 1 – Physical scale model (left). Upstream flume and point gauge (right)
Figure 3 – Free surface views. Bottom left: k-ε RNG model. Bottom right: LES.
Figure 3 – Free surface views. Bottom left: k-ε RNG model. Bottom right: LES.
Figure 4 – Water levels: physical model (maximum values) and CFD results (mean values)
Figure 4 – Water levels: physical model (maximum values) and CFD results (mean values)
Figure 5 – Instantaneous pressures [Pa] and velocities [m/s] at model scale (bay center)
Figure 5 – Instantaneous pressures [Pa] and velocities [m/s] at model scale (bay center)

Keywords

CFD validation, hydro-combined, k-ε RNG, LES, pressure spectrum

REFERENCES

ADRIAN R. J. (2007). “Hairpin vortex organization in wall turbulence.” Phys. Fluids 19(4), 041301.
DEWALS B., ARCHAMBEAU P., RULOT F., PIROTTON M. and ERPICUM S. (2013). “Physical and
Numerical Modelling in Low-Head Structures Design.” Proc. International Workshop on Hydraulic
Design of Low-Head Structures, Aachen, Germany, Bundesanstalt für Wasserbau Publ., D.B. BUNG
and S. PAGLIARA Editors, pp.11-30.
GRENANDER, U. (1959). Probability and Statistics: The Harald Cramér Volume. Wiley.
HIRT, C. W. and NICHOLS B. D. (1981). “Volume of fluid (VOF) method for the dynamics of free
boundaries.” Journal of Computational Physics 39(1): 201-225.
JOHNSON M. C. and SAVAGE B. M. (2006). “Physical and numerical comparison of flow over ogee
spillway in the presence of tailwater.” J. Hydraulic Eng. 132(12): 1353–1357.
KHAN L.A., WICKLEIN E.A., RASHID M., EBNER L.L. and RICHARDS N.A. (2004).
“Computational fluid dynamics modeling of turbine intake hydraulics at a hydropower plant.” Journal
of Hydraulic Research, 42:1, 61-69
LAROCQUE L.A., IMRAN J. and CHAUDHRY M. (2013). “3D numerical simulation of partial breach
dam-break flow using the LES and k–ϵ turbulence models.” Jl of Hydraulic Research, 51:2, 145-157
LI S., LAI Y., WEBER L., MATOS SILVA J. and PATEL V.C. (2004). “Validation of a threedimensional numerical model for water-pump intakes.” Journal of Hydraulic Research, 42:3, 282-292
NOVAK P., GUINOT V., JEFFREY A. and REEVE D.E. (2010). “Hydraulic modelling – An
introduction.” Spon Press, London and New York, ISBN 978-0-419-25010-4, 616 pp.

Embankment Dams Overtopping Breach: A Numerical Investigation of Hydraulic Results

Embankment Dams Overtopping Breach: A Numerical Investigation of Hydraulic Results

Mahdi EbrahimiMirali MohammadiSayed Mohammad Hadi Meshkati & Farhad Imanshoar

Abstract

The overtopping breach is the most probable reason of embankment dam failures. Hence, the investigation of the mentioned phenomenon is one of the vital hydraulic issues. This research paper tries to utilize three numerical models, i.e., BREACH, HEC-RAS, and FLOW-3D for modeling the hydraulic outcomes of overtopping breach phenomenon. Furthermore, the outputs have been compared with experimental model results given by authors. The BREACH model presents a desired prediction for the peak flow. The HEC-RAS model has a more realistic performance in terms of the peak flow prediction, its occurrence time (5-s difference with observed status), and maximum flow depth. The variations diagram in the reservoir water level during the breach process has a descending trend. Whereas it initially ascended; and then, it experienced a descending trend in the observed status. The FLOW-3D model computes the flow depth, flow velocity, and Froude number due to the physical model breach. Moreover, it revealed a peak flow damping equals to 5% and 5-s difference in the peak flow occurrence time at 4-m distance from the physical model downstream. In addition, the current research work demonstrates the mentioned numerical models and provides a possible comprehensive perspective for a dam breach scope. They also help to achieve the various hydraulic parameters computations. Besides, they may calculate unmeasured parameters using the experimental data.

월류 현상은 제방 댐 실패의 가장 유력한 원인입니다. 따라서 언급된 현상에 대한 조사는 중요한 수리학적 문제 중 하나입니다.

본 연구 논문에서는 월류 침해 현상의 수리적 결과를 모델링하기 위해 BREACH, HEC-RAS 및 FLOW-3D의 세 가지 수치 모델을 활용하려고 합니다. 또한 출력은 저자가 제공한 실험 모델 결과와 비교되었습니다. BREACH 모델은 최대 유량에 대해 원하는 예측을 제시합니다.

HEC-RAS 모델은 최고유량 예측, 발생시간(관찰상태와 5초 차이), 최대유량수심 측면에서 보다 현실적인 성능을 가지고 있습니다. 위반 과정 중 저수지 수위의 변동 다이어그램은 감소하는 추세를 보입니다. 처음에는 상승했지만 그런 다음 관찰된 상태가 감소하는 추세를 경험했습니다.

FLOW-3D 모델은 물리적 모델 위반으로 인한 흐름 깊이, 흐름 속도 및 Froude 수를 계산합니다. 또한, 실제 모델 하류로부터 4m 거리에서 최대유량 발생시간이 5%, 5초 차이에 해당하는 최대유량 감쇠를 나타냈습니다.

또한, 현재 연구 작업은 언급된 수치 모델을 보여주고 댐 침해 범위에 대한 가능한 포괄적인 관점을 제공합니다. 또한 다양한 유압 매개변수 계산을 수행하는 데 도움이 됩니다. 게다가 실험 데이터를 사용하여 측정되지 않은 매개변수를 계산할 수도 있습니다.

Keywords

DOI

  • https://doi.org/10.1007/s40996-024-01387-9

References

  • Association of state dam safety officials (2023) Kentucky, USA. Available from https://damsafety.org
  • ASTM D1557 (2007) Standard test methods for laboratory compaction characteristics of soil using standard effort. West Conshohocken, PA, USA
  • ASTM D422–63 (2002) Standard test method for particle size analysis of soils
  • Azimi H, Shabanlou S (2016) Comparison of subcritical and supercritical flow patterns within triangular channels along the side weir. Int J Nonlinear Sci Numer Simul 17(7–8):361–368Article MathSciNet Google Scholar 
  • Azimi H, Shabanlou S (2018) Numerical study of bed slope change effect of circular channel with side weir in supercritical flow conditions. Appl Water Sci 8(6):166Article ADS Google Scholar 
  • Azimi H, Shabanlou S, Kardar S (2017) Characteristics of hydraulic jump in U-shaped channels. Arab J Sci Eng 42:3751–3760Article Google Scholar 
  • Brunner GW (2016) HEC-RAS Reference Manual, version 5.0. Hydrologic Engineering Center, Institute for Water Resources, US Army Corps of Engineers, Davis, California
  • Brunner GW (2016) HEC-RAS users Manual, version 5.0. Hydrologic Engineering Center, Institute for Water Resources, US Army Corps of Engineers, Davis, California
  • Chanson H, Wang H (2013) Unsteady discharge calibration of a large V-notch weir. Flow Meas Instrum 29:19–24Article Google Scholar 
  • Committee on Dam Safety (2019) ICOLD incident database bulletin 99 update: statistical analysis of dam failures, technical report, international commission on large dams. Available from: https://www.icoldchile.cl/boletines/188.pdf
  • Engomoen B, Witter DT, Knight K, Luebke TA (2014) Design Standards No 13: Embankment Dams. United States Bureau of Reclamation
  • Flow Science Corporation (2017) Flow-3D v11.0 User Manual. Available from: http://flow3d.com
  • Froehlich DC (2016) Predicting peak discharge from gradually breached embankment dam. J Hydrol Eng 21(11):04016041Article Google Scholar 
  • Hakimzadeh H, Nourani V, Amini AB (2014) Genetic programming simulation of dam breach hydrograph and peak outflow discharge. J Hydrol Eng 19:757–768Article Google Scholar 
  • Hooshyaripor F, Tahershamsi A, Golian S (2014) Application of copula method and neural networks for predicting peak outflow from breached embankments. J Hydro-Environ Res 8(3):292–303Article Google Scholar 
  • Irmakunal CI (2019) Two-dimensional dam break analyses of Berdan dam. MSC thesis, Middle East Technical University, Turkey
  • kumar Gupta A, Narang I, Goyal P, (2020) Dam break analysis of JAWAI dam PALI, Rajasthan using HEC-RAS. IOSR J Mech Civ Eng 17(2):43–52Google Scholar 
  • Mo C, Cen W, Le X, Ban H, Ruan Y, Lai S, Shen Y (2023) Simulation of dam-break flood and risk assessment: a case study of Chengbi river dam in Baise, China. J Hydroinformatics 25(4):1276–1294Article Google Scholar 
  • Morris M, Kortenhaus A, Visser P (2009) Modelling breach initiation and growth. FLOODsite report: T06–08–02, FLOODsite Consortium, Wallingford, UK
  • Novak P, Moffat AIB, Nalluri C, Narayanan RAIB (2017) Hydraulic structures. CRC PressGoogle Scholar 
  • Pierce MW, Thornton CI, Abt SR (2010) Predicting peak outflow from breached embankment dams. J Hydrol Eng 15(5):338–349Article Google Scholar 
  • Saberi O (2016) Embankment dam failure outflow hydrograph development. PhD thesis, Graz University of Technology, Austria
  • Sylvestre J, Sylvestre P (2018) User’s guide for BRCH GUI. 2018. Available from: http://rivermechanics.net
  • USACE) 2004) General design and construction considerations for Earth and rockfill dams, US Army Corps of Engineers, Washington DC, USA
  • USBR (1987) Design of small dams, Bureau of Reclamation, Water Resources Technical Publication
  • Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method. Pearson education
  • Wang Z, Bowles DS (2006) Three-dimensional non-cohesive earthen dam breach model. Part 1: theory and methodology. Adv Water Resour 29(10):1528–1545Article ADS Google Scholar 
  • Webby MG (1996) Discussion of peak outflow from breached embankment dam by David C. Froehlich. J Water Resour Plan Manag 122(4):316–317
  • Wu W, Marsooli R, He Z (2012) Depth-averaged two-dimensional model of unsteady flow and sediment transport due to noncohesive embankment break/breaching. J Hydraul Eng 138(6):503–516Article Google Scholar 
  • Xu Y, Zhang LM (2009) Breaching parameters for earth and rockfill dams. J Geotech Geoenviron Eng 135(12):1957–1970Article Google Scholar 
Coupled CFD-DEM simulation of interfacial fluid–particle interaction during binder jet 3D printing

Coupled CFD-DEM simulation of interfacial fluid–particle interaction during binder jet 3D printing

바인더 제트 3D 프린팅 중 계면 유체-입자 상호 작용에 대한 CFD-DEM 결합 시뮬레이션

Joshua J. Wagner, C. Fred Higgs III

https://doi.org/10.1016/j.cma.2024.116747

Abstract

The coupled dynamics of interfacial fluid phases and unconstrained solid particles during the binder jet 3D printing process govern the final quality and performance of the resulting components. The present work proposes a computational fluid dynamics (CFD) and discrete element method (DEM) framework capable of simulating the complex interfacial fluid–particle interaction that occurs when binder microdroplets are deposited into a powder bed. The CFD solver uses a volume-of-fluid (VOF) method for capturing liquid–gas multifluid flows and relies on block-structured adaptive mesh refinement (AMR) to localize grid refinement around evolving fluid–fluid interfaces. The DEM module resolves six degrees of freedom particle motion and accounts for particle contact, cohesion, and rolling resistance. Fully-resolved CFD-DEM coupling is achieved through a fictitious domain immersed boundary (IB) approach. An improved method for enforcing three-phase contact lines with a VOF-IB extension technique is introduced. We present several simulations of binder jet primitive formation using realistic process parameters and material properties. The DEM particle systems are experimentally calibrated to reproduce the cohesion behavior of physical nickel alloy powder feedstocks. We demonstrate the proposed model’s ability to resolve the interdependent fluid and particle dynamics underlying the process by directly comparing simulated primitive granules with one-to-one experimental counterparts obtained from an in-house validation apparatus. This computational framework provides unprecedented insight into the fundamental mechanisms of binder jet 3D printing and presents a versatile new approach for process parameter optimization and defect mitigation that avoids the inherent challenges of experiments.

바인더 젯 3D 프린팅 공정 중 계면 유체 상과 구속되지 않은 고체 입자의 결합 역학이 결과 구성 요소의 최종 품질과 성능을 좌우합니다. 본 연구는 바인더 미세액적이 분말층에 증착될 때 발생하는 복잡한 계면 유체-입자 상호작용을 시뮬레이션할 수 있는 전산유체역학(CFD) 및 이산요소법(DEM) 프레임워크를 제안합니다.

CFD 솔버는 액체-가스 다중유체 흐름을 포착하기 위해 VOF(유체량) 방법을 사용하고 블록 구조 적응형 메쉬 세분화(AMR)를 사용하여 진화하는 유체-유체 인터페이스 주위의 그리드 세분화를 국지화합니다. DEM 모듈은 6개의 자유도 입자 운동을 해결하고 입자 접촉, 응집력 및 구름 저항을 설명합니다.

완전 분해된 CFD-DEM 결합은 가상 도메인 침지 경계(IB) 접근 방식을 통해 달성됩니다. VOF-IB 확장 기술을 사용하여 3상 접촉 라인을 강화하는 향상된 방법이 도입되었습니다. 현실적인 공정 매개변수와 재료 특성을 사용하여 바인더 제트 기본 형성에 대한 여러 시뮬레이션을 제시합니다.

DEM 입자 시스템은 물리적 니켈 합금 분말 공급원료의 응집 거동을 재현하기 위해 실험적으로 보정되었습니다. 우리는 시뮬레이션된 기본 과립과 내부 검증 장치에서 얻은 일대일 실험 대응물을 직접 비교하여 프로세스의 기본이 되는 상호 의존적인 유체 및 입자 역학을 해결하는 제안된 모델의 능력을 보여줍니다.

이 계산 프레임워크는 바인더 제트 3D 프린팅의 기본 메커니즘에 대한 전례 없는 통찰력을 제공하고 실험에 내재된 문제를 피하는 공정 매개변수 최적화 및 결함 완화를 위한 다용도의 새로운 접근 방식을 제시합니다.

Introduction

Binder jet 3D printing (BJ3DP) is a powder bed additive manufacturing (AM) technology capable of fabricating geometrically complex components from advanced engineering materials, such as metallic superalloys and ultra-high temperature ceramics [1], [2]. As illustrated in Fig. 1(a), the process is comprised of many repetitive print cycles, each contributing a new cross-sectional layer on top of a preceding one to form a 3D CAD-specified geometry. The feedstock material is first delivered from a hopper to a build plate and then spread into a thin layer by a counter-rotating roller. After powder spreading, a print head containing many individual inkjet nozzles traverses over the powder bed while precisely jetting binder microdroplets onto select regions of the spread layer. Following binder deposition, the build plate lowers by a specified layer thickness, leaving a thin void space at the top of the job box that the subsequent powder layer will occupy. This cycle repeats until the full geometries are formed layer by layer. Powder bed fusion (PBF) methods follow a similar procedure, except they instead use a laser or electron beam to selectively melt and fuse the powder material. Compared to PBF, binder jetting offers several distinct advantages, including faster build rates, enhanced scalability for large production volumes, reduced machine and operational costs, and a wider selection of suitable feedstock materials [2]. However, binder jetted parts generally possess inferior mechanical properties and reduced dimensional accuracy [3]. As a result, widescale adoption of BJ3DP to fabricate high-performance, mission-critical components, such as those common to the aerospace and defense sectors, is contingent on novel process improvements and innovations [4].

A major obstacle hindering the advancement of BJ3DP is our limited understanding of how various printing parameters and material properties collectively influence the underlying physical mechanisms of the process and their effect on the resulting components. To date, the vast majority of research efforts to uncover these relationships have relied mainly on experimental approaches [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], which are often expensive and time-consuming and have inherent physical restrictions on what can be measured and observed. For these reasons, there is a rapidly growing interest in using computational models to circumvent the challenges of experimental investigations and facilitate a deeper understanding of the process’s fundamental phenomena. While significant progress has been made in developing and deploying numerical frameworks aimed at powder spreading [20], [21], [22], [23], [24], [25], [26], [27] and sintering [28], [29], [30], [31], [32], simulating the interfacial fluid–particle interaction (IFPI) in the binder deposition stage is still in its infancy. In their exhaustive review, Mostafaei et al. [2] point out the lack of computational models capable of resolving the coupled fluid and particle dynamics associated with binder jetting and suggest that the development of such tools is critical to further improving the process and enhancing the quality of its end-use components.

We define IFPI as a multiphase flow regime characterized by immiscible fluid phases separated by dynamic interfaces that intersect the surfaces of moving solid particles. As illustrated in Fig. 1(b), an elaborate IFPI occurs when a binder droplet impacts the powder bed in BJ3DP. The momentum transferred from the impacting droplet may cause powder compaction, cratering, and particle ejection. These ballistic disturbances can have deleterious effects on surface texture and lead to the formation of large void spaces inside the part [5], [13]. After impact, the droplet spreads laterally on the bed surface and vertically into the pore network, driven initially by inertial impact forces and then solely by capillary action [33]. Attractive capillary forces exerted on mutually wetted particles tend to draw them inward towards each other, forming a packed cluster of bound particles referred to as a primitive [34]. A single-drop primitive is the most fundamental building element of a BJ3DP part, and the interaction leading to its formation has important implications on the final part characteristics, such as its mechanical properties, resolution, and dimensional accuracy. Generally, binder droplets are deposited successively as the print head traverses over the powder bed. The traversal speed and jetting frequency are set such that consecutive droplets coalesce in the bed, creating a multi-drop primitive line instead of a single-drop primitive granule. The binder must be jetted with sufficient velocity to penetrate the powder bed deep enough to provide adequate interlayer binding; however, a higher impact velocity leads to more pronounced ballistic effects.

A computational framework equipped to simulate the interdependent fluid and particle dynamics in BJ3DP would allow for unprecedented observational and measurement capability at temporal and spatial resolutions not currently achievable by state-of-the-art imaging technology, namely synchrotron X-ray imaging [13], [14], [18], [19]. Unfortunately, BJ3DP presents significant numerical challenges that have slowed the development of suitable modeling frameworks; the most significant of which are as follows:

  • 1.Incorporating dynamic fluid–fluid interfaces with complex topological features remains a nontrivial task for standard mesh-based CFD codes. There are two broad categories encompassing the methods used to handle interfacial flows: interface tracking and interface capturing [35]. Interface capturing techniques, such as the popular volume-of-fluid (VOF) [36] and level-set methods [37], [38], are better suited for problems with interfaces that become heavily distorted or when coalescence and fragmentation occur frequently; however, they are less accurate in resolving surface tension and boundary layer effects compared to interface tracking methods like front-tracking [39], arbitrary Lagrangian–Eulerian [40], and space–time finite element formulations [41]. Since interfacial forces become increasingly dominant at decreasing length scales, inaccurate surface tension calculations can significantly deteriorate the fidelity of IFPI simulations involving <100 μm droplets and particles.
  • 2.Dynamic powder systems are often modeled using the discrete element method (DEM) introduced by Cundall and Strack [42]. For IFPI problems, a CFD-DEM coupling scheme is required to exchange information between the fluid and particle solvers. Fully-resolved CFD-DEM coupling suggests that the flow field around individual particle surfaces is resolved on the CFD mesh [43], [44]. In contrast, unresolved coupling volume averages the effect of the dispersed solid phase on the continuous fluid phases [45], [46], [47], [48]. Comparatively, the former is computationally expensive but provides detailed information about the IFPI in question and is more appropriate when contact line dynamics are significant. However, since the pore structure of a powder bed is convoluted and evolves with time, resolving such solid–fluid interfaces on a computational mesh presents similar challenges as fluid–fluid interfaces discussed in the previous point. Although various algorithms have been developed to deform unstructured meshes to accommodate moving solid surfaces (see Bazilevs et al. [49] for an overview of such methods), they can be prohibitively expensive when frequent topology changes require mesh regeneration rather than just modification through nodal displacement. The pore network in a powder bed undergoes many topology changes as particles come in and out of contact with each other, constantly closing and opening new flow channels. Non-body-conforming structured grid approaches that rely on immersed boundary (IB) methods to embed the particles in the flow field can be better suited for such cases [50]. Nevertheless, accurately representing these complex pore geometries on Cartesian grids requires extremely high mesh resolutions, which can impose significant computational costs.
  • 3.Capillary effects depend on the contact angle at solid–liquid–gas intersections. Since mesh nodes do not coincide with a particle surface when using an IB method on structured grids, imposing contact angle boundary conditions at three-phase contact lines is not straightforward.

While these issues also pertain to PBF process modeling, resolving particle motion is generally less crucial for analyzing melt pool dynamics compared to primitive formation in BJ3DP. Therefore, at present, the vast majority of computational process models of PBF assume static powder beds and avoid many of the complications described above, see, e.g., [51], [52], [53], [54], [55], [56], [57], [58], [59]. Li et al. [60] presented the first 2D fully-resolved CFD-DEM simulations of the interaction between the melt pool, powder particles, surrounding gas, and metal vapor in PBF. Following this work, Yu and Zhao [61], [62] published similar melt pool IFPI simulations in 3D; however, contact line dynamics and capillary forces were not considered. Compared to PBF, relatively little work has been published regarding the computational modeling of binder deposition in BJ3DP. Employing the open-source VOF code Gerris [63], Tan [33] first simulated droplet impact on a powder bed with appropriate binder jet parameters, namely droplet size and impact velocity. However, similar to most PBF melt pool simulations described in the current literature, the powder bed was fixed in place and not allowed to respond to the interacting fluid phases. Furthermore, a simple face-centered cubic packing of non-contacting, monosized particles was considered, which does not provide a realistic pore structure for AM powder beds. Building upon this approach, we presented a framework to simulate droplet impact on static powder beds with more practical particle size distributions and packing arrangements [64]. In a study similar to [33], [64], Deng et al. [65] used the VOF capability in Ansys Fluent to examine the lateral and vertical spreading of a binder droplet impacting a fixed bimodal powder bed with body-centered packing. Li et al. [66] also adopted Fluent to conduct 2D simulations of a 100 μm diameter droplet impacting substrates with spherical roughness patterns meant to represent the surface of a simplified powder bed with monosized particles. The commercial VOF-based software FLOW-3D offers an AM module centered on process modeling of various AM technologies, including BJ3DP. However, like the above studies, particle motion is still not considered in this codebase. Ur Rehman et al. [67] employed FLOW-3D to examine microdroplet impact on a fixed stainless steel powder bed. Using OpenFOAM, Erhard et al. [68] presented simulations of different droplet impact spacings and patterns on static sand particles.

Recently, Fuchs et al. [69] introduced an impressive multipurpose smoothed particle hydrodynamics (SPH) framework capable of resolving IFPI in various AM methods, including both PBF and BJ3DP. In contrast to a combined CFD-DEM approach, this model relies entirely on SPH meshfree discretization of both the fluid and solid governing equations. The authors performed several prototype simulations demonstrating an 80 μm diameter droplet impacting an unconstrained powder bed at different speeds. While the powder bed responds to the hydrodynamic forces imparted by the impacting droplet, the particle motion is inconsistent with experimental time-resolved observations of the process [13]. Specifically, the ballistic effects, such as particle ejection and bed deformation, were drastically subdued, even in simulations using a droplet velocity ∼ 5× that of typical jetting conditions. This behavior could be caused by excessive damping in the inter-particle contact force computations within their SPH framework. Moreover, the wetted particles did not appear to be significantly influenced by the strong capillary forces exerted by the binder as no primitive agglomeration occurred. The authors mention that the objective of these simulations was to demonstrate their codebase’s broad capabilities and that some unrealistic process parameters were used to improve computational efficiency and stability, which could explain the deviations from experimental observations.

In the present paper, we develop a novel 3D CFD-DEM numerical framework for simulating fully-resolved IFPI during binder jetting with realistic material properties and process parameters. The CFD module is based on the VOF method for capturing binder–air interfaces. Surface tension effects are realized through the continuum surface force (CSF) method with height function calculations of interface curvature. Central to our fluid solver is a proprietary block-structured AMR library with hierarchical octree grid nesting to focus enhanced grid resolution near fluid–fluid interfaces. The GPU-accelerated DEM module considers six degrees of freedom particle motion and includes models based on Hertz-Mindlin contact, van der Waals cohesion, and viscoelastic rolling resistance. The CFD and DEM modules are coupled to achieve fully-resolved IFPI using an IB approach in which Lagrangian solid particles are mapped to the underlying Eulerian fluid mesh through a solid volume fraction field. An improved VOF-IB extension algorithm is introduced to enforce the contact angle at three-phase intersections. This provides robust capillary flow behavior and accurate computations of the fluid-induced forces and torques acting on individual wetted particles in densely packed powder beds.

We deploy our integrated codebase for direct numerical simulations of single-drop primitive formation with powder beds whose particle size distributions are generated from corresponding laboratory samples. These simulations use jetting parameters similar to those employed in current BJ3DP machines, fluid properties that match commonly used aqueous polymeric binders, and powder properties specific to nickel alloy feedstocks. The cohesion behavior of the DEM powder is calibrated based on the angle of repose of the laboratory powder systems. The resulting primitive granules are compared with those obtained from one-to-one experiments conducted using a dedicated in-house test apparatus. Finally, we demonstrate how the proposed framework can simulate more complex and realistic printing operations involving multi-drop primitive lines.

Section snippets

Mathematical description of interfacial fluid–particle interaction

This section briefly describes the governing equations of fluid and particle dynamics underlying the CFD and DEM solvers. Our unified framework follows an Eulerian–Lagrangian approach, wherein the Navier–Stokes equations of incompressible flow are discretized on an Eulerian grid to describe the motion of the binder liquid and surrounding gas, and the Newton–Euler equations account for the positions and orientations of the Lagrangian powder particles. The mathematical foundation for

CFD solver for incompressible flow with multifluid interfaces

This section details the numerical methodology used in our CFD module to solve the Navier–Stokes equations of incompressible flow. First, we introduce the VOF method for capturing the interfaces between the binder and air phases. This approach allows us to solve the fluid dynamics equations considering only a single continuum field with spatial and temporal variations in fluid properties. Next, we describe the time integration procedure using a fractional-step projection algorithm for

DEM solver for solid particle dynamics

This section covers the numerical procedure for tracking the motion of individual powder particles with DEM. The Newton–Euler equations (Eqs. (10), (11)) are ordinary differential equations (ODEs) for which many established numerical integrators are available. In general, the most challenging aspects of DEM involve processing particle collisions in a computationally efficient manner and dealing with small time step constraints that result from stiff materials, such as metallic AM powders. The

Unified CFD-DEM solver

The preceding sections have introduced the CFD and DEM solution algorithms separately. Here, we discuss the integrated CFD-DEM solution algorithm and related details.

Binder jet process modeling and validation experiments

In this section, we deploy our CFD-DEM framework to simulate the IFPI occurring during the binder droplet deposition stage of the BJ3DP process. The first simulations attempt to reproduce experimental single-drop primitive granules extracted from four nickel alloy powder samples with varying particle size distributions. The experiments are conducted with a dedicated in-house test apparatus that allows for the precision deposition of individual binder microdroplets into a powder bed sample. The

Conclusions

This paper introduces a coupled CFD-DEM framework capable of fully-resolved simulation of the interfacial fluid–particle interaction occurring in the binder jet 3D printing process. The interfacial flow of binder and surrounding air is captured with the VOF method and surface tension effects are incorporated using the CSF technique augmented by height function curvature calculations. Block-structured AMR is employed to provide localized grid refinement around the evolving liquid–gas interface.

CRediT authorship contribution statement

Joshua J. Wagner: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing. C. Fred Higgs III: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Writing – original draft, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by a NASA Space Technology Research Fellowship, United States of America, Grant No. 80NSSC19K1171. Partial support was also provided through an AIAA Foundation Orville, USA and Wilbur Wright Graduate Award, USA . The authors would like to gratefully acknowledge Dr. Craig Smith of NASA Glenn Research Center for the valuable input he provided on this project.

References (155)

NUMERICAL ANALYSIS OF THE HYDRODYNAMICS CHARACTERISTICS OF TORPEDO ANCHOR INSTALLATION UNDER THE INFLUENCE OF OCEAN CURRENTS

魚雷錨擲錨過程受海流擲下之運移特性數值分析

번역된 기고 제목: 해류의 영향에 따른 어뢰 앵커 설치의 유체 역학 특성에 대한 수치 분석

Translated title of the contribution: NUMERICAL ANALYSIS OF THE HYDRODYNAMICS CHARACTERISTICS OF TORPEDO ANCHOR INSTALLATION UNDER THE INFLUENCE OF OCEAN CURRENTS

L. Y. Chen, R. Y. Yang

Abstract

The gravity-installed anchor (GIA) is a type of the anchor foundation that is installed by penetrating the seabed using the weight of the anchor body. It has the advantages of high installation efficiency, low cost, and no requirement of additional installation facilities. The GIA type used in this study is the torpedo anchor, which has been ap-plied in practical cases widely. The purpose of this study is to investigate the numerical analysis of the anchor trans-porting during the installation of the torpedo anchor under the action of ocean currents. Therefore, this article con-siders external environmental conditions and the different forms of torpedo anchors by using computational fluid dynamics (CFD) software, FLOW-3D, to simulate the fluid-solid interaction effect on the torpedo anchor. The falling time, impact velocity, displaced angle, and horizontal displacement of the torpedo anchor were observed at an installation height (i.e., the distance between the seabed and the anchor release height) of 85 meters. The obtained results show that when the current velocity is greater, the torpedo anchor will have a larger displaced angle, which will affect the impact velocity of the anchor on the seabed and may cause insufficient penetration depth, leading to installation failure.

중력설치형 앵커(GIA)는 앵커 본체의 무게를 이용하여 해저를 관통하여 설치하는 앵커 기초의 일종이다. 설치 효율성이 높고, 비용이 저렴하며, 추가 설치 시설이 필요하지 않다는 장점이 있습니다. 본 연구에서 사용된 GIA 유형은 어뢰앵커로 실제 사례에 널리 적용되어 왔다.

본 연구의 목적은 해류의 작용에 따라 어뢰앵커 설치 시 앵커 이송에 대한 수치해석을 연구하는 것이다. 따라서 이 기사에서는 어뢰 앵커에 대한 유체-고체 상호 작용 효과를 시뮬레이션하기 위해 전산유체역학(CFD) 소프트웨어인 FLOW-3D를 사용하여 외부 환경 조건과 다양한 형태의 어뢰 앵커를 고려합니다.

어뢰앵커의 낙하시간, 충격속도, 변위각, 수평변위 등은 설치높이(즉, 해저와 앵커 해제 높이 ​​사이의 거리) 85m에서 관찰되었다. 얻은 결과는 현재 속도가 더 높을 때 어뢰 앵커의 변위 각도가 더 커져 해저에 대한 앵커의 충격 속도에 영향을 미치고 침투 깊이가 부족하여 설치 실패로 이어질 수 있음을 보여줍니다.

  • Ocean currentsEngineering & Materials Science100%
  • AnchorsEngineering & Materials Science74%
  • Numerical analysisEngineering & Materials Science63%
  • HydrodynamicsEngineering & Materials Science62%
  • GravitationEngineering & Materials Science9%
  • Computational fluid dynamicsEngineering & Materials Science4%
  • FluidsEngineering & Materials Science3%
  • CostsEngineering & Materials Science
  • 해류
  • 앵커
  • 수치해석
  • 유체 역학
  • 중력
  • 전산유체역학
Fig. 3. Free surface and substrate profiles in all Sp and Ls cases at t = 1 s, t = 3 s, and t = 5 s, arranged left to right (note: the colour contours correspond to the horizontal component of the flow velocity (u), expressed in m/s).

Numerical investigation of dam break flow over erodible beds with diverse substrate level variations

다양한 기질 수준 변화를 갖는 침식성 층 위의 댐 파손 흐름에 대한 수치 조사

Alireza Khoshkonesh1, Blaise Nsom2, Saeid Okhravi3*, Fariba Ahmadi Dehrashid4, Payam Heidarian5,
Silvia DiFrancesco6
1 Department of Geography, School of Social Sciences, History, and Philosophy, Birkbeck University of London, London, UK.
2 Université de Bretagne Occidentale. IRDL/UBO UMR CNRS 6027. Rue de Kergoat, 29285 Brest, France.
3 Institute of Hydrology, Slovak Academy of Sciences, Dúbravská cesta 9, 84104, Bratislava, Slovak Republic.
4Department of Water Science and Engineering, Faculty of Agriculture, Bu-Ali Sina University, 65178-38695, Hamedan, Iran.
5 Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, 25123 Brescia, Italy.
6Niccol`o Cusano University, via Don C. Gnocchi 3, 00166 Rome, Italy. * Corresponding author. Tel.: +421-944624921. E-mail: saeid.okhravi@savba.sk

Abstract

This study aimed to comprehensively investigate the influence of substrate level difference and material composition on dam break wave evolution over two different erodible beds. Utilizing the Volume of Fluid (VOF) method, we tracked free surface advection and reproduced wave evolution using experimental data from the literature. For model validation, a comprehensive sensitivity analysis encompassed mesh resolution, turbulence simulation methods, and bed load transport equations. The implementation of Large Eddy Simulation (LES), non-equilibrium sediment flux, and van Rijn’s (1984) bed load formula yielded higher accuracy compared to alternative approaches. The findings emphasize the significant effect of substrate level difference and material composition on dam break morphodynamic characteristics. Decreasing substrate level disparity led to reduced flow velocity, wavefront progression, free surface height, substrate erosion, and other pertinent parameters. Initial air entrapment proved substantial at the wavefront, illustrating pronounced air-water interaction along the bottom interface. The Shields parameter experienced a one-third reduction as substrate level difference quadrupled, with the highest near-bed concentration observed at the wavefront. This research provides fresh insights into the complex interplay of factors governing dam break wave propagation and morphological changes, advancing our comprehension of this intricate phenomenon.

이 연구는 두 개의 서로 다른 침식층에 대한 댐 파괴파 진화에 대한 기질 수준 차이와 재료 구성의 영향을 종합적으로 조사하는 것을 목표로 했습니다. VOF(유체량) 방법을 활용하여 자유 표면 이류를 추적하고 문헌의 실험 데이터를 사용하여 파동 진화를 재현했습니다.

모델 검증을 위해 메쉬 해상도, 난류 시뮬레이션 방법 및 침대 하중 전달 방정식을 포함하는 포괄적인 민감도 분석을 수행했습니다. LES(Large Eddy Simulation), 비평형 퇴적물 플럭스 및 van Rijn(1984)의 하상 부하 공식의 구현은 대체 접근 방식에 비해 더 높은 정확도를 산출했습니다.

연구 결과는 댐 붕괴 형태역학적 특성에 대한 기질 수준 차이와 재료 구성의 중요한 영향을 강조합니다. 기판 수준 차이가 감소하면 유속, 파면 진행, 자유 표면 높이, 기판 침식 및 기타 관련 매개변수가 감소했습니다.

초기 공기 포집은 파면에서 상당한 것으로 입증되었으며, 이는 바닥 경계면을 따라 뚜렷한 공기-물 상호 작용을 보여줍니다. 기판 레벨 차이가 4배로 증가함에 따라 Shields 매개변수는 1/3로 감소했으며, 파면에서 가장 높은 베드 근처 농도가 관찰되었습니다.

이 연구는 댐 파괴파 전파와 형태학적 변화를 지배하는 요인들의 복잡한 상호 작용에 대한 새로운 통찰력을 제공하여 이 복잡한 현상에 대한 이해를 향상시킵니다.

Keywords

Dam break; Substrate level difference; Erodible bed; Sediment transport; Computational fluid dynamics CFD.

Fig. 3. Free surface and substrate profiles in all Sp and Ls cases at t = 1 s, t = 3 s, and t = 5 s, arranged left to right (note: the colour contours
correspond to the horizontal component of the flow velocity (u), expressed in m/s).
Fig. 3. Free surface and substrate profiles in all Sp and Ls cases at t = 1 s, t = 3 s, and t = 5 s, arranged left to right (note: the colour contours correspond to the horizontal component of the flow velocity (u), expressed in m/s).

REFERENCES

Aleixo, R., Soares-Frazão, S., Zech, Y., 2010. Velocity profiles in
dam-break flows: water and sediment layers. In: Proc. Int. Conf.
on Fluvial Hydraulics “River Flow 2010”, pp. 533–540.
An, S., Ku, H., Julien, P.Y., 2015. Numerical modelling of local
scour caused by submerged jets. Maejo Int. J. Sci. Technol., 9, 3,
328–343.
Bahmanpouri, F., Daliri, M., Khoshkonesh, A., Namin, M.M.,
Buccino, M., 2021. Bed compaction effect on dam break flow over
erodible bed; experimental and numerical modeling. J. Hydrol.,
594, 125645. https://doi.org/10.1016/j.jhydrol.2020.125645
Baklanov, A., 2007. Environmental risk and assessment modelling
– scientific needs and expected advancements. In: Ebel, A.,
Davitashvili, T. (Eds.): Air, Water and Soil Quality Modelling
for Risk and Impact Assessment Springer, Dordrecht, pp. 29–44.
Biscarini, C., Di Francesco, S., Nardi, F., Manciola, P., 2013.
Detailed simulation of complex hydraulic problems with
macroscopic and mesoscopic mathematical methods. Math.
Probl. Eng., 928309. https://doi.org/10.1155/2013/928309
Cao, Z., Pender, G., Wallis, S., Carling, P., 2004. Computational
dam-break hydraulics over erodible sediment bed. J. Hydraul.
Eng., 130, 7, 689–703.
Catucci, D., Briganti, R., Heller, V., 2021. Numerical validation of novel
scaling laws for air entrainment in water. Proc. R. Soc. A, 477, 2255,20210339. https://doi.org/10.1098/rspa.2021.0339
Dehrashid, F.A., Heidari, M., Rahimi, H., Khoshkonesh, A., Yuan,
S., Tang, X., Lu, C., Wang, X., 2023. CFD modeling the flow
dynamics in an open channel with double-layered vegetation.
Model. Earth Syst. Environ., 9, 1, 543–555.
Desombre, J., Morichon, D., Mory, M., 2013. RANS v2-f simulation
of a swash event: Detailed flow structure. Coastal Eng., 71, 1–12.
Dodangeh, E., Afzalimehr, H., 2022. Incipient motion of sediment
particles in the presence of bed forms under decelerating and
accelerating flows. J. Hydrol. Hydromech., 70, 1, 89–102.
Dong, Z., Wang, J., Vetsch, D.F., Boes, R.M., Tan, G., 2019.
Numerical simulation of air entrainment on stepped
spillways. In: E-proceedings of the 38th IAHR World Congress
(pp. 1494). September 1–6, 2019, Panama City, Panama. DOI:
10.3850/38WC092019-0755
Flow3D [computer software]. 2023. Santa Fe, NM: Flow Science,
Inc.
Fraccarollo, L., Capart, H., 2002. Riemann wave description of
erosional dam-break flows. J. Fluid Mech., 461, 183–228.
Gu, Z., Wang, T., Meng, W., Yu, C.H., An, R., 2023. Numerical
investigation of silted-up dam-break flow with different silted-up
sediment heights. Water Supply, 23, 2, 599–614.
Gualtieri, P., De Felice, S., Pasquino, V., Doria, G.P., 2018. Use of
conventional flow resistance equations and a model for the
Nikuradse roughness in vegetated flows at high submergence. J.
Hydrol. Hydromech., 66, 1, 107–120.
Heller, V., 2011. Scale effects in physical hydraulic engineering
models. J. Hydraul. Res., 49, 3, 293–306.
Hirt, C.W., 2003. Modeling turbulent entrainment of air at a free
surface. Flow Science, Inc.
Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for
the dynamics of free boundaries. J. Comput. Phys., 39, 1, 201–
225.
Issakhov, A., Zhandaulet, Y., Nogaeva, A., 2018. Numerical
simulation of dam break flow for various forms of the obstacle
by VOF method. Int. J. Multiphase Flow, 109, 191–206.
Khayyer, A., Gotoh, H., 2010. On particle-based simulation of a dam
break over a wet bed. J. Hydraul. Res., 48, 2, 238–249.
Khoshkonesh, A., Daliri, M., Riaz, K., Dehrashid, F.A.,
Bahmanpouri, F., Di Francesco, S., 2022. Dam-break flow
dynamics over a stepped channel with vegetation. J. Hydrol., 613,128395. https://doi.org/10.1016/j.jhydrol.2022.128395
Khoshkonesh, A., Nsom, B., Gohari, S., Banejad, H., 2019.
A comprehensive study on dam-break flow over dry and wet
beds. Ocean Eng., 188, 106279.
https://doi.org/10.1016/j.oceaneng.2019.106279
Khoshkonesh, A., Sadeghi, S.H., Gohari, S., Karimpour, S., Oodi,
S., Di Francesco, S., 2023. Study of dam-break flow over a
vegetated channel with and without a drop. Water Resour.
Manage., 37, 5, 2107–2123.
Khosravi, K., Chegini, A.H.N., Cooper, J., Mao, L., Habibnejad, M.,
Shahedi, K., Binns, A., 2021. A laboratory investigation of bedload transport of gravel sediments under dam break flow. Int. J.
Sediment Res., 36, 2, 229–234.
Kim, Y., Zhou, Z., Hsu, T.J., Puleo, J.A., 2017. Large eddy
simulation of dam‐break‐driven swash on a rough‐planar beach.
J. Geophys. Res.: Oceans, 122, 2, 1274–1296.
Kocaman, S., Ozmen-Cagatay, H., 2012. The effect of lateral
channel contraction on dam break flows: Laboratory experiment.
J. Hydrol., 432, 145–153.
Leal, J.G., Ferreira, R.M., Cardoso, A.H., 2006. Dam-break wavefront celerity. J. Hydraul. Eng., 132, 1, 69–76.
Leal, J.G.A.B., Ferreira, R.M., Cardoso, A.H., 2003. Dam-break
wave propagation over a cohesionless erodible bed. In: Proc.
30rd IAHR Congress, 100, 261–268.
Li, Y. L., Ma, Y., Deng, R., Jiang, D.P., Hu, Z., 2019. Research on
dam-break induced tsunami bore acting on the triangular
breakwater based on high order 3D CLSVOF-THINC/WLICIBM approaching. Ocean Eng., 182, 645–659.
Li, Y.L., Yu, C.H., 2019. Research on dam-break flow induced front
wave impacting a vertical wall based on the CLSVOF and level
set methods. Ocean Eng., 178, 442–462.
Mei, S., Chen, S., Zhong, Q., Shan, Y., 2022. Detailed numerical
modeling for breach hydrograph and morphology evolution
during landslide dam breaching. Landslides, 19, 12, 2925–2949.
Meng, W., Yu, C.H., Li, J., An, R., 2022. Three-dimensional simulation
of silted-up dam-break flow striking a rigid structure. Ocean Eng.,
261, 112042. https://doi.org/10.1016/j.oceaneng.2022.112042
Meyer-Peter, E., Müller, R., 1948. Formulas for bed-load transport.
In: IAHSR 2nd meeting, Stockholm, appendix 2. IAHR.
Nielsen, P., 1984. Field measurements of time-averaged suspended
sediment concentrations under waves. Coastal Eng., 8, 1, 51–72.
Nielsen, P., 2018. Bed shear stress, surface shape and velocity field
near the tips of dam-breaks, tsunami and wave runup. Coastal
Eng., 138, 126–131.
Nsom, B., Latrache, N., Ramifidisoa, L., Khoshkonesh, A., 2019.
Analytical solution to the stability of gravity-driven stratified
flow of two liquids over an inclined plane. In: 24th French
Mechanics Congress in Brest. Brest, p. 244178.
Nsom, B., Ravelo, B., Ndong, W., 2008. Flow regimes in horizontal
viscous dam-break flow of Cayous mud. Appl. Rheol., 18, 4,
43577-1. https://doi.org/10.1515/arh-2008-0012
Oguzhan, S., Aksoy, A.O., 2020. Experimental investigation of the
effect of vegetation on dam break flood waves. J. Hydrol.
Hydromech., 68, 3, 231–241.
Okhravi, S., Gohari, S., Alemi, M., Maia, R., 2022. Effects of bedmaterial gradation on clear water scour at single and group of
piles. J. Hydrol. Hydromech., 70, 1, 114–127.
Okhravi, S., Gohari, S., Alemi, M., Maia, R., 2023. Numerical
modeling of local scour of non-uniform graded sediment for two
arrangements of pile groups. Int. J. Sediment Res., 38, 4, 597–614.
Parambath, A., 2010. Impact of tsunamis on near shore wind power
units. Master’s Thesis. Texas A&M University. Available
electronically from https://hdl.handle.net/1969.1/ETD-TAMU2010-12-8919
Pintado-Patiño, J.C., Puleo, J.A., Krafft, D., Torres-Freyermuth, A.,

  • Hydrodynamics and sediment transport under a dambreak-driven swash: An experimental study. Coastal Eng., 170,
  • https://doi.org/10.1016/j.coastaleng.2021.103986
    Riaz, K., Aslam, H.M.S., Yaseen, M.W., Ahmad, H.H.,
    Khoshkonesh, A., Noshin, S., 2022. Flood frequency analysis
    and hydraulic design of bridge at Mashan on river Kunhar. Arch.
    Hydroengineering Environ. Mech., 69, 1, 1–12.
    Ritter, A., 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift
    des Vereines Deutscher Ingenieure, 36, 33, 947–954. (In
    German.)
    Smagorinsky, J., 1963. General circulation experiments with the
    primitive equations: I. The basic experiment. Mon. Weather
    Rev., 91, 3, 99–164.
    Soulsby, R.L., 1997. Dynamics of marine sands: a manual for
    practical applications. Oceanogr. Lit. Rev., 9, 44, 947.
    Spinewine, B., Capart, H., 2013. Intense bed-load due to a sudden
    dam-break. J. Fluid Mech., 731, 579–614.
    Van Rijn, L.C., 1984. Sediment transport, part I: bed load transport.
    J. Hydraul. Eng., 110, 10, 1431–1456.
    Vosoughi, F., Rakhshandehroo, G., Nikoo, M.R., Sadegh, M.,
  • Experimental study and numerical verification of
    silted-up dam break. J. Hydrol., 590, 125267.
    https://doi.org/10.1016/j.jhydrol.2020.125267
    Wu, W., Wang, S.S., 2008. One-dimensional explicit finite-volume
    model for sediment transport. J. Hydraul. Res., 46, 1, 87–98.
    Xu, T., Huai, W., Liu, H., 2023. MPS-based simulation of
    dam-break wave propagation over wet beds with a
    sediment layer. Ocean Eng., 281, 115035.
    https://doi.org/10.1016/j.oceaneng.2023.115035
    Yang, S., Yang, W., Qin, S., Li, Q., Yang, B., 2018. Numerical study
    on characteristics of dam-break wave. Ocean Eng., 159, 358–371.
    Yao, G.F., 2004. Development of new pressure-velocity solvers in
    FLOW-3D. Flow Science, Inc., USA.
Fig. 3. (a–c) Snapshots of the CtFD simulation of laser-beam irradiation: (a) Top, (b) longitudinal vertical cross-sectional, and (c) transversal vertical cross-sectional views. (d) z-position of the solid/liquid interface during melting and solidification.

Solute segregation in a rapidly solidified Hastelloy-X Ni-based superalloy during laser powder bed fusion investigated by phase-field simulations and computational thermal-fluid dynamics

Masayuki Okugawa ab, Kenji Saito a, Haruki Yoshima a, Katsuhiko Sawaizumi a, Sukeharu Nomoto c, Makoto Watanabe c, Takayoshi Nakano ab, Yuichiro Koizumi abShow moreAdd to MendeleyShareCite

https://doi.org/10.1016/j.addma.2024.104079

Get rights and content Under a Creative Commons license open access

Abstract

Solute segregation significantly affects material properties and is a critical issue in the laser powder-bed fusion (LPBF) additive manufacturing (AM) of Ni-based superalloys. To the best of our knowledge, this is the first study to demonstrate a computational thermal-fluid dynamics (CtFD) simulation coupled multi-phase-field (MPF) simulation with a multicomponent-composition model of Ni-based superalloy to predict solute segregation under solidification conditions in LPBF. The MPF simulation of the Hastelloy-X superalloy reproduced the experimentally observed submicron-sized cell structure. Significant solute segregations were formed within interdendritic regions during solidification at high cooling rates of up to 10K s-1, a characteristic feature of LPBF. Solute segregation caused a decrease in the solidus temperature (TS), with a reduction of up to 30.4 K, which increases the risk of liquation cracks during LPBF. In addition, the segregation triggers the formation of carbide phases, which increases the susceptibility to ductility dip cracking. Conversely, we found that the decrease in TS is suppressed at the melt-pool boundary regions, where re-remelting occurs during the stacking of the layer above. Controlling the re-remelting behavior is deemed to be crucial for designing crack-free alloys. Thus, we demonstrated that solute segregation at the various interfacial regions of Ni-based multicomponent alloys can be predicted by the conventional MPF simulation. The design of crack-free Ni-based superalloys can be expedited by MPF simulations of a broad range of element combinations and their concentrations in multicomponent Ni-based superalloys.

Graphical abstract

Keywords

Laser powder-bed fusion, Hastelloy-X Nickel-based superalloy, solute element segregation, computational thermal-fluid dynamics simulation, phase-field method

1. Introduction

Additive manufacturing (AM) technologies have attracted considerable attention as they allow us to easily build three-dimensional (3D) parts with complex geometries. Among the wide range of available AM techniques, laser powder-bed fusion (LPBF) has emerged as a preferred technique for metal AM [1][2][3][4][5]. In LPBF, metal products are built layer-by-layer by scanning laser, which fuse metal powder particles into bulk solids.

Significant attempts have been made to integrate LPBF techniques within the aerospace industry, with a particular focus on weldable Ni-based superalloys, such as IN718 [6][7][8], IN625 [9][10], and Hastelloy-X (HX) [11][12][13][14]. Non-weldable alloys, such as IN738LC [15][16] and CMSX-4 [1][17] are also suitable for their sufficient creep resistance under higher temperature conditions. However, non-weldable alloys are difficult to build using LPBF because of their susceptibility to cracking during the process. In general, a macro solute-segregation during solidification is suppressed by the rapid cooling conditions (up to 108 K s-1) unique to the LPBF process [18]. However, the solute segregation still occurs in the interdendritic regions that are smaller than the micrometer scale [5][19][20][21]; these regions are suggested to be related to the hot cracks in LPBF-fabricated parts. Therefore, an understanding of solute segregation is essential for the fabrication of reliable LPBF-fabricated parts while avoiding cracks.

The multiphase-field (MPF) method has gained popularity for modeling the microstructure evolution and solute segregation under rapid cooling conditions [5][20][21][22][23][24][25][26][27][28]. Moreover, quantifiable predictions have been achieved by combining the MPF method with temperature distribution analysis methods such as the finite-element method (FEM) [20] and computational thermal-fluid dynamics (CtFD) simulations [28]. These aforementioned studies have used binary-approximated multicomponent systems, such as Ni–Nb binary alloys, to simulate IN718 alloys. While MPF simulations using binary alloy systems can effectively reproduce microstructure formations and segregation behaviors, the binary approximation might be affected by the chemical interactions between the removed solute elements in the target multicomponent alloy. The limit of absolute stability predicted by the Mullins-Sekerka theory [29] is also crucial because the limit velocity is close to the solidification rate in the LPBF process and is different in multicomponent and binary-approximated systems. The difference between the solidus and liquidus temperatures, ΔT0, directly determines the absolute stability according to the Mullins-Sekerka theory. For example, the ΔT0 values of IN718 and its binary-approximated Ni–5 wt.%Nb alloy are 134 K [28] and 71 K [30], respectively. The solidification rate compared to the limit of absolute stability, i.e., the relative non-equilibrium of solidification, changes by simplification of the system. It is therefore important to use the composition of the actual multicomponent system in such simulations. However, to the best of our knowledge, there is no MPF simulation using a multicomponent model coupled with a temperature analysis simulation to predict solute segregation in a Ni-based superalloy.

In this study, we demonstrate that the conventional MPF model can reproduce experimentally observed dendritic structures by performing a phase-field simulation using the temperature distribution obtained by a CtFD simulation of a multicomponent Ni-based alloy (conventional solid-solution hardening-type HX). The MPF simulation revealed that the segregation behavior of solute elements largely depends on the regions of the melt pool, such as the cell boundary, the interior of the melt-pool boundary, and heat-affected regions. The sensitivities of the various interfaces to liquation and solidification cracks are compared based on the predicted concentration distributions. Moreover, the feasibility of using the conventional MPF model for LPBF is discussed in terms of the absolute stability limit.

2. Methods

2.1. Laser-beam irradiation experiments

Rolled and recrystallized HX ingots with dimensions of 20 × 50 × 10 mm were used as the specimens for laser-irradiation experiments. The specimens were irradiated with a laser beam scanned along straight lines of 10 mm in length using a laser AM machine (EOS 290 M, EOS) equipped with a 400 W Yb-fiber laser. Irradiation was performed with a beam power of P = 300 W and a scanning speed of V = 600 mm s-1, which are the conditions generally used in the LPBF fabrication of Ni-based superalloy [8]. The corresponding line energy was 0.5 J mm-1. The samples were cut perpendicular to the beam-scanning direction for cross-sectional observation using a field-emission scanning electron microscope (FE-SEM, JEOL JSM 6500). Crystal orientation analysis was performed by electron backscatter diffraction (EBSD). The sizes of each crystal grain and their aspect ratios were evaluated by analyzing the EBSD data.

2.2. CtFD simulation

CtFD simulations of the laser-beam irradiation of HX were performed using a 3D thermo-fluid analysis software (Flow Science FLOW-3D® with Flow-3D Weld module). A Gaussian heat source model was used, in which the irradiation intensity distribution of the beam is regarded as a symmetrical Gaussian distribution over the entire beam. The distribution of the beam irradiation intensity is expressed by the following equation.(1)q̇=2ηPπR2exp−2r2R2.

Here, P is the power, R is the effective beam radius, r is the actual beam radius, and η is the beam absorption rate of the substrate. To improve the accuracy of the model, η was calculated by assuming multiple reflections using the Fresnel equation:(2)�=1−121+1−�cos�21+1+�cos�2+�2−2�cos�+2cos2��2+2�cos�+2cos2�.

ε is the Fresnel coefficient and θ is the incident angle of the laser. A local laser melt causes the vaporization of the material and results in a high vapor pressure. This vapor pressure acts as a recoil pressure on the surface, pushing the weld pool down. The recoil pressure is reproduced using the following equation.(3)precoil=Ap0exp∆HLVRTV1−TVT.

Here, p0 is the atmospheric pressure, ∆HLV is the latent heat of vaporization, R is the gas constant, and TV is the boiling point at the saturated vapor pressure. A is a ratio coefficient that is generally assumed to be 0.54, indicating that the recoil pressure due to evaporation is 54% of the vapor pressure at equilibrium on the liquid surface.

Table 1 shows the parameters used in the simulations. Most parameters were evaluated using an alloy physical property calculation software (Sente software JMatPro v11). The values in a previously published study [31] were used for the emissivity and the Stefan–Boltzmann constant, and the values for pure Ni [32] were used for the heat of vaporization and vaporization temperatures. The Fresnel coefficient, which determines the beam absorption efficiency, was used as a fitting parameter to reproduce the morphology of the experimentally observed melt region, and a Fresnel coefficient of 0.12 was used in this study.

Table 1. Parameters used in the CtFD simulations.

ParameterSymbolValueReference
Density at 298.15 Kρ8.24 g cm-3[]
Liquidus temperatureTL1628.15 K[]
Solidus temperatureTS1533.15 K[]
Viscosity at TLη6.8 g m-1 s-1[]
Specific heat at 298.15 KCP0.439 J g-1 K-1[]
Thermal conductivity at 298.15 Kλ10.3 W m-1 K-1[]
Surface tension at TLγL1.85 J m-2[]
Temperature coefficient of surface tensiondγL/dT–2.5 × 10−4 J m-2 K-1[]
EmissivityΕ0.27[31]
Stefan–Boltzmann constantσ5.67 × 10-8 W m-2 K-4[31]
Heat of fusionΔHSL2.76 × 102 J g-1[32]
Heat of vaporizationΔHLV4.29 × 10J g-1[32]
Vaporization temperatureTV3110 K[32]

Calculated using JMatPro v11.

The dimensions of the computational domain of the numerical model were 4.0 mm in the beam-scanning direction, 0.4 mm in width, and 0.3 mm in height. A uniform mesh size of 10 μm was applied throughout the computational domain. The boundary condition of continuity was applied to all boundaries except for the top surface. The temperature was initially set to 300 K. P and V were set to their experimental values, i.e., 300 W and 600 mm s-1, respectively. Solidification conditions based on the temperature gradient, G, the solidification rate, R, and the cooling rate were evaluated, and the obtained temperature distribution was used in the MPF simulations.

2.3. MPF simulation

Two-dimensional MPF simulations weakly coupled with the CtFD simulation were performed using the Microstructure Evolution Simulation Software (MICRESS) [33][34][35][36][37] with the TQ-Interface for Thermo-Calc [38]. A simplified HX alloy composition of Ni-21.4Cr-17.6Fe-0.46Mn-8.80Mo-0.39Si-0.50W-1.10Co-0.08 C (mass %) was used in this study. The Gibbs free energy and diffusion coefficient of the system were calculated using the TCNI9 thermodynamic database [39] and the MOBNi5 mobility database [40]. Τhe equilibrium phase diagram calculated using Thermo-Calc indicates that the face-centered cubic (FCC) and σ phases appear as the equilibrium solid phases [19]. However, according to the time-temperature-transformation (TTT) diagram [41], the phases are formed after the sample is maintained for tens of hours in a temperature range of 1073 to 1173 K. Therefore, only the liquid and FCC phases were assumed to appear in the MPF simulations. The simulation domain was 5 × 100 μm, and the grid size Δx and interface width were set to 0.025 and 0.1 µm, respectively. The interfacial mobility between the solid and liquid phases was set to 1.0 × 10-8 m4 J-1 s-1. Initially, one crystalline nucleus with a [100] crystal orientation was placed at the left bottom of the simulation domain, with the liquid phase occupying the remainder of the domain. The model was solidified under the temperature field distribution obtained by the CtFD simulation. The concentration distribution and crystal orientation of the solidified model were examined. The primary dendrite arm space (PDAS) was compared to the experimental PDAS measured by the cross-sectional SEM observation.

In an actual LPBF process, solidified layers are remelted and resolidified during the stacking of the one layer above, thereby greatly affecting solute element distributions in those regions. Therefore, remelting and resolidification simulations were performed to examine the effect of remelting on solute segregation. The solidified model was remelted and resolidified by applying a time-dependent temperature field shifted by 60 μm in the height direction, assuming reheating during the stacking of the upper layer (i.e., the upper 40 μm region of the simulation box was remelted and resolidified). The changes in the composition distribution and formed microstructure were investigated.

3. Results

3.1. Experimental observation of melt pool

Fig. 1 shows a cross-sectional optical microscopy image and corresponding inverse pole figure (IPF) orientation maps obtained from the laser-melted region of HX. The dashed line indicates the fusion line. A deep melted region was formed by keyhole-mode melting due to the vaporization of the metal and resultant recoil pressure. Epitaxial growth from the unmelted region was observed. Columnar crystal grains with an average diameter of 5.46 ± 0.32 μm and an aspect ratio of 3.61 ± 0.13 appeared at the melt regions (Figs. 1b–1d). In addition, crystal grains growing in the z direction could be observed in the lower center.

Fig. 1

Fig. 2a shows a cross-sectional backscattering electron image (BEI) obtained from the laser-melted region indicated by the black square in Fig. 1a. The bright particles with a diameter of approximately 2 μm observed outside the melt pool. It is well known that M6C, M23C6, σ, and μ precipitate phases are formed in Hastelloy-X [41]. These precipitates mainly consisted of Mo, Cr, Fe, and Ni; The μ and M6C phases are rich in Mo, while the σ and M23C6 phases are rich in Cr. The SEM energy dispersive X-ray spectroscopy analysis suggested that the bright particles are the stable precipitates as shown in Fig. S2 and Table S1. Conversely, there are no carbides in the melt pool. This suggests that the cooling rate is extremely high during LPBF, which prevents the formation of a stable carbide during solidification. Figs. 2b–2f show magnified BEI images at different height positions indicated in Fig. 2a. Bright regions are observed between the cells, which become fragmentary at the center of the melt pool, as indicated by the yellow arrow heads in Figs. 2e and 2f.

Fig. 2

3.2. CtFD simulation

Figs. 3a–3c show snapshots of the CtFD simulation of HX at 2.72 ms, with the temperature indicated in color. A melt pool with an elongated teardrop shape formed and keyhole-mode melting was observed at the front of the melt region. The cooling rate, temperature gradient (G), and solidification rate (R) were evaluated from the temporal change in the temperature distribution of the CtFD simulation results. The z-position of the solid/liquid interface during the melting and solidification processes is shown in Fig. 3d. The interface goes down rapidly during melting and then rises during solidification. The MPF simulation of the microstructure formation during solidification was performed using the temperature distribution. Moreover, the microstructure formation process during the fabrication of the upper layer was investigated by remelting and resolidifying the solidified layer using the same temperature distribution with a 60 μm upward shift, corresponding to the layer thickness commonly used in the LPBF of Ni-based superalloys.

Fig. 3

Figs. 4a–4c show the changes in the cooling rate, temperature gradient, and solidification rate in the center line of the melt pool parallel to the z direction. To output the solidification conditions at the solid/liquid interface in the melt pool, only the data of the mesh where the solid phase ratio was close to 0.5 were plotted. Solidification occurred where the cooling rate was in the range of 2.1 × 105–1.6 × 10K s-1G was in the range of 3.6 × 105–1.9 × 10K m-1, and R was in the range of 8.2 × 10−2–6.3 × 10−1 m s-1. The cooling rate was the highest near the fusion line and decreased as the interface approached the center of the melt region (Fig. 4a). G also exhibited the highest value in the regions near the fusion line and decreased throughout the solid/liquid interface toward the center of the melt pool (Fig. 4b). R had the lowest value near the fusion line and increased as the interface approached the center of the melt region (Fig. 4c).

Fig. 4

3.3. MPF simulations coupled with CtFD simulation

MPF simulations of solidification, remelting, and resolidification were performed using the temperature-time distribution obtained by the CtFD simulation. Fig. 5 shows the MPF solidified models colored by phase and Mo concentration. All the computational domains show the FCC phase after the solidification (Fig. 5a). Dendrites grew parallel to the heat flow direction, and solute segregations were observed in the interdendritic regions. At the bottom of the melt pool (Fig. 5d), planar interface growth occurred before the formation of primary dendrites. The bottom of the melt pool is the turning point of the solid/liquid interface from the downward motion in melting to the upward motion in solidification. Thus, the solidification rate at the boundary is zero, and is extremely low immediately above the molt-pool boundary. Here, the lower limit of the solidification rate (R) for dendritic growth can be represented by the constitutional supercooling criterion [29]Vcs = (G × DL) / ΔT, and planar interface growth occurs at R < VcsDL and ΔT denote the diffusion coefficient in the liquid and the equilibrium freezing range, respectively. The results suggest that planar interface growth occurs at the bottom of the melt pool, resulting in a dark region with a different solute element distribution. Some of the primary dendrites were diminished by competition with other dendrites. In addition, secondary dendrite arms could be seen in the upper regions (Fig. 5c), where solidification occurred at a lower cooling rate. The fragmentation of the solute segregation near the secondary dendrite arms is similar to that observed in the experimental melt pool shown in Figs. 2e and 2f, and the secondary dendrite arms are suggested to have appeared at the center of the melt region. Fig. 6 shows the PDASs measured from the MPF simulation models, compared to the experimental PDASs measured by the cross-sectional SEM observation of the laser-melted regions (Fig. 2). The PDAS obtained by the MPF simulation become larger as the solidification progress. Ghosh et al. [21] evident by the phase-field method that the PDAS decreases as the cooling rate increases under the rapid cooling conditions obtained by the finite element analysis. In this study, the cooling rate was decreased as the interface approached the center of the melt region (Fig. 4a), and the trends in PDAS changes with respect to cooling rate is same as the reported trend [21]. The simulated trends of the PDAS with the position in the melt pool agreed well with the experimental trends. However, all PDASs in the simulation were larger than those observed in the experiment at the same positions. Ode et al. [42] reported that PDAS differences between 2D and 3D MPF simulations can be represented by PDAS2D = 1.12 × PDAS3D owing to differences in the effects of the interfacial energy and diffusivity. We also performed 2D and 3D MPF simulations under the solidification conditions of G = 1.94 × 10K m-1 and R = 0.82 m s-1 (Fig. S1), and found that the PDAS from the 2D MPF simulation was 1.26 times larger than that from the 3D simulation. Therefore, the cell structure obtained by the CtFD simulation coupled with the 2D MPF simulation agreed well with the experimental results over the entire melt pool region considering the dimensional effects.

Fig. 5
Fig. 6

Fig. 7b1 and 7c1 show the concentration profiles of the solidified model along the growth direction indicated by dashed lines in Fig. 7a. The differences in concentrations from the alloy composition are also shown in Fig. 7b2 and 7c2. Cr, Mo, C, Mn, and W were segregated to the interdendritic regions, while Si, Fe, and Co were depressed. The solute segregation behavior agrees with the experimentally observation [43] and the prediction by the Scheil-Gulliver simulation [19]. Segregation occurred to the highest degree in Mo, while the ratio of segregation to the alloy composition was remarkable in C. The concentration fluctuations correlated with the position in the melt pool and decreased at the center of the melt pool, which was suggested to correspond to the lower cooling rate in this region. Conversely, droplets that appeared between secondary dendrite arms in the upper regions of the simulation domain exhibited a locally high segregation of solute elements, with the same amount of segregation as that at the bottom of the melt pool.

Fig. 7

3.4. Remelting and resolidification simulation

The solidified model was subjected to remelting and resolidification conditions by shifting the temperature profile upward by 60 µm to reveal the effect of reheating on the solute segregation behavior. Figs. 8a and 8b shows the simulation domains of the HX model after resolidification, colored by phase and Mo concentration. The magnified MPF models during the resolidification of the regions indicated by rectangles in Figs. 8a and 8b are also shown as Figs. 8c and 8d. Dendrites grew from the bottom of the remelted region, with the segregation of solute elements occurring in the interdendritic regions. The entire domain become the FCC phase after the resolidification, as shown in Fig. 8a. The bottom of the remelted regions exhibited a different microstructure, and Mo was depressed at the remelted regions, rather than the interdendritic regions. The different solute segregation behavior [44] and the microstructure formation [45] at the melt pool boundary is also observed in LPBF manufactured 316 L stainless steel. We found that this microstructure was formed by further remelting during the resolidification process, which is shown in Fig. 9. Here, the solidified HX model was heated, and the interdendritic regions were preferentially melted while concentration fluctuations were maintained (Fig. 9a1 and 9a2). Subsequently, planer interface growth occurs near the melt pool boundary where the solidification rate is almost zero, and the dendrites outside of the boundary are grown epitaxially (Fig. 9b1 and 9b2). However, these remelted again because of the temperature rise (Fig. 9c1 and 9c2, and the temperature-time profile shown in Fig. 9e). The remelted regions then cooled and solidified with the abnormal solute segregations (Fig. 9d1 and 9d2). Then, dendrite grows from amplified fluctuations under the solidification rate larger than the criterion of constitutional supercooling (Fig. 9d1, 9d2, and Fig. 8d). It has been reported [46][47] that temperature rising owning to latent heat affects microstructure formation: phase-field simulations of a Ni–Al binary alloy suggest that the release of latent heat during solidification increases the average temperature of the system [46] and strongly influences the solidification conditions [47]. In this study, the release of latent heat during solidification is considered in CtFD simulations for calculating the temperature distribution, and the temperature increase is suggested to have also occurred due to the release of latent heat.

Fig. 8
Fig. 9

Fig. 10b1 and 10c1 show the solute element concentration line profiles of the resolidified model along the growth direction indicated by dashed lines in Fig. 10a. Fig. 10b2 and 10c2 show the corresponding differences in concentration from the alloy composition. The segregation behavior of solute elements at the interdendritic regions (Fig. 10b1 and 10b2) was the same as that in the solidified model (Figs. 7b1 and 7b2). Here, Cr, Mo, C, Mn, and W were segregated to the interdendritic regions, while Si, Fe, and Co were depressed. However, the concentration fluctuations at the interdendritic regions were larger than those in the solidified model. Moreover, the segregation of the outside of the melt pool, i.e., the heat-affected zone, was remarkable throughout remelting and resolidification. Different segregation behaviors were observed in the re-remelted region: Mo, Si, Mn, and W were segregated, while Ni, Fe, and Co were depressed. These solute segregations caused by remelting are expected to heavily influence the crack behavior.

Fig. 10

4. Discussion

4.1. Effect of segregation of solute elements on liquation cracking susceptibility

Strong solute segregation was observed between the interdendritic regions of the solidified alloy (Fig. 7). In addition, the solute segregation behavior was significantly affected by remelting and resolidification and varied across the alloy. Solute segregation can be categorized by the regions shown in Fig. 11a1–11a4, namely the cell boundary (Fig. 11a1), interior of the melt-pool boundary (Fig. 11a2), re-remelted regions (Fig. 11a3), and heat-affected regions (Fig. 11a4). The concentration profiles of these regions are shown in Fig. 11b1–11b4. Solute segregation was the highest in the cell boundary region. The solute segregation in the heat-affected region was almost the same as that in the cell boundary region, but seemed to have been attenuated by reheating during remelting and resolidification. The interior of the melt-pool boundary region also had the same tendency for solute segregation. However, the amount of Cr segregation was smaller than that of Mo. A decrease in the Cr concentration was also mitigated, and the concentration remained the same as that in the alloy composition. Fig. 11c1–11c4 show the chemical potentials of the solute elements for the FCC phase at 1073 K calculated using the compositions of those interfacial regions. All the interfacial regions showed non-constant chemical potentials for each element along the perpendicular direction, but the fluctuations of the chemical potentials differed by the type of interfaces. In particular, the fluctuation of the chemical potential of C at the cell boundary region was the largest, suggesting it can be relaxed easily by heat treatment. On the other hand, the fluctuations of the other elements in all the regions were small. The solute segregations are most likely to remain after the heat treatment and are supposed to affect the cracking susceptibilities.

Fig. 11

The solidus temperatures TS, the difference between the liquidus and solidus temperatures (i.e., the brittle temperature range (BTR)), and the fractions of the equilibrium precipitate phases at 1073 K of the interfacial regions were calculated as the liquation, solidification, and ductility dip cracking susceptibilities, respectively. At the cell boundary (Fig. 12a1), interior of the melt-pool boundary (Fig. 12a1), and heat-affected regions (Fig. 12a1), the internal and interfacial regions exhibited higher and lower TS compared to that of the alloy composition, respectively. The lowest Ts was obtained with the composition at the cell boundary region, which is the largest solute-segregated region. It has been suggested that strong segregations of solute elements in LPBF lead to liquation cracks [16]. This study also supports this suggestion, and liquation cracks are more likely to occur at the interfacial regions indicated by predicting the solute segregation behavior using the MPF model. Additionally, the BTRs of the cell boundary, interior of the melt-pool boundary, and heat-affected regions were wider at the interdendritic regions, and solidification cracks were also likely to occur in these regions. Moreover, within the solute segregation regions, the fraction of the precipitate phases in these interfacial regions was larger than that calculated using the alloy composition (Fig. 12c1, 12c2, and 12c4). This indicates that ductility dip cracking is also likely to occur at the cell boundary, interior of the melt-pool boundary, and in heat-affected regions. Contrarily, we found that the re-remelted region exhibited a higher TS and smaller BTR even in the interfacial region (Fig. 12a3 and 12b3), where the solute segregation behavior was different from that of the other regions. In addition, the re-remelting region exhibited less precipitation compared with the other segregated regions (Fig. 12c3). The re-remelting caused by the latent heat can attenuate solute segregation, prevent Ts from decreasing, decrease the BTR, and decrease the amount of precipitate phases. Alloys with a large amount of latent heat are expected to increase the re-remelting region, thereby decreasing the susceptibility to liquation and ductility dip cracks due to solute element segregation. This can be a guide for designing alloys for the LPBF process. As mentioned in Section 3.4, the microstructure [45] and the solute segregation behavior [44] at the melt pool boundary of LPBF-manufactured 316 L stainless steel are observed, and they are different from that of the interdendritic regions. Experimental observations of the solute segregation behavior in the LPBF-fabricated Ni-based alloys are currently underway.

Fig. 12

4.2. Applicability of the conventional MPF simulation to microstructure formation under LPBF

As the solidification growth rate increases, segregation coefficients approach 1, and the fluctuation of the solid/liquid interface is suppressed by the interfacial tension. The interface growth occurs in a flat fashion instead of having a cellular morphology at a velocity above the absolute stability limit, Ras, predicted by the Mullins-Sekerka theory [29]Ras = (ΔT0 DL) / (k Γ) where ΔT0DLk, and Γ are the difference between the liquidus and solidus temperatures, equilibrium segregation coefficient, the diffusivity of liquid, and the Gibbs-Thomson coefficient, respectively.

The Ras of HX was calculated using the equation and the thermodynamic parameters obtained by the TCNI9 thermodynamic database [39]. The calculated Ras of HX was 3.9 m s-1 and is ten times larger than that of the Ni–Nb alloy (approximately 0.4 m s-1[20]. The HX alloy was solidified under R values in the range of 8.2 × 10−2–6.3 × 10−1 m s-1. The theoretically calculated criterion is larger than the evaluated R, and is in agreement with the experiment in which dendritic growth is observed in the melt pool (Fig. 5). In contrast, Karayagiz et al. [20] reported that the R of the Ni–Nb binary alloy under LPBF was as high as approximately 2 m s-1, and planar interface growth was observed to be predominant under the high-growth-rate conditions. These experimentally observed microstructures agree well with the prediction by the Mullins-Sekerka theory about the relationship between the morphology and solidification rates.

In this study, the solidification microstructure formed by the laser-beam irradiation of an HX multicomponent Ni-based superalloy was reproduced by a conventional MPF simulation, in which the system was assumed to be in a quasi-equilibrium condition. Boussinot et al. [24] also suggested that the conventional phase-field model can be applied to simulate the microstructure of an IN718 multicomponent Ni-based superalloy in LPBF. In contrast, Kagayaski et al. [20] suggested that the conventional MPF simulation cannot be applied to the solidification of the Ni-Nb binary alloy system and that the finite interface dissipation model proposed by Steinbach et al. [48][49] is necessary to simulate the high solidification rates observed in LPBF. The difference in the applicability of the conventional MPF method to HX and Ni–Nb binary alloys is presumed to arise from the differences in the non-equilibrium degree of these systems under the high solidification rates of LPBF. The results suggest that Ras can be used as a simple index to apply the conventional MPF model for solidification in LPBF. Solidification becomes a non-equilibrium process as the solidification rate approaches the limit of absolute stability, Ras. In this study, the solidification of the HX multicomponent system occurred under a relatively low solidification rate compared to Ras, and the microstructure of the conventional MPF model was successfully reproduced in the physical experiment. However, note that the limit of absolute stability predicted by the Mullins-Sekerka theory was originally proposed for solidification in a binary alloy system, and further investigation is required to consider its applicability to multicomponent alloy systems. Moreover, the fast solidification, such as in the LPBF process, causes segregation coefficient approaching a value of 1 [20][21][25] corresponds to a diffusion length that is on the order of the atomic interface thickness. When the segregation coefficient approaches 1, solute undercooling disappears; hence, there is no driving force to amplify fluctuations regardless of whether interfacial tension is present. This phenomenon should be further investigated in future studies.

5. Conclusions

We simulated solute segregation in a multicomponent HX alloy under the LPBF process by an MPF simulation using the temperature distributions obtained by a CtFD simulation. We set the parameters of the CtFD simulation to match the melt pool shape formed in the laser-irradiation experiment and found that solidification occurred under high cooling rates of up to 1.6 × 10K s-1.

MPF simulations using the temperature distributions from CtFD simulation could reproduce the experimentally observed PDAS and revealed that significant solute segregation occurred at the interdendritic regions. Equilibrium thermodynamic calculations using the alloy compositions of the segregated regions when considering crack sensitivities suggested a decrease in the solidus temperature and an increase in the amount of carbide precipitation, thereby increasing the susceptibility to liquation and ductility dip cracks in these regions. Notably, these changes were suppressed at the melt-pool boundary region, where re-remelting occurred during the stacking of the layer above. This effect can be used to achieve a novel in-process segregation attenuation.

Our study revealed that a conventional MPF simulation weakly coupled with a CtFD simulation can be used to study the solidification of multicomponent alloys in LPBF, contrary to the cases of binary alloys investigated in previous studies. We discussed the applicability of the conventional MPF model to the LPBF process in terms of the limit of absolute stability, Ras, and suggested that alloys with a high limit velocity, i.e., multicomponent alloys, can be simulated using the conventional MPF model even under the high solidification velocity conditions of LPBF.

CRediT authorship contribution statement

Masayuki Okugawa: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Takayoshi Nakano: Writing – review & editing, Validation, Supervision, Funding acquisition. Yuichiro Koizumi: Writing – review & editing, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Sukeharu Nomoto: Writing – review & editing, Validation, Investigation. Makoto Watanabe: Writing – review & editing, Validation, Supervision, Funding acquisition. Katsuhiko Sawaizumi: Validation, Software, Investigation, Formal analysis, Data curation. Kenji Saito: Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. Haruki Yoshima: Visualization, Validation, Software, Investigation, Formal analysis, Data curation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

Acknowledgments

This work was partly supported by the Cabinet Office, Government of Japan, Cross-ministerial Strategic Innovation Promotion Program (SIP), “Materials Integration for Revolutionary Design System of Structural Materials,” (funding agency: The Japan Science and Technology Agency), by JSPS KAKENHI Grant Numbers 21H05018 and 21H05193, and by CREST Nanomechanics: Elucidation of macroscale mechanical properties based on understanding nanoscale dynamics for innovative mechanical materials (Grant Number: JPMJCR2194) from the Japan Science and Technology Agency (JST). The authors would like to thank Mr. H. Kawabata and Mr. K. Kimura for their technical support with the sample preparations and laser beam irradiation experiments.

Appendix A. Supplementary material

Download : Download Word document (654KB)

Supplementary material.

Data availability

Data will be made available on request.

References

Schematic diagram of HP-LPBF melting process.

Modeling and numerical studies of high-precision laser powder bed fusion

Yi Wei ;Genyu Chen;Nengru Tao;Wei Zhou
https://doi.org/10.1063/5.0191504

In order to comprehensively reveal the evolutionary dynamics of the molten pool and the state of motion of the fluid during the high-precision laser powder bed fusion (HP-LPBF) process, this study aims to deeply investigate the specific manifestations of the multiphase flow, solidification phenomena, and heat transfer during the process by means of numerical simulation methods. Numerical simulation models of SS316L single-layer HP-LPBF formation with single and double tracks were constructed using the discrete element method and the computational fluid dynamics method. The effects of various factors such as Marangoni convection, surface tension, vapor recoil, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool have been paid attention to during the model construction process. The results show that the molten pool exhibits a “comet” shape, in which the temperature gradient at the front end of the pool is significantly larger than that at the tail end, with the highest temperature gradient up to 1.69 × 108 K/s. It is also found that the depth of the second track is larger than that of the first one, and the process parameter window has been determined preliminarily. In addition, the application of HP-LPBF technology helps to reduce the surface roughness and minimize the forming size.

Topics

Heat transferNonequilibrium thermodynamicsSolidification processComputer simulationDiscrete element methodLasersMass transferFluid mechanicsComputational fluid dynamicsMultiphase flows

I. INTRODUCTION

Laser powder bed fusion (LPBF) has become a research hotspot in the field of additive manufacturing of metals due to its advantages of high-dimensional accuracy, good surface quality, high density, and high material utilization.1,2 With the rapid development of electronics, medical, automotive, biotechnology, energy, communication, and optics, the demand for microfabrication technology is increasing day by day.3 High-precision laser powder bed fusion (HP-LPBF) is one of the key manufacturing technologies for tiny parts in the fields of electronics, medical, automotive, biotechnology, energy, communication, and optics because of its process characteristics such as small focal spot diameter, small powder particle size, and thin powder layup layer thickness.4–13 Compared with LPBF, HP-LPBF has the significant advantages of smaller focal spot diameter, smaller powder particle size, and thinner layer thickness. These advantages make HP-LPBF perform better in producing micro-fine parts, high surface quality, and parts with excellent mechanical properties.

HP-LPBF is in the exploratory stage, and researchers have already done some exploratory studies on the focal spot diameter, the amount of defocusing, and the powder particle size. In order to explore the influence of changing the laser focal spot diameter on the LPBF process characteristics of the law, Wildman et al.14 studied five groups of different focal spot diameter LPBF forming 316L stainless steel (SS316L) processing effect, the smallest focal spot diameter of 26 μm, and the results confirm that changing the focal spot diameter can be achieved to achieve the energy control, so as to control the quality of forming. Subsequently, Mclouth et al.15 proposed the laser out-of-focus amount (focal spot diameter) parameter, which characterizes the distance between the forming plane and the laser focal plane. The laser energy density was controlled by varying the defocusing amount while keeping the laser parameters constant. Sample preparation at different focal positions was investigated, and their microstructures were characterized. The results show that the samples at the focal plane have finer microstructure than those away from the focal plane, which is the effect of higher power density and smaller focal spot diameter. In order to explore the influence of changing the powder particle size on the characteristics of the LPBF process, Qian et al.16 carried out single-track scanning simulations on powder beds with average powder particle sizes of 70 and 40 μm, respectively, and the results showed that the melt tracks sizes were close to each other under the same process parameters for the two particle-size distributions and that the molten pool of powder beds with small particles was more elongated and the edges of the melt tracks were relatively flat. In order to explore the superiority of HP-LPBF technology, Xu et al.17 conducted a comparative analysis of HP-LPBF and conventional LPBF of SS316L. The results showed that the average surface roughness of the top surface after forming by HP-LPBF could reach 3.40 μm. Once again, it was verified that HP-LPBF had higher forming quality than conventional LPBF. On this basis, Wei et al.6 comparatively analyzed the effects of different laser focal spot diameters on different powder particle sizes formed by LPBF. The results showed that the smaller the laser focal spot diameter, the fewer the defects on the top and side surfaces. The above research results confirm that reducing the laser focal spot diameter can obtain higher energy density and thus better forming quality.

LPBF involves a variety of complex systems and mechanisms, and the final quality of the part is influenced by a large number of process parameters.18–24 Some research results have shown that there are more than 50 factors affecting the quality of the specimen. The influencing factors are mainly categorized into three main groups: (1) laser parameters, (2) powder parameters, and (3) equipment parameters, which interact with each other to determine the final specimen quality. With the continuous development of technologies such as computational materials science and computational fluid dynamics (CFD), the method of studying the influence of different factors on the forming quality of LPBF forming process has been shifted from time-consuming and laborious experimental characterization to the use of numerical simulation methods. As a result, more and more researchers are adopting this approach for their studies. Currently, numerical simulation studies on LPBF are mainly focused on the exploration of molten pool, temperature distribution, and residual stresses.

  1. Finite element simulation based on continuum mechanics and free surface fluid flow modeling based on fluid dynamics are two common approaches to study the behavior of LPBF molten pool.25–28 Finite element simulation focuses on the temperature and thermal stress fields, treats the powder bed as a continuum, and determines the molten pool size by plotting the elemental temperature above the melting point. In contrast, fluid dynamics modeling can simulate the 2D or 3D morphology of the metal powder pile and obtain the powder size and distribution by certain algorithms.29 The flow in the molten pool is mainly affected by recoil pressure and the Marangoni effect. By simulating the molten pool formation, it is possible to predict defects, molten pool shape, and flow characteristics, as well as the effect of process parameters on the molten pool geometry.30–34 In addition, other researchers have been conducted to optimize the laser processing parameters through different simulation methods and experimental data.35–46 Crystal growth during solidification is studied to further understand the effect of laser parameters on dendritic morphology and solute segregation.47–54 A multi-scale system has been developed to describe the fused deposition process during 3D printing, which is combined with the conductive heat transfer model and the dendritic solidification model.55,56
  2. Relevant scholars have adopted various different methods for simulation, such as sequential coupling theory,57 Lagrangian and Eulerian thermal models,58 birth–death element method,25 and finite element method,59 in order to reveal the physical phenomena of the laser melting process and optimize the process parameters. Luo et al.60 compared the LPBF temperature field and molten pool under double ellipsoidal and Gaussian heat sources by ANSYS APDL and found that the diffusion of the laser energy in the powder significantly affects the molten pool size and the temperature field.
  3. The thermal stresses obtained from the simulation correlate with the actual cracks,61 and local preheating can effectively reduce the residual stresses.62 A three-dimensional thermodynamic finite element model investigated the temperature and stress variations during laser-assisted fabrication and found that powder-to-solid conversion increases the temperature gradient, stresses, and warpage.63 Other scholars have predicted residual stresses and part deflection for LPBF specimens and investigated the effects of deposition pattern, heat, laser power, and scanning strategy on residual stresses, noting that high-temperature gradients lead to higher residual stresses.64–67 

In short, the process of LPBF forming SS316L is extremely complex and usually involves drastic multi-scale physicochemical changes that will only take place on a very small scale. Existing literature employs DEM-based mesoscopic-scale numerical simulations to investigate the effects of process parameters on the molten pool dynamics of LPBF-formed SS316L. However, a few studies have been reported on the key mechanisms of heating and solidification, spatter, and convective behavior of the molten pool of HP-LPBF-formed SS316L with small laser focal spot diameters. In this paper, the geometrical properties of coarse and fine powder particles under three-dimensional conditions were first calculated using DEM. Then, numerical simulation models for single-track and double-track cases in the single-layer HP-LPBF forming SS316L process were developed at mesoscopic scale using the CFD method. The flow genesis of the melt in the single-track and double-track molten pools is discussed, and their 3D morphology and dimensional characteristics are discussed. In addition, the effects of laser process parameters, powder particle size, and laser focal spot diameter on the temperature field, characterization information, and defects in the molten pool are discussed.

II. MODELING

A. 3D powder bed modeling

HP-LPBF is an advanced processing technique for preparing target parts layer by layer stacking, the process of which involves repetitive spreading and melting of powders. In this process, both the powder spreading and the morphology of the powder bed are closely related to the results of the subsequent melting process, while the melted surface also affects the uniform distribution of the next layer of powder. For this reason, this chapter focuses on the modeling of the physical action during the powder spreading process and the theory of DEM to establish the numerical model of the powder bed, so as to lay a solid foundation for the accuracy of volume of fluid (VOF) and CFD.

1. DEM

DEM is a numerical technique for calculating the interaction of a large number of particles, which calculates the forces and motions of the spheres by considering each powder sphere as an independent unit. The motion of the powder particles follows the laws of classical Newtonian mechanics, including translational and rotational,38,68–70 which are expressed as follows:����¨=���+∑��ij,

(1)����¨=∑�(�ij×�ij),

(2)

where �� is the mass of unit particle i in kg, ��¨ is the advective acceleration in m/s2, And g is the gravitational acceleration in m/s2. �ij is the force in contact with the neighboring particle � in N. �� is the rotational inertia of the unit particle � in kg · m2. ��¨ is the unit particle � angular acceleration in rad/s2. �ij is the vector pointing from unit particle � to the contact point of neighboring particle �⁠.

Equations (1) and (2) can be used to calculate the velocity and angular velocity variations of powder particles to determine their positions and velocities. A three-dimensional powder bed model of SS316L was developed using DEM. The powder particles are assumed to be perfect spheres, and the substrate and walls are assumed to be rigid. To describe the contact between the powder particles and between the particles and the substrate, a non-slip Hertz–Mindlin nonlinear spring-damping model71 was used with the following expression:�hz=��������+��[(�����ij−�eff����)−(�����+�eff����)],

(3)

where �hz is the force calculated using the Hertzian in M. �� and �� are the radius of unit particles � and � in m, respectively. �� is the overlap size of the two powder particles in m. ��⁠, �� are the elastic constants in the normal and tangential directions, respectively. �ij is the unit vector connecting the centerlines of the two powder particles. �eff is the effective mass of the two powder particles in kg. �� and �� are the viscoelastic damping constants in the normal and tangential directions, respectively. �� and �� are the components of the relative velocities of the two powder particles. ��� is the displacement vector between two spherical particles. The schematic diagram of overlapping powder particles is shown in Fig. 1.

FIG. 1.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of overlapping powder particles.

Because the particle size of the powder used for HP-LPBF is much smaller than 100 μm, the effect of van der Waals forces must be considered. Therefore, the cohesive force �jkr of the Hertz–Mindlin model was used instead of van der Waals forces,72 with the following expression:�jkr=−4��0�*�1.5+4�*3�*�3,

(4)1�*=(1−��2)��+(1−��2)��,

(5)1�*=1��+1��,

(6)

where �* is the equivalent Young’s modulus in GPa; �* is the equivalent particle radius in m; �0 is the surface energy of the powder particles in J/m2; α is the contact radius in m; �� and �� are the Young’s modulus of the unit particles � and �⁠, respectively, in GPa; and �� and �� are the Poisson’s ratio of the unit particles � and �⁠, respectively.

2. Model building

Figure 2 shows a 3D powder bed model generated using DEM with a coarse powder geometry of 1000 × 400 × 30 μm3. The powder layer thickness is 30 μm, and the powder bed porosity is 40%. The average particle size of this spherical powder is 31.7 μm and is normally distributed in the range of 15–53 μm. The geometry of the fine powder was 1000 × 400 × 20 μm3, with a layer thickness of 20 μm, and the powder bed porosity of 40%. The average particle size of this spherical powder is 11.5 μm and is normally distributed in the range of 5–25 μm. After the 3D powder bed model is generated, it needs to be imported into the CFD simulation software for calculation, and the imported geometric model is shown in Fig. 3. This geometric model is mainly composed of three parts: protective gas, powder bed, and substrate. Under the premise of ensuring the accuracy of the calculation, the mesh size is set to 3 μm, and the total number of coarse powder meshes is 1 704 940. The total number of fine powder meshes is 3 982 250.

FIG. 2.

VIEW LARGEDOWNLOAD SLIDE

Three-dimensional powder bed model: (a) coarse powder, (b) fine powder.

FIG. 3.

VIEW LARGEDOWNLOAD SLIDE

Geometric modeling of the powder bed computational domain: (a) coarse powder, (b) fine powder.

B. Modeling of fluid mechanics simulation

In order to solve the flow, melting, and solidification problems involved in HP-LPBF molten pool, the study must follow the three governing equations of conservation of mass, conservation of energy, and conservation of momentum.73 The VOF method, which is the most widely used in fluid dynamics, is used to solve the molten pool dynamics model.

1. VOF

VOF is a method for tracking the free interface between the gas and liquid phases on the molten pool surface. The core idea of the method is to define a volume fraction function F within each grid, indicating the proportion of the grid space occupied by the material, 0 ≤ F ≤ 1 in Fig. 4. Specifically, when F = 0, the grid is empty and belongs to the gas-phase region; when F = 1, the grid is completely filled with material and belongs to the liquid-phase region; and when 0 < F < 1, the grid contains free surfaces and belongs to the mixed region. The direction normal to the free surface is the direction of the fastest change in the volume fraction F (the direction of the gradient of the volume fraction), and the direction of the gradient of the volume fraction can be calculated from the values of the volume fractions in the neighboring grids.74 The equations controlling the VOF are expressed as follows:𝛻����+�⋅(��→)=0,

(7)

where t is the time in s and �→ is the liquid velocity in m/s.

FIG. 4.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of VOF.

The material parameters of the mixing zone are altered due to the inclusion of both the gas and liquid phases. Therefore, in order to represent the density of the mixing zone, the average density �¯ is used, which is expressed as follows:72�¯=(1−�1)�gas+�1�metal,

(8)

where �1 is the proportion of liquid phase, �gas is the density of protective gas in kg/m3, and �metal is the density of metal in kg/m3.

2. Control equations and boundary conditions

Figure 5 is a schematic diagram of the HP-LPBF melting process. First, the laser light strikes a localized area of the material and rapidly heats up the area. Next, the energy absorbed in the region is diffused through a variety of pathways (heat conduction, heat convection, and surface radiation), and this process triggers complex phase transition phenomena (melting, evaporation, and solidification). In metals undergoing melting, the driving forces include surface tension and the Marangoni effect, recoil due to evaporation, and buoyancy due to gravity and uneven density. The above physical phenomena interact with each other and do not occur independently.

FIG. 5.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of HP-LPBF melting process.

  1. Laser heat sourceThe Gaussian surface heat source model is used as the laser heat source model with the following expression:�=2�0����2exp(−2�12��2),(9)where � is the heat flow density in W/m2, �0 is the absorption rate of SS316L, �� is the radius of the laser focal spot in m, and �1 is the radial distance from the center of the laser focal spot in m. The laser focal spot can be used for a wide range of applications.
  2. Energy absorptionThe formula for calculating the laser absorption �0 of SS316L is as follows:�0=0.365(�0[1+�0(�−20)]/�)0.5,(10)where �0 is the direct current resistivity of SS316L at 20 °C in Ω m, �0 is the resistance temperature coefficient in ppm/°C, � is the temperature in °C, and � is the laser wavelength in m.
  3. Heat transferThe basic principle of heat transfer is conservation of energy, which is expressed as follows:𝛻𝛻𝛻�(��)��+�·(��→�)=�·(�0����)+��,(11)where � is the density of liquid phase SS316L in kg/m3, �� is the specific heat capacity of SS316L in J/(kg K), 𝛻� is the gradient operator, t is the time in s, T is the temperature in K, 𝛻�� is the temperature gradient, �→ is the velocity vector, �0 is the coefficient of thermal conduction of SS316L in W/(m K), and  �� is the thermal energy dissipation term in the molten pool.
  4. Molten pool flowThe following three conditions need to be satisfied for the molten pool to flow:
    • Conservation of mass with the following expression:𝛻�·(��→)=0.(12)
    • Conservation of momentum (Navier–Stokes equation) with the following expression:𝛻𝛻𝛻𝛻���→��+�(�→·�)�→=�·[−pI+�(��→+(��→)�)]+�,(13)where � is the pressure in Pa exerted on the liquid phase SS316L microelement, � is the unit matrix, � is the fluid viscosity in N s/m2, and � is the volumetric force (gravity, atmospheric pressure, surface tension, vapor recoil, and the Marangoni effect).
    • Conservation of energy, see Eq. (11)
  5. Surface tension and the Marangoni effectThe effect of temperature on the surface tension coefficient is considered and set as a linear relationship with the following expression:�=�0−��dT(�−��),(14)where � is the surface tension of the molten pool at temperature T in N/m, �� is the melting temperature of SS316L in K, �0 is the surface tension of the molten pool at temperature �� in Pa, and σdσ/ dT is the surface tension temperature coefficient in N/(m K).In general, surface tension decreases with increasing temperature. A temperature gradient causes a gradient in surface tension that drives the liquid to flow, known as the Marangoni effect.
  6. Metal vapor recoilAt higher input energy densities, the maximum temperature of the molten pool surface reaches the evaporation temperature of the material, and a gasification recoil pressure occurs vertically downward toward the molten pool surface, which will be the dominant driving force for the molten pool flow.75 The expression is as follows:��=0.54�� exp ���−���0���,(15)where �� is the gasification recoil pressure in Pa, �� is the ambient pressure in kPa, �� is the latent heat of evaporation in J/kg, �0 is the gas constant in J/(mol K), T is the surface temperature of the molten pool in K, and Te is the evaporation temperature in K.
  7. Solid–liquid–gas phase transitionWhen the laser hits the powder layer, the powder goes through three stages: heating, melting, and solidification. During the solidification phase, mutual transformations between solid, liquid, and gaseous states occur. At this point, the latent heat of phase transition absorbed or released during the phase transition needs to be considered.68 The phase transition is represented based on the relationship between energy and temperature with the following expression:�=�����,(�<��),�(��)+�−����−����,(��<�<��)�(��)+(�−��)����,(��<�),,(16)where �� and �� are solid and liquid phase density, respectively, of SS316L in kg/m3. �� and �� unit volume of solid and liquid phase-specific heat capacity, respectively, of SS316L in J/(kg K). �� and ��⁠, respectively, are the solidification temperature and melting temperature of SS316L in K. �� is the latent heat of the phase transition of SS316L melting in J/kg.

3. Assumptions

The CFD model was computed using the commercial software package FLOW-3D.76 In order to simplify the calculation and solution process while ensuring the accuracy of the results, the model makes the following assumptions:

  1. It is assumed that the effects of thermal stress and material solid-phase thermal expansion on the calculation results are negligible.
  2. The molten pool flow is assumed to be a Newtonian incompressible laminar flow, while the effects of liquid thermal expansion and density on the results are neglected.
  3. It is assumed that the surface tension can be simplified to an equivalent pressure acting on the free surface of the molten pool, and the effect of chemical composition on the results is negligible.
  4. Neglecting the effect of the gas flow field on the molten pool.
  5. The mass loss due to evaporation of the liquid metal is not considered.
  6. The influence of the plasma effect of the molten metal on the calculation results is neglected.

It is worth noting that the formulation of assumptions requires a trade-off between accuracy and computational efficiency. In the above models, some physical phenomena that have a small effect or high difficulty on the calculation results are simplified or ignored. Such simplifications make numerical simulations more efficient and computationally tractable, while still yielding accurate results.

4. Initial conditions

The preheating temperature of the substrate was set to 393 K, at which time all materials were in the solid state and the flow rate was zero.

5. Material parameters

The material used is SS316L and the relevant parameters required for numerical simulations are shown in Table I.46,77,78

TABLE I.

SS316L-related parameters.

PropertySymbolValue
Density of solid metal (kg/m3�metal 7980 
Solid phase line temperature (K) �� 1658 
Liquid phase line temperature (K) �� 1723 
Vaporization temperature (K) �� 3090 
Latent heat of melting (⁠ J/kg⁠) �� 2.60×105 
Latent heat of evaporation (⁠ J/kg⁠) �� 7.45×106 
Surface tension of liquid phase (N /m⁠) � 1.60 
Liquid metal viscosity (kg/m s) �� 6×10−3 
Gaseous metal viscosity (kg/m s) �gas 1.85×10−5 
Temperature coefficient of surface tension (N/m K) ��/�T 0.80×10−3 
Molar mass (⁠ kg/mol⁠) 0.05 593 
Emissivity � 0.26 
Laser absorption �0 0.35 
Ambient pressure (kPa) �� 101 325 
Ambient temperature (K) �0 300 
Stefan–Boltzmann constant (W/m2 K4� 5.67×10−8 
Thermal conductivity of metals (⁠ W/m K⁠) � 24.55 
Density of protective gas (kg/m3�gas 1.25 
Coefficient of thermal expansion (/K) �� 16×10−6 
Generalized gas constant (⁠ J/mol K⁠) 8.314 

III. RESULTS AND DISCUSSION

With the objective of studying in depth the evolutionary patterns of single-track and double-track molten pool development, detailed observations were made for certain specific locations in the model, as shown in Fig. 6. In this figure, P1 and P2 represent the longitudinal tangents to the centers of the two melt tracks in the XZ plane, while L1 is the transverse profile in the YZ plane. The scanning direction is positive and negative along the X axis. Points A and B are the locations of the centers of the molten pool of the first and second melt tracks, respectively (x = 1.995 × 10−4, y = 5 × 10−7, and z = −4.85 × 10−5).

FIG. 6.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of observation position.

A. Single-track simulation

A series of single-track molten pool simulation experiments were carried out in order to investigate the influence law of laser power as well as scanning speed on the HP-LPBF process. Figure 7 demonstrates the evolution of the 3D morphology and temperature field of the single-track molten pool in the time period of 50–500 μs under a laser power of 100 W and a scanning speed of 800 mm/s. The powder bed is in the natural cooling state. When t = 50 μs, the powder is heated by the laser heat and rapidly melts and settles to form the initial molten pool. This process is accompanied by partial melting of the substrate and solidification together with the melted powder. The molten pool rapidly expands with increasing width, depth, length, and temperature, as shown in Fig. 7(a). When t = 150 μs, the molten pool expands more obviously, and the temperature starts to transfer to the surrounding area, forming a heat-affected zone. At this point, the width of the molten pool tends to stabilize, and the temperature in the center of the molten pool has reached its peak and remains largely stable. However, the phenomenon of molten pool spatter was also observed in this process, as shown in Fig. 7(b). As time advances, when t = 300 μs, solidification begins to occur at the tail of the molten pool, and tiny ripples are produced on the solidified surface. This is due to the fact that the melt flows toward the region with large temperature gradient under the influence of Marangoni convection and solidifies together with the melt at the end of the bath. At this point, the temperature gradient at the front of the bath is significantly larger than at the end. While the width of the molten pool was gradually reduced, the shape of the molten pool was gradually changed to a “comet” shape. In addition, a slight depression was observed at the top of the bath because the peak temperature at the surface of the bath reached the evaporation temperature, which resulted in a recoil pressure perpendicular to the surface of the bath downward, creating a depressed region. As the laser focal spot moves and is paired with the Marangoni convection of the melt, these recessed areas will be filled in as shown in Fig. 7(c). It has been shown that the depressed regions are the result of the coupled effect of Marangoni convection, recoil pressure, and surface tension.79 By t = 500 μs, the width and height of the molten pool stabilize and show a “comet” shape in Fig. 7(d).

FIG. 7.

VIEW LARGEDOWNLOAD SLIDE

Single-track molten pool process: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠.

Figure 8 depicts the velocity vector diagram of the P1 profile in a single-track molten pool, the length of the arrows represents the magnitude of the velocity, and the maximum velocity is about 2.36 m/s. When t = 50 μs, the molten pool takes shape, and the velocities at the two ends of the pool are the largest. The variation of the velocities at the front end is especially more significant in Fig. 8(a). As the time advances to t = 150 μs, the molten pool expands rapidly, in which the velocity at the tail increases and changes more significantly, while the velocity at the front is relatively small. At this stage, the melt moves backward from the center of the molten pool, which in turn expands the molten pool area. The melt at the back end of the molten pool center flows backward along the edge of the molten pool surface and then converges along the edge of the molten pool to the bottom center, rising to form a closed loop. Similarly, a similar closed loop is formed at the front end of the center of the bath, but with a shorter path. However, a large portion of the melt in the center of the closed loop formed at the front end of the bath is in a nearly stationary state. The main cause of this melt flow phenomenon is the effect of temperature gradient and surface tension (the Marangoni effect), as shown in Figs. 8(b) and 8(e). This dynamic behavior of the melt tends to form an “elliptical” pool. At t = 300 μs, the tendency of the above two melt flows to close the loop is more prominent and faster in Fig. 8(c). When t = 500 μs, the velocity vector of the molten pool shows a stable trend, and the closed loop of melt flow also remains stable. With the gradual laser focal spot movement, the melt is gradually solidified at its tail, and finally, a continuous and stable single track is formed in Fig. 8(d).

FIG. 8.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of single-track molten pool velocity in XZ longitudinal section: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠, (e) molten pool flow.

In order to explore in depth the transient evolution of the molten pool, the evolution of the single-track temperature field and the melt flow was monitored in the YZ cross section. Figure 9(a) shows the state of the powder bed at the initial moment. When t = 250 μs, the laser focal spot acts on the powder bed and the powder starts to melt and gradually collects in the molten pool. At this time, the substrate will also start to melt, and the melt flow mainly moves in the downward and outward directions and the velocity is maximum at the edges in Fig. 9(b). When t = 300 μs, the width and depth of the molten pool increase due to the recoil pressure. At this time, the melt flows more slowly at the center, but the direction of motion is still downward in Fig. 9(c). When t = 350 μs, the width and depth of the molten pool further increase, at which time the intensity of the melt flow reaches its peak and the direction of motion remains the same in Fig. 9(d). When t = 400 μs, the melt starts to move upward, and the surrounding powder or molten material gradually fills up, causing the surface of the molten pool to begin to flatten. At this time, the maximum velocity of the melt is at the center of the bath, while the velocity at the edge is close to zero, and the edge of the melt starts to solidify in Fig. 9(e). When t = 450 μs, the melt continues to move upward, forming a convex surface of the melt track. However, the melt movement slows down, as shown in Fig. 9(f). When t = 500 μs, the melt further moves upward and its speed gradually becomes smaller. At the same time, the melt solidifies further, as shown in Fig. 9(g). When t = 550 μs, the melt track is basically formed into a single track with a similar “mountain” shape. At this stage, the velocity is close to zero only at the center of the molten pool, and the flow behavior of the melt is poor in Fig. 9(h). At t = 600 μs, the melt stops moving and solidification is rapidly completed. Up to this point, a single track is formed in Fig. 9(i). During the laser action on the powder bed, the substrate melts and combines with the molten state powder. The powder-to-powder fusion is like the convergence of water droplets, which are rapidly fused by surface tension. However, the fusion between the molten state powder and the substrate occurs driven by surface tension, and the molten powder around the molten pool is pulled toward the substrate (a wetting effect occurs), which ultimately results in the formation of a monolithic whole.38,80,81

FIG. 9.

VIEW LARGEDOWNLOAD SLIDE

Evolution of single-track molten pool temperature and melt flow in the YZ cross section: (a) t = 0  ��⁠, (b) t = 250  ��⁠, (c) t = 300  ��⁠, (d) t = 350  ��⁠, (e) t = 400  ��⁠, (f) t = 450  ��⁠, (g) t = 500  ��⁠, (h) t = 550  ��⁠, (i) t = 600  ��⁠.

The wetting ability between the liquid metal and the solid substrate in the molten pool directly affects the degree of balling of the melt,82,83 and the wetting ability can be measured by the contact angle of a single track in Fig. 10. A smaller value of contact angle represents better wettability. The contact angle α can be calculated by�=�1−�22,

(17)

where �1 and �2 are the contact angles of the left and right regions, respectively.

FIG. 10.

VIEW LARGEDOWNLOAD SLIDE

Schematic of contact angle.

Relevant studies have confirmed that the wettability is better at a contact angle α around or below 40°.84 After measurement, a single-track contact angle α of about 33° was obtained under this process parameter, which further confirms the good wettability.

B. Double-track simulation

In order to deeply investigate the influence of hatch spacing on the characteristics of the HP-LPBF process, a series of double-track molten pool simulation experiments were systematically carried out. Figure 11 shows in detail the dynamic changes of the 3D morphology and temperature field of the double-track molten pool in the time period of 2050–2500 μs under the conditions of laser power of 100 W, scanning speed of 800 mm/s, and hatch spacing of 0.06 mm. By comparing the study with Fig. 7, it is observed that the basic characteristics of the 3D morphology and temperature field of the second track are similar to those of the first track. However, there are subtle differences between them. The first track exhibits a basically symmetric shape, but the second track morphology shows a slight deviation influenced by the difference in thermal diffusion rate between the solidified metal and the powder. Otherwise, the other characteristic information is almost the same as that of the first track. Figure 12 shows the velocity vector plot of the P2 profile in the double-track molten pool, with a maximum velocity of about 2.63 m/s. The melt dynamics at both ends of the pool are more stable at t = 2050 μs, where the maximum rate of the second track is only 1/3 of that of the first one. Other than that, the rest of the information is almost no significant difference from the characteristic information of the first track. Figure 13 demonstrates a detailed observation of the double-track temperature field and melts flow in the YZ cross section, and a comparative study with Fig. 9 reveals that the width of the second track is slightly wider. In addition, after the melt direction shifts from bottom to top, the first track undergoes four time periods (50 μs) to reach full solidification, while the second track takes five time periods. This is due to the presence of significant heat buildup in the powder bed after the forming of the first track, resulting in a longer dynamic time of the melt and an increased molten pool lifetime. In conclusion, the level of specimen forming can be significantly optimized by adjusting the laser power and hatch spacing.

FIG. 11.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool process: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 12.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of double-track molten pool velocity in XZ longitudinal section: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 13.

VIEW LARGEDOWNLOAD SLIDE

Evolution of double-track molten pool temperature and melt flow in the YZ cross section: (a) t = 2250  ��⁠, (b) t = 2300  ��⁠, (c) t = 2350  ��⁠, (d) t = 2400  ��⁠, (e) t = 2450  ��⁠, (f) t = 2500  ��⁠, (g) t = 2550  ��⁠, (h) t = 2600  ��⁠, (i) t = 2650  ��⁠.

In order to quantitatively detect the molten pool dimensions as well as the remolten region dimensions, the molten pool characterization information in Fig. 14 is constructed by drawing the boundary on the YZ cross section based on the isothermal surface of the liquid phase line. It can be observed that the heights of the first track and second track are basically the same, but the depth of the second track increases relative to the first track. The molten pool width is mainly positively correlated with the laser power as well as the scanning speed (the laser line energy density �⁠). However, the remelted zone width is negatively correlated with the hatch spacing (the overlapping ratio). Overall, the forming quality of the specimens can be directly influenced by adjusting the laser power, scanning speed, and hatch spacing.

FIG. 14.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool characterization information on YZ cross section.

In order to study the variation rule of the temperature in the center of the molten pool with time, Fig. 15 demonstrates the temperature variation curves with time for two reference points, A and B. Among them, the red dotted line indicates the liquid phase line temperature of SS316L. From the figure, it can be seen that the maximum temperature at the center of the molten pool in the first track is lower than that in the second track, which is mainly due to the heat accumulation generated after passing through the first track. The maximum temperature gradient was calculated to be 1.69 × 108 K/s. When the laser scanned the first track, the temperature in the center of the molten pool of the second track increased slightly. Similarly, when the laser scanned the second track, a similar situation existed in the first track. Since the temperature gradient in the second track is larger than that in the first track, the residence time of the liquid phase in the molten pool of the first track is longer than that of the second track.

FIG. 15.

VIEW LARGEDOWNLOAD SLIDE

Temperature profiles as a function of time for two reference points A and B.

C. Simulation analysis of molten pool under different process parameters

In order to deeply investigate the effects of various process parameters on the mesoscopic-scale temperature field, molten pool characteristic information and defects of HP-LPBF, numerical simulation experiments on mesoscopic-scale laser power, scanning speed, and hatch spacing of double-track molten pools were carried out.

1. Laser power

Figure 16 shows the effects of different laser power on the morphology and temperature field of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. When P = 50 W, a smaller molten pool is formed due to the lower heat generated by the Gaussian light source per unit time. This leads to a smaller track width, which results in adjacent track not lapping properly and the presence of a large number of unmelted powder particles, resulting in an increase in the number of defects, such as pores in the specimen. The surface of the track is relatively flat, and the depth is small. In addition, the temperature gradient before and after the molten pool was large, and the depression location appeared at the biased front end in Fig. 16(a). When P = 100 W, the surface of the track is flat and smooth with excellent lap. Due to the Marangoni effect, the velocity field of the molten pool is in the form of “vortex,” and the melt has good fluidity, and the maximum velocity reaches 2.15 m/s in Fig. 16(b). When P = 200 W, the heat generated by the Gaussian light source per unit time is too large, resulting in the melt rapidly reaching the evaporation temperature, generating a huge recoil pressure, forming a large molten pool, and the surface of the track is obviously raised. The melt movement is intense, especially the closed loop at the center end of the molten pool. At this time, the depth and width of the molten pool are large, leading to the expansion of the remolten region and the increased chance of the appearance of porosity defects in Fig. 16(c). The results show that at low laser power, the surface tension in the molten pool is dominant. At high laser power, recoil pressure is its main role.

FIG. 16.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different laser powers: (a) P = 50 W, (b) P = 100 W, (c) P = 200 W.

Table II shows the effect of different laser powers on the characteristic information of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. The negative overlapping ratio in the table indicates that the melt tracks are not lapped, and 26/29 indicates the melt depth of the first track/second track. It can be seen that with the increase in laser power, the melt depth, melt width, melt height, and remelted zone show a gradual increase. At the same time, the overlapping ratio also increases. Especially in the process of laser power from 50 to 200 W, the melting depth and melting width increased the most, which increased nearly 2 and 1.5 times, respectively. Meanwhile, the overlapping ratio also increases with the increase in laser power, which indicates that the melting and fusion of materials are better at high laser power. On the other hand, the dimensions of the molten pool did not change uniformly with the change of laser power. Specifically, the depth-to-width ratio of the molten pool increased from about 0.30 to 0.39 during the increase from 50 to 120 W, which further indicates that the effective heat transfer in the vertical direction is greater than that in the horizontal direction with the increase in laser power. This dimensional response to laser power is mainly affected by the recoil pressure and also by the difference in the densification degree between the powder layer and the metal substrate. In addition, according to the experimental results, the contact angle shows a tendency to increase and then decrease during the process of laser power increase, and always stays within the range of less than 33°. Therefore, in practical applications, it is necessary to select the appropriate laser power according to the specific needs in order to achieve the best processing results.

TABLE II.

Double-track molten pool characterization information at different laser powers.

Laser power (W)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
50 16 54 11 −10 23 
100 26/29 74 14 18 23.33 33 
200 37/45 116 21 52 93.33 28 

2. Scanning speed

Figure 17 demonstrates the effect of different scanning speeds on the morphology and temperature field of the double-track molten pool at a laser power of 100 W and a hatch spacing of 0.06 mm. With the gradual increase in scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. When � = 200 mm/s, the slow scanning speed causes the material to absorb too much heat, which is very easy to trigger the overburning phenomenon. At this point, the molten pool is larger and the surface morphology is uneven. This situation is consistent with the previously discussed scenario with high laser power in Fig. 17(a). However, when � = 1600 mm/s, the scanning speed is too fast, resulting in the material not being able to absorb sufficient heat, which triggers the powder particles that fail to melt completely to have a direct effect on the bonding of the melt to the substrate. At this time, the molten pool volume is relatively small and the neighboring melt track cannot lap properly. This result is consistent with the previously discussed case of low laser power in Fig. 17(b). Overall, the ratio of the laser power to the scanning speed (the line energy density �⁠) has a direct effect on the temperature field and surface morphology of the molten pool.

FIG. 17.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different scanning speed: (a)  � = 200 mm/s, (b)  � = 1600 mm/s.

Table III shows the effects of different scanning speed on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and hatch spacing of 0.06 mm. It can be seen that the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. With the increase in scanning speed, the melt depth, melt width, melt height, remelted zone, and overlapping ratio show a gradual decreasing trend. Among them, the melt depth and melt width decreased faster, while the melt height and remolten region decreased relatively slowly. In addition, when the scanning speed was increased from 200 to 800 mm/s, the decreasing speeds of melt depth and melt width were significantly accelerated, while the decreasing speeds of overlapping ratio were relatively slow. When the scanning speed was further increased to 1600 mm/s, the decreasing speeds of melt depth and melt width were further accelerated, and the un-lapped condition of the melt channel also appeared. In addition, the contact angle increases and then decreases with the scanning speed, and both are lower than 33°. Therefore, when selecting the scanning speed, it is necessary to make reasonable trade-offs according to the specific situation, and take into account the factors of melt depth, melt width, melt height, remolten region, and overlapping ratio, in order to achieve the best processing results.

TABLE III.

Double-track molten pool characterization information at different scanning speeds.

Scanning speed (mm/s)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
200 55/68 182 19/32 124 203.33 22 
1600 13 50 11 −16.67 31 

3. Hatch spacing

Figure 18 shows the effect of different hatch spacing on the morphology and temperature field of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. The surface morphology and temperature field of the first track and second track are basically the same, but slightly different. The first track shows a basically symmetric morphology along the scanning direction, while the second track shows a slight offset due to the difference in the heat transfer rate between the solidified material and the powder particles. When the hatch spacing is too small, the overlapping ratio increases and the probability of defects caused by remelting phenomenon grows. When the hatch spacing is too large, the neighboring melt track cannot overlap properly, and the powder particles are not completely melted, leading to an increase in the number of holes. In conclusion, the ratio of the line energy density � to the hatch spacing (the volume energy density E) has a significant effect on the temperature field and surface morphology of the molten pool.

FIG. 18.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different hatch spacings: (a) H = 0.03 mm, (b) H = 0.12 mm.

Table IV shows the effects of different hatch spacing on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. It can be seen that the hatch spacing has little effect on the melt depth, melt width, and melt height, but has some effect on the remolten region. With the gradual expansion of hatch spacing, the remolten region shows a gradual decrease. At the same time, the overlapping ratio also decreased with the increase in hatch spacing. In addition, it is observed that the contact angle shows a tendency to increase and then remain stable when the hatch spacing increases, which has a more limited effect on it. Therefore, trade-offs and decisions need to be made on a case-by-case basis when selecting the hatch spacing.

TABLE IV.

Double-track molten pool characterization information at different hatch spacings.

Hatch spacing (mm)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
0.03 25/27 82 14 59 173.33 30 
0.12 26 78 14 −35 33 

In summary, the laser power, scanning speed, and hatch spacing have a significant effect on the formation of the molten pool, and the correct selection of these three process parameters is crucial to ensure the forming quality. In addition, the melt depth of the second track is slightly larger than that of the first track at higher line energy density � and volume energy density E. This is mainly due to the fact that a large amount of heat accumulation is generated after the first track, forming a larger molten pool volume, which leads to an increase in the melt depth.

D. Simulation analysis of molten pool with powder particle size and laser focal spot diameter

Figure 19 demonstrates the effect of different powder particle sizes and laser focal spot diameters on the morphology and temperature field of the double-track molten pool under a laser power of 100 W, a scanning speed of 800 mm/s, and a hatch spacing of 0.06 mm. In the process of melting coarse powder with small laser focal spot diameter, the laser energy cannot completely melt the larger powder particles, resulting in their partial melting and further generating excessive pore defects. The larger powder particles tend to generate zigzag molten pool edges, which cause an increase in the roughness of the melt track surface. In addition, the molten pool is also prone to generate the present spatter phenomenon, which can directly affect the quality of forming. The volume of the formed molten pool is relatively small, while the melt depth, melt width, and melt height are all smaller relative to the fine powder in Fig. 19(a). In the process of melting fine powders with a large laser focal spot diameter, the laser energy is able to melt the fine powder particles sufficiently, even to the point of overmelting. This results in a large number of fine spatters being generated at the edge of the molten pool, which causes porosity defects in the melt track in Fig. 19(b). In addition, the maximum velocity of the molten pool is larger for large powder particle sizes compared to small powder particle sizes, which indicates that the temperature gradient in the molten pool is larger for large powder particle sizes and the melt motion is more intense. However, the size of the laser focal spot diameter has a relatively small effect on the melt motion. However, a larger focal spot diameter induces a larger melt volume with greater depth, width, and height. In conclusion, a small powder size helps to reduce the surface roughness of the specimen, and a small laser spot diameter reduces the minimum forming size of a single track.

FIG. 19.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool with different powder particle size and laser focal spot diameter: (a) focal spot = 25 μm, coarse powder, (b) focal spot = 80 μm, fine powder.

Table V shows the maximum temperature gradient at the reference point for different powder sizes and laser focal spot diameters. As can be seen from the table, the maximum temperature gradient is lower than that of HP-LPBF for both coarse powders with a small laser spot diameter and fine powders with a large spot diameter, a phenomenon that leads to an increase in the heat transfer rate of HP-LPBF, which in turn leads to a corresponding increase in the cooling rate and, ultimately, to the formation of finer microstructures.

TABLE V.

Maximum temperature gradient at the reference point for different powder particle sizes and laser focal spot diameters.

Laser power (W)Scanning speed (mm/s)Hatch spacing (mm)Average powder size (μm)Laser focal spot diameter (μm)Maximum temperature gradient (×107 K/s)
100 800 0.06 31.7 25 7.89 
11.5 80 7.11 

IV. CONCLUSIONS

In this study, the geometrical characteristics of 3D coarse and fine powder particles were first calculated using DEM and then numerical simulations of single track and double track in the process of forming SS316L from monolayer HP-LPBF at mesoscopic scale were developed using CFD method. The effects of Marangoni convection, surface tension, recoil pressure, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool were considered in this model. The effects of laser power, scanning speed, and hatch spacing on the dynamics of the single-track and double-track molten pools, as well as on other characteristic information, were investigated. The effects of the powder particle size on the molten pool were investigated comparatively with the laser focal spot diameter. The main conclusions are as follows:

  1. The results show that the temperature gradient at the front of the molten pool is significantly larger than that at the tail, and the molten pool exhibits a “comet” morphology. At the top of the molten pool, there is a slightly concave region, which is the result of the coupling of Marangoni convection, recoil pressure, and surface tension. The melt flow forms two closed loops, which are mainly influenced by temperature gradients and surface tension. This special dynamic behavior of the melt tends to form an “elliptical” molten pool and an almost “mountain” shape in single-track forming.
  2. The basic characteristics of the three-dimensional morphology and temperature field of the second track are similar to those of the first track, but there are subtle differences. The first track exhibits a basically symmetrical shape; however, due to the difference in thermal diffusion rates between the solidified metal and the powder, a slight asymmetry in the molten pool morphology of the second track occurs. After forming through the first track, there is a significant heat buildup in the powder bed, resulting in a longer dynamic time of the melt, which increases the life of the molten pool. The heights of the first track and second track remained essentially the same, but the depth of the second track was greater relative to the first track. In addition, the maximum temperature gradient was 1.69 × 108 K/s during HP-LPBF forming.
  3. At low laser power, the surface tension in the molten pool plays a dominant role. At high laser power, recoil pressure becomes the main influencing factor. With the increase of laser power, the effective heat transfer in the vertical direction is superior to that in the horizontal direction. With the gradual increase of scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. In addition, the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. Too large or too small hatch spacing will lead to remelting or non-lap phenomenon, which in turn causes the formation of defects.
  4. When using a small laser focal spot diameter, it is difficult to completely melt large powder particle sizes, resulting in partial melting and excessive porosity generation. At the same time, large powder particles produce curved edges of the molten pool, resulting in increased surface roughness of the melt track. In addition, spatter occurs, which directly affects the forming quality. At small focal spot diameters, the molten pool volume is relatively small, and the melt depth, the melt width, and the melt height are correspondingly small. Taken together, the small powder particle size helps to reduce surface roughness, while the small spot diameter reduces the forming size.

REFERENCES

  1. S. L. Sing and W. Y. Yeong , “ Laser powder bed fusion for metal additive manufacturing: Perspectives on recent developments,” Virtual Phys. Prototyping. 15, 359–370 (2020).https://doi.org/10.1080/17452759.2020.1779999
    Google ScholarCrossref
  2. A. M. Khorasani , I. G. Jithin , J. K. Veetil , and A. H. Ghasemi , “ A review of technological improvements in laser-based powder bed fusion of metal printers,” Int. J. Adv. Manuf. Technol. 108, 191–209 (2020).https://doi.org/10.1007/s00170-020-05361-3
    Google ScholarCrossref
  3. Y. Qin , A. Brockett , Y. Ma , A. Razali , J. Zhao , C. Harrison , W. Pan , X. Dai , and D. Loziak , “ Micro-manufacturing: Research, technology outcomes and development issues,” Int. J. Adv. Manuf. Technol. 47, 821–837 (2010).https://doi.org/10.1007/s00170-009-2411-2
    Google ScholarCrossref
  4. B. Nagarajan , Z. Hu , X. Song , W. Zhai , and J. Wei , “ Development of micro selective laser melting: The state of the art and future perspectives,” Engineering. 5, 702–720 (2019).https://doi.org/10.1016/j.eng.2019.07.002
    Google ScholarCrossref
  5. Y. Wei , G. Chen , W. Li , Y. Zhou , Z. Nie , J. Xu , and W. Zhou , “ Micro selective laser melting of SS316L: Single tracks, defects, microstructures and thermal/mechanical properties,” Opt. Laser Technol. 145, 107469 (2022).https://doi.org/10.1016/j.optlastec.2021.107469
    Google ScholarCrossref
  6. Y. Wei , G. Chen , W. Li , M. Li , Y. Zhou , Z. Nie , and J. Xu , “ Process optimization of micro selective laser melting and comparison of different laser diameter for forming different powder,” Opt. Laser Technol. 150, 107953 (2022).https://doi.org/10.1016/j.optlastec.2022.107953
    Google ScholarCrossref
  7. H. Zhiheng , B. Nagarajan , X. Song , R. Huang , W. Zhai , and J. Wei , “ Formation of SS316L single tracks in micro selective laser melting: Surface, geometry, and defects,” Adv. Mater. Sci. Eng. 2019, 9451406.https://doi.org/10.1155/2019/9451406
    Crossref
  8. B. Nagarajan , Z. Hu , S. Gao , X. Song , R. Huang , M. Seita , and J. Wei , “ Effect of in-situ laser remelting on the microstructure of SS316L fabricated by micro selective laser melting,” in Advanced Surface Enhancement, edited by Sho Itoh and Shashwat Shukla , Lecture Notes in Mechanical Engineering ( Springer Singapore, Singapore, 2020), pp. 330–336.
    Google ScholarCrossref
  9. H. Zhiheng , B. Nagarajan , X. Song , R. Huang , W. Zhai , and J. Wei , “ Tailoring surface roughness of micro selective laser melted SS316L by in-situ laser remelting,” in Advanced Surface Enhancement, edited by Sho Itoh and Shashwat Shukla , Lecture Notes in Mechanical Engineering ( Springer Singapore, Singapore, 2020), pp. 337–343.
    Google Scholar
  10. J. Fu , Z. Hu , X. Song , W. Zhai , Y. Long , H. Li , and M. Fu , “ Micro selective laser melting of NiTi shape memory alloy: Defects, microstructures and thermal/mechanical properties,” Opt. Laser Technol. 131, 106374 (2020).https://doi.org/10.1016/j.optlastec.2020.106374
    Google ScholarCrossref
  11. E. Abele and M. Kniepkamp , “ Analysis and optimisation of vertical surface roughness in micro selective laser melting,” Surf. Topogr.: Metrol. Prop. 3, 034007 (2015).https://doi.org/10.1088/2051-672X/3/3/034007
    Google ScholarCrossref
  12. S. Qu , J. Ding , J. Fu , M. Fu , B. Zhang , and X. Song , “ High-precision laser powder bed fusion processing of pure copper,” Addit. Manuf. 48, 102417 (2021).https://doi.org/10.1016/j.addma.2021.102417
    Google ScholarCrossref
  13. Y. Wei , G. Chen , M. Li , W. Li , Y. Zhou , J. Xu , and Z. wei , “ High-precision laser powder bed fusion of 18Ni300 maraging steel and its SiC reinforcement composite materials,” J. Manuf. Process. 84, 750–763 (2022).https://doi.org/10.1016/j.jmapro.2022.10.049
    Google ScholarCrossref
  14. B. Liu , R. Wildman , T. Christopher , I. Ashcroft , and H. Richard , “ Investigation the effect of particle size distribution on processing parameters optimisation in selective laser melting process,” in 2011 International Solid Freeform Fabrication Symposium ( University of Texas at Austin, 2011).
    Google Scholar
  15. T. D. McLouth , G. E. Bean , D. B. Witkin , S. D. Sitzman , P. M. Adams , D. N. Patel , W. Park , J.-M. Yang , and R. J. Zaldivar , “ The effect of laser focus shift on microstructural variation of Inconel 718 produced by selective laser melting,” Mater. Des. 149, 205–213 (2018).https://doi.org/10.1016/j.matdes.2018.04.019
    Google ScholarCrossref
  16. Y. Qian , Y. Wentao , and L. Feng , “ Mesoscopic simulations of powder bed fusion: Research progresses and conditions,” Electromachining Mould 06, 46–52 (2017).https://doi.org/10.3969/j.issn.1009-279X.2017.06.012
    Google Scholar
  17. J. Fu , S. Qu , J. Ding , X. Song , and M. W. Fu , “ Comparison of the microstructure, mechanical properties and distortion of stainless Steel 316L fabricated by micro and conventional laser powder bed fusion,” Addit. Manuf. 44, 102067 (2021).https://doi.org/10.1016/j.addma.2021.102067
    Google ScholarCrossref
  18. N. T. Aboulkhair , I. Maskery , C. Tuck , I. Ashcroft , and N. M. Everitt , “ The microstructure and mechanical properties of selectively laser Melted AlSi10Mg: The effect of a conventional T6-like heat treatment,” Mater. Sci. Eng. A 667, 139–146 (2016).https://doi.org/10.1016/j.msea.2016.04.092
    Google ScholarCrossref
  19. S. Y. Chen , J. C. Huang , C. T. Pan , C. H. Lin , T. L. Yang , Y. S. Huang , C. H. Ou , L. Y. Chen , D. Y. Lin , H. K. Lin , T. H. Li , J. S. C. Jang , and C. C. Yang , “ Microstructure and mechanical properties of open-cell porous Ti-6Al-4V fabricated by selective laser melting,” J. Alloys Compd. 713, 248–254 (2017).https://doi.org/10.1016/j.jallcom.2017.04.190
    Google ScholarCrossref
  20. Y. Bai , Y. Yang , D. Wang , and M. Zhang , “ Influence mechanism of parameters process and mechanical properties evolution mechanism of Maraging steel 300 by selective laser melting,” Mater. Sci. Eng. A 703, 116–123 (2017).https://doi.org/10.1016/j.msea.2017.06.033
    Google ScholarCrossref
  21. Y. Bai , Y. Yang , Z. Xiao , M. Zhang , and D. Wang , “ Process optimization and mechanical property evolution of AlSiMg0.75 by selective laser melting,” Mater. Des. 140, 257–266 (2018).https://doi.org/10.1016/j.matdes.2017.11.045
    Google ScholarCrossref
  22. Y. Liu , M. Zhang , W. Shi , Y. Ma , and J. Yang , “ Study on performance optimization of 316L stainless steel parts by high-efficiency selective laser melting,” Opt. Laser Technol. 138, 106872 (2021).https://doi.org/10.1016/j.optlastec.2020.106872
    Google ScholarCrossref
  23. D. Gu , Y.-C. Hagedorn , W. Meiners , G. Meng , R. J. S. Batista , K. Wissenbach , and R. Poprawe , “ Densification behavior, microstructure evolution, and wear performance of selective laser melting processed commercially pure titanium,” Acta Mater. 60, 3849–3860 (2012).https://doi.org/10.1016/j.actamat.2012.04.006
    Google ScholarCrossref
  24. N. Read , W. Wang , K. Essa , and M. M. Attallah , “ Selective laser melting of AlSi10Mg alloy: Process optimisation and mechanical properties development,” Mater. Des. 65, 417–424 (2015).https://doi.org/10.1016/j.matdes.2014.09.044
    Google ScholarCrossref
  25. I. A. Roberts , C. J. Wang , R. Esterlein , M. Stanford , and D. J. Mynors , “ A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing,” Int. J. Mach. Tools Manuf. 49(12–13), 916–923 (2009).https://doi.org/10.1016/j.ijmachtools.2009.07.004
    Google ScholarCrossref
  26. K. Dai and L. Shaw , “ Finite element analysis of the effect of volume shrinkage during laser densification,” Acta Mater. 53(18), 4743–4754 (2005).https://doi.org/10.1016/j.actamat.2005.06.014
    Google ScholarCrossref
  27. K. Carolin , E. Attar , and P. Heinl , “ Mesoscopic simulation of selective beam melting processes,” J. Mater. Process. Technol. 211(6), 978–987 (2011).https://doi.org/10.1016/j.jmatprotec.2010.12.016
    Google ScholarCrossref
  28. F.-J. Gürtler , M. Karg , K.-H. Leitz , and M. Schmidt , “ Simulation of laser beam melting of steel powders using the three-dimensional volume of fluid method,” Phys. Procedia 41, 881–886 (2013).https://doi.org/10.1016/j.phpro.2013.03.162
    Google ScholarCrossref
  29. P. Meakin and R. Jullien , “ Restructuring effects in the rain model for random deposition,” J. Phys. France 48(10), 1651–1662 (1987).https://doi.org/10.1051/jphys:0198700480100165100
    Google ScholarCrossref
  30. J-m Wang , G-h Liu , Y-l Fang , and W-k Li , “ Marangoni effect in nonequilibrium multiphase system of material processing,” Rev. Chem. Eng. 32(5), 551–585 (2016).https://doi.org/10.1515/revce-2015-0067
    Google ScholarCrossref
  31. W. Ye , S. Zhang , L. L. Mendez , M. Farias , J. Li , B. Xu , P. Li , and Y. Zhang , “ Numerical simulation of the melting and alloying processes of elemental titanium and boron powders using selective laser alloying,” J. Manuf. Process. 64, 1235–1247 (2021).https://doi.org/10.1016/j.jmapro.2021.02.044
    Google ScholarCrossref
  32. U. S. Bertoli , A. J. Wolfer , M. J. Matthews , J.-P. R. Delplanque , and J. M. Schoenung , “ On the limitations of volumetric energy density as a design parameter for selective laser melting,” Mater. Des. 113, 331–340 (2017).https://doi.org/10.1016/j.matdes.2016.10.037
    Google ScholarCrossref
  33. W. E. King , H. D. Barth , V. M. Castillo , G. F. Gallegos , J. W. Gibbs , D. E. Hahn , C. Kamath , and A. M. Rubenchik , “ Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing,” J. Mater. Process. Technol. 214(12), 2915–2925 (2014).https://doi.org/10.1016/j.jmatprotec.2014.06.005
    Google ScholarCrossref
  34. L. Cao , “ Numerical simulation of the impact of laying powder on selective laser melting single-pass formation,” Int. J. Heat Mass Transfer 141, 1036–1048 (2019).https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.053
    Google ScholarCrossref
  35. L. Huang , X. Hua , D. Wu , and F. Li , “ Numerical study of keyhole instability and porosity formation mechanism in laser welding of aluminum alloy and steel,” J. Mater. Process. Technol. 252, 421–431 (2018).https://doi.org/10.1016/j.jmatprotec.2017.10.011
    Google ScholarCrossref
  36. K. Q. Le , C. Tang , and C. H. Wong , “ On the study of keyhole-mode melting in selective laser melting process,” Int. J. Therm. Sci. 145, 105992 (2019).https://doi.org/10.1016/j.ijthermalsci.2019.105992
    Google ScholarCrossref
  37. J.-H. Cho and S.-J. Na , “ Theoretical analysis of keyhole dynamics in polarized laser drilling,” J. Phys. D: Appl. Phys. 40(24), 7638 (2007).https://doi.org/10.1088/0022-3727/40/24/007
    Google ScholarCrossref
  38. W. Ye , “ Mechanism analysis of selective laser melting and metallurgy process based on base element powder of titanium and boron,” Ph.D. dissertation ( Nanchang University, 2021).
    Google Scholar
  39. R. Ammer , M. Markl , U. Ljungblad , C. Körner , and U. Rüde , “ Simulating fast electron beam melting with a parallel thermal free surface lattice Boltzmann method,” Comput. Math. Appl. 67(2), 318–330 (2014).https://doi.org/10.1016/j.camwa.2013.10.001
    Google ScholarCrossref
  40. H. Chen , Q. Wei , S. Wen , Z. Li , and Y. Shi , “ Flow behavior of powder particles in layering process of selective laser melting: Numerical modeling and experimental verification based on discrete element method,” Int. J. Mach. Tools Manuf. 123, 146–159 (2017).https://doi.org/10.1016/j.ijmachtools.2017.08.004
    Google ScholarCrossref
  41. F. Verhaeghe , T. Craeghs , J. Heulens , and L. Pandelaers , “ A pragmatic model for selective laser melting with evaporation,” Acta Mater. 57(20), 6006–6012 (2009).https://doi.org/10.1016/j.actamat.2009.08.027
    Google ScholarCrossref
  42. C. H. Fu and Y. B. Guo , “ Three-dimensional temperature gradient mechanism in selective laser melting of Ti-6Al-4V,” J. Manuf. Sci. Eng. 136(6), 061004 (2014).https://doi.org/10.1115/1.4028539
    Google ScholarCrossref
  43. Y. Xiang , Z. Shuzhe , L. Junfeng , W. Zhengying , Y. Lixiang , and J. Lihao , “ Numerical simulation and experimental verification for selective laser single track melting forming of Ti6Al4V,” J. Zhejiang Univ. (Eng. Sci.) 53(11), 2102–2109 + 2117 (2019).https://doi.org/10.3785/j.issn.1008-973X.2019.11.007
    Google Scholar
  44. Q. He , H. Xia , J. Liu , X. Ao , and S. Lin , “ Modeling and numerical studies of selective laser melting: Multiphase flow, solidification and heat transfer,” Mater. Des. 196, 109115 (2020).https://doi.org/10.1016/j.matdes.2020.109115
    Google ScholarCrossref
  45. L. Cao , “ Mesoscopic-scale numerical simulation including the influence of process parameters on SLM single-layer multi-pass formation,” Metall. Mater. Trans. A 51, 4130–4145 (2020).https://doi.org/10.1007/s11661-020-05831-z
    Google ScholarCrossref
  46. L. Cao , “ Mesoscopic-scale numerical investigation including the influence of process parameters on LPBF multi-layer multi-path formation,” Comput. Model. Eng. Sci. 126(1), 5–23 (2021).https://doi.org/10.32604/cmes.2021.014693
    Google ScholarCrossref
  47. H. Yin and S. D. Felicelli , “ Dendrite growth simulation during solidification in the LENS process,” Acta Mater. 58(4), 1455–1465 (2010).https://doi.org/10.1016/j.actamat.2009.10.053
    Google ScholarCrossref
  48. P. Nie , O. A. Ojo , and Z. Li , “ Numerical modeling of microstructure evolution during laser additive manufacturing of a nickel-based superalloy,” Acta Mater. 77, 85–95 (2014).https://doi.org/10.1016/j.actamat.2014.05.039
    Google ScholarCrossref
  49. Z. Liu and H. Qi , “ Effects of substrate crystallographic orientations on crystal growth and microstructure formation in laser powder deposition of nickel-based superalloy,” Acta Mater. 87, 248–258 (2015).https://doi.org/10.1016/j.actamat.2014.12.046
    Google ScholarCrossref
  50. L. Wei , L. Xin , W. Meng , and H. Weidong , “ Cellular automaton simulation of the molten pool of laser solid forming process,” Acta Phys. Sin. 64(01), 018103–018363 (2015).https://doi.org/10.7498/aps.64.018103
    Google ScholarCrossref
  51. R. Acharya , J. A. Sharon , and A. Staroselsky , “ Prediction of microstructure in laser powder bed fusion process,” Acta Mater. 124, 360–371 (2017).https://doi.org/10.1016/j.actamat.2016.11.018
    Google ScholarCrossref
  52. M. R. Rolchigo and R. LeSar , “ Modeling of binary alloy solidification under conditions representative of additive manufacturing,” Comput. Mater. Sci. 150, 535–545 (2018).https://doi.org/10.1016/j.commatsci.2018.04.004
    Google ScholarCrossref
  53. S. Geng , P. Jiang , L. Guo , X. Gao , and G. Mi , “ Multi-scale simulation of grain/sub-grain structure evolution during solidification in laser welding of aluminum alloys,” Int. J. Heat Mass Transfer 149, 119252 (2020).https://doi.org/10.1016/j.ijheatmasstransfer.2019.119252
    Google ScholarCrossref
  54. W. L. Wang , W. Q. Liu , X. Yang , R. R. Xu , and Q. Y. Dai , “ Multi-scale simulation of columnar-to-equiaxed transition during laser selective melting of rare earth magnesium alloy,” J. Mater. Sci. Technol. 119, 11–24 (2022).https://doi.org/10.1016/j.jmst.2021.12.029
    Google ScholarCrossref
  55. Q. Xia , J. Yang , and Y. Li , “ On the conservative phase-field method with the N-component incompressible flows,” Phys. Fluids 35, 012120 (2023).https://doi.org/10.1063/5.0135490
    Google ScholarCrossref
  56. Q. Xia , G. Sun , J. Kim , and Y. Li , “ Multi-scale modeling and simulation of additive manufacturing based on fused deposition technique,” Phys. Fluids 35, 034116 (2023).https://doi.org/10.1063/5.0141316
    Google ScholarCrossref
  57. A. Hussein , L. Hao , C. Yan , and R. Everson , “ Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting,” Mater. Des. 52, 638–647 (2013).https://doi.org/10.1016/j.matdes.2013.05.070
    Google ScholarCrossref
  58. J. Ding , P. Colegrove , J. Mehnen , S. Ganguly , P. M. Sequeira Almeida , F. Wang , and S. Williams , “ Thermo-mechanical analysis of wire and arc additive layer manufacturing process on large multi-layer parts,” Comput. Mater. Sci. 50(12), 3315–3322 (2011).https://doi.org/10.1016/j.commatsci.2011.06.023
    Google ScholarCrossref
  59. Y. Du , X. You , F. Qiao , L. Guo , and Z. Liu , “ A model for predicting the temperature field during selective laser melting,” Results Phys. 12, 52–60 (2019).https://doi.org/10.1016/j.rinp.2018.11.031
    Google ScholarCrossref
  60. X. Luo , M. Liu , L. Zhenhua , H. Li , and J. Shen , “ Effect of different heat-source models on calculated temperature field of selective laser melted 18Ni300,” Chin. J. Lasers 48(14), 1402005–1402062 (2021).https://doi.org/10.3788/CJL202148.1402005
    Google ScholarCrossref
  61. J. F. Li , L. Li , and F. H. Stott , “ Thermal stresses and their implication on cracking during laser melting of ceramic materials,” Acta Mater. 52(14), 4385–4398 (2004).https://doi.org/10.1016/j.actamat.2004.06.005
    Google ScholarCrossref
  62. P. Aggarangsi and J. L. Beuth , “ Localized preheating approaches for reducing residual stress in additive manufacturing,” paper presented at the 2006 International Solid Freeform Fabrication Symposium, The University of Texas in Austin on August 14–16, 2006.
  63. K. Dai and L. Shaw , “ Thermal and mechanical finite element modeling of laser forming from metal and ceramic powders,” Acta Mater. 52(1), 69–80 (2004).https://doi.org/10.1016/j.actamat.2003.08.028
    Google ScholarCrossref
  64. A. H. Nickel , D. M. Barnett , and F. B. Prinz , “ Thermal stresses and deposition patterns in layered manufacturing,” Mater. Sci. Eng. A 317(1–2), 59–64 (2001).https://doi.org/10.1016/S0921-5093(01)01179-0
    Google ScholarCrossref
  65. M. F. Zaeh and G. Branner , “ Investigations on residual stresses and deformations in selective laser melting,” Prod. Eng. 4(1), 35–45 (2010).https://doi.org/10.1007/s11740-009-0192-y
    Google ScholarCrossref
  66. P. Bian , J. Shi , Y. Liu , and Y. Xie , “ Influence of laser power and scanning strategy on residual stress distribution in additively manufactured 316L steel,” Opt. Laser Technol. 132, 106477 (2020).https://doi.org/10.1016/j.optlastec.2020.106477
    Google ScholarCrossref
  67. B. M. Marques , C. M. Andrade , D. M. Neto , M. C. Oliveira , J. L. Alves , and L. F. Menezes , “ Numerical analysis of residual stresses in parts produced by selective laser melting process,” Procedia Manuf. 47, 1170–1177 (2020).https://doi.org/10.1016/j.promfg.2020.04.167
    Google ScholarCrossref
  68. W. Mu , “ Numerical simulation of SLM forming process and research and prediction of forming properties,” MA thesis ( Anhui Jianzhu University, 2022).
    Google Scholar
  69. Y. Zhang , “ Multi-scale multi-physics modeling of laser powder bed fusion process of metallic materials with experiment validation,” Ph.D. dissertation ( Purdue University, 2018).
    Google Scholar
  70. Y. Qian , “ Mesoscopic simulation studies of key processing issues for powder bed fusion technology,” Ph.D. dissertation ( Tsinghua University, 2019).
    Google Scholar
  71. N. V. Brilliantov , S. Frank , J.-M. Hertzsch , and T. Pöschel , “ Model for collisions in granular gases,” Phys. Rev. E 53(5), 5382–5392 (1996).https://doi.org/10.1103/PhysRevE.53.5382
    Google ScholarCrossref
  72. Z. Xiao , “ Research on microscale selective laser melting process of high strength pure copper specimens,” MA thesis ( Hunan University, 2022).
    Google Scholar
  73. Z. Li , K. Mukai , M. Zeze , and K. C. Mills , “ Determination of the surface tension of liquid stainless steel,” J. Mater. Sci. 40(9–10), 2191–2195 (2005).https://doi.org/10.1007/s10853-005-1931-x
    Google ScholarCrossref
  74. R. Scardovelli and S. Zaleski , “ Analytical relations connecting linear interfaces and volume fractions in rectangular grids,” J. Comput. Phys. 164(1), 228–237 (2000).https://doi.org/10.1006/jcph.2000.6567
    Google ScholarCrossref
  75. D.-W. Cho , W.-I. Cho , and S.-J. Na , “ Modeling and simulation of arc: Laser and hybrid welding process,” J. Manuf. Process. 16(1), 26–55 (2014).https://doi.org/10.1016/j.jmapro.2013.06.012
    Google ScholarCrossref
    76.Flow3D. Version 11.1.0: User Manual ( FlowScience, Santa Fe, NM, USA, 2015).
  76. Y. Tian , L. Yang , D. Zhao , Y. Huang , and J. Pan , “ Numerical analysis of powder bed generation and single track forming for selective laser melting of ss316l stainless steel,” J. Manuf. Process. 58, 964–974 (2020).https://doi.org/10.1016/j.jmapro.2020.09.002
    Google ScholarCrossref
  77. C. Tang , K. Q. Le , and C. H. Wong , “ Physics of humping formation in laser powder bed fusion,” Int. J. Heat Mass Transfer 149, 119172 (2020).https://doi.org/10.1016/j.ijheatmasstransfer.2019.119172
    Google ScholarCrossref
  78. L. Cao , “ Mesoscopic-scale simulation of pore evolution during laser powder bed fusion process,” Comput. Mater. Sci. 179, 109686 (2020).https://doi.org/10.1016/j.commatsci.2020.109686
    Google ScholarCrossref
  79. R. Li , J. Liu , Y. Shi , W. Li , and W. Jiang , “ Balling behavior of stainless steel and nickel powder during selective laser melting process,” Int. J. Adv. Manuf. Technol. 59(9–12), 1025–1035 (2012).https://doi.org/10.1007/s00170-011-3566-1
    Google ScholarCrossref
  80. S. A. Khairallah and A. Anderson , “ Mesoscopic simulation model of selective laser melting of stainless steel powder,” J. Mater. Process. Technol. 214(11), 2627–2636 (2014).https://doi.org/10.1016/j.jmatprotec.2014.06.001
    Google ScholarCrossref
  81. J. Liu , D. Gu , H. Chen , D. Dai , and H. Zhang , “ Influence of substrate surface morphology on wetting behavior of tracks during selective laser melting of aluminum-based alloys,” J. Zhejiang Univ. Sci. A 19(2), 111–121 (2018).https://doi.org/10.1631/jzus.A1700599
    Google ScholarCrossref
  82. L. Li , J. Li , and T. Fan , “ Phase-field modeling of wetting and balling dynamics in powder bed fusion process,” Phys. Fluids 33, 042116 (2021).https://doi.org/10.1063/5.0046771
    Google ScholarCrossref
  83. X. Nie , Z. Hu , H. Zhu , Z. Hu , L. Ke , and X. Zeng , “ Analysis of processing parameters and characteristics of selective laser melted high strength Al-Cu-Mg alloys: from single tracks to cubic samples,” J. Mater. Process. Technol. 256, 69–77 (2018).https://doi.org/10.1016/j.jmatprotec.2018.01.030
    Google ScholarCrossref
Figure 3. Computed contour of velocity magnitude (m/s) for Run 1 to Run 15.

FLOW-3D 소프트웨어를 이용한 유입구 및 배플 위치가 침전조 제거 효율에 미치는 영향

Ali Poorkarimi1
Khaled Mafakheri2
Shahrzad Maleki2

Journal of Hydraulic Structures
J. Hydraul. Struct., 2023; 9(4): 76-87
DOI: 10.22055/jhs.2024.44817.1265

Abstract

중력에 의한 침전은 부유 물질을 제거하기 위해 물과 폐수 처리 공정에 널리 적용됩니다. 이 연구에서는 침전조의 제거 효율에 대한 입구 및 배플 위치의 영향을 간략하게 설명합니다. 실험은 CCD(중심복합설계) 방법론을 기반으로 수행되었습니다. 전산유체역학(CFD)은 유압 설계, 미래 발전소에 대한 계획 연구, 토목 유지 관리 및 공급 효율성과 관련된 복잡한 문제를 모델링하고 분석하는 데 광범위하게 사용됩니다. 본 연구에서는 입구 높이, 입구로부터 배플까지의 거리, 배플 높이의 다양한 조건에 따른 영향을 조사하였다. CCD 접근 방식을 사용하여 얻은 데이터를 분석하면 축소된 2차 모델이 R2 = 0.77의 결정 계수로 부유 물질 제거를 예측할 수 있음이 나타났습니다. 연구 결과, 유입구와 배플의 부적절한 위치는 침전조의 효율에 부정적인 영향을 미칠 수 있음을 보여주었습니다. 입구 높이, 배플 거리, 배플 높이의 최적 값은 각각 0.87m, 0.77m, 0.56m였으며 제거 효율은 80.6%였습니다.

Sedimentation due to gravitation is applied widely in water and wastewater treatment processes to remove suspended solids. This study outlines the effect of the inlet and baffle position on the removal efficiency of sedimentation tanks. Experiments were carried out based on the central composite design (CCD) methodology. Computational fluid dynamics (CFD) is used extensively to model and analyze complex issues related to hydraulic design, planning studies for future generating stations, civil maintenance, and supply efficiency. In this study, the effect of different conditions of inlet elevation, baffle’s distance from the inlet, and baffle height were investigated. Analysis of the obtained data with a CCD approach illustrated that the reduced quadratic model can predict the suspended solids removal with a coefficient of determination of R2 = 0.77. The results showed that the inappropriate position of the inlet and the baffle can have a negative effect on the efficiency of the sedimentation tank. The optimal values of inlet elevation, baffle distance, and baffle height were 0.87 m, 0.77 m, and 0.56 m respectively with 80.6% removal efficiency.

Keywords

Sedimentation tank, Particle removal, Central Composite Design, Computational
Fluid Dynamics, Flow-3D

Figure 3. Computed contour of velocity magnitude (m/s) for Run 1 to Run 15.
Figure 3. Computed contour of velocity magnitude (m/s) for Run 1 to Run 15.

References

  1. Shahrokhi, M., F. Rostami, M.A. Md. Said, S.R.S. Yazdi, and Syafalni, (2013). Experimental
    investigation of the influence of baffle position on the flow field, sediment concentration, and
    efficiency of rectangular primary sedimentation tanks. Journal of Hydraulic Engineering,.
    139(1): p. 88-94.
  2. Shahrokhi, M., F. Rostami, M.A.M. Said, and S.R.S. Yazdi, (2012). The effect of number of
    baffles on the improvement efficiency of primary sedimentation tanks. Applied Mathematical
    Modelling,. 36(8): p. 3725-3735.
  3. Borna, M., A. Janfeshan, E. Merufinia, and A. Asnaashari, (2014). Numerical simulations of
    distribution and sediment transmission in pre-settled pools using Finite Volume Method and
    comparison with experimental results. Journal of Civil Engineering and Urbanism,. 4(3): p.
    287-292.
  4. Rad, M.J., P.E. Firoozabadi, and F. Rostami, (2022). Numerical Investigation of the Effect
    Dimensions of Rectangular Sedimentation Tanks on Its Hydraulic Efficiency Using Flow-3D
    Software. Acta Technica Jaurinensis,. 15(4): p. 207-220.
  5. Hirom, K. and T.T. Devi, (2022). Application of computational fluid dynamics in sedimentation
    tank design and its recent developments: A review. Water, Air, & Soil Pollution,. 233: p. 1-
    26.
  6. Shahrokhi, M., F. Rostami, M.A.M. Said, S.-R. Sabbagh-Yazdi, S. Syafalni, and R. Abdullah,
    (2012). The effect of baffle angle on primary sedimentation tank efficiency. Canadian Journal
    of Civil Engineering,. 39(3): p. 293-303.
  7. Tarpagkou, R. and A. Pantokratoras, (2014). The influence of lamellar settler in sedimentation
    tanks for potable water treatment—A computational fluid dynamic study. Powder
    Technology,. 268: p. 139-149.
  8. Ekama, G. and P. Marais, (2004). Assessing the applicability of the 1D flux theory to full-scale
    secondary settling tank design with a 2D hydrodynamic model. Water research,. 38(3): p. 495-
    506.
  9. Gharagozian, A., (1998). Circular secondary clarifier investigations using a numerical model.,
    University of California, Los Angeles.
  10. Shahrokhi, M., F. Rostami, and M.A.M. Said, (2013). Numerical modeling of baffle location
    effects on the flow pattern of primary sedimentation tanks. Applied Mathematical Modelling,.
    37(6): p. 4486-4496.
  11. Razmi, A.M., R. Bakhtyar, B. Firoozabadi, and D.A. Barry, (2013). Experiments and
    numerical modeling of baffle configuration effects on the performance of sedimentation tanks.
    Canadian Journal of Civil Engineering,. 40(2): p. 140-150.
  12. Liu, Y., P. Zhang, and W. Wei, (2016). Simulation of effect of a baffle on the flow patterns
    and hydraulic efficiency in a sedimentation tank. Desalination and Water Treatment,. 57(54):
    p. 25950-25959.
  13. Saeedi, E., E. Behnamtalab, and S. Salehi Neyshabouri, (2020). Numerical simulation of baffle
    effect on the performance of sedimentation basin. Water and environment journal,. 34(2): p.
    212-222.
  14. Miri, J.K., B. Aminnejad, and A. Zahiri, (2023). Numerical Study of Flow Pattern, Sediment
    Field and Effect of the Arrangement of Guiding Blades (Baffles) on Sedimentation in PreSedimentation Basins by Numerical Models. Water Resources,. 50(1): p. 68-81.
  15. Heydari, M.M., M. Rahbani, and S.M.M. Jamal, (2014). Experimental and numerical
    investigations of baffle effect on the removal efficiency of sedimentation basin. Advances in
    Environmental Biology,: p. 1015-1022.
  16. Guo, H., S.J. Ki, S. Oh, Y.M. Kim, S. Wang, and J.H. Kim, (2017). Numerical simulation of
    separation process for enhancing fine particle removal in tertiary sedimentation tank mounting
    adjustable baffle. Chemical engineering science,. 158: p. 21-29.

Figure 1 | Schematic of the present research model with dimensions and macro-roughnesses installed.

On the hydraulic performance of the inclined drops: the effect of downstreammacro-roughness elements

경사 낙하의 수력학적 성능: 하류 거시 거칠기 요소의 영향

Farhoud Kalateh a,*, Ehsan Aminvash a and Rasoul Daneshfaraz b
a Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran
b Faculty of Engineering, University of Maragheh, Maragheh, Iran
*Corresponding author. E-mail: f.kalateh@gmail.com

ABSTRACT

The main goal of the present study is to investigate the effects of macro-roughnesses downstream of the inclined drop through numerical models. Due to the vital importance of geometrical properties of the macro-roughnesses in the hydraulic performance and efficient energy dissipation downstream of inclined drops, two different geometries of macro-roughnesses, i.e., semi-circular and triangular geometries, have been investigated using the Flow-3D model. Numerical simulation showed that with the flow rate increase and relative critical depth, the flow energy consumption has decreased. Also, relative energy dissipation increases with the increase in height and slope angle, so that this amount of increase in energy loss compared to the smooth bed in semi-circular and triangular elements is 86.39 and 76.80%, respectively, in the inclined drop with a height of 15 cm and 86.99 and 65.78% in the drop with a height of 20 cm. The Froude number downstream on the uneven bed has been dramatically reduced, so this amount of reduction has been approximately 47 and 54% compared to the control condition. The relative depth of the downstream has also increased due to the turbulence of the flow on the uneven bed with the increase in the flow rate.

본 연구의 주요 목표는 수치 모델을 통해 경사 낙하 하류의 거시 거칠기 효과를 조사하는 것입니다. 수력학적 성능과 경사 낙하 하류의 효율적인 에너지 소산에서 거시 거칠기의 기하학적 특성이 매우 중요하기 때문에 두 가지 서로 다른 거시 거칠기 형상, 즉 반원형 및 삼각형 형상이 Flow를 사용하여 조사되었습니다.

3D 모델 수치 시뮬레이션을 통해 유량이 증가하고 상대 임계 깊이가 증가함에 따라 유동 에너지 소비가 감소하는 것으로 나타났습니다. 또한, 높이와 경사각이 증가함에 따라 상대적인 에너지 소산도 증가하는데, 반원형 요소와 삼각형 요소에서 평활층에 비해 에너지 손실의 증가량은 경사낙하에서 각각 86.39%와 76.80%입니다.

높이 15cm, 높이 20cm의 드롭에서 86.99%, 65.78%입니다. 고르지 못한 베드 하류의 프루드 수가 극적으로 감소하여 이 감소량은 대조 조건에 비해 약 47%와 54%였습니다. 유속이 증가함에 따라 고르지 못한 층에서의 흐름의 난류로 인해 하류의 상대적 깊이도 증가했습니다.

Key words

flow energy dissipation, Froude number, inclined drop, numerical simulation

Figure 1 | Schematic of the present research model with dimensions and macro-roughnesses installed.
Figure 1 | Schematic of the present research model with dimensions and macro-roughnesses installed.
Figure 2 | Meshing, boundary condition, and solution field network
Figure 2 | Meshing, boundary condition, and solution field network

REFERENCES

Abbaspour, A., Taghavianpour, T. & Arvanaghi, H. 2019 Experimental study of the hydraulic jump on the reverse bed with porous screens.
Applied Water Science 9, 155.
Abbaspour, A., Shiravani, P. & Hosseinzadeh Dalir, A. 2021 Experimental study of the energy dissipation on rough ramps. ISH Journal of
Hydraulic Engineering 27, 334–342.
Akib, S., Ahmed, A. A., Imran, H. M., Mahidin, M. F., Ahmed, H. S. & Rahman, S. 2015 Properties of a hydraulic jump over apparent
corrugated beds. Dam Engineering 25, 65–77.
AlTalib, A. N., Mohammed, A. Y. & Hayawi, H. A. 2015 Hydraulic jump and energy dissipation downstream stepped weir. Flow
Measurement and Instrumentation 69, 101616.
Bayon-Barrachina, A. & Lopez-Jimenez, P. A. 2015 Numerical analysis of hydraulic jumps using OpenFOAM. Journal of Hydroinformatics
17, 662–678.
Canovaro, F. & Solari, L. 2007 Dissipative analogies between a schematic macro-roughness arrangement and step–pool morphology. Earth
Surface Processes and Landforms: The Journal of the British Geomorphological Research Group 32, 1628–1640.
Daneshfaraz, R., Ghaderi, A., Akhtari, A. & Di Francesco, S. 2020 On the effect of block roughness in ogee spill-ways with flip buckets. Fluids
5, 182.
Daneshfaraz, R., Aminvash, E., Di Francesco, S., Najibi, A. & Abraham, J. 2021a Three-dimensional study of the effect of block roughness
geometry on inclined drop. Numerical Methods in Civil Engineering 6, 1–9.
Daneshfaraz, R., Aminvash, E., Ghaderi, A., Abraham, J. & Bagherzadeh, M. 2021b SVM performance for predicting the effect of horizontal
screen diameters on the hydraulic parameters of a vertical drop. Applied Science 11, 4238.
Daneshfaraz, R., Aminvash, E., Ghaderi, A., Kuriqi, A. & Abraham, J. 2021c Three-dimensional investigation of hydraulic properties of
vertical drop in the presence of step and grid dissipators. Symmetry 13, 895.
Dey, S. & Sarkar, A. 2008 Characteristics of turbulent flow in submerged jumps on rough beds. Journal of Engineering Mechanics 134, 49–59.
Ead, S. A. & Rajaratnam, N. 2002 Hydraulic jumps on corrugated beds. Journal of Hydraulic Engineering 128, 656–663.
Fang, H., Han, X., He, G. & Dey, S. 2018 Influence of permeable beds on hydraulically macro-rough flow. Journal of Fluid Mechanics 847,
552–590.
Federico, I., Marrone, S., Colagrossi, A., Aristodemo, F. & Antuono, M. 2019 Simulating 2D open-channel flows through an SPH model.
European Journal of Mechanics-B/Fluids 34, 35–46.
Ghaderi, A., Dasineh, M., Aristodemo, F. & Aricò, C. 2021 Numerical simulations of the flow field of a submerged hydraulic jump over
triangular macroroughnesses. Water 13, 674.
Ghare, A. D., Ingl, R. N., Porey, P. D. & Gokhale, S. S. 2010 Block ramp design for efficient energy dissipation. Journal of Energy Dissipation
136, 1–5.
Habibzadeh, A., Rajaratnam, N. & Loewen, M. 2019 Characteristics of the flow field downstream of free and submerged hydraulic jumps.
Proceedings of the Institution of Civil Engineers-Water Management 172, 180–194.
Hajiahmadi, A., Ghaeini-Hessaroeyeh, M. & Khanjani, M. J. 2021 Experimental evaluation of vertical shaft efficiency in vortex flow energy
dissipation. International Journal of Civil Engineering 19, 1445–1455.

Katourani, S. & Kashefipour, S. M. 2012 Effect of the geometric characteristics of baffle on hydraulic flow condition in baffled apron drop.
Irrigation Sciences and Engineering 37, 51–59.
Kurdistani, S. M., Varaki, M. E. & Moayedi Moshkaposhti, M. 2024 Apron and macro roughness as scour countermeasures downstream of
block ramps. ISH Journal of Hydraulic Engineering 1–9.
Lopardo, R. A. 2013 Extreme velocity fluctuations below free hydraulic jumps. Journal of Engineering 1–5.
Mahmoudi-Rad, M. & Najafzadeh, M. 2023 Experimental evaluation of the energy dissipation efficiency of the vortex flow section of drop
shafts. Scientific Reports 13, 1679.
Matin, M. A., Hasan, M. & Islam, M. R. 2018 Experiment on hydraulic jump in sudden expansion in a sloping rectangular channel. Journal of
Civil Engineering 36, 65–77.
Moghadam, K. F., Banihashemi, M. A., Badiei, P. & Shirkavand, A. 2019 A numerical approach to solve fluid-solid two-phase flows using time
splitting projection method with a pressure correction technique. Progress in Computational Fluid Dynamics, an International Journal
19, 357–367.
Moghadam, K. F., Banihashemi, M. A., Badiei, P. & Shirkavand, A. 2020 A time-splitting pressure-correction projection method for complete
two-fluid modeling of a local scour hole. International Journal of Sediment Research 35, 395–407.
Moradi-SabzKoohi, A., Kashefipour, S. M. & Bina, M. 2011 Experimental comparison of energy dissipation on drop structures. JWSS –
Isfahan University of Technology 15, 209–223. (in Persian).
Mouaze, D., Murzyn, F. & Chaplin, J. R. 2005 Free surface length scale estimation in hydraulic jumps. Journal of Fluids Engineering 127,
1191–1193.
Nicosia, A., Carollo, F. G. & Ferro, V. 2023 Effects of boulder arrangement on flow resistance due to macro-scale bed roughness. Water 15,
349.
Ohtsu, I. & Yasuda, Y. 1991 Hydraulic jump in sloping channel. Journal of Hydraulic Engineering 117, 905–921.
Pagliara, S. & Palermo, M. 2012 Effect of stilling basin geometry on the dissipative process in the presence of block ramps. Journal of
Irrigation and Drainage Engineering 138, 1027–1031.
Pagliara, S., Das, R. & Palermo, M. 2008 Energy dissipation on submerged block ramps. Journal of Irrigation and Drainage Engineering 134,
527–532.
Pagliara, S., Roshni, T. & Palermo, M. 2015 Energy dissipation over large-scale roughness for both transition and uniform flow conditions.
International Journal of Civil Engineering 13, 341–346.
Parsaie, A., Dehdar-Behbahani, S. & Haghiabi, A. H. 2016 Numerical modeling of cavitation on spillway’s flip bucket. Frontiers of Structural
and Civil Engineering 10, 438–444.
Pourabdollah, N., Heidarpour, M. & Abedi Koupai, J. 2018 Characteristics of free and submerged hydraulic jumps in different stilling basins.
In: Proceedings of the Institution of Civil Engineers-Water Management. Thomas Telford Ltd, pp. 1–11.
Roushangar, K. & Ghasempour, R. 2019 Evaluation of the impact of channel geometry and rough elements arrangement in hydraulic jump
energy dissipation via SVM. Journal of Hydroinformatics 21, 92–103.
Samadi-Boroujeni, H., Ghazali, M., Gorbani, B. & Nafchi, R. F. 2013 Effect of triangular corrugated beds on the hydraulic jump
characteristics. Canadian Journal of Civil Engineering 40, 841–847.
Shekari, Y., Javan, M. & Eghbalzadeh, A. 2014 Three-dimensional numerical study of submerged hydraulic jumps. Arabian Journal for
Science and Engineering 39, 6969–6981.
Tokyay, N. D., Evcimen, T. U. & Şimsek, Ç. 2011 Forced hydraulic jump on non-protruding rough beds. Canadian Journal of Civil
Engineering 38, 1136–1144.
Wagner, W. E. 1956 Hydraulic model studies of the check intake structure-potholes East canal. Bureau of Reclamation Hydraulic Laboratory
Report Hyd, 411.
Witt, A., Gulliver, J. S. & Shen, L. 2018 Numerical investigation of vorticity and bubble clustering in an air-entraining hydraulic jump.
Computers & Fluids 172, 162–180.

Lab-on-a-Chip 시스템의 혈류 역학에 대한 검토: 엔지니어링 관점

Review on Blood Flow Dynamics in Lab-on-a-Chip Systems: An Engineering Perspective

  • Bin-Jie Lai
  • Li-Tao Zhu
  • Zhe Chen*
  • Bo Ouyang*
  • , and 
  • Zheng-Hong Luo*

Abstract

다양한 수송 메커니즘 하에서, “LOC(lab-on-a-chip)” 시스템에서 유동 전단 속도 조건과 밀접한 관련이 있는 혈류 역학은 다양한 수송 현상을 초래하는 것으로 밝혀졌습니다.

본 연구는 적혈구의 동적 혈액 점도 및 탄성 거동과 같은 점탄성 특성의 역할을 통해 LOC 시스템의 혈류 패턴을 조사합니다. 모세관 및 전기삼투압의 주요 매개변수를 통해 LOC 시스템의 혈액 수송 현상에 대한 연구는 실험적, 이론적 및 수많은 수치적 접근 방식을 통해 제공됩니다.

전기 삼투압 점탄성 흐름에 의해 유발되는 교란은 특히 향후 연구 기회를 위해 혈액 및 기타 점탄성 유체를 취급하는 LOC 장치의 혼합 및 분리 기능 향상에 논의되고 적용됩니다. 또한, 본 연구는 보다 정확하고 단순화된 혈류 모델에 대한 요구와 전기역학 효과 하에서 점탄성 유체 흐름에 대한 수치 연구에 대한 강조와 같은 LOC 시스템 하에서 혈류 역학의 수치 모델링의 문제를 식별합니다.

전기역학 현상을 연구하는 동안 제타 전위 조건에 대한 보다 실용적인 가정도 강조됩니다. 본 연구는 모세관 및 전기삼투압에 의해 구동되는 미세유체 시스템의 혈류 역학에 대한 포괄적이고 학제적인 관점을 제공하는 것을 목표로 한다.

KEYWORDS: 

1. Introduction

1.1. Microfluidic Flow in Lab-on-a-Chip (LOC) Systems

Over the past several decades, the ability to control and utilize fluid flow patterns at microscales has gained considerable interest across a myriad of scientific and engineering disciplines, leading to growing interest in scientific research of microfluidics. 

(1) Microfluidics, an interdisciplinary field that straddles physics, engineering, and biotechnology, is dedicated to the behavior, precise control, and manipulation of fluids geometrically constrained to a small, typically submillimeter, scale. 

(2) The engineering community has increasingly focused on microfluidics, exploring different driving forces to enhance working fluid transport, with the aim of accurately and efficiently describing, controlling, designing, and applying microfluidic flow principles and transport phenomena, particularly for miniaturized applications. 

(3) This attention has chiefly been fueled by the potential to revolutionize diagnostic and therapeutic techniques in the biomedical and pharmaceutical sectorsUnder various driving forces in microfluidic flows, intriguing transport phenomena have bolstered confidence in sustainable and efficient applications in fields such as pharmaceutical, biochemical, and environmental science. The “lab-on-a-chip” (LOC) system harnesses microfluidic flow to enable fluid processing and the execution of laboratory tasks on a chip-sized scale. LOC systems have played a vital role in the miniaturization of laboratory operations such as mixing, chemical reaction, separation, flow control, and detection on small devices, where a wide variety of fluids is adapted. Biological fluid flow like blood and other viscoelastic fluids are notably studied among the many working fluids commonly utilized by LOC systems, owing to the optimization in small fluid sample volumed, rapid response times, precise control, and easy manipulation of flow patterns offered by the system under various driving forces. 

(4)The driving forces in blood flow can be categorized as passive or active transport mechanisms and, in some cases, both. Under various transport mechanisms, the unique design of microchannels enables different functionalities in driving, mixing, separating, and diagnosing blood and drug delivery in the blood. 

(5) Understanding and manipulating these driving forces are crucial for optimizing the performance of a LOC system. Such knowledge presents the opportunity to achieve higher efficiency and reliability in addressing cellular level challenges in medical diagnostics, forensic studies, cancer detection, and other fundamental research areas, for applications of point-of-care (POC) devices. 

(6)

1.2. Engineering Approach of Microfluidic Transport Phenomena in LOC Systems

Different transport mechanisms exhibit unique properties at submillimeter length scales in microfluidic devices, leading to significant transport phenomena that differ from those of macroscale flows. An in-depth understanding of these unique transport phenomena under microfluidic systems is often required in fluidic mechanics to fully harness the potential functionality of a LOC system to obtain systematically designed and precisely controlled transport of microfluids under their respective driving force. Fluid mechanics is considered a vital component in chemical engineering, enabling the analysis of fluid behaviors in various unit designs, ranging from large-scale reactors to separation units. Transport phenomena in fluid mechanics provide a conceptual framework for analytically and descriptively explaining why and how experimental results and physiological phenomena occur. The Navier–Stokes (N–S) equation, along with other governing equations, is often adapted to accurately describe fluid dynamics by accounting for pressure, surface properties, velocity, and temperature variations over space and time. In addition, limiting factors and nonidealities for these governing equations should be considered to impose corrections for empirical consistency before physical models are assembled for more accurate controls and efficiency. Microfluidic flow systems often deviate from ideal conditions, requiring adjustments to the standard governing equations. These deviations could arise from factors such as viscous effects, surface interactions, and non-Newtonian fluid properties from different microfluid types and geometrical layouts of microchannels. Addressing these nonidealities supports the refining of theoretical models and prediction accuracy for microfluidic flow behaviors.

The analytical calculation of coupled nonlinear governing equations, which describes the material and energy balances of systems under ideal conditions, often requires considerable computational efforts. However, advancements in computation capabilities, cost reduction, and improved accuracy have made numerical simulations using different numerical and modeling methods a powerful tool for effectively solving these complex coupled equations and modeling various transport phenomena. Computational fluid dynamics (CFD) is a numerical technique used to investigate the spatial and temporal distribution of various flow parameters. It serves as a critical approach to provide insights and reasoning for decision-making regarding the optimal designs involving fluid dynamics, even prior to complex physical model prototyping and experimental procedures. The integration of experimental data, theoretical analysis, and reliable numerical simulations from CFD enables systematic variation of analytical parameters through quantitative analysis, where adjustment to delivery of blood flow and other working fluids in LOC systems can be achieved.

Numerical methods such as the Finite-Difference Method (FDM), Finite-Element-Method (FEM), and Finite-Volume Method (FVM) are heavily employed in CFD and offer diverse approaches to achieve discretization of Eulerian flow equations through filling a mesh of the flow domain. A more in-depth review of numerical methods in CFD and its application for blood flow simulation is provided in Section 2.2.2.

1.3. Scope of the Review

In this Review, we explore and characterize the blood flow phenomena within the LOC systems, utilizing both physiological and engineering modeling approaches. Similar approaches will be taken to discuss capillary-driven flow and electric-osmotic flow (EOF) under electrokinetic phenomena as a passive and active transport scheme, respectively, for blood transport in LOC systems. Such an analysis aims to bridge the gap between physical (experimental) and engineering (analytical) perspectives in studying and manipulating blood flow delivery by different driving forces in LOC systems. Moreover, the Review hopes to benefit the interests of not only blood flow control in LOC devices but also the transport of viscoelastic fluids, which are less studied in the literature compared to that of Newtonian fluids, in LOC systems.

Section 2 examines the complex interplay between viscoelastic properties of blood and blood flow patterns under shear flow in LOC systems, while engineering numerical modeling approaches for blood flow are presented for assistance. Sections 3 and 4 look into the theoretical principles, numerical governing equations, and modeling methodologies for capillary driven flow and EOF in LOC systems as well as their impact on blood flow dynamics through the quantification of key parameters of the two driving forces. Section 5 concludes the characterized blood flow transport processes in LOC systems under these two forces. Additionally, prospective areas of research in improving the functionality of LOC devices employing blood and other viscoelastic fluids and potentially justifying mechanisms underlying microfluidic flow patterns outside of LOC systems are presented. Finally, the challenges encountered in the numerical studies of blood flow under LOC systems are acknowledged, paving the way for further research.

2. Blood Flow Phenomena

ARTICLE SECTIONS

Jump To


2.1. Physiological Blood Flow Behavior

Blood, an essential physiological fluid in the human body, serves the vital role of transporting oxygen and nutrients throughout the body. Additionally, blood is responsible for suspending various blood cells including erythrocytes (red blood cells or RBCs), leukocytes (white blood cells), and thrombocytes (blood platelets) in a plasma medium.Among the cells mentioned above, red blood cells (RBCs) comprise approximately 40–45% of the volume of healthy blood. 

(7) An RBC possesses an inherent elastic property with a biconcave shape of an average diameter of 8 μm and a thickness of 2 μm. This biconcave shape maximizes the surface-to-volume ratio, allowing RBCs to endure significant distortion while maintaining their functionality. 

(8,9) Additionally, the biconcave shape optimizes gas exchange, facilitating efficient uptake of oxygen due to the increased surface area. The inherent elasticity of RBCs allows them to undergo substantial distortion from their original biconcave shape and exhibits high flexibility, particularly in narrow channels.RBC deformability enables the cell to deform from a biconcave shape to a parachute-like configuration, despite minor differences in RBC shape dynamics under shear flow between initial cell locations. As shown in Figure 1(a), RBCs initiating with different resting shapes and orientations displaying display a similar deformation pattern 

(10) in terms of its shape. Shear flow induces an inward bending of the cell at the rear position of the rim to the final bending position, 

(11) resulting in an alignment toward the same position of the flow direction.

Figure 1. Images of varying deformation of RBCs and different dynamic blood flow behaviors. (a) The deforming shape behavior of RBCs at four different initiating positions under the same experimental conditions of a flow from left to right, (10) (b) RBC aggregation, (13) (c) CFL region. (18) Reproduced with permission from ref (10). Copyright 2011 Elsevier. Reproduced with permission from ref (13). Copyright 2022 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/. Reproduced with permission from ref (18). Copyright 2019 Elsevier.

The flexible property of RBCs enables them to navigate through narrow capillaries and traverse a complex network of blood vessels. The deformability of RBCs depends on various factors, including the channel geometry, RBC concentration, and the elastic properties of the RBC membrane. 

(12) Both flexibility and deformability are vital in the process of oxygen exchange among blood and tissues throughout the body, allowing cells to flow in vessels even smaller than the original cell size prior to deforming.As RBCs serve as major components in blood, their collective dynamics also hugely affect blood rheology. RBCs exhibit an aggregation phenomenon due to cell to cell interactions, such as adhesion forces, among populated cells, inducing unique blood flow patterns and rheological behaviors in microfluidic systems. For blood flow in large vessels between a diameter of 1 and 3 cm, where shear rates are not high, a constant viscosity and Newtonian behavior for blood can be assumed. However, under low shear rate conditions (0.1 s

–1) in smaller vessels such as the arteries and venules, which are within a diameter of 0.2 mm to 1 cm, blood exhibits non-Newtonian properties, such as shear-thinning viscosity and viscoelasticity due to RBC aggregation and deformability. The nonlinear viscoelastic property of blood gives rise to a complex relationship between viscosity and shear rate, primarily influenced by the highly elastic behavior of RBCs. A wide range of research on the transient behavior of the RBC shape and aggregation characteristics under varied flow circumstances has been conducted, aiming to obtain a better understanding of the interaction between blood flow shear forces from confined flows.

For a better understanding of the unique blood flow structures and rheological behaviors in microfluidic systems, some blood flow patterns are introduced in the following section.

2.1.1. RBC Aggregation

RBC aggregation is a vital phenomenon to be considered when designing LOC devices due to its impact on the viscosity of the bulk flow. Under conditions of low shear rate, such as in stagnant or low flow rate regions, RBCs tend to aggregate, forming structures known as rouleaux, resembling stacks of coins as shown in Figure 1(b). 

(13) The aggregation of RBCs increases the viscosity at the aggregated region, 

(14) hence slowing down the overall blood flow. However, when exposed to high shear rates, RBC aggregates disaggregate. As shear rates continue to increase, RBCs tend to deform, elongating and aligning themselves with the direction of the flow. 

(15) Such a dynamic shift in behavior from the cells in response to the shear rate forms the basis of the viscoelastic properties observed in whole blood. In essence, the viscosity of the blood varies according to the shear rate conditions, which are related to the velocity gradient of the system. It is significant to take the intricate relationship between shear rate conditions and the change of blood viscosity due to RBC aggregation into account since various flow driving conditions may induce varied effects on the degree of aggregation.

2.1.2. Fåhræus-Lindqvist Effect

The Fåhræus–Lindqvist (FL) effect describes the gradual decrease in the apparent viscosity of blood as the channel diameter decreases. 

(16) This effect is attributed to the migration of RBCs toward the central region in the microchannel, where the flow rate is higher, due to the presence of higher pressure and asymmetric distribution of shear forces. This migration of RBCs, typically observed at blood vessels less than 0.3 mm, toward the higher flow rate region contributes to the change in blood viscosity, which becomes dependent on the channel size. Simultaneously, the increase of the RBC concentration in the central region of the microchannel results in the formation of a less viscous region close to the microchannel wall. This region called the Cell-Free Layer (CFL), is primarily composed of plasma. 

(17) The combination of the FL effect and the following CFL formation provides a unique phenomenon that is often utilized in passive and active plasma separation mechanisms, involving branched and constriction channels for various applications in plasma separation using microfluidic systems.

2.1.3. Cell-Free Layer Formation

In microfluidic blood flow, RBCs form aggregates at the microchannel core and result in a region that is mostly devoid of RBCs near the microchannel walls, as shown in Figure 1(c). 

(18) The region is known as the cell-free layer (CFL). The CFL region is often known to possess a lower viscosity compared to other regions within the blood flow due to the lower viscosity value of plasma when compared to that of the aggregated RBCs. Therefore, a thicker CFL region composed of plasma correlates to a reduced apparent whole blood viscosity. 

(19) A thicker CFL region is often established following the RBC aggregation at the microchannel core under conditions of decreasing the tube diameter. Apart from the dependence on the RBC concentration in the microchannel core, the CFL thickness is also affected by the volume concentration of RBCs, or hematocrit, in whole blood, as well as the deformability of RBCs. Given the influence CFL thickness has on blood flow rheological parameters such as blood flow rate, which is strongly dependent on whole blood viscosity, investigating CFL thickness under shear flow is crucial for LOC systems accounting for blood flow.

2.1.4. Plasma Skimming in Bifurcation Networks

The uneven arrangement of RBCs in bifurcating microchannels, commonly termed skimming bifurcation, arises from the axial migration of RBCs within flowing streams. This uneven distribution contributes to variations in viscosity across differing sizes of bifurcating channels but offers a stabilizing effect. Notably, higher flow rates in microchannels are associated with increased hematocrit levels, resulting in higher viscosity compared with those with lower flow rates. Parametric investigations on bifurcation angle, 

(20) thickness of the CFL, 

(21) and RBC dynamics, including aggregation and deformation, 

(22) may alter the varying viscosity of blood and its flow behavior within microchannels.

2.2. Modeling on Blood Flow Dynamics

2.2.1. Blood Properties and Mathematical Models of Blood Rheology

Under different shear rate conditions in blood flow, the elastic characteristics and dynamic changes of the RBC induce a complex velocity and stress relationship, resulting in the incompatibility of blood flow characterization through standard presumptions of constant viscosity used for Newtonian fluid flow. Blood flow is categorized as a viscoelastic non-Newtonian fluid flow where constitutive equations governing this type of flow take into consideration the nonlinear viscometric properties of blood. To mathematically characterize the evolving blood viscosity and the relationship between the elasticity of RBC and the shear blood flow, respectively, across space and time of the system, a stress tensor (τ) defined by constitutive models is often coupled in the Navier–Stokes equation to account for the collective impact of the constant dynamic viscosity (η) and the elasticity from RBCs on blood flow.The dynamic viscosity of blood is heavily dependent on the shear stress applied to the cell and various parameters from the blood such as hematocrit value, plasma viscosity, mechanical properties of the RBC membrane, and red blood cell aggregation rate. The apparent blood viscosity is considered convenient for the characterization of the relationship between the evolving blood viscosity and shear rate, which can be defined by Casson’s law, as shown in eq 1.

𝜇=𝜏0𝛾˙+2𝜂𝜏0𝛾˙⎯⎯⎯⎯⎯⎯⎯√+𝜂�=�0�˙+2��0�˙+�

(1)where τ

0 is the yield stress–stress required to initiate blood flow motion, η is the Casson rheological constant, and γ̇ is the shear rate. The value of Casson’s law parameters under blood with normal hematocrit level can be defined as τ

0 = 0.0056 Pa and η = 0.0035 Pa·s. 

(23) With the known property of blood and Casson’s law parameters, an approximation can be made to the dynamic viscosity under various flow condition domains. The Power Law model is often employed to characterize the dynamic viscosity in relation to the shear rate, since precise solutions exist for specific geometries and flow circumstances, acting as a fundamental standard for definition. The Carreau and Carreau–Yasuda models can be advantageous over the Power Law model due to their ability to evaluate the dynamic viscosity at low to zero shear rate conditions. However, none of the above-mentioned models consider the memory or other elastic behavior of blood and its RBCs. Some other commonly used mathematical models and their constants for the non-Newtonian viscosity property characterization of blood are listed in Table 1 below. 

(24−26)Table 1. Comparison of Various Non-Newtonian Models for Blood Viscosity 

(24−26)

ModelNon-Newtonian ViscosityParameters
Power Law(2)n = 0.61, k = 0.42
Carreau(3)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 3.1736 s, m = 2.406, a = 0.254
Walburn–Schneck(4)C1 = 0.000797 Pa·s, C2 = 0.0608 Pa·s, C3 = 0.00499, C4 = 14.585 g–1, TPMA = 25 g/L
Carreau–Yasuda(5)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 1.902 s, n = 0.22, a = 1.25
Quemada(6)μp = 0.0012 Pa·s, k = 2.07, k0 = 4.33, γ̇c = 1.88 s–1

The blood rheology is commonly known to be influenced by two key physiological factors, namely, the hematocrit value (H

t) and the fibrinogen concentration (c

f), with an average value of 42% and 0.252 gd·L

–1, respectively. Particularly in low shear conditions, the presence of varying fibrinogen concentrations affects the tendency for aggregation and rouleaux formation, while the occurrence of aggregation is contingent upon specific levels of hematocrit. 

(27) The study from Apostolidis et al. 

(28) modifies the Casson model through emphasizing its reliance on hematocrit and fibrinogen concentration parameter values, owing to the extensive knowledge of the two physiological blood parameters.The viscoelastic response of blood is heavily dependent on the elasticity of the RBC, which is defined by the relationship between the deformation and stress relaxation from RBCs under a specific location of shear flow as a function of the velocity field. The stress tensor is usually characterized by constitutive equations such as the Upper-Convected Maxwell Model 

(29) and the Oldroyd-B model 

(30) to track the molecule effects under shear from different driving forces. The prominent non-Newtonian features, such as shear thinning and yield stress, have played a vital role in the characterization of blood rheology, particularly with respect to the evaluation of yield stress under low shear conditions. The nature of stress measurement in blood, typically on the order of 1 mPa, is challenging due to its low magnitude. The occurrence of the CFL complicates the measurement further due to the significant decrease in apparent viscosity near the wall over time and a consequential disparity in viscosity compared to the bulk region.In addition to shear thinning viscosity and yield stress, the formation of aggregation (rouleaux) from RBCs under low shear rates also contributes to the viscoelasticity under transient flow 

(31) and thixotropy 

(32) of whole blood. Given the difficulty in evaluating viscoelastic behavior of blood under low strain magnitudes and limitations in generalized Newtonian models, the utilization of viscoelastic models is advocated to encompass elasticity and delineate non-shear components within the stress tensor. Extending from the Oldroyd-B model, Anand et al. 

(33) developed a viscoelastic model framework for adapting elasticity within blood samples and predicting non-shear stress components. However, to also address the thixotropic effects, the model developed by Horner et al. 

(34) serves as a more comprehensive approach than the viscoelastic model from Anand et al. Thixotropy 

(32) typically occurs from the structural change of the rouleaux, where low shear rate conditions induce rouleaux formation. Correspondingly, elasticity increases, while elasticity is more representative of the isolated RBCs, under high shear rate conditions. The model of Horner et al. 

(34) considers the contribution of rouleaux to shear stress, taking into account factors such as the characteristic time for Brownian aggregation, shear-induced aggregation, and shear-induced breakage. Subsequent advancements in the model from Horner et al. often revolve around refining the three aforementioned key terms for a more substantial characterization of rouleaux dynamics. Notably, this has led to the recently developed mHAWB model 

(35) and other model iterations to enhance the accuracy of elastic and viscoelastic contributions to blood rheology, including the recently improved model suggested by Armstrong et al. 

(36)

2.2.2. Numerical Methods (FDM, FEM, FVM)

Numerical simulation has become increasingly more significant in analyzing the geometry, boundary layers of flow, and nonlinearity of hyperbolic viscoelastic flow constitutive equations. CFD is a powerful and efficient tool utilizing numerical methods to solve the governing hydrodynamic equations, such as the Navier–Stokes (N–S) equation, continuity equation, and energy conservation equation, for qualitative evaluation of fluid motion dynamics under different parameters. CFD overcomes the challenge of analytically solving nonlinear forms of differential equations by employing numerical methods such as the Finite-Difference Method (FDM), Finite-Element Method (FEM), and Finite-Volume Method (FVM) to discretize and solve the partial differential equations (PDEs), allowing for qualitative reproduction of transport phenomena and experimental observations. Different numerical methods are chosen to cope with various transport systems for optimization of the accuracy of the result and control of error during the discretization process.FDM is a straightforward approach to discretizing PDEs, replacing the continuum representation of equations with a set of finite-difference equations, which is typically applied to structured grids for efficient implementation in CFD programs. 

(37) However, FDM is often limited to simple geometries such as rectangular or block-shaped geometries and struggles with curved boundaries. In contrast, FEM divides the fluid domain into small finite grids or elements, approximating PDEs through a local description of physics. 

(38) All elements contribute to a large, sparse matrix solver. However, FEM may not always provide accurate results for systems involving significant deformation and aggregation of particles like RBCs due to large distortion of grids. 

(39) FVM evaluates PDEs following the conservation laws and discretizes the selected flow domain into small but finite size control volumes, with each grid at the center of a finite volume. 

(40) The divergence theorem allows the conversion of volume integrals of PDEs with divergence terms into surface integrals of surface fluxes across cell boundaries. Due to its conservation property, FVM offers efficient outcomes when dealing with PDEs that embody mass, momentum, and energy conservation principles. Furthermore, widely accessible software packages like the OpenFOAM toolbox 

(41) include a viscoelastic solver, making it an attractive option for viscoelastic fluid flow modeling. 

(42)

2.2.3. Modeling Methods of Blood Flow Dynamics

The complexity in the blood flow simulation arises from deformability and aggregation that RBCs exhibit during their interaction with neighboring cells under different shear rate conditions induced by blood flow. Numerical models coupled with simulation programs have been applied as a groundbreaking method to predict such unique rheological behavior exhibited by RBCs and whole blood. The conventional approach of a single-phase flow simulation is often applied to blood flow simulations within large vessels possessing a moderate shear rate. However, such a method assumes the properties of plasma, RBCs and other cellular components to be evenly distributed as average density and viscosity in blood, resulting in the inability to simulate the mechanical dynamics, such as RBC aggregation under high-shear flow field, inherent in RBCs. To accurately describe the asymmetric distribution of RBC and blood flow, multiphase flow simulation, where numerical simulations of blood flows are often modeled as two immiscible phases, RBCs and blood plasma, is proposed. A common assumption is that RBCs exhibit non-Newtonian behavior while the plasma is treated as a continuous Newtonian phase.Numerous multiphase numerical models have been proposed to simulate the influence of RBCs on blood flow dynamics by different assumptions. In large-scale simulations (above the millimeter range), continuum-based methods are wildly used due to their lower computational demands. 

(43) Eulerian multiphase flow simulations offer the solution of a set of conservation equations for each separate phase and couple the phases through common pressure and interphase exchange coefficients. Xu et al. 

(44) utilized the combined finite-discrete element method (FDEM) to replicate the dynamic behavior and distortion of RBCs subjected to fluidic forces, utilizing the Johnson–Kendall–Roberts model 

(45) to define the adhesive forces of cell-to-cell interactions. The iterative direct-forcing immersed boundary method (IBM) is commonly employed in simulations of the fluid–cell interface of blood. This method effectively captures the intricacies of the thin and flexible RBC membranes within various external flow fields. 

(46) The study by Xu et al. 

(44) also adopts this approach to bridge the fluid dynamics and RBC deformation through IBM. Yoon and You utilized the Maxwell model to define the viscosity of the RBC membrane. 

(47) It was discovered that the Maxwell model could represent the stress relaxation and unloading processes of the cell. Furthermore, the reduced flexibility of an RBC under particular situations such as infection is specified, which was unattainable by the Kelvin–Voigt model 

(48) when compared to the Maxwell model in the literature. The Yeoh hyperplastic material model was also adapted to predict the nonlinear elasticity property of RBCs with FEM employed to discretize the RBC membrane using shell-type elements. Gracka et al. 

(49) developed a numerical CFD model with a finite-volume parallel solver for multiphase blood flow simulation, where an updated Maxwell viscoelasticity model and a Discrete Phase Model are adopted. In the study, the adapted IBM, based on unstructured grids, simulates the flow behavior and shape change of the RBCs through fluid-structure coupling. It was found that the hybrid Euler–Lagrange (E–L) approach 

(50) for the development of the multiphase model offered better results in the simulated CFL region in the microchannels.To study the dynamics of individual behaviors of RBCs and the consequent non-Newtonian blood flow, cell-shape-resolved computational models are often adapted. The use of the boundary integral method has become prevalent in minimizing computational expenses, particularly in the exclusive determination of fluid velocity on the surfaces of RBCs, incorporating the option of employing IBM or particle-based techniques. The cell-shaped-resolved method has enabled an examination of cell to cell interactions within complex ambient or pulsatile flow conditions 

(51) surrounding RBC membranes. Recently, Rydquist et al. 

(52) have looked to integrate statistical information from macroscale simulations to obtain a comprehensive overview of RBC behavior within the immediate proximity of the flow through introduction of respective models characterizing membrane shape definition, tension, bending stresses of RBC membranes.At a macroscopic scale, continuum models have conventionally been adapted for assessing blood flow dynamics through the application of elasticity theory and fluid dynamics. However, particle-based methods are known for their simplicity and adaptability in modeling complex multiscale fluid structures. Meshless methods, such as the boundary element method (BEM), smoothed particle hydrodynamics (SPH), and dissipative particle dynamics (DPD), are often used in particle-based characterization of RBCs and the surrounding fluid. By representing the fluid as discrete particles, meshless methods provide insights into the status and movement of the multiphase fluid. These methods allow for the investigation of cellular structures and microscopic interactions that affect blood rheology. Non-confronting mesh methods like IBM can also be used to couple a fluid solver such as FEM, FVM, or the Lattice Boltzmann Method (LBM) through membrane representation of RBCs. In comparison to conventional CFD methods, LBM has been viewed as a favorable numerical approach for solving the N–S equations and the simulation of multiphase flows. LBM exhibits the notable advantage of being amenable to high-performance parallel computing environments due to its inherently local dynamics. In contrast to DPD and SPH where RBC membranes are modeled as physically interconnected particles, LBM employs the IBM to account for the deformation dynamics of RBCs 

(53,54) under shear flows in complex channel geometries. 

(54,55) However, it is essential to acknowledge that the utilization of LBM in simulating RBC flows often entails a significant computational overhead, being a primary challenge in this context. Krüger et al. 

(56) proposed utilizing LBM as a fluid solver, IBM to couple the fluid and FEM to compute the response of membranes to deformation under immersed fluids. This approach decouples the fluid and membranes but necessitates significant computational effort due to the requirements of both meshes and particles.Despite the accuracy of current blood flow models, simulating complex conditions remains challenging because of the high computational load and cost. Balachandran Nair et al. 

(57) suggested a reduced order model of RBC under the framework of DEM, where the RBC is represented by overlapping constituent rigid spheres. The Morse potential force is adapted to account for the RBC aggregation exhibited by cell to cell interactions among RBCs at different distances. Based upon the IBM, the reduced-order RBC model is adapted to simulate blood flow transport for validation under both single and multiple RBCs with a resolved CFD-DEM solver. 

(58) In the resolved CFD-DEM model, particle sizes are larger than the grid size for a more accurate computation of the surrounding flow field. A continuous forcing approach is taken to describe the momentum source of the governing equation prior to discretization, which is different from a Direct Forcing Method (DFM). 

(59) As no body-conforming moving mesh is required, the continuous forcing approach offers lower complexity and reduced cost when compared to the DFM. Piquet et al. 

(60) highlighted the high complexity of the DFM due to its reliance on calculating an additional immersed boundary flux for the velocity field to ensure its divergence-free condition.The fluid–structure interaction (FSI) method has been advocated to connect the dynamic interplay of RBC membranes and fluid plasma within blood flow such as the coupling of continuum–particle interactions. However, such methodology is generally adapted for anatomical configurations such as arteries 

(61,62) and capillaries, 

(63) where both the structural components and the fluid domain undergo substantial deformation due to the moving boundaries. Due to the scope of the Review being blood flow simulation within microchannels of LOC devices without deformable boundaries, the Review of the FSI method will not be further carried out.In general, three numerical methods are broadly used: mesh-based, particle-based, and hybrid mesh–particle techniques, based on the spatial scale and the fundamental numerical approach, mesh-based methods tend to neglect the effects of individual particles, assuming a continuum and being efficient in terms of time and cost. However, the particle-based approach highlights more of the microscopic and mesoscopic level, where the influence of individual RBCs is considered. A review from Freund et al. 

(64) addressed the three numerical methodologies and their respective modeling approaches of RBC dynamics. Given the complex mechanics and the diverse levels of study concerning numerical simulations of blood and cellular flow, a broad spectrum of numerical methods for blood has been subjected to extensive review. 

(64−70) Ye at al. 

(65) offered an extensive review of the application of the DPD, SPH, and LBM for numerical simulations of RBC, while Rathnayaka et al. 

(67) conducted a review of the particle-based numerical modeling for liquid marbles through drawing parallels to the transport of RBCs in microchannels. A comparative analysis between conventional CFD methods and particle-based approaches for cellular and blood flow dynamic simulation can be found under the review by Arabghahestani et al. 

(66) Literature by Li et al. 

(68) and Beris et al. 

(69) offer an overview of both continuum-based models at micro/macroscales and multiscale particle-based models encompassing various length and temporal dimensions. Furthermore, these reviews deliberate upon the potential of coupling continuum-particle methods for blood plasma and RBC modeling. Arciero et al. 

(70) investigated various modeling approaches encompassing cellular interactions, such as cell to cell or plasma interactions and the individual cellular phases. A concise overview of the reviews is provided in Table 2 for reference.

Table 2. List of Reviews for Numerical Approaches Employed in Blood Flow Simulation

ReferenceNumerical methods
Li et al. (2013) (68)Continuum-based modeling (BIM), particle-based modeling (LBM, LB-FE, SPH, DPD)
Freund (2014) (64)RBC dynamic modeling (continuum-based modeling, complementary discrete microstructure modeling), blood flow dynamic modeling (FDM, IBM, LBM, particle-mesh methods, coupled boundary integral and mesh-based methods, DPD)
Ye et al. (2016) (65)DPD, SPH, LBM, coupled IBM-Smoothed DPD
Arciero et al. (2017) (70)LBM, IBM, DPD, conventional CFD Methods (FDM, FVM, FEM)
Arabghahestani et al. (2019) (66)Particle-based methods (LBM, DPD, direct simulation Monte Carlo, molecular dynamics), SPH, conventional CFD methods (FDM, FVM, FEM)
Beris et al. (2021) (69)DPD, smoothed DPD, IBM, LBM, BIM
Rathnayaka (2022) (67)SPH, CG, LBM

3. Capillary Driven Blood Flow in LOC Systems

ARTICLE SECTIONS

Jump To


3.1. Capillary Driven Flow Phenomena

Capillary driven (CD) flow is a pivotal mechanism in passive microfluidic flow systems 

(9) such as the blood circulation system and LOC systems. 

(71) CD flow is essentially the movement of a liquid to flow against drag forces, where the capillary effect exerts a force on the liquid at the borders, causing a liquid–air meniscus to flow despite gravity or other drag forces. A capillary pressure drops across the liquid–air interface with surface tension in the capillary radius and contact angle. The capillary effect depends heavily on the interaction between the different properties of surface materials. Different values of contact angles can be manipulated and obtained under varying levels of surface wettability treatments to manipulate the surface properties, resulting in different CD blood delivery rates for medical diagnostic device microchannels. CD flow techniques are appealing for many LOC devices, because they require no external energy. However, due to the passive property of liquid propulsion by capillary forces and the long-term instability of surface treatments on channel walls, the adaptability of CD flow in geometrically complex LOC devices may be limited.

3.2. Theoretical and Numerical Modeling of Capillary Driven Blood Flow

3.2.1. Theoretical Basis and Assumptions of Microfluidic Flow

The study of transport phenomena regarding either blood flow driven by capillary forces or externally applied forces under microfluid systems all demands a comprehensive recognition of the significant differences in flow dynamics between microscale and macroscale. The fundamental assumptions and principles behind fluid transport at the microscale are discussed in this section. Such a comprehension will lay the groundwork for the following analysis of the theoretical basis of capillary forces and their role in blood transport in LOC systems.

At the macroscale, fluid dynamics are often strongly influenced by gravity due to considerable fluid mass. However, the high surface to volume ratio at the microscale shifts the balance toward surface forces (e.g., surface tension and viscous forces), much larger than the inertial force. This difference gives rise to transport phenomena unique to microscale fluid transport, such as the prevalence of laminar flow due to a very low Reynolds number (generally lower than 1). Moreover, the fluid in a microfluidic system is often assumed to be incompressible due to the small flow velocity, indicating constant fluid density in both space and time.Microfluidic flow behaviors are governed by the fundamental principles of mass and momentum conservation, which are encapsulated in the continuity equation and the Navier–Stokes (N–S) equation. The continuity equation describes the conservation of mass, while the N–S equation captures the spatial and temporal variations in velocity, pressure, and other physical parameters. Under the assumption of the negligible influence of gravity in microfluidic systems, the continuity equation and the Eulerian representation of the incompressible N–S equation can be expressed as follows:

∇·𝐮⇀=0∇·�⇀=0

(7)

−∇𝑝+𝜇∇2𝐮⇀+∇·𝝉⇀−𝐅⇀=0−∇�+�∇2�⇀+∇·�⇀−�⇀=0

(8)Here, p is the pressure, u is the fluid viscosity, 

𝝉⇀�⇀ represents the stress tensor, and F is the body force exerted by external forces if present.

3.2.2. Theoretical Basis and Modeling of Capillary Force in LOC Systems

The capillary force is often the major driving force to manipulate and transport blood without an externally applied force in LOC systems. Forces induced by the capillary effect impact the free surface of fluids and are represented not directly in the Navier–Stokes equations but through the pressure boundary conditions of the pressure term p. For hydrophilic surfaces, the liquid generally induces a contact angle between 0° and 30°, encouraging the spread and attraction of fluid under a positive cos θ condition. For this condition, the pressure drop becomes positive and generates a spontaneous flow forward. A hydrophobic solid surface repels the fluid, inducing minimal contact. Generally, hydrophobic solids exhibit a contact angle larger than 90°, inducing a negative value of cos θ. Such a value will result in a negative pressure drop and a flow in the opposite direction. The induced contact angle is often utilized to measure the wall exposure of various surface treatments on channel walls where different wettability gradients and surface tension effects for CD flows are established. Contact angles between different interfaces are obtainable through standard values or experimental methods for reference. 

(72)For the characterization of the induced force by the capillary effect, the Young–Laplace (Y–L) equation 

(73) is widely employed. In the equation, the capillary is considered a pressure boundary condition between the two interphases. Through the Y–L equation, the capillary pressure force can be determined, and subsequently, the continuity and momentum balance equations can be solved to obtain the blood filling rate. Kim et al. 

(74) studied the effects of concentration and exposure time of a nonionic surfactant, Silwet L-77, on the performance of a polydimethylsiloxane (PDMS) microchannel in terms of plasma and blood self-separation. The study characterized the capillary pressure force by incorporating the Y–L equation and further evaluated the effects of the changing contact angle due to different levels of applied channel wall surface treatments. The expression of the Y–L equation utilized by Kim et al. 

(74) is as follows:

𝑃=−𝜎(cos𝜃b+cos𝜃tℎ+cos𝜃l+cos𝜃r𝑤)�=−�(cos⁡�b+cos⁡�tℎ+cos⁡�l+cos⁡�r�)

(9)where σ is the surface tension of the liquid and θ

bθ

tθ

l, and θ

r are the contact angle values between the liquid and the bottom, top, left, and right walls, respectively. A numerical simulation through Coventor software is performed to evaluate the dynamic changes in the filling rate within the microchannel. The simulation results for the blood filling rate in the microchannel are expressed at a specific time stamp, shown in Figure 2. The results portray an increasing instantaneous filling rate of blood in the microchannel following the decrease in contact angle induced by a higher concentration of the nonionic surfactant treated to the microchannel wall.

Figure 2. Numerical simulation of filling rate of capillary driven blood flow under various contact angle conditions at a specific timestamp. (74) Reproduced with permission from ref (74). Copyright 2010 Elsevier.

When in contact with hydrophilic or hydrophobic surfaces, blood forms a meniscus with a contact angle due to surface tension. The Lucas–Washburn (L–W) equation 

(75) is one of the pioneering theoretical definitions for the position of the meniscus over time. In addition, the L–W equation provides the possibility for research to obtain the velocity of the blood formed meniscus through the derivation of the meniscus position. The L–W equation 

(75) can be shown below:

𝐿(𝑡)=𝑅𝜎cos(𝜃)𝑡2𝜇⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�(�)=��⁡cos(�)�2�

(10)Here L(t) represents the distance of the liquid driven by the capillary forces. However, the generalized L–W equation solely assumes the constant physical properties from a Newtonian fluid rather than considering the non-Newtonian fluid behavior of blood. Cito et al. 

(76) constructed an enhanced version of the L–W equation incorporating the power law to consider the RBC aggregation and the FL effect. The non-Newtonian fluid apparent viscosity under the Power Law model is defined as

𝜇=𝑘·(𝛾˙)𝑛−1�=�·(�˙)�−1

(11)where γ̇ is the strain rate tensor defined as 

𝛾˙=12𝛾˙𝑖𝑗𝛾˙𝑗𝑖⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�˙=12�˙���˙��. The stress tensor term τ is computed as τ = μγ̇

ij. The updated L–W equation by Cito 

(76) is expressed as

𝐿(𝑡)=𝑅[(𝑛+13𝑛+1)(𝜎cos(𝜃)𝑅𝑘)1/𝑛𝑡]𝑛/𝑛+1�(�)=�[(�+13�+1)(�⁡cos(�)��)1/��]�/�+1

(12)where k is the flow consistency index and n is the power law index, respectively. The power law index, from the Power Law model, characterizes the extent of the non-Newtonian behavior of blood. Both the consistency and power law index rely on blood properties such as hematocrit, the appearance of the FL effect, the formation of RBC aggregates, etc. The updated L–W equation computes the location and velocity of blood flow caused by capillary forces at specified time points within the LOC devices, taking into account the effects of blood flow characteristics such as RBC aggregation and the FL effect on dynamic blood viscosity.Apart from the blood flow behaviors triggered by inherent blood properties, unique flow conditions driven by capillary forces that are portrayed under different microchannel geometries also hold crucial implications for CD blood delivery. Berthier et al. 

(77) studied the spontaneous Concus–Finn condition, the condition to initiate the spontaneous capillary flow within a V-groove microchannel, as shown in Figure 3(a) both experimentally and numerically. Through experimental studies, the spontaneous Concus–Finn filament development of capillary driven blood flow is observed, as shown in Figure 3(b), while the dynamic development of blood flow is numerically simulated through CFD simulation.

Figure 3. (a) Sketch of the cross-section of Berthier’s V-groove microchannel, (b) experimental view of blood in the V-groove microchannel, (78) (c) illustration of the dynamic change of the extension of filament from FLOW 3D under capillary flow at three increasing time intervals. (78) Reproduced with permission from ref (78). Copyright 2014 Elsevier.

Berthier et al. 

(77) characterized the contact angle needed for the initiation of the capillary driving force at a zero-inlet pressure, through the half-angle (α) of the V-groove geometry layout, and its relation to the Concus–Finn filament as shown below:

𝜃<𝜋2−𝛼sin𝛼1+2(ℎ2/𝑤)sin𝛼<cos𝜃{�<�2−�sin⁡�1+2(ℎ2/�)⁡sin⁡�<cos⁡�

(13)Three possible regimes were concluded based on the contact angle value for the initiation of flow and development of Concus–Finn filament:

𝜃>𝜃1𝜃1>𝜃>𝜃0𝜃0no SCFSCF without a Concus−Finn filamentSCF without a Concus−Finn filament{�>�1no SCF�1>�>�0SCF without a Concus−Finn filament�0SCF without a Concus−Finn filament

(14)Under Newton’s Law, the force balance with low Reynolds and Capillary numbers results in the neglect of inertial terms. The force balance between the capillary forces and the viscous force induced by the channel wall is proposed to derive the analytical fluid velocity. This relation between the two forces offers insights into the average flow velocity and the penetration distance function dependent on time. The apparent blood viscosity is defined by Berthier et al. 

(78) through Casson’s law, 

(23) given in eq 1. The research used the FLOW-3D program from Flow Science Inc. software, which solves transient, free-surface problems using the FDM in multiple dimensions. The Volume of Fluid (VOF) method 

(79) is utilized to locate and track the dynamic extension of filament throughout the advancing interface within the channel ahead of the main flow at three progressing time stamps, as depicted in Figure 3(c).

4. Electro-osmotic Flow (EOF) in LOC Systems

ARTICLE SECTIONS

Jump To


The utilization of external forces, such as electric fields, has significantly broadened the possibility of manipulating microfluidic flow in LOC systems. 

(80) Externally applied electric field forces induce a fluid flow from the movement of ions in fluid terms as the “electro-osmotic flow” (EOF).Unique transport phenomena, such as enhanced flow velocity and flow instability, induced by non-Newtonian fluids, particularly viscoelastic fluids, under EOF, have sparked considerable interest in microfluidic devices with simple or complicated geometries within channels. 

(81) However, compared to the study of Newtonian fluids and even other electro-osmotic viscoelastic fluid flows, the literature focusing on the theoretical and numerical modeling of electro-osmotic blood flow is limited due to the complexity of blood properties. Consequently, to obtain a more comprehensive understanding of the complex blood flow behavior under EOF, theoretical and numerical studies of the transport phenomena in the EOF section will be based on the studies of different viscoelastic fluids under EOF rather than that of blood specifically. Despite this limitation, we believe these studies offer valuable insights that can help understand the complex behavior of blood flow under EOF.

4.1. EOF Phenomena

Electro-osmotic flow occurs at the interface between the microchannel wall and bulk phase solution. When in contact with the bulk phase, solution ions are absorbed or dissociated at the solid–liquid interface, resulting in the formation of a charge layer, as shown in Figure 4. This charged channel surface wall interacts with both negative and positive ions in the bulk sample, causing repulsion and attraction forces to create a thin layer of immobilized counterions, known as the Stern layer. The induced electric potential from the wall gradually decreases with an increase in the distance from the wall. The Stern layer potential, commonly termed the zeta potential, controls the intensity of the electrostatic interactions between mobile counterions and, consequently, the drag force from the applied electric field. Next to the Stern layer is the diffuse mobile layer, mainly composed of a mobile counterion. These two layers constitute the “electrical double layer” (EDL), the thickness of which is directly proportional to the ionic strength (concentration) of the bulk fluid. The relationship between the two parameters is characterized by a Debye length (λ

D), expressed as

𝜆𝐷=𝜖𝑘B𝑇2(𝑍𝑒)2𝑐0⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√��=��B�2(��)2�0

(15)where ϵ is the permittivity of the electrolyte solution, k

B is the Boltzmann constant, T is the electron temperature, Z is the integer valence number, e is the elementary charge, and c

0 is the ionic density.

Figure 4. Schematic diagram of an electro-osmotic flow in a microchannel with negative surface charge. (82) Reproduced with permission from ref (82). Copyright 2012 Woodhead Publishing.

When an electric field is applied perpendicular to the EDL, viscous drag is generated due to the movement of excess ions in the EDL. Electro-osmotic forces can be attributed to the externally applied electric potential (ϕ) and the zeta potential, the system wall induced potential by charged walls (ψ). As illustrated in Figure 4, the majority of ions in the bulk phase have a uniform velocity profile, except for a shear rate condition confined within an extremely thin Stern layer. Therefore, EOF displays a unique characteristic of a “near flat” or plug flow velocity profile, different from the parabolic flow typically induced by pressure-driven microfluidic flow (Hagen–Poiseuille flow). The plug-shaped velocity profile of the EOF possesses a high shear rate above the Stern layer.Overall, the EOF velocity magnitude is typically proportional to the Debye Length (λ

D), zeta potential, and magnitude of the externally applied electric field, while a more viscous liquid reduces the EOF velocity.

4.2. Modeling on Electro-osmotic Viscoelastic Fluid Flow

4.2.1. Theoretical Basis of EOF Mechanisms

The EOF of an incompressible viscoelastic fluid is commonly governed by the continuity and incompressible N–S equations, as shown in eqs 7 and 8, where the stress tensor and the electrostatic force term are coupled. The electro-osmotic body force term F, representing the body force exerted by the externally applied electric force, is defined as 

𝐹⇀=𝑝𝐸𝐸⇀�⇀=���⇀, where ρ

E and 

𝐸⇀�⇀ are the net electric charge density and the applied external electric field, respectively.Numerous models are established to theoretically study the externally applied electric potential and the system wall induced potential by charged walls. The following Laplace equation, expressed as eq 16, is generally adapted and solved to calculate the externally applied potential (ϕ).

∇2𝜙=0∇2�=0

(16)Ion diffusion under applied electric fields, together with mass transport resulting from convection and diffusion, transports ionic solutions in bulk flow under electrokinetic processes. The Nernst–Planck equation can describe these transport methods, including convection, diffusion, and electro-diffusion. Therefore, the Nernst–Planck equation is used to determine the distribution of the ions within the electrolyte. The electric potential induced by the charged channel walls follows the Poisson–Nernst–Plank (PNP) equation, which can be written as eq 17.

∇·[𝐷𝑖∇𝑛𝑖−𝑢⇀𝑛𝑖+𝑛𝑖𝐷𝑖𝑧𝑖𝑒𝑘𝑏𝑇∇(𝜙+𝜓)]=0∇·[��∇��−�⇀��+����������∇(�+�)]=0

(17)where D

in

i, and z

i are the diffusion coefficient, ionic concentration, and ionic valence of the ionic species I, respectively. However, due to the high nonlinearity and numerical stiffness introduced by different lengths and time scales from the PNP equations, the Poisson–Boltzmann (PB) model is often considered the major simplified method of the PNP equation to characterize the potential distribution of the EDL region in microchannels. In the PB model, it is assumed that the ionic species in the fluid follow the Boltzmann distribution. This model is typically valid for steady-state problems where charge transport can be considered negligible, the EDLs do not overlap with each other, and the intrinsic potentials are low. It provides a simplified representation of the potential distribution in the EDL region. The PB equation governing the EDL electric potential distribution is described as

∇2𝜓=(2𝑒𝑧𝑛0𝜀𝜀0)sinh(𝑧𝑒𝜓𝑘b𝑇)∇2�=(2���0��0)⁡sinh(����b�)

(18)where n

0 is the ion bulk concentration, z is the ionic valence, and ε

0 is the electric permittivity in the vacuum. Under low electric potential conditions, an even further simplified model to illustrate the EOF phenomena is the Debye–Hückel (DH) model. The DH model is derived by obtaining a charge density term by expanding the exponential term of the Boltzmann equation in a Taylor series.

4.2.2. EOF Modeling for Viscoelastic Fluids

Many studies through numerical modeling were performed to obtain a deeper understanding of the effect exhibited by externally applied electric fields on viscoelastic flow in microchannels under various geometrical designs. Bello et al. 

(83) found that methylcellulose solution, a non-Newtonian polymer solution, resulted in stronger electro-osmotic mobility in experiments when compared to the predictions by the Helmholtz–Smoluchowski equation, which is commonly used to define the velocity of EOF of a Newtonian fluid. Being one of the pioneers to identify the discrepancies between the EOF of Newtonian and non-Newtonian fluids, Bello et al. attributed such discrepancies to the presence of a very high shear rate in the EDL, resulting in a change in the orientation of the polymer molecules. Park and Lee 

(84) utilized the FVM to solve the PB equation for the characterization of the electric field induced force. In the study, the concept of fractional calculus for the Oldroyd-B model was adapted to illustrate the elastic and memory effects of viscoelastic fluids in a straight microchannel They observed that fluid elasticity and increased ratio of viscoelastic fluid contribution to overall fluid viscosity had a significant impact on the volumetric flow rate and sensitivity of velocity to electric field strength compared to Newtonian fluids. Afonso et al. 

(85) derived an analytical expression for EOF of viscoelastic fluid between parallel plates using the DH model to account for a zeta potential condition below 25 mV. The study established the understanding of the electro-osmotic viscoelastic fluid flow under low zeta potential conditions. Apart from the electrokinetic forces, pressure forces can also be coupled with EOF to generate a unique fluid flow behavior within the microchannel. Sousa et al. 

(86) analytically studied the flow of a standard viscoelastic solution by combining the pressure gradient force with an externally applied electric force. It was found that, at a near wall skimming layer and the outer layer away from the wall, macromolecules migrating away from surface walls in viscoelastic fluids are observed. In the study, the Phan-Thien Tanner (PTT) constitutive model is utilized to characterize the viscoelastic properties of the solution. The approach is found to be valid when the EDL is much thinner than the skimming layer under an enhanced flow rate. Zhao and Yang 

(87) solved the PB equation and Carreau model for the characterization of the EOF mechanism and non-Newtonian fluid respectively through the FEM. The numerical results depict that, different from the EOF of Newtonian fluids, non-Newtonian fluids led to an increase of electro-osmotic mobility for shear thinning fluids but the opposite for shear thickening fluids.Like other fluid transport driving forces, EOF within unique geometrical layouts also portrays unique transport phenomena. Pimenta and Alves 

(88) utilized the FVM to perform numerical simulations of the EOF of viscoelastic fluids considering the PB equation and the Oldroyd-B model, in a cross-slot and flow-focusing microdevices. It was found that electroelastic instabilities are formed due to the development of large stresses inside the EDL with streamlined curvature at geometry corners. Bezerra et al. 

(89) used the FDM to numerically analyze the vortex formation and flow instability from an electro-osmotic non-Newtonian fluid flow in a microchannel with a nozzle geometry and parallel wall geometry setting. The PNP equation is utilized to characterize the charge motion in the EOF and the PTT model for non-Newtonian flow characterization. A constriction geometry is commonly utilized in blood flow adapted in LOC systems due to the change in blood flow behavior under narrow dimensions in a microchannel. Ji et al. 

(90) recently studied the EOF of viscoelastic fluid in a constriction microchannel connected by two relatively big reservoirs on both ends (as seen in Figure 5) filled with the polyacrylamide polymer solution, a viscoelastic fluid, and an incompressible monovalent binary electrolyte solution KCl.

Figure 5. Schematic diagram of a negatively charged constriction microchannel connected to two reservoirs at both ends. An electro-osmotic flow is induced in the system by the induced potential difference between the anode and cathode. (90) Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

In studying the EOF of viscoelastic fluids, the Oldroyd-B model is often utilized to characterize the polymeric stress tensor and the deformation rate of the fluid. The Oldroyd-B model is expressed as follows:

𝜏=𝜂p𝜆(𝐜−𝐈)�=�p�(�−�)

(19)where η

p, λ, c, and I represent the polymer dynamic viscosity, polymer relaxation time, symmetric conformation tensor of the polymer molecules, and the identity matrix, respectively.A log-conformation tensor approach is taken to prevent convergence difficulty induced by the viscoelastic properties. The conformation tensor (c) in the polymeric stress tensor term is redefined by a new tensor (Θ) based on the natural logarithm of the c. The new tensor is defined as

Θ=ln(𝐜)=𝐑ln(𝚲)𝐑Θ=ln(�)=�⁡ln(�)�

(20)in which Λ is the diagonal matrix and R is the orthogonal matrix.Under the new conformation tensor, the induced EOF of a viscoelastic fluid is governed by the continuity and N–S equations adapting the Oldroyd-B model, which is expressed as

∂𝚯∂𝑡+𝐮·∇𝚯=𝛀Θ−ΘΩ+2𝐁+1𝜆(eΘ−𝐈)∂�∂�+�·∇�=�Θ−ΘΩ+2�+1�(eΘ−�)

(21)where Ω and B represent the anti-symmetric matrix and the symmetric traceless matrix of the decomposition of the velocity gradient tensor ∇u, respectively. The conformation tensor can be recovered by c = exp(Θ). The PB model and Laplace equation are utilized to characterize the charged channel wall induced potential and the externally applied potential.The governing equations are numerically solved through the FVM by RheoTool, 

(42) an open-source viscoelastic EOF solver on the OpenFOAM platform. A SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm was applied to solve the velocity-pressure coupling. The pressure field and velocity field were computed by the PCG (Preconditioned Conjugate Gradient) solver and the PBiCG (Preconditioned Biconjugate Gradient) solver, respectively.Ranging magnitudes of an applied electric field or fluid concentration induce both different streamlines and velocity magnitudes at various locations and times of the microchannel. In the study performed by Ji et al., 

(90) notable fluctuation of streamlines and vortex formation is formed at the upper stream entrance of the constriction as shown in Figure 6(a) and (b), respectively, due to the increase of electrokinetic effect, which is seen as a result of the increase in polymeric stress (τ

xx). 

(90) The contraction geometry enhances the EOF velocity within the constriction channel under high E

app condition (600 V/cm). Such phenomena can be attributed to the dependence of electro-osmotic viscoelastic fluid flow on the system wall surface and bulk fluid properties. 

(91)

Figure 6. Schematic diagram of vortex formation and streamlines of EOF depicting flow instability at (a) 1.71 s and (b) 1.75 s. Spatial distribution of the elastic normal stress at (c) high Eapp condition. Streamline of an electro-osmotic flow under Eapp of 600 V/cm (90) for (d) non-Newtonian and (e) Newtonian fluid through a constriction geometry. Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

As elastic normal stress exceeds the local shear stress, flow instability and vortex formation occur. The induced elastic stress under EOF not only enhances the instability of the flow but often generates an irregular secondary flow leading to strong disturbance. 

(92) It is also vital to consider the effect of the constriction layout of microchannels on the alteration of the field strength within the system. The contraction geometry enhances a larger electric field strength compared with other locations of the channel outside the constriction region, resulting in a higher velocity gradient and stronger extension on the polymer within the viscoelastic solution. Following the high shear flow condition, a higher magnitude of stretch for polymer molecules in viscoelastic fluids exhibits larger elastic stresses and enhancement of vortex formation at the region. 

(93)As shown in Figure 6(c), significant elastic normal stress occurs at the inlet of the constriction microchannel. Such occurrence of a polymeric flow can be attributed to the dominating elongational flow, giving rise to high deformation of the polymers within the viscoelastic fluid flow, resulting in higher elastic stress from the polymers. Such phenomena at the entrance result in the difference in velocity streamline as circled in Figure 6(d) compared to that of the Newtonian fluid at the constriction entrance in Figure 6(e). 

(90) The difference between the Newtonian and polymer solution at the exit, as circled in Figure 6(d) and (e), can be attributed to the extrudate swell effect of polymers 

(94) within the viscoelastic fluid flow. The extrudate swell effect illustrates that, as polymers emerge from the constriction exit, they tend to contract in the flow direction and grow in the normal direction, resulting in an extrudate diameter greater than the channel size. The deformation of polymers within the polymeric flow at both the entrance and exit of the contraction channel facilitates the change in shear stress conditions of the flow, leading to the alteration in streamlines of flows for each region.

4.3. EOF Applications in LOC Systems

4.3.1. Mixing in LOC Systems

Rather than relying on the micromixing controlled by molecular diffusion under low Reynolds number conditions, active mixers actively leverage convective instability and vortex formation induced by electro-osmotic flows from alternating current (AC) or direct current (DC) electric fields. Such adaptation is recognized as significant breakthroughs for promotion of fluid mixing in chemical and biological applications such as drug delivery, medical diagnostics, chemical synthesis, and so on. 

(95)Many researchers proposed novel designs of electro-osmosis micromixers coupled with numerical simulations in conjunction with experimental findings to increase their understanding of the role of flow instability and vortex formation in the mixing process under electrokinetic phenomena. Matsubara and Narumi 

(96) numerically modeled the mixing process in a microchannel with four electrodes on each side of the microchannel wall, which generated a disruption through unstable electro-osmotic vortices. It was found that particle mixing was sensitive to both the convection effect induced by the main and secondary vortex within the micromixer and the change in oscillation frequency caused by the supplied AC voltage when the Reynolds number was varied. Qaderi et al. 

(97) adapted the PNP equation to numerically study the effect of the geometry and zeta potential configuration of the microchannel on the mixing process with a combined electro-osmotic pressure driven flow. It was reported that the application of heterogeneous zeta potential configuration enhances the mixing efficiency by around 23% while the height of the hurdles increases the mixing efficiency at most 48.1%. Cho et al. 

(98) utilized the PB model and Laplace equation to numerically simulate the electro-osmotic non-Newtonian fluid mixing process within a wavy and block layout of microchannel walls. The Power Law model is adapted to describe the fluid rheological characteristic. It was found that shear-thinning fluids possess a higher volumetric flow rate, which could result in poorer mixing efficiency compared to that of Newtonian fluids. Numerous studies have revealed that flow instability and vortex generation, in particular secondary vortices produced by barriers or greater magnitudes of heterogeneous zeta potential distribution, enhance mixing by increasing bulk flow velocity and reducing flow distance.To better understand the mechanism of disturbance formed in the system due to externally applied forces, known as electrokinetic instability, literature often utilize the Rayleigh (Ra) number, 

(1) as described below:

𝑅𝑎𝑣=𝑢ev𝑢eo=(𝛾−1𝛾+1)2𝑊𝛿2𝐸el2𝐻2𝜁𝛿Ra�=�ev�eo=(�−1�+1)2��2�el2�2��

(22)where γ is the conductivity ratio of the two streams and can be written as 

𝛾=𝜎el,H𝜎el,L�=�el,H�el,L. The Ra number characterizes the ratio between electroviscous and electro-osmotic flow. A high Ra

v value often results in good mixing. It is evident that fluid properties such as the conductivity (σ) of the two streams play a key role in the formation of disturbances to enhance mixing in microsystems. At the same time, electrokinetic parameters like the zeta potential (ζ) in the Ra number is critical in the characterization of electro-osmotic velocity and a slip boundary condition at the microchannel wall.To understand the mixing result along the channel, the concentration field can be defined and simulated under the assumption of steady state conditions and constant diffusion coefficient for each of the working fluid within the system through the convection–diffusion equation as below:

∂𝑐𝒊∂𝑡+∇⇀(𝑐𝑖𝑢⇀−𝐷𝑖∇⇀𝑐𝒊)=0∂��∂�+∇⇀(���⇀−��∇⇀��)=0

(23)where c

i is the species concentration of species i and D

i is the diffusion coefficient of the corresponding species.The standard deviation of concentration (σ

sd) can be adapted to evaluate the mixing quality of the system. 

(97) The standard deviation for concentration at a specific portion of the channel may be calculated using the equation below:

𝜎sd=∫10(𝐶∗(𝑦∗)−𝐶m)2d𝑦∗∫10d𝑦∗⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯�sd=∫01(�*(�*)−�m)2d�*∫01d�*

(24)where C*(y*) and C

m are the non-dimensional concentration profile and the mean concentration at the portion, respectively. C* is the non-dimensional concentration and can be calculated as 

𝐶∗=𝐶𝐶ref�*=��ref, where C

ref is the reference concentration defined as the bulk solution concentration. The mean concentration profile can be calculated as 

𝐶m=∫10(𝐶∗(𝑦∗)d𝑦∗∫10d𝑦∗�m=∫01(�*(�*)d�*∫01d�*. With the standard deviation of concentration, the mixing efficiency 

(97) can then be calculated as below:

𝜀𝑥=1−𝜎sd𝜎sd,0��=1−�sd�sd,0

(25)where σ

sd,0 is the standard derivation of the case of no mixing. The value of the mixing efficiency is typically utilized in conjunction with the simulated flow field and concentration field to explore the effect of geometrical and electrokinetic parameters on the optimization of the mixing results.

5. Summary

ARTICLE SECTIONS

Jump To


5.1. Conclusion

Viscoelastic fluids such as blood flow in LOC systems are an essential topic to proceed with diagnostic analysis and research through microdevices in the biomedical and pharmaceutical industries. The complex blood flow behavior is tightly controlled by the viscoelastic characteristics of blood such as the dynamic viscosity and the elastic property of RBCs under various shear rate conditions. Furthermore, the flow behaviors under varied driving forces promote an array of microfluidic transport phenomena that are critical to the management of blood flow and other adapted viscoelastic fluids in LOC systems. This review addressed the blood flow phenomena, the complicated interplay between shear rate and blood flow behaviors, and their numerical modeling under LOC systems through the lens of the viscoelasticity characteristic. Furthermore, a theoretical understanding of capillary forces and externally applied electric forces leads to an in-depth investigation of the relationship between blood flow patterns and the key parameters of the two driving forces, the latter of which is introduced through the lens of viscoelastic fluids, coupling numerical modeling to improve the knowledge of blood flow manipulation in LOC systems. The flow disturbances triggered by the EOF of viscoelastic fluids and their impact on blood flow patterns have been deeply investigated due to their important role and applications in LOC devices. Continuous advancements of various numerical modeling methods with experimental findings through more efficient and less computationally heavy methods have served as an encouraging sign of establishing more accurate illustrations of the mechanisms for multiphase blood and other viscoelastic fluid flow transport phenomena driven by various forces. Such progress is fundamental for the manipulation of unique transport phenomena, such as the generated disturbances, to optimize functionalities offered by microdevices in LOC systems.

The following section will provide further insights into the employment of studied blood transport phenomena to improve the functionality of micro devices adapting LOC technology. A discussion of the novel roles that external driving forces play in microfluidic flow behaviors is also provided. Limitations in the computational modeling of blood flow and electrokinetic phenomena in LOC systems will also be emphasized, which may provide valuable insights for future research endeavors. These discussions aim to provide guidance and opportunities for new paths in the ongoing development of LOC devices that adapt blood flow.

5.2. Future Directions

5.2.1. Electro-osmosis Mixing in LOC Systems

Despite substantial research, mixing results through flow instability and vortex formation phenomena induced by electro-osmotic mixing still deviate from the effective mixing results offered by chaotic mixing results such as those seen in turbulent flows. However, recent discoveries of a mixing phenomenon that is generally observed under turbulent flows are found within electro-osmosis micromixers under low Reynolds number conditions. Zhao 

(99) experimentally discovered a rapid mixing process in an AC applied micromixer, where the power spectrum of concentration under an applied voltage of 20 V

p-p induces a −5/3 slope within a frequency range. This value of the slope is considered as the O–C spectrum in macroflows, which is often visible under relatively high Re conditions, such as the Taylor microscale Reynolds number Re > 500 in turbulent flows. 

(100) However, the Re value in the studied system is less than 1 at the specific location and applied voltage. A secondary flow is also suggested to occur close to microchannel walls, being attributed to the increase of convective instability within the system.Despite the experimental phenomenon proposed by Zhao et al., 

(99) the range of effects induced by vital parameters of an EOF mixing system on the enhanced mixing results and mechanisms of disturbance generated by the turbulent-like flow instability is not further characterized. Such a gap in knowledge may hinder the adaptability and commercialization of the discovery of micromixers. One of the parameters for further evaluation is the conductivity gradient of the fluid flow. A relatively strong conductivity gradient (5000:1) was adopted in the system due to the conductive properties of the two fluids. The high conductivity gradients may contribute to the relatively large Rayleigh number and differences in EDL layer thickness, resulting in an unusual disturbance in laminar flow conditions and enhanced mixing results. However, high conductivity gradients are not always achievable by the working fluids due to diverse fluid properties. The reliance on turbulent-like phenomena and rapid mixing results in a large conductivity gradient should be established to prevent the limited application of fluids for the mixing system. In addition, the proposed system utilizes distinct zeta potential distributions at the top and bottom walls due to their difference in material choices, which may be attributed to the flow instability phenomena. Further studies should be made on varying zeta potential magnitude and distribution to evaluate their effect on the slip boundary conditions of the flow and the large shear rate condition close to the channel wall of EOF. Such a study can potentially offer an optimized condition in zeta potential magnitude through material choices and geometrical layout of the zeta potential for better mixing results and manipulation of mixing fluid dynamics. The two vital parameters mentioned above can be varied with the aid of numerical simulation to understand the effect of parameters on the interaction between electro-osmotic forces and electroviscous forces. At the same time, the relationship of developed streamlines of the simulated velocity and concentration field, following their relationship with the mixing results, under the impact of these key parameters can foster more insight into the range of impact that the two parameters have on the proposed phenomena and the microfluidic dynamic principles of disturbances.

In addition, many of the current investigations of electrokinetic mixers commonly emphasize the fluid dynamics of mixing for Newtonian fluids, while the utilization of biofluids, primarily viscoelastic fluids such as blood, and their distinctive response under shear forces in these novel mixing processes of LOC systems are significantly less studied. To develop more compatible microdevice designs and efficient mixing outcomes for the biomedical industry, it is necessary to fill the knowledge gaps in the literature on electro-osmotic mixing for biofluids, where properties of elasticity, dynamic viscosity, and intricate relationship with shear flow from the fluid are further considered.

5.2.2. Electro-osmosis Separation in LOC Systems

Particle separation in LOC devices, particularly in biological research and diagnostics, is another area where disturbances may play a significant role in optimization. 

(101) Plasma analysis in LOC systems under precise control of blood flow phenomena and blood/plasma separation procedures can detect vital information about infectious diseases from particular antibodies and foreign nucleic acids for medical treatments, diagnostics, and research, 

(102) offering more efficient results and simple operating procedures compared to that of the traditional centrifugation method for blood and plasma separation. However, the adaptability of LOC devices for blood and plasma separation is often hindered by microchannel clogging, where flow velocity and plasma yield from LOC devices is reduced due to occasional RBC migration and aggregation at the filtration entrance of microdevices. 

(103)It is important to note that the EOF induces flow instability close to microchannel walls, which may provide further solutions to clogging for the separation process of the LOC systems. Mohammadi et al. 

(104) offered an anti-clogging effect of RBCs at the blood and plasma separating device filtration entry, adjacent to the surface wall, through RBC disaggregation under high shear rate conditions generated by a forward and reverse EOF direction.

Further theoretical and numerical research can be conducted to characterize the effect of high shear rate conditions near microchannel walls toward the detachment of binding blood cells on surfaces and the reversibility of aggregation. Through numerical modeling with varying electrokinetic parameters to induce different degrees of disturbances or shear conditions at channel walls, it may be possible to optimize and better understand the process of disrupting the forces that bind cells to surface walls and aggregated cells at filtration pores. RBCs that migrate close to microchannel walls are often attracted by the adhesion force between the RBC and the solid surface originating from the van der Waals forces. Following RBC migration and attachment by adhesive forces adjacent to the microchannel walls as shown in Figure 7, the increase in viscosity at the region causes a lower shear condition and encourages RBC aggregation (cell–cell interaction), which clogs filtering pores or microchannels and reduces flow velocity at filtration region. Both the impact that shear forces and disturbances may induce on cell binding forces with surface walls and other cells leading to aggregation may suggest further characterization. Kinetic parameters such as activation energy and the rate-determining step for cell binding composition attachment and detachment should be considered for modeling the dynamics of RBCs and blood flows under external forces in LOC separation devices.

Figure 7. Schematic representations of clogging at a microchannel pore following the sequence of RBC migration, cell attachment to channel walls, and aggregation. (105) Reproduced with permission from ref (105). Copyright 2018 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

5.2.3. Relationship between External Forces and Microfluidic Systems

In blood flow, a thicker CFL suggests a lower blood viscosity, suggesting a complex relationship between shear stress and shear rate, affecting the blood viscosity and blood flow. Despite some experimental and numerical studies on electro-osmotic non-Newtonian fluid flow, limited literature has performed an in-depth investigation of the role that applied electric forces and other external forces could play in the process of CFL formation. Additional studies on how shear rates from external forces affect CFL formation and microfluidic flow dynamics can shed light on the mechanism of the contribution induced by external driving forces to the development of a separate phase of layer, similar to CFL, close to the microchannel walls and distinct from the surrounding fluid within the system, then influencing microfluidic flow dynamics.One of the mechanisms of phenomena to be explored is the formation of the Exclusion Zone (EZ) region following a “Self-Induced Flow” (SIF) phenomenon discovered by Li and Pollack, 

(106) as shown in Figure 8(a) and (b), respectively. A spontaneous sustained axial flow is observed when hydrophilic materials are immersed in water, resulting in the buildup of a negative layer of charges, defined as the EZ, after water molecules absorb infrared radiation (IR) energy and break down into H and OH

+.

Figure 8. Schematic representations of (a) the Exclusion Zone region and (b) the Self Induced Flow through visualization of microsphere movement within a microchannel. (106) Reproduced with permission from ref (106). Copyright 2020 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

Despite the finding of such a phenomenon, the specific mechanism and role of IR energy have yet to be defined for the process of EZ development. To further develop an understanding of the role of IR energy in such phenomena, a feasible study may be seen through the lens of the relationships between external forces and microfluidic flow. In the phenomena, the increase of SIF velocity under a rise of IR radiation resonant characteristics is shown in the participation of the external electric field near the microchannel walls under electro-osmotic viscoelastic fluid flow systems. The buildup of negative charges at the hydrophilic surfaces in EZ is analogous to the mechanism of electrical double layer formation. Indeed, research has initiated the exploration of the core mechanisms for EZ formation through the lens of the electrokinetic phenomena. 

(107) Such a similarity of the role of IR energy and the transport phenomena of SIF with electrokinetic phenomena paves the way for the definition of the unknown SIF phenomena and EZ formation. Furthermore, Li and Pollack 

(106) suggest whether CFL formation might contribute to a SIF of blood using solely IR radiation, a commonly available source of energy in nature, as an external driving force. The proposition may be proven feasible with the presence of the CFL region next to the negatively charged hydrophilic endothelial glycocalyx layer, coating the luminal side of blood vessels. 

(108) Further research can dive into the resonating characteristics between the formation of the CFL region next to the hydrophilic endothelial glycocalyx layer and that of the EZ formation close to hydrophilic microchannel walls. Indeed, an increase in IR energy is known to rapidly accelerate EZ formation and SIF velocity, depicting similarity to the increase in the magnitude of electric field forces and greater shear rates at microchannel walls affecting CFL formation and EOF velocity. Such correlation depicts a future direction in whether SIF blood flow can be observed and characterized theoretically further through the lens of the relationship between blood flow and shear forces exhibited by external energy.

The intricate link between the CFL and external forces, more specifically the externally applied electric field, can receive further attention to provide a more complete framework for the mechanisms between IR radiation and EZ formation. Such characterization may also contribute to a greater comprehension of the role IR can play in CFL formation next to the endothelial glycocalyx layer as well as its role as a driving force to propel blood flow, similar to the SIF, but without the commonly assumed pressure force from heart contraction as a source of driving force.

5.3. Challenges

Although there have been significant improvements in blood flow modeling under LOC systems over the past decade, there are still notable constraints that may require special attention for numerical simulation applications to benefit the adaptability of the designs and functionalities of LOC devices. Several points that require special attention are mentioned below:

1.The majority of CFD models operate under the relationship between the viscoelasticity of blood and the shear rate conditions of flow. The relative effect exhibited by the presence of highly populated RBCs in whole blood and their forces amongst the cells themselves under complex flows often remains unclearly defined. Furthermore, the full range of cell populations in whole blood requires a much more computational load for numerical modeling. Therefore, a vital goal for future research is to evaluate a reduced modeling method where the impact of cell–cell interaction on the viscoelastic property of blood is considered.
2.Current computational methods on hemodynamics rely on continuum models based upon non-Newtonian rheology at the macroscale rather than at molecular and cellular levels. Careful considerations should be made for the development of a constructive framework for the physical and temporal scales of micro/nanoscale systems to evaluate the intricate relationship between fluid driving forces, dynamic viscosity, and elasticity.
3.Viscoelastic fluids under the impact of externally applied electric forces often deviate from the assumptions of no-slip boundary conditions due to the unique flow conditions induced by externally applied forces. Furthermore, the mechanism of vortex formation and viscoelastic flow instability at laminar flow conditions should be better defined through the lens of the microfluidic flow phenomenon to optimize the prediction of viscoelastic flow across different geometrical layouts. Mathematical models and numerical methods are needed to better predict such disturbance caused by external forces and the viscoelasticity of fluids at such a small scale.
4.Under practical situations, zeta potential distribution at channel walls frequently deviates from the common assumption of a constant distribution because of manufacturing faults or inherent surface charges prior to the introduction of electrokinetic influence. These discrepancies frequently lead to inconsistent surface potential distribution, such as excess positive ions at relatively more negatively charged walls. Accordingly, unpredicted vortex formation and flow instability may occur. Therefore, careful consideration should be given to these discrepancies and how they could trigger the transport process and unexpected results of a microdevice.

Author Information

ARTICLE SECTIONS

Jump To


  • Corresponding Authors
    • Zhe Chen – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: zaccooky@sjtu.edu.cn
    • Bo Ouyang – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: bouy93@sjtu.edu.cn
    • Zheng-Hong Luo – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-9011-6020; Email: luozh@sjtu.edu.cn
  • Authors
    • Bin-Jie Lai – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0009-0002-8133-5381
    • Li-Tao Zhu – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-6514-8864
  • NotesThe authors declare no competing financial interest.

Acknowledgments

ARTICLE SECTIONS

Jump To


This work was supported by the National Natural Science Foundation of China (No. 22238005) and the Postdoctoral Research Foundation of China (No. GZC20231576).

Vocabulary

ARTICLE SECTIONS

Jump To


Microfluidicsthe field of technological and scientific study that investigates fluid flow in channels with dimensions between 1 and 1000 μm
Lab-on-a-Chip Technologythe field of research and technological development aimed at integrating the micro/nanofluidic characteristics to conduct laboratory processes on handheld devices
Computational Fluid Dynamics (CFD)the method utilizing computational abilities to predict physical fluid flow behaviors mathematically through solving the governing equations of corresponding fluid flows
Shear Ratethe rate of change in velocity where one layer of fluid moves past the adjacent layer
Viscoelasticitythe property holding both elasticity and viscosity characteristics relying on the magnitude of applied shear stress and time-dependent strain
Electro-osmosisthe flow of fluid under an applied electric field when charged solid surface is in contact with the bulk fluid
Vortexthe rotating motion of a fluid revolving an axis line

References

ARTICLE SECTIONS

Jump To


This article references 108 other publications.

  1. 1Neethirajan, S.; Kobayashi, I.; Nakajima, M.; Wu, D.; Nandagopal, S.; Lin, F. Microfluidics for food, agriculture and biosystems industries. Lab Chip 201111 (9), 1574– 1586,  DOI: 10.1039/c0lc00230eViewGoogle Scholar
  2. 2Whitesides, G. M. The origins and the future of microfluidics. Nature 2006442 (7101), 368– 373,  DOI: 10.1038/nature05058ViewGoogle Scholar
  3. 3Burklund, A.; Tadimety, A.; Nie, Y.; Hao, N.; Zhang, J. X. J. Chapter One – Advances in diagnostic microfluidics; Elsevier, 2020; DOI:  DOI: 10.1016/bs.acc.2019.08.001 .ViewGoogle Scholar
  4. 4Abdulbari, H. A. Chapter 12 – Lab-on-a-chip for analysis of blood. In Nanotechnology for Hematology, Blood Transfusion, and Artificial Blood; Denizli, A., Nguyen, T. A., Rajan, M., Alam, M. F., Rahman, K., Eds.; Elsevier, 2022; pp 265– 283.ViewGoogle Scholar
  5. 5Vladisavljević, G. T.; Khalid, N.; Neves, M. A.; Kuroiwa, T.; Nakajima, M.; Uemura, K.; Ichikawa, S.; Kobayashi, I. Industrial lab-on-a-chip: Design, applications and scale-up for drug discovery and delivery. Advanced Drug Delivery Reviews 201365 (11), 1626– 1663,  DOI: 10.1016/j.addr.2013.07.017ViewGoogle Scholar
  6. 6Kersaudy-Kerhoas, M.; Dhariwal, R.; Desmulliez, M. P. Y.; Jouvet, L. Hydrodynamic blood plasma separation in microfluidic channels. Microfluid. Nanofluid. 20108 (1), 105– 114,  DOI: 10.1007/s10404-009-0450-5ViewGoogle Scholar
  7. 7Popel, A. S.; Johnson, P. C. Microcirculation and Hemorheology. Annu. Rev. Fluid Mech. 200537 (1), 43– 69,  DOI: 10.1146/annurev.fluid.37.042604.133933ViewGoogle Scholar
  8. 8Fedosov, D. A.; Peltomäki, M.; Gompper, G. Deformation and dynamics of red blood cells in flow through cylindrical microchannels. Soft Matter 201410 (24), 4258– 4267,  DOI: 10.1039/C4SM00248BViewGoogle Scholar
  9. 9Chakraborty, S. Dynamics of capillary flow of blood into a microfluidic channel. Lab Chip 20055 (4), 421– 430,  DOI: 10.1039/b414566fViewGoogle Scholar
  10. 10Tomaiuolo, G.; Guido, S. Start-up shape dynamics of red blood cells in microcapillary flow. Microvascular Research 201182 (1), 35– 41,  DOI: 10.1016/j.mvr.2011.03.004ViewGoogle Scholar
  11. 11Sherwood, J. M.; Dusting, J.; Kaliviotis, E.; Balabani, S. The effect of red blood cell aggregation on velocity and cell-depleted layer characteristics of blood in a bifurcating microchannel. Biomicrofluidics 20126 (2), 24119,  DOI: 10.1063/1.4717755ViewGoogle Scholar
  12. 12Nader, E.; Skinner, S.; Romana, M.; Fort, R.; Lemonne, N.; Guillot, N.; Gauthier, A.; Antoine-Jonville, S.; Renoux, C.; Hardy-Dessources, M.-D. Blood Rheology: Key Parameters, Impact on Blood Flow, Role in Sickle Cell Disease and Effects of Exercise. Frontiers in Physiology 201910, 01329,  DOI: 10.3389/fphys.2019.01329ViewGoogle Scholar
  13. 13Trejo-Soto, C.; Lázaro, G. R.; Pagonabarraga, I.; Hernández-Machado, A. Microfluidics Approach to the Mechanical Properties of Red Blood Cell Membrane and Their Effect on Blood Rheology. Membranes 202212 (2), 217,  DOI: 10.3390/membranes12020217ViewGoogle Scholar
  14. 14Wagner, C.; Steffen, P.; Svetina, S. Aggregation of red blood cells: From rouleaux to clot formation. Comptes Rendus Physique 201314 (6), 459– 469,  DOI: 10.1016/j.crhy.2013.04.004ViewGoogle Scholar
  15. 15Kim, H.; Zhbanov, A.; Yang, S. Microfluidic Systems for Blood and Blood Cell Characterization. Biosensors 202313 (1), 13,  DOI: 10.3390/bios13010013ViewGoogle Scholar
  16. 16Fåhræus, R.; Lindqvist, T. THE VISCOSITY OF THE BLOOD IN NARROW CAPILLARY TUBES. American Journal of Physiology-Legacy Content 193196 (3), 562– 568,  DOI: 10.1152/ajplegacy.1931.96.3.562ViewGoogle Scholar
  17. 17Ascolese, M.; Farina, A.; Fasano, A. The Fåhræus-Lindqvist effect in small blood vessels: how does it help the heart?. J. Biol. Phys. 201945 (4), 379– 394,  DOI: 10.1007/s10867-019-09534-4ViewGoogle Scholar
  18. 18Bento, D.; Fernandes, C. S.; Miranda, J. M.; Lima, R. In vitro blood flow visualizations and cell-free layer (CFL) measurements in a microchannel network. Experimental Thermal and Fluid Science 2019109, 109847,  DOI: 10.1016/j.expthermflusci.2019.109847ViewGoogle Scholar
  19. 19Namgung, B.; Ong, P. K.; Wong, Y. H.; Lim, D.; Chun, K. J.; Kim, S. A comparative study of histogram-based thresholding methods for the determination of cell-free layer width in small blood vessels. Physiological Measurement 201031 (9), N61,  DOI: 10.1088/0967-3334/31/9/N01ViewGoogle Scholar
  20. 20Hymel, S. J.; Lan, H.; Fujioka, H.; Khismatullin, D. B. Cell trapping in Y-junction microchannels: A numerical study of the bifurcation angle effect in inertial microfluidics. Phys. Fluids (1994) 201931 (8), 082003,  DOI: 10.1063/1.5113516ViewGoogle Scholar
  21. 21Li, X.; Popel, A. S.; Karniadakis, G. E. Blood-plasma separation in Y-shaped bifurcating microfluidic channels: a dissipative particle dynamics simulation study. Phys. Biol. 20129 (2), 026010,  DOI: 10.1088/1478-3975/9/2/026010ViewGoogle Scholar
  22. 22Yin, X.; Thomas, T.; Zhang, J. Multiple red blood cell flows through microvascular bifurcations: Cell free layer, cell trajectory, and hematocrit separation. Microvascular Research 201389, 47– 56,  DOI: 10.1016/j.mvr.2013.05.002ViewGoogle Scholar
  23. 23Shibeshi, S. S.; Collins, W. E. The Rheology of Blood Flow in a Branched Arterial System. Appl. Rheol 200515 (6), 398– 405,  DOI: 10.1515/arh-2005-0020ViewGoogle Scholar
  24. 24Sequeira, A.; Janela, J. An Overview of Some Mathematical Models of Blood Rheology. In A Portrait of State-of-the-Art Research at the Technical University of Lisbon; Pereira, M. S., Ed.; Springer Netherlands: Dordrecht, 2007; pp 65– 87.ViewGoogle Scholar
  25. 25Walburn, F. J.; Schneck, D. J. A constitutive equation for whole human blood. Biorheology 197613, 201– 210,  DOI: 10.3233/BIR-1976-13307ViewGoogle Scholar
  26. 26Quemada, D. A rheological model for studying the hematocrit dependence of red cell-red cell and red cell-protein interactions in blood. Biorheology 198118, 501– 516,  DOI: 10.3233/BIR-1981-183-615ViewGoogle Scholar
  27. 27Varchanis, S.; Dimakopoulos, Y.; Wagner, C.; Tsamopoulos, J. How viscoelastic is human blood plasma?. Soft Matter 201814 (21), 4238– 4251,  DOI: 10.1039/C8SM00061AViewGoogle Scholar
  28. 28Apostolidis, A. J.; Moyer, A. P.; Beris, A. N. Non-Newtonian effects in simulations of coronary arterial blood flow. J. Non-Newtonian Fluid Mech. 2016233, 155– 165,  DOI: 10.1016/j.jnnfm.2016.03.008ViewGoogle Scholar
  29. 29Luo, X. Y.; Kuang, Z. B. A study on the constitutive equation of blood. J. Biomech. 199225 (8), 929– 934,  DOI: 10.1016/0021-9290(92)90233-QViewGoogle Scholar
  30. 30Oldroyd, J. G.; Wilson, A. H. On the formulation of rheological equations of state. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1950200 (1063), 523– 541,  DOI: 10.1098/rspa.1950.0035ViewGoogle Scholar
  31. 31Prado, G.; Farutin, A.; Misbah, C.; Bureau, L. Viscoelastic transient of confined red blood cells. Biophys J. 2015108 (9), 2126– 2136,  DOI: 10.1016/j.bpj.2015.03.046ViewGoogle Scholar
  32. 32Huang, C. R.; Pan, W. D.; Chen, H. Q.; Copley, A. L. Thixotropic properties of whole blood from healthy human subjects. Biorheology 198724 (6), 795– 801,  DOI: 10.3233/BIR-1987-24630ViewGoogle Scholar
  33. 33Anand, M.; Kwack, J.; Masud, A. A new generalized Oldroyd-B model for blood flow in complex geometries. International Journal of Engineering Science 201372, 78– 88,  DOI: 10.1016/j.ijengsci.2013.06.009ViewGoogle Scholar
  34. 34Horner, J. S.; Armstrong, M. J.; Wagner, N. J.; Beris, A. N. Investigation of blood rheology under steady and unidirectional large amplitude oscillatory shear. J. Rheol. 201862 (2), 577– 591,  DOI: 10.1122/1.5017623ViewGoogle Scholar
  35. 35Horner, J. S.; Armstrong, M. J.; Wagner, N. J.; Beris, A. N. Measurements of human blood viscoelasticity and thixotropy under steady and transient shear and constitutive modeling thereof. J. Rheol. 201963 (5), 799– 813,  DOI: 10.1122/1.5108737ViewGoogle Scholar
  36. 36Armstrong, M.; Tussing, J. A methodology for adding thixotropy to Oldroyd-8 family of viscoelastic models for characterization of human blood. Phys. Fluids 202032 (9), 094111,  DOI: 10.1063/5.0022501ViewGoogle Scholar
  37. 37Crank, J.; Nicolson, P. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Mathematical Proceedings of the Cambridge Philosophical Society 194743 (1), 50– 67,  DOI: 10.1017/S0305004100023197ViewGoogle Scholar
  38. 38Clough, R. W. Original formulation of the finite element method. Finite Elements in Analysis and Design 19907 (2), 89– 101,  DOI: 10.1016/0168-874X(90)90001-UViewGoogle Scholar
  39. 39Liu, W. K.; Liu, Y.; Farrell, D.; Zhang, L.; Wang, X. S.; Fukui, Y.; Patankar, N.; Zhang, Y.; Bajaj, C.; Lee, J.Immersed finite element method and its applications to biological systems. Computer Methods in Applied Mechanics and Engineering 2006195 (13), 1722– 1749,  DOI: 10.1016/j.cma.2005.05.049ViewGoogle Scholar
  40. 40Lopes, D.; Agujetas, R.; Puga, H.; Teixeira, J.; Lima, R.; Alejo, J. P.; Ferrera, C. Analysis of finite element and finite volume methods for fluid-structure interaction simulation of blood flow in a real stenosed artery. International Journal of Mechanical Sciences 2021207, 106650,  DOI: 10.1016/j.ijmecsci.2021.106650ViewGoogle Scholar
  41. 41Favero, J. L.; Secchi, A. R.; Cardozo, N. S. M.; Jasak, H. Viscoelastic flow analysis using the software OpenFOAM and differential constitutive equations. J. Non-Newtonian Fluid Mech. 2010165 (23), 1625– 1636,  DOI: 10.1016/j.jnnfm.2010.08.010ViewGoogle Scholar
  42. 42Pimenta, F.; Alves, M. A. Stabilization of an open-source finite-volume solver for viscoelastic fluid flows. J. Non-Newtonian Fluid Mech. 2017239, 85– 104,  DOI: 10.1016/j.jnnfm.2016.12.002ViewGoogle Scholar
  43. 43Chee, C. Y.; Lee, H. P.; Lu, C. Using 3D fluid-structure interaction model to analyse the biomechanical properties of erythrocyte. Phys. Lett. A 2008372 (9), 1357– 1362,  DOI: 10.1016/j.physleta.2007.09.067ViewGoogle Scholar
  44. 44Xu, D.; Kaliviotis, E.; Munjiza, A.; Avital, E.; Ji, C.; Williams, J. Large scale simulation of red blood cell aggregation in shear flows. J. Biomech. 201346 (11), 1810– 1817,  DOI: 10.1016/j.jbiomech.2013.05.010ViewGoogle Scholar
  45. 45Johnson, K. L.; Kendall, K.; Roberts, A. Surface energy and the contact of elastic solids. Proceedings of the royal society of London. A. mathematical and physical sciences 1971324 (1558), 301– 313,  DOI: 10.1098/rspa.1971.0141ViewGoogle Scholar
  46. 46Shi, L.; Pan, T.-W.; Glowinski, R. Deformation of a single red blood cell in bounded Poiseuille flows. Phys. Rev. E 201285 (1), 016307,  DOI: 10.1103/PhysRevE.85.016307ViewGoogle Scholar
  47. 47Yoon, D.; You, D. Continuum modeling of deformation and aggregation of red blood cells. J. Biomech. 201649 (11), 2267– 2279,  DOI: 10.1016/j.jbiomech.2015.11.027ViewGoogle Scholar
  48. 48Mainardi, F.; Spada, G. Creep, relaxation and viscosity properties for basic fractional models in rheology. European Physical Journal Special Topics 2011193 (1), 133– 160,  DOI: 10.1140/epjst/e2011-01387-1ViewGoogle Scholar
  49. 49Gracka, M.; Lima, R.; Miranda, J. M.; Student, S.; Melka, B.; Ostrowski, Z. Red blood cells tracking and cell-free layer formation in a microchannel with hyperbolic contraction: A CFD model validation. Computer Methods and Programs in Biomedicine 2022226, 107117,  DOI: 10.1016/j.cmpb.2022.107117ViewGoogle Scholar
  50. 50Aryan, H.; Beigzadeh, B.; Siavashi, M. Euler-Lagrange numerical simulation of improved magnetic drug delivery in a three-dimensional CT-based carotid artery bifurcation. Computer Methods and Programs in Biomedicine 2022219, 106778,  DOI: 10.1016/j.cmpb.2022.106778ViewGoogle Scholar
  51. 51Czaja, B.; Závodszky, G.; Azizi Tarksalooyeh, V.; Hoekstra, A. G. Cell-resolved blood flow simulations of saccular aneurysms: effects of pulsatility and aspect ratio. J. R Soc. Interface 201815 (146), 20180485,  DOI: 10.1098/rsif.2018.0485ViewGoogle Scholar
  52. 52Rydquist, G.; Esmaily, M. A cell-resolved, Lagrangian solver for modeling red blood cell dynamics in macroscale flows. J. Comput. Phys. 2022461, 111204,  DOI: 10.1016/j.jcp.2022.111204ViewGoogle Scholar
  53. 53Dadvand, A.; Baghalnezhad, M.; Mirzaee, I.; Khoo, B. C.; Ghoreishi, S. An immersed boundary-lattice Boltzmann approach to study the dynamics of elastic membranes in viscous shear flows. Journal of Computational Science 20145 (5), 709– 718,  DOI: 10.1016/j.jocs.2014.06.006ViewGoogle Scholar
  54. 54Krüger, T.; Holmes, D.; Coveney, P. V. Deformability-based red blood cell separation in deterministic lateral displacement devices─A simulation study. Biomicrofluidics 20148 (5), 054114,  DOI: 10.1063/1.4897913ViewGoogle Scholar
  55. 55Takeishi, N.; Ito, H.; Kaneko, M.; Wada, S. Deformation of a Red Blood Cell in a Narrow Rectangular Microchannel. Micromachines 201910 (3), 199,  DOI: 10.3390/mi10030199ViewGoogle Scholar
  56. 56Krüger, T.; Varnik, F.; Raabe, D. Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method. Computers & Mathematics with Applications 201161 (12), 3485– 3505,  DOI: 10.1016/j.camwa.2010.03.057ViewGoogle Scholar
  57. 57Balachandran Nair, A. N.; Pirker, S.; Umundum, T.; Saeedipour, M. A reduced-order model for deformable particles with application in bio-microfluidics. Computational Particle Mechanics 20207 (3), 593– 601,  DOI: 10.1007/s40571-019-00283-8ViewGoogle Scholar
  58. 58Balachandran Nair, A. N.; Pirker, S.; Saeedipour, M. Resolved CFD-DEM simulation of blood flow with a reduced-order RBC model. Computational Particle Mechanics 20229 (4), 759– 774,  DOI: 10.1007/s40571-021-00441-xViewGoogle Scholar
  59. 59Mittal, R.; Iaccarino, G. IMMERSED BOUNDARY METHODS. Annu. Rev. Fluid Mech. 200537 (1), 239– 261,  DOI: 10.1146/annurev.fluid.37.061903.175743ViewGoogle Scholar
  60. 60Piquet, A.; Roussel, O.; Hadjadj, A. A comparative study of Brinkman penalization and direct-forcing immersed boundary methods for compressible viscous flows. Computers & Fluids 2016136, 272– 284,  DOI: 10.1016/j.compfluid.2016.06.001ViewGoogle Scholar
  61. 61Akerkouch, L.; Le, T. B. A Hybrid Continuum-Particle Approach for Fluid-Structure Interaction Simulation of Red Blood Cells in Fluid Flows. Fluids 20216 (4), 139,  DOI: 10.3390/fluids6040139ViewGoogle Scholar
  62. 62Barker, A. T.; Cai, X.-C. Scalable parallel methods for monolithic coupling in fluid-structure interaction with application to blood flow modeling. J. Comput. Phys. 2010229 (3), 642– 659,  DOI: 10.1016/j.jcp.2009.10.001ViewGoogle Scholar
  63. 63Cetin, A.; Sahin, M. A monolithic fluid-structure interaction framework applied to red blood cells. International Journal for Numerical Methods in Biomedical Engineering 201935 (2), e3171  DOI: 10.1002/cnm.3171ViewGoogle Scholar
  64. 64Freund, J. B. Numerical Simulation of Flowing Blood Cells. Annu. Rev. Fluid Mech. 201446 (1), 67– 95,  DOI: 10.1146/annurev-fluid-010313-141349ViewGoogle Scholar
  65. 65Ye, T.; Phan-Thien, N.; Lim, C. T. Particle-based simulations of red blood cells─A review. J. Biomech. 201649 (11), 2255– 2266,  DOI: 10.1016/j.jbiomech.2015.11.050ViewGoogle Scholar
  66. 66Arabghahestani, M.; Poozesh, S.; Akafuah, N. K. Advances in Computational Fluid Mechanics in Cellular Flow Manipulation: A Review. Applied Sciences 20199 (19), 4041,  DOI: 10.3390/app9194041ViewGoogle Scholar
  67. 67Rathnayaka, C. M.; From, C. S.; Geekiyanage, N. M.; Gu, Y. T.; Nguyen, N. T.; Sauret, E. Particle-Based Numerical Modelling of Liquid Marbles: Recent Advances and Future Perspectives. Archives of Computational Methods in Engineering 202229 (5), 3021– 3039,  DOI: 10.1007/s11831-021-09683-7ViewGoogle Scholar
  68. 68Li, X.; Vlahovska, P. M.; Karniadakis, G. E. Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease. Soft Matter 20139 (1), 28– 37,  DOI: 10.1039/C2SM26891DViewGoogle Scholar
  69. 69Beris, A. N.; Horner, J. S.; Jariwala, S.; Armstrong, M. J.; Wagner, N. J. Recent advances in blood rheology: a review. Soft Matter 202117 (47), 10591– 10613,  DOI: 10.1039/D1SM01212FViewGoogle Scholar
  70. 70Arciero, J.; Causin, P.; Malgaroli, F. Mathematical methods for modeling the microcirculation. AIMS Biophysics 20174 (3), 362– 399,  DOI: 10.3934/biophy.2017.3.362ViewGoogle Scholar
  71. 71Maria, M. S.; Chandra, T. S.; Sen, A. K. Capillary flow-driven blood plasma separation and on-chip analyte detection in microfluidic devices. Microfluid. Nanofluid. 201721 (4), 72,  DOI: 10.1007/s10404-017-1907-6ViewGoogle Scholar
  72. 72Huhtamäki, T.; Tian, X.; Korhonen, J. T.; Ras, R. H. A. Surface-wetting characterization using contact-angle measurements. Nat. Protoc. 201813 (7), 1521– 1538,  DOI: 10.1038/s41596-018-0003-zViewGoogle Scholar
  73. 73Young, T., III. An essay on the cohesion of fluids. Philosophical Transactions of the Royal Society of London 180595, 65– 87,  DOI: 10.1098/rstl.1805.0005ViewGoogle Scholar
  74. 74Kim, Y. C.; Kim, S.-H.; Kim, D.; Park, S.-J.; Park, J.-K. Plasma extraction in a capillary-driven microfluidic device using surfactant-added poly(dimethylsiloxane). Sens. Actuators, B 2010145 (2), 861– 868,  DOI: 10.1016/j.snb.2010.01.017ViewGoogle Scholar
  75. 75Washburn, E. W. The Dynamics of Capillary Flow. Physical Review 192117 (3), 273– 283,  DOI: 10.1103/PhysRev.17.273ViewGoogle Scholar
  76. 76Cito, S.; Ahn, Y. C.; Pallares, J.; Duarte, R. M.; Chen, Z.; Madou, M.; Katakis, I. Visualization and measurement of capillary-driven blood flow using spectral domain optical coherence tomography. Microfluid Nanofluidics 201213 (2), 227– 237,  DOI: 10.1007/s10404-012-0950-6ViewGoogle Scholar
  77. 77Berthier, E.; Dostie, A. M.; Lee, U. N.; Berthier, J.; Theberge, A. B. Open Microfluidic Capillary Systems. Anal Chem. 201991 (14), 8739– 8750,  DOI: 10.1021/acs.analchem.9b01429ViewGoogle Scholar
  78. 78Berthier, J.; Brakke, K. A.; Furlani, E. P.; Karampelas, I. H.; Poher, V.; Gosselin, D.; Cubizolles, M.; Pouteau, P. Whole blood spontaneous capillary flow in narrow V-groove microchannels. Sens. Actuators, B 2015206, 258– 267,  DOI: 10.1016/j.snb.2014.09.040ViewGoogle Scholar
  79. 79Hirt, C. W.; Nichols, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 198139 (1), 201– 225,  DOI: 10.1016/0021-9991(81)90145-5ViewGoogle Scholar
  80. 80Chen, J.-L.; Shih, W.-H.; Hsieh, W.-H. AC electro-osmotic micromixer using a face-to-face, asymmetric pair of planar electrodes. Sens. Actuators, B 2013188, 11– 21,  DOI: 10.1016/j.snb.2013.07.012ViewGoogle Scholar
  81. 81Zhao, C.; Yang, C. Electrokinetics of non-Newtonian fluids: A review. Advances in Colloid and Interface Science 2013201-202, 94– 108,  DOI: 10.1016/j.cis.2013.09.001ViewGoogle Scholar
  82. 82Oh, K. W. 6 – Lab-on-chip (LOC) devices and microfluidics for biomedical applications. In MEMS for Biomedical Applications; Bhansali, S., Vasudev, A., Eds.; Woodhead Publishing, 2012; pp 150– 171.ViewGoogle Scholar
  83. 83Bello, M. S.; De Besi, P.; Rezzonico, R.; Righetti, P. G.; Casiraghi, E. Electroosmosis of polymer solutions in fused silica capillaries. ELECTROPHORESIS 199415 (1), 623– 626,  DOI: 10.1002/elps.1150150186ViewGoogle Scholar
  84. 84Park, H. M.; Lee, W. M. Effect of viscoelasticity on the flow pattern and the volumetric flow rate in electroosmotic flows through a microchannel. Lab Chip 20088 (7), 1163– 1170,  DOI: 10.1039/b800185eViewGoogle Scholar
  85. 85Afonso, A. M.; Alves, M. A.; Pinho, F. T. Analytical solution of mixed electro-osmotic/pressure driven flows of viscoelastic fluids in microchannels. J. Non-Newtonian Fluid Mech. 2009159 (1), 50– 63,  DOI: 10.1016/j.jnnfm.2009.01.006ViewGoogle Scholar
  86. 86Sousa, J. J.; Afonso, A. M.; Pinho, F. T.; Alves, M. A. Effect of the skimming layer on electro-osmotic─Poiseuille flows of viscoelastic fluids. Microfluid. Nanofluid. 201110 (1), 107– 122,  DOI: 10.1007/s10404-010-0651-yViewGoogle Scholar
  87. 87Zhao, C.; Yang, C. Electro-osmotic mobility of non-Newtonian fluids. Biomicrofluidics 20115 (1), 014110,  DOI: 10.1063/1.3571278ViewGoogle Scholar
  88. 88Pimenta, F.; Alves, M. A. Electro-elastic instabilities in cross-shaped microchannels. J. Non-Newtonian Fluid Mech. 2018259, 61– 77,  DOI: 10.1016/j.jnnfm.2018.04.004ViewGoogle Scholar
  89. 89Bezerra, W. S.; Castelo, A.; Afonso, A. M. Numerical Study of Electro-Osmotic Fluid Flow and Vortex Formation. Micromachines (Basel) 201910 (12), 796,  DOI: 10.3390/mi10120796ViewGoogle Scholar
  90. 90Ji, J.; Qian, S.; Liu, Z. Electroosmotic Flow of Viscoelastic Fluid through a Constriction Microchannel. Micromachines (Basel) 202112 (4), 417,  DOI: 10.3390/mi12040417ViewGoogle Scholar
  91. 91Zhao, C.; Yang, C. Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels. Applied Mathematics and Computation 2009211 (2), 502– 509,  DOI: 10.1016/j.amc.2009.01.068ViewGoogle Scholar
  92. 92Gerum, R.; Mirzahossein, E.; Eroles, M.; Elsterer, J.; Mainka, A.; Bauer, A.; Sonntag, S.; Winterl, A.; Bartl, J.; Fischer, L. Viscoelastic properties of suspended cells measured with shear flow deformation cytometry. Elife 202211, e78823,  DOI: 10.7554/eLife.78823ViewGoogle Scholar
  93. 93Sadek, S. H.; Pinho, F. T.; Alves, M. A. Electro-elastic flow instabilities of viscoelastic fluids in contraction/expansion micro-geometries. J. Non-Newtonian Fluid Mech. 2020283, 104293,  DOI: 10.1016/j.jnnfm.2020.104293ViewGoogle Scholar
  94. 94Spanjaards, M.; Peters, G.; Hulsen, M.; Anderson, P. Numerical Study of the Effect of Thixotropy on Extrudate Swell. Polymers 202113 (24), 4383,  DOI: 10.3390/polym13244383ViewGoogle Scholar
  95. 95Rashidi, S.; Bafekr, H.; Valipour, M. S.; Esfahani, J. A. A review on the application, simulation, and experiment of the electrokinetic mixers. Chemical Engineering and Processing – Process Intensification 2018126, 108– 122,  DOI: 10.1016/j.cep.2018.02.021ViewGoogle Scholar
  96. 96Matsubara, K.; Narumi, T. Microfluidic mixing using unsteady electroosmotic vortices produced by a staggered array of electrodes. Chemical Engineering Journal 2016288, 638– 647,  DOI: 10.1016/j.cej.2015.12.013ViewGoogle Scholar
  97. 97Qaderi, A.; Jamaati, J.; Bahiraei, M. CFD simulation of combined electroosmotic-pressure driven micro-mixing in a microchannel equipped with triangular hurdle and zeta-potential heterogeneity. Chemical Engineering Science 2019199, 463– 477,  DOI: 10.1016/j.ces.2019.01.034ViewGoogle Scholar
  98. 98Cho, C.-C.; Chen, C.-L.; Chen, C. o.-K. Mixing enhancement in crisscross micromixer using aperiodic electrokinetic perturbing flows. International Journal of Heat and Mass Transfer 201255 (11), 2926– 2933,  DOI: 10.1016/j.ijheatmasstransfer.2012.02.006ViewGoogle Scholar
  99. 99Zhao, W.; Yang, F.; Wang, K.; Bai, J.; Wang, G. Rapid mixing by turbulent-like electrokinetic microflow. Chemical Engineering Science 2017165, 113– 121,  DOI: 10.1016/j.ces.2017.02.027ViewGoogle Scholar
  100. 100Tran, T.; Chakraborty, P.; Guttenberg, N.; Prescott, A.; Kellay, H.; Goldburg, W.; Goldenfeld, N.; Gioia, G. Macroscopic effects of the spectral structure in turbulent flows. Nat. Phys. 20106 (6), 438– 441,  DOI: 10.1038/nphys1674ViewGoogle Scholar
  101. 101Toner, M.; Irimia, D. Blood-on-a-chip. Annu. Rev. Biomed Eng. 20057, 77– 103,  DOI: 10.1146/annurev.bioeng.7.011205.135108ViewGoogle Scholar
  102. 102Maria, M. S.; Rakesh, P. E.; Chandra, T. S.; Sen, A. K. Capillary flow of blood in a microchannel with differential wetting for blood plasma separation and on-chip glucose detection. Biomicrofluidics 201610 (5), 054108,  DOI: 10.1063/1.4962874ViewGoogle Scholar
  103. 103Tripathi, S.; Varun Kumar, Y. V. B.; Prabhakar, A.; Joshi, S. S.; Agrawal, A. Passive blood plasma separation at the microscale: a review of design principles and microdevices. Journal of Micromechanics and Microengineering 201525 (8), 083001,  DOI: 10.1088/0960-1317/25/8/083001ViewGoogle Scholar
  104. 104Mohammadi, M.; Madadi, H.; Casals-Terré, J. Microfluidic point-of-care blood panel based on a novel technique: Reversible electroosmotic flow. Biomicrofluidics 20159 (5), 054106,  DOI: 10.1063/1.4930865ViewGoogle Scholar
  105. 105Kang, D. H.; Kim, K.; Kim, Y. J. An anti-clogging method for improving the performance and lifespan of blood plasma separation devices in real-time and continuous microfluidic systems. Sci. Rep 20188 (1), 17015,  DOI: 10.1038/s41598-018-35235-4ViewGoogle Scholar
  106. 106Li, Z.; Pollack, G. H. Surface-induced flow: A natural microscopic engine using infrared energy as fuel. Science Advances 20206 (19), eaba0941  DOI: 10.1126/sciadv.aba0941ViewGoogle Scholar
  107. 107Mercado-Uribe, H.; Guevara-Pantoja, F. J.; García-Muñoz, W.; García-Maldonado, J. S.; Méndez-Alcaraz, J. M.; Ruiz-Suárez, J. C. On the evolution of the exclusion zone produced by hydrophilic surfaces: A contracted description. J. Chem. Phys. 2021154 (19), 194902,  DOI: 10.1063/5.0043084ViewGoogle Scholar
  108. 108Yalcin, O.; Jani, V. P.; Johnson, P. C.; Cabrales, P. Implications Enzymatic Degradation of the Endothelial Glycocalyx on the Microvascular Hemodynamics and the Arteriolar Red Cell Free Layer of the Rat Cremaster Muscle. Front Physiol 20189, 168,  DOI: 10.3389/fphys.2018.00168ViewGoogle Scholar
Fig. 9 From: An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

Abstract

웨어의 두 가지 서로 다른 배열(즉, 직선형 웨어와 직사각형 미로 웨어)을 사용하여 웨어 모양, 웨어 간격, 웨어의 오리피스 존재, 흐름 영역에 대한 바닥 경사와 같은 기하학적 매개변수의 영향을 평가했습니다.

유량과 수심의 관계, 수심 평균 속도의 변화와 분포, 난류 특성, 어도에서의 에너지 소산. 흐름 조건에 미치는 영향을 조사하기 위해 FLOW-3D® 소프트웨어를 사용하여 전산 유체 역학 시뮬레이션을 수행했습니다.

수치 모델은 계산된 표면 프로파일과 속도를 문헌의 실험적으로 측정된 값과 비교하여 검증되었습니다. 수치 모델과 실험 데이터의 결과, 급락유동의 표면 프로파일과 표준화된 속도 프로파일에 대한 평균 제곱근 오차와 평균 절대 백분율 오차가 각각 0.014m와 3.11%로 나타나 수치 모델의 능력을 확인했습니다.

수영장과 둑의 흐름 특성을 예측합니다. 각 모델에 대해 L/B = 1.83(L: 웨어 거리, B: 수로 폭) 값에서 급락 흐름이 발생할 수 있고 L/B = 0.61에서 스트리밍 흐름이 발생할 수 있습니다. 직사각형 미로보 모델은 기존 모델보다 무차원 방류량(Q+)이 더 큽니다.

수중 흐름의 기존 보와 직사각형 미로 보의 경우 Q는 각각 1.56과 1.47h에 비례합니다(h: 보 위 수심). 기존 웨어의 풀 내 평균 깊이 속도는 직사각형 미로 웨어의 평균 깊이 속도보다 높습니다.

그러나 주어진 방류량, 바닥 경사 및 웨어 간격에 대해 난류 운동 에너지(TKE) 및 난류 강도(TI) 값은 기존 웨어에 비해 직사각형 미로 웨어에서 더 높습니다. 기존의 웨어는 직사각형 미로 웨어보다 에너지 소산이 더 낮습니다.

더 낮은 TKE 및 TI 값은 미로 웨어 상단, 웨어 하류 벽 모서리, 웨어 측벽과 채널 벽 사이에서 관찰되었습니다. 보와 바닥 경사면 사이의 거리가 증가함에 따라 평균 깊이 속도, 난류 운동 에너지의 평균값 및 난류 강도가 증가하고 수영장의 체적 에너지 소산이 감소했습니다.

둑에 개구부가 있으면 평균 깊이 속도와 TI 값이 증가하고 풀 내에서 가장 높은 TKE 범위가 감소하여 두 모델 모두에서 물고기를 위한 휴식 공간이 더 넓어지고(TKE가 낮아짐) 에너지 소산율이 감소했습니다.

Two different arrangements of the weir (i.e., straight weir and rectangular labyrinth weir) were used to evaluate the effects of geometric parameters such as weir shape, weir spacing, presence of an orifice at the weir, and bed slope on the flow regime and the relationship between discharge and depth, variation and distribution of depth-averaged velocity, turbulence characteristics, and energy dissipation at the fishway. Computational fluid dynamics simulations were performed using FLOW-3D® software to examine the effects on flow conditions. The numerical model was validated by comparing the calculated surface profiles and velocities with experimentally measured values from the literature. The results of the numerical model and experimental data showed that the root-mean-square error and mean absolute percentage error for the surface profiles and normalized velocity profiles of plunging flows were 0.014 m and 3.11%, respectively, confirming the ability of the numerical model to predict the flow characteristics of the pool and weir. A plunging flow can occur at values of L/B = 1.83 (L: distance of the weir, B: width of the channel) and streaming flow at L/B = 0.61 for each model. The rectangular labyrinth weir model has larger dimensionless discharge values (Q+) than the conventional model. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q is proportional to 1.56 and 1.47h, respectively (h: the water depth above the weir). The average depth velocity in the pool of a conventional weir is higher than that of a rectangular labyrinth weir. However, for a given discharge, bed slope, and weir spacing, the turbulent kinetic energy (TKE) and turbulence intensity (TI) values are higher for a rectangular labyrinth weir compared to conventional weir. The conventional weir has lower energy dissipation than the rectangular labyrinth weir. Lower TKE and TI values were observed at the top of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall. As the distance between the weirs and the bottom slope increased, the average depth velocity, the average value of turbulent kinetic energy and the turbulence intensity increased, and the volumetric energy dissipation in the pool decreased. The presence of an opening in the weir increased the average depth velocity and TI values and decreased the range of highest TKE within the pool, resulted in larger resting areas for fish (lower TKE), and decreased the energy dissipation rates in both models.

1 Introduction

Artificial barriers such as detour dams, weirs, and culverts in lakes and rivers prevent fish from migrating and completing the upstream and downstream movement cycle. This chain is related to the life stage of the fish, its location, and the type of migration. Several riverine fish species instinctively migrate upstream for spawning and other needs. Conversely, downstream migration is a characteristic of early life stages [1]. A fish ladder is a waterway that allows one or more fish species to cross a specific obstacle. These structures are constructed near detour dams and other transverse structures that have prevented such migration by allowing fish to overcome obstacles [2]. The flow pattern in fish ladders influences safe and comfortable passage for ascending fish. The flow’s strong turbulence can reduce the fish’s speed, injure them, and delay or prevent them from exiting the fish ladder. In adult fish, spawning migrations are usually complex, and delays are critical to reproductive success [3].

Various fish ladders/fishways include vertical slots, denil, rock ramps, and pool weirs [1]. The choice of fish ladder usually depends on many factors, including water elevation, space available for construction, and fish species. Pool and weir structures are among the most important fish ladders that help fish overcome obstacles in streams or rivers and swim upstream [1]. Because they are easy to construct and maintain, this type of fish ladder has received considerable attention from researchers and practitioners. Such a fish ladder consists of a sloping-floor channel with series of pools directly separated by a series of weirs [4]. These fish ladders, with or without underwater openings, are generally well-suited for slopes of 10% or less [12]. Within these pools, flow velocities are low and provide resting areas for fish after they enter the fish ladder. After resting in the pools, fish overcome these weirs by blasting or jumping over them [2]. There may also be an opening in the flooded portion of the weir through which the fish can swim instead of jumping over the weir. Design parameters such as the length of the pool, the height of the weir, the slope of the bottom, and the water discharge are the most important factors in determining the hydraulic structure of this type of fish ladder [3]. The flow over the weir depends on the flow depth at a given slope S0 and the pool length, either “plunging” or “streaming.” In plunging flow, the water column h over each weir creates a water jet that releases energy through turbulent mixing and diffusion mechanisms [5]. The dimensionless discharges for plunging (Q+) and streaming (Q*) flows are shown in Fig. 1, where Q is the total discharge, B is the width of the channel, w is the weir height, S0 is the slope of the bottom, h is the water depth above the weir, d is the flow depth, and g is the acceleration due to gravity. The maximum velocity occurs near the top of the weir for plunging flow. At the water’s surface, it drops to about half [6].

figure 1
Fig. 1

Extensive experimental studies have been conducted to investigate flow patterns for various physical geometries (i.e., bed slope, pool length, and weir height) [2]. Guiny et al. [7] modified the standard design by adding vertical slots, orifices, and weirs in fishways. The efficiency of the orifices and vertical slots was related to the velocities at their entrances. In the laboratory experiments of Yagci [8], the three-dimensional (3D) mean flow and turbulence structure of a pool weir fishway combined with an orifice and a slot is investigated. It is shown that the energy dissipation per unit volume and the discharge have a linear relationship.

Considering the beneficial characteristics reported in the limited studies of researchers on the labyrinth weir in the pool-weir-type fishway, and knowing that the characteristics of flow in pool-weir-type fishways are highly dependent on the geometry of the weir, an alternative design of the rectangular labyrinth weir instead of the straight weirs in the pool-weir-type fishway is investigated in this study [79]. Kim [10] conducted experiments to compare the hydraulic characteristics of three different weir types in a pool-weir-type fishway. The results show that a straight, rectangular weir with a notch is preferable to a zigzag or trapezoidal weir. Studies on natural fish passes show that pass ability can be improved by lengthening the weir’s crest [7]. Zhong et al. [11] investigated the semi-rigid weir’s hydraulic performance in the fishway’s flow field with a pool weir. The results showed that this type of fishway performed better with a lower invert slope and a smaller radius ratio but with a larger pool spacing.

Considering that an alternative method to study the flow characteristics in a fishway with a pool weir is based on numerical methods and modeling from computational fluid dynamics (CFD), which can easily change the geometry of the fishway for different flow fields, this study uses the powerful package CFD and the software FLOW-3D to evaluate the proposed weir design and compare it with the conventional one to extend the application of the fishway. The main objective of this study was to evaluate the hydraulic performance of the rectangular labyrinth pool and the weir with submerged openings in different hydraulic configurations. The primary objective of creating a new weir configuration for suitable flow patterns is evaluated based on the swimming capabilities of different fish species. Specifically, the following questions will be answered: (a) How do the various hydraulic and geometric parameters relate to the effects of water velocity and turbulence, expressed as turbulent kinetic energy (TKE) and turbulence intensity (TI) within the fishway, i.e., are conventional weirs more affected by hydraulics than rectangular labyrinth weirs? (b) Which weir configurations have the greatest effect on fish performance in the fishway? (c) In the presence of an orifice plate, does the performance of each weir configuration differ with different weir spacing, bed gradients, and flow regimes from that without an orifice plate?

2 Materials and Methods

2.1 Physical Model Configuration

This paper focuses on Ead et al. [6]’s laboratory experiments as a reference, testing ten pool weirs (Fig. 2). The experimental flume was 6 m long, 0.56 m wide, and 0.6 m high, with a bottom slope of 10%. Field measurements were made at steady flow with a maximum flow rate of 0.165 m3/s. Discharge was measured with magnetic flow meters in the inlets and water level with point meters (see Ead et al. [6]. for more details). Table 1 summarizes the experimental conditions considered for model calibration in this study.

figure 2
Fig. 2

Table 1 Experimental conditions considered for calibration

Full size table

2.2 Numerical Models

Computational fluid dynamics (CFD) simulations were performed using FLOW-3D® v11.2 to validate a series of experimental liner pool weirs by Ead et al. [6] and to investigate the effects of the rectangular labyrinth pool weir with an orifice. The dimensions of the channel and data collection areas in the numerical models are the same as those of the laboratory model. Two types of pool weirs were considered: conventional and labyrinth. The proposed rectangular labyrinth pool weirs have a symmetrical cross section and are sized to fit within the experimental channel. The conventional pool weir model had a pool length of l = 0.685 and 0.342 m, a weir height of w = 0.141 m, a weir width of B = 0.56 m, and a channel slope of S0 = 5 and 10%. The rectangular labyrinth weirs have the same front width as the offset, i.e., a = b = c = 0.186 m. A square underwater opening with a width of 0.05 m and a depth of 0.05 m was created in the middle of the weir. The weir configuration considered in the present study is shown in Fig. 3.

figure 3
Fig. 3

2.3 Governing Equations

FLOW-3D® software solves the Navier–Stokes–Reynolds equations for three-dimensional analysis of incompressible flows using the fluid-volume method on a gridded domain. FLOW -3D® uses an advanced free surface flow tracking algorithm (TruVOF) developed by Hirt and Nichols [12], where fluid configurations are defined in terms of a VOF function F (xyzt). In this case, F (fluid fraction) represents the volume fraction occupied by the fluid: F = 1 in cells filled with fluid and F = 0 in cells without fluid (empty areas) [413]. The free surface area is at an intermediate value of F. (Typically, F = 0.5, but the user can specify a different intermediate value.) The equations in Cartesian coordinates (xyz) applicable to the model are as follows:

�f∂�∂�+∂(���x)∂�+∂(���y)∂�+∂(���z)∂�=�SOR

(1)

∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�x+�x

(2)

∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�y+�y

(3)

∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�z+�z

(4)

where (uvw) are the velocity components, (AxAyAz) are the flow area components, (Gx, Gy, Gz) are the mass accelerations, and (fxfyfz) are the viscous accelerations in the directions (xyz), ρ is the fluid density, RSOR is the spring term, Vf is the volume fraction associated with the flow, and P is the pressure. The kε turbulence model (RNG) was used in this study to solve the turbulence of the flow field. This model is a modified version of the standard kε model that improves performance. The model is a two-equation model; the first equation (Eq. 5) expresses the turbulence’s energy, called turbulent kinetic energy (k) [14]. The second equation (Eq. 6) is the turbulent dissipation rate (ε), which determines the rate of dissipation of kinetic energy [15]. These equations are expressed as follows Dasineh et al. [4]:

∂(��)∂�+∂(����)∂��=∂∂��[������∂�∂��]+��−�ε

(5)

∂(�ε)∂�+∂(�ε��)∂��=∂∂��[�ε�eff∂ε∂��]+�1εε��k−�2ε�ε2�

(6)

In these equations, k is the turbulent kinetic energy, ε is the turbulent energy consumption rate, Gk is the generation of turbulent kinetic energy by the average velocity gradient, with empirical constants αε = αk = 1.39, C1ε = 1.42, and C2ε = 1.68, eff is the effective viscosity, μeff = μ + μt [15]. Here, μ is the hydrodynamic density coefficient, and μt is the turbulent density of the fluid.

2.4 Meshing and the Boundary Conditions in the Model Setup

The numerical area is divided into three mesh blocks in the X-direction. The meshes are divided into different sizes, a containing mesh block for the entire spatial domain and a nested block with refined cells for the domain of interest. Three different sizes were selected for each of the grid blocks. By comparing the accuracy of their results based on the experimental data, the reasonable mesh for the solution domain was finally selected. The convergence index method (GCI) evaluated the mesh sensitivity analysis. Based on this method, many researchers, such as Ahmadi et al. [16] and Ahmadi et al. [15], have studied the independence of numerical results from mesh size. Three different mesh sizes with a refinement ratio (r) of 1.33 were used to perform the convergence index method. The refinement ratio is the ratio between the larger and smaller mesh sizes (r = Gcoarse/Gfine). According to the recommendation of Celik et al. [17], the recommended number for the refinement ratio is 1.3, which gives acceptable results. Table 2 shows the characteristics of the three mesh sizes selected for mesh sensitivity analysis.Table 2 Characteristics of the meshes tested in the convergence analysis

Full size table

The results of u1 = umax (u1 = velocity component along the x1 axis and umax = maximum velocity of u1 in a section perpendicular to the invert of the fishway) at Q = 0.035 m3/s, × 1/l = 0.66, and Y1/b = 0 in the pool of conventional weir No. 4, obtained from the output results of the software, were used to evaluate the accuracy of the calculation range. As shown in Fig. 4x1 = the distance from a given weir in the x-direction, Y1 = the water depth measured in the y-direction, Y0 = the vertical distance in the Cartesian coordinate system, h = the water column at the crest, b = the distance between the two points of maximum velocity umax and zero velocity, and l = the pool length.

figure 4
Fig. 4

The apparent index of convergence (p) in the GCI method is calculated as follows:

�=ln⁡(�3−�2)(�2−�1)/ln⁡(�)

(7)

f1f2, and f3 are the hydraulic parameters obtained from the numerical simulation (f1 corresponds to the small mesh), and r is the refinement ratio. The following equation defines the convergence index of the fine mesh:

GCIfine=1.25|ε|��−1

(8)

Here, ε = (f2 − f1)/f1 is the relative error, and f2 and f3 are the values of hydraulic parameters considered for medium and small grids, respectively. GCI12 and GCI23 dimensionless indices can be calculated as:

GCI12=1.25|�2−�1�1|��−1

(9)

Then, the independence of the network is preserved. The convergence index of the network parameters obtained by Eqs. (7)–(9) for all three network variables is shown in Table 3. Since the GCI values for the smaller grid (GCI12) are lower compared to coarse grid (GCI23), it can be concluded that the independence of the grid is almost achieved. No further change in the grid size of the solution domain is required. The calculated values (GCI23/rpGCI12) are close to 1, which shows that the numerical results obtained are within the convergence range. As a result, the meshing of the solution domain consisting of a block mesh with a mesh size of 0.012 m and a block mesh within a larger block mesh with a mesh size of 0.009 m was selected as the optimal mesh (Fig. 5).Table 3 GCI calculation

Full size table

figure 5
Fig. 5

The boundary conditions applied to the area are shown in Fig. 6. The boundary condition of specific flow rate (volume flow rate-Q) was used for the inlet of the flow. For the downstream boundary, the flow output (outflow-O) condition did not affect the flow in the solution area. For the Zmax boundary, the specified pressure boundary condition was used along with the fluid fraction = 0 (P). This type of boundary condition considers free surface or atmospheric pressure conditions (Ghaderi et al. [19]). The wall boundary condition is defined for the bottom of the channel, which acts like a virtual wall without friction (W). The boundary between mesh blocks and walls were considered a symmetrical condition (S).

figure 6
Fig. 6

The convergence of the steady-state solutions was controlled during the simulations by monitoring the changes in discharge at the inlet boundary conditions. Figure 7 shows the time series plots of the discharge obtained from the Model A for the three main discharges from the numerical results. The 8 s to reach the flow equilibrium is suitable for the case of the fish ladder with pool and weir. Almost all discharge fluctuations in the models are insignificant in time, and the flow has reached relative stability. The computation time for the simulations was between 6 and 8 h using a personal computer with eight cores of a CPU (Intel Core i7-7700K @ 4.20 GHz and 16 GB RAM).

figure 7
Fig. 7

3 Results

3.1 Verification of Numerical Results

Quantitative outcomes, including free surface and normalized velocity profiles obtained using FLOW-3D software, were reviewed and compared with the results of Ead et al. [6]. The fourth pool was selected to present the results and compare the experiment and simulation. For each quantity, the percentage of mean absolute error (MAPE (%)) and root-mean-square error (RMSE) are calculated. Equations (10) and (11) show the method used to calculate the errors.

MAPE(%)100×1�∑1�|�exp−�num�exp|

(10)

RMSE(−)1�∑1�(�exp−�num)2

(11)

Here, Xexp is the value of the laboratory data, Xnum is the numerical data value, and n is the amount of data. As shown in Fig. 8, let x1 = distance from a given weir in the x-direction and Y1 = water depth in the y-direction from the bottom. The trend of the surface profiles for each of the numerical results is the same as that of the laboratory results. The surface profiles of the plunging flows drop after the flow enters and then rises to approach the next weir. The RMSE and MAPE error values for Model A are 0.014 m and 3.11%, respectively, indicating acceptable agreement between numerical and laboratory results. Figure 9 shows the velocity vectors and plunging flow from the numerical results, where x and y are horizontal and vertical to the flow direction, respectively. It can be seen that the jet in the fish ladder pool has a relatively high velocity. The two vortices, i.e., the enclosed vortex rotating clockwise behind the weir and the surface vortex rotating counterclockwise above the jet, are observed for the regime of incident flow. The point where the jet meets the fish passage bed is shown in the figure. The normalized velocity profiles upstream and downstream of the impact points are shown in Fig. 10. The figure shows that the numerical results agree well with the experimental data of Ead et al. [6].

figure 8
Fig. 8
figure 9
Fig. 9
figure 10
Fig. 10

3.2 Flow Regime and Discharge-Depth Relationship

Depending on the geometric shape of the fishway, including the distance of the weir, the slope of the bottom, the height of the weir, and the flow conditions, the flow regime in the fishway is divided into three categories: dipping, transitional, and flow regimes [4]. In the plunging flow regime, the flow enters the pool through the weir, impacts the bottom of the fishway, and forms a hydraulic jump causing two eddies [220]. In the streamwise flow regime, the surface of the flow passing over the weir is almost parallel to the bottom of the channel. The transitional regime has intermediate flow characteristics between the submerged and flow regimes. To predict the flow regime created in the fishway, Ead et al. [6] proposed two dimensionless parameters, Qt* and L/w, where Qt* is the dimensionless discharge, L is the distance between weirs, and w is the height of the weir:

��∗=���0���

(12)

Q is the total discharge, B is the width of the channel, S0 is the slope of the bed, and g is the gravity acceleration. Figure 11 shows different ranges for each flow regime based on the slope of the bed and the distance between the pools in this study. The results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22] were used for this comparison. The distance between the pools affects the changes in the regime of the fish ladder. So, if you decrease the distance between weirs, the flow regime more likely becomes. This study determined all three flow regimes in a fish ladder. When the corresponding range of Qt* is less than 0.6, the flow regime can dip at values of L/B = 1.83. If the corresponding range of Qt* is greater than 0.5, transitional flow may occur at L/B = 1.22. On the other hand, when Qt* is greater than 1, streamwise flow can occur at values of L/B = 0.61. These observations agree well with the results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22].

figure 11
Fig. 11

For plunging flows, another dimensionless discharge (Q+) versus h/w given by Ead et al. [6] was used for further evaluation:

�+=��ℎ�ℎ=23�d�

(13)

where h is the water depth above the weir, and Cd is the discharge coefficient. Figure 12a compares the numerical and experimental results of Ead et al. [6]. In this figure, Rehbock’s empirical equation is used to estimate the discharge coefficient of Ead et al. [6].

�d=0.57+0.075ℎ�

(14)

figure 12
Fig. 12

The numerical results for the conventional weir (Model A) and the rectangular labyrinth weir (Model B) of this study agree well with the laboratory results of Ead et al. [6]. When comparing models A and B, it is also found that a rectangular labyrinth weir has larger Q + values than the conventional weir as the length of the weir crest increases for a given channel width and fixed headwater elevation. In Fig. 12b, Models A and B’s flow depth plot shows the plunging flow regime. The power trend lines drawn through the data are the best-fit lines. The data shown in Fig. 12b are for different bed slopes and weir geometries. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q can be assumed to be proportional to 1.56 and 1.47h, respectively. In the results of Ead et al. [6], Q is proportional to 1.5h. If we assume that the flow through the orifice is Qo and the total outflow is Q, the change in the ratio of Qo/Q to total outflow for models A and B can be shown in Fig. 13. For both models, the flow through the orifice decreases as the total flow increases. A logarithmic trend line was also found between the total outflow and the dimensionless ratio Qo/Q.

figure 13
Fig. 13

3.3 Depth-Averaged Velocity Distributions

To ensure that the target fish species can pass the fish ladder with maximum efficiency, the average velocity in the fish ladder should be low enough [4]. Therefore, the average velocity in depth should be as much as possible below the critical swimming velocities of the target fishes at a constant flow depth in the pool [20]. The contour plot of depth-averaged velocity was used instead of another direction, such as longitudinal velocity because fish are more sensitive to depth-averaged flow velocity than to its direction under different hydraulic conditions. Figure 14 shows the distribution of depth-averaged velocity in the pool for Models A and B in two cases with and without orifice plates. Model A’s velocity within the pool differs slightly in the spanwise direction. However, no significant variation in velocity was observed. The flow is gradually directed to the sides as it passes through the rectangular labyrinth weir. This increases the velocity at the sides of the channel. Therefore, the high-velocity zone is located at the sides. The low velocity is in the downstream apex of the weir. This area may be suitable for swimming target fish. The presence of an opening in the weir increases the flow velocity at the opening and in the pool’s center, especially in Model A. The flow velocity increase caused by the models’ opening varied from 7.7 to 12.48%. Figure 15 illustrates the effect of the inverted slope on the averaged depth velocity distribution in the pool at low and high discharge. At constant discharge, flow velocity increases with increasing bed slope. In general, high flow velocity was found in the weir toe sidewall and the weir and channel sidewalls.

figure 14
Fig. 14
figure 15
Fig. 15

On the other hand, for a constant bed slope, the high-velocity area of the pool increases due to the increase in runoff. For both bed slopes and different discharges, the most appropriate path for fish to travel from upstream to downstream is through the middle of the cross section and along the top of the rectangular labyrinth weirs. The maximum dominant velocities for Model B at S0 = 5% were 0.83 and 1.01 m/s; at S0 = 10%, they were 1.12 and 1.61 m/s at low and high flows, respectively. The low mean velocities for the same distance and S0 = 5 and 10% were 0.17 and 0.26 m/s, respectively.

Figure 16 shows the contour of the averaged depth velocity for various distances from the weir at low and high discharge. The contour plot shows a large variation in velocity within short distances from the weir. At L/B = 0.61, velocities are low upstream and downstream of the top of the weir. The high velocities occur in the side walls of the weir and the channel. At L/B = 1.22, the low-velocity zone displaces the higher velocity in most of the pool. Higher velocities were found only on the sides of the channel. As the discharge increases, the velocity zone in the pool becomes wider. At L/B = 1.83, there is an area of higher velocities only upstream of the crest and on the sides of the weir. At high discharge, the prevailing maximum velocities for L/B = 0.61, 1.22, and 1.83 were 1.46, 1.65, and 1.84 m/s, respectively. As the distance between weirs increases, the range of maximum velocity increases.

figure 16
Fig. 16

On the other hand, the low mean velocity for these distances was 0.27, 0.44, and 0.72 m/s, respectively. Thus, the low-velocity zone decreases with increasing distance between weirs. Figure 17 shows the pattern distribution of streamlines along with the velocity contour at various distances from the weir for Q = 0.05 m3/s. A stream-like flow is generally formed in the pool at a small distance between weirs (L/B = 0.61). The rotation cell under the jet forms clockwise between the two weirs. At the distances between the spillways (L/B = 1.22), the transition regime of the flow is formed. The transition regime occurs when or shortly after the weir is flooded. The rotation cell under the jet is clockwise smaller than the flow regime and larger than the submergence regime. At a distance L/B = 1.83, a plunging flow is formed so that the plunging jet dips into the pool and extends downstream to the center of the pool. The clockwise rotation of the cell is bounded by the dipping jet of the weir and is located between the bottom and the side walls of the weir and the channel.

figure 17
Fig. 17

Figure 18 shows the average depth velocity bar graph for each weir at different bed slopes and with and without orifice plates. As the distance between weirs increases, all models’ average depth velocity increases. As the slope of the bottom increases and an orifice plate is present, the average depth velocity in the pool increases. In addition, the average pool depth velocity increases as the discharge increases. Among the models, Model A’s average depth velocity is higher than Model B’s. The variation in velocity ranged from 8.11 to 12.24% for the models without an orifice plate and from 10.26 to 16.87% for the models with an orifice plate.

figure 18
Fig. 18

3.4 Turbulence Characteristics

The turbulent kinetic energy is one of the important parameters reflecting the turbulent properties of the flow field [23]. When the k value is high, more energy and a longer transit time are required to migrate the target species. The turbulent kinetic energy is defined as follows:

�=12(�x′2+�y′2+�z′2)

(15)

where uxuy, and uz are fluctuating velocities in the xy, and z directions, respectively. An illustration of the TKE and the effects of the geometric arrangement of the weir and the presence of an opening in the weir is shown in Fig. 19. For a given bed slope, in Model A, the highest TKE values are uniformly distributed in the weir’s upstream portion in the channel’s cross section. In contrast, for the rectangular labyrinth weir (Model B), the highest TKE values are concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value in Models A and B is 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%). In the downstream portion of the conventional weir and within the crest of the weir and the walls of the rectangular labyrinth, there was a much lower TKE value that provided the best conditions for fish to recover in the pool between the weirs. The average of the lowest TKE for bottom slopes of 5 and 10% in Model A is 0.041 and 0.056 J/kg, and for Model B, is 0.047 and 0.064 J/kg. The presence of an opening in the weirs reduces the area of the highest TKE within the pool. It also increases the resting areas for fish (lower TKE). The highest TKE at the highest bottom slope in Models A and B with an orifice is 0.208 and 0.191 J/kg, respectively.

figure 19
Fig. 19

Figure 20 shows the effect of slope on the longitudinal distribution of TKE in the pools. TKE values significantly increase for a given discharge with an increasing bottom slope. Thus, for a low bed slope (S0 = 5%), a large pool area has expanded with average values of 0.131 and 0.168 J/kg for low and high discharge, respectively. For a bed slope of S0 = 10%, the average TKE values are 0.176 and 0.234 J/kg. Furthermore, as the discharge increases, the area with high TKE values within the pool increases. Lower TKE values are observed at the apex of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall for both bottom slopes. The effect of distance between weirs on TKE is shown in Fig. 21. Low TKE values were observed at low discharge and short distances between weirs. Low TKE values are located at the top of the rectangular labyrinth weir and the downstream corner of the weir wall. There is a maximum value of TKE at the large distances between weirs, L/B = 1.83, along the center line of the pool, where the dip jet meets the bottom of the bed. At high discharge, the maximum TKE value for the distance L/B = 0.61, 1.22, and 1.83 was 0.246, 0.322, and 0.417 J/kg, respectively. In addition, the maximum TKE range increases with the distance between weirs.

figure 20
Fig. 20
figure 21
Fig. 21

For TKE size, the average value (TKEave) is plotted against q in Fig. 22. For all models, the TKE values increase with increasing q. For example, in models A and B with L/B = 0.61 and a slope of 10%, the TKE value increases by 41.66 and 86.95%, respectively, as q increases from 0.1 to 0.27 m2/s. The TKE values in Model B are higher than Model A for a given discharge, bed slope, and weir distance. The TKEave in Model B is higher compared to Model A, ranging from 31.46 to 57.94%. The presence of an orifice in the weir reduces the TKE values in both weirs. The intensity of the reduction is greater in Model B. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, an orifice reduces TKEave values by 60.35 and 19.04%, respectively. For each model, increasing the bed slope increases the TKEave values in the pool. For example, for Model B with q = 0.18 m2/s, increasing the bed slope from 5 to 10% increases the TKEave value by 14.34%. Increasing the distance between weirs increases the TKEave values in the pool. For example, in Model B with S0 = 10% and q = 0.3 m2/s, the TKEave in the pool increases by 34.22% if you increase the distance between weirs from L/B = 0.61 to L/B = 0.183.

figure 22
Fig. 22

Cotel et al. [24] suggested that turbulence intensity (TI) is a suitable parameter for studying fish swimming performance. Figure 23 shows the plot of TI and the effects of the geometric arrangement of the weir and the presence of an orifice. In Model A, the highest TI values are found upstream of the weirs and are evenly distributed across the cross section of the channel. The TI values increase as you move upstream to downstream in the pool. For the rectangular labyrinth weir, the highest TI values were concentrated on the sides of the pool, between the top of the weir and the side wall of the channel, and along the top of the weir. Downstream of the conventional weir, within the apex of the weir, and at the corners of the walls of the rectangular labyrinth weir, the percentage of TI was low. At the highest discharge, the average range of TI in Models A and B was 24–45% and 15–62%, respectively. The diversity of TI is greater in the rectangular labyrinth weir than the conventional weir. Fish swimming performance is reduced due to higher turbulence intensity. However, fish species may prefer different disturbance intensities depending on their swimming abilities; for example, Salmo trutta prefers a disturbance intensity of 18–53% [25]. Kupferschmidt and Zhu [26] found a higher range of TI for fishways, such as natural rock weirs, of 40–60%. The presence of an orifice in the weir increases TI values within the pool, especially along the middle portion of the cross section of the fishway. With an orifice in the weir, the average range of TI in Models A and B was 28–59% and 22–73%, respectively.

figure 23
Fig. 23

The effect of bed slope on TI variation is shown in Fig. 24. TI increases in different pool areas as the bed slope increases for a given discharge. For a low bed slope (S0 = 5%), a large pool area has increased from 38 to 63% and from 56 to 71% for low and high discharge, respectively. For a bed slope of S0 = 10%, the average values of TI are 45–67% and 61–73% for low and high discharge, respectively. Therefore, as runoff increases, the area with high TI values within the pool increases. A lower TI is observed for both bottom slopes in the corner of the wall, downstream of the crest walls, and between the side walls in the weir and channel. Figure 25 compares weir spacing with the distribution of TI values within the pool. The TI values are low at low flows and short distances between weirs. A maximum value of TI occurs at long spacing and where the plunging stream impinges on the bed and the area around the bed. TI ranges from 36 to 57%, 58–72%, and 47–76% for the highest flow in a wide pool area for L/B = 0.61, 1.22, and 1.83, respectively.

figure 24
Fig. 24
figure 25
Fig. 25

The average value of turbulence intensity (TIave) is plotted against q in Fig. 26. The increase in TI values with the increase in q values is seen in all models. For example, the average values of TI for Models A and B at L/B = 0.61 and slope of 10% increased from 23.9 to 33.5% and from 42 to 51.8%, respectively, with the increase in q from 0.1 to 0.27 m2/s. For a given discharge, a given gradient, and a given spacing of weirs, the TIave is higher in Model B than Model A. The presence of an orifice in the weirs increases the TI values in both types. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, the presence of an orifice increases TIave from 23.9 to 37.1% and from 42 to 48.8%, respectively. For each model, TIave in the pool increases with increasing bed slope. For Model B with q = 0.18 m2/s, TIave increases from 37.5 to 45.8% when you increase the invert slope from 5 to 10%. Increasing the distance between weirs increases the TIave in the pool. In Model B with S0 = 10% and q = 0.3 m2/s, the TIave in the pool increases from 51.8 to 63.7% as the distance between weirs increases from L/B = 0.61 to L/B = 0.183.

figure 26
Fig. 26

3.5 Energy Dissipation

To facilitate the passage of various target species through the pool of fishways, it is necessary to pay attention to the energy dissipation of the flow and to keep the flow velocity in the pool slow. The average volumetric energy dissipation (k) in the pool is calculated using the following basic formula:

�=����0��

(16)

where ρ is the water density, and H is the average water depth of the pool. The change in k versus Q for all models at two bottom slopes, S0 = 5%, and S0 = 10%, is shown in Fig. 27. Like the results of Yagci [8] and Kupferschmidt and Zhu [26], at a constant bottom slope, the energy dissipation in the pool increases with increasing discharge. The trend of change in k as a function of Q from the present study at a bottom gradient of S0 = 5% is also consistent with the results of Kupferschmidt and Zhu [26] for the fishway with rock weir. The only difference between the results is the geometry of the fishway and the combination of boulders instead of a solid wall. Comparison of the models shows that the conventional model has lower energy dissipation than the rectangular labyrinth for a given discharge. Also, increasing the distance between weirs decreases the volumetric energy dissipation for each model with the same bed slope. Increasing the slope of the bottom leads to an increase in volumetric energy dissipation, and an opening in the weir leads to a decrease in volumetric energy dissipation for both models. Therefore, as a guideline for volumetric energy dissipation, if the value within the pool is too high, the increased distance of the weir, the decreased slope of the bed, or the creation of an opening in the weir would decrease the volumetric dissipation rate.

figure 27
Fig. 27

To evaluate the energy dissipation inside the pool, the general method of energy difference in two sections can use:

ε=�1−�2�1

(17)

where ε is the energy dissipation rate, and E1 and E2 are the specific energies in Sects. 1 and 2, respectively. The distance between Sects. 1 and 2 is the same. (L is the distance between two upstream and downstream weirs.) Figure 28 shows the changes in ε relative to q (flow per unit width). The rectangular labyrinth weir (Model B) has a higher energy dissipation rate than the conventional weir (Model A) at a constant bottom gradient. For example, at S0 = 5%, L/B = 0.61, and q = 0.08 m3/s.m, the energy dissipation rate in Model A (conventional weir) was 0.261. In Model B (rectangular labyrinth weir), however, it was 0.338 (22.75% increase). For each model, the energy dissipation rate within the pool increases as the slope of the bottom increases. For Model B with L/B = 1.83 and q = 0.178 m3/s.m, the energy dissipation rate at S0 = 5% and 10% is 0.305 and 0.358, respectively (14.8% increase). Figure 29 shows an orifice’s effect on the pools’ energy dissipation rate. With an orifice in the weir, both models’ energy dissipation rates decreased. Thus, the reduction in energy dissipation rate varied from 7.32 to 9.48% for Model A and from 8.46 to 10.57 for Model B.

figure 28
Fig. 28
figure 29
Fig. 29

4 Discussion

This study consisted of entirely of numerical analysis. Although this study was limited to two weirs, the hydraulic performance and flow characteristics in a pooled fishway are highlighted by the rectangular labyrinth weir and its comparison with the conventional straight weir. The study compared the numerical simulations with laboratory experiments in terms of surface profiles, velocity vectors, and flow characteristics in a fish ladder pool. The results indicate agreement between the numerical and laboratory data, supporting the reliability of the numerical model in capturing the observed phenomena.

When the configuration of the weir changes to a rectangular labyrinth weir, the flow characteristics, the maximum and minimum area, and even the location of each hydraulic parameter change compared to a conventional weir. In the rectangular labyrinth weir, the flow is gradually directed to the sides as it passes the weir. This increases the velocity at the sides of the channel [21]. Therefore, the high-velocity area is located on the sides. In the downstream apex of the weir, the flow velocity is low, and this area may be suitable for swimming target fish. However, no significant change in velocity was observed at the conventional weir within the fish ladder. This resulted in an average increase in TKE of 32% and an average increase in TI of about 17% compared to conventional weirs.

In addition, there is a slight difference in the flow regime for both weir configurations. In addition, the rectangular labyrinth weir has a higher energy dissipation rate for a given discharge and constant bottom slope than the conventional weir. By reducing the distance between the weirs, this becomes even more intense. Finally, the presence of an orifice in both configurations of the weir increased the flow velocity at the orifice and in the middle of the pool, reducing the highest TKE value and increasing the values of TI within the pool of the fish ladder. This resulted in a reduction in volumetric energy dissipation for both weir configurations.

The results of this study will help the reader understand the direct effects of the governing geometric parameters on the hydraulic characteristics of a fishway with a pool and weir. However, due to the limited configurations of the study, further investigation is needed to evaluate the position of the weir’s crest on the flow direction and the difference in flow characteristics when combining boulders instead of a solid wall for this type of labyrinth weir [26]. In addition, hydraulic engineers and biologists must work together to design an effective fishway with rectangular labyrinth configurations. The migration habits of the target species should be considered when designing the most appropriate design [27]. Parametric studies and field observations are recommended to determine the perfect design criteria.

The current study focused on comparing a rectangular labyrinth weir with a conventional straight weir. Further research can explore other weir configurations, such as variations in crest position, different shapes of labyrinth weirs, or the use of boulders instead of solid walls. This would help understand the influence of different geometric parameters on hydraulic characteristics.

5 Conclusions

A new layout of the weir was evaluated, namely a rectangular labyrinth weir compared to a straight weir in a pool and weir system. The differences between the weirs were highlighted, particularly how variations in the geometry of the structures, such as the shape of the weir, the spacing of the weir, the presence of an opening at the weir, and the slope of the bottom, affect the hydraulics within the structures. The main findings of this study are as follows:

  • The calculated dimensionless discharge (Qt*) confirmed three different flow regimes: when the corresponding range of Qt* is smaller than 0.6, the regime of plunging flow occurs for values of L/B = 1.83. (L: distance of the weir; B: channel width). When the corresponding range of Qt* is greater than 0.5, transitional flow occurs at L/B = 1.22. On the other hand, if Qt* is greater than 1, the streaming flow is at values of L/B = 0.61.
  • For the conventional weir and the rectangular labyrinth weir with the plunging flow, it can be assumed that the discharge (Q) is proportional to 1.56 and 1.47h, respectively (h: water depth above the weir). This information is useful for estimating the discharge based on water depth in practical applications.
  • In the rectangular labyrinth weir, the high-velocity zone is located on the side walls between the top of the weir and the channel wall. A high-velocity variation within short distances of the weir. Low velocity occurs within the downstream apex of the weir. This area may be suitable for swimming target fish.
  • As the distance between weirs increased, the zone of maximum velocity increased. However, the zone of low speed decreased. The prevailing maximum velocity for a rectangular labyrinth weir at L/B = 0.61, 1.22, and 1.83 was 1.46, 1.65, and 1.84 m/s, respectively. The low mean velocities for these distances were 0.27, 0.44, and 0.72 m/s, respectively. This finding highlights the importance of weir spacing in determining the flow characteristics within the fishway.
  • The presence of an orifice in the weir increased the flow velocity at the orifice and in the middle of the pool, especially in a conventional weir. The increase ranged from 7.7 to 12.48%.
  • For a given bottom slope, in a conventional weir, the highest values of turbulent kinetic energy (TKE) are uniformly distributed in the upstream part of the weir in the cross section of the channel. In contrast, for the rectangular labyrinth weir, the highest TKE values were concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value for the conventional and the rectangular labyrinth weir was 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%).
  • For a given discharge, bottom slope, and weir spacing, the average values of TI are higher for the rectangular labyrinth weir than for the conventional weir. At the highest discharge, the average range of turbulence intensity (TI) for the conventional and rectangular labyrinth weirs was between 24 and 45% and 15% and 62%, respectively. This reveals that the rectangular labyrinth weir may generate more turbulent flow conditions within the fishway.
  • For a given discharge and constant bottom slope, the rectangular labyrinth weir has a higher energy dissipation rate than the conventional weir (22.75 and 34.86%).
  • Increasing the distance between weirs decreased volumetric energy dissipation. However, increasing the gradient increased volumetric energy dissipation. The presence of an opening in the weir resulted in a decrease in volumetric energy dissipation for both model types.

Availability of data and materials

Data is contained within the article.

References

  1. Katopodis C (1992) Introduction to fishway design, working document. Freshwater Institute, Central Arctic Region
  2. Marriner, B.A.; Baki, A.B.M.; Zhu, D.Z.; Thiem, J.D.; Cooke, S.J.; Katopodis, C.: Field and numerical assessment of turning pool hydraulics in a vertical slot fishway. Ecol. Eng. 63, 88–101 (2014). https://doi.org/10.1016/j.ecoleng.2013.12.010Article Google Scholar 
  3. Dasineh, M.; Ghaderi, A.; Bagherzadeh, M.; Ahmadi, M.; Kuriqi, A.: Prediction of hydraulic jumps on a triangular bed roughness using numerical modeling and soft computing methods. Mathematics 9, 3135 (2021)Article Google Scholar 
  4. Silva, A.T.; Bermúdez, M.; Santos, J.M.; Rabuñal, J.R.; Puertas, J.: Pool-type fishway design for a potamodromous cyprinid in the Iberian Peninsula: the Iberian barbel—synthesis and future directions. Sustainability 12, 3387 (2020). https://doi.org/10.3390/su12083387Article Google Scholar 
  5. Santos, J.M.; Branco, P.; Katopodis, C.; Ferreira, T.; Pinheiro, A.: Retrofitting pool-and-weir fishways to improve passage performance of benthic fishes: effect of boulder density and fishway discharge. Ecol. Eng. 73, 335–344 (2014). https://doi.org/10.1016/j.ecoleng.2014.09.065Article Google Scholar 
  6. Ead, S.; Katopodis, C.; Sikora, G.; Rajaratnam, N.J.J.: Flow regimes and structure in pool and weir fishways. J. Environ. Eng. Sci. 3, 379–390 (2004)Article Google Scholar 
  7. Guiny, E.; Ervine, D.A.; Armstrong, J.D.: Hydraulic and biological aspects of fish passes for Atlantic salmon. J. Hydraul. Eng. 131, 542–553 (2005)Article Google Scholar 
  8. Yagci, O.: Hydraulic aspects of pool-weir fishways as ecologically friendly water structure. Ecol. Eng. 36, 36–46 (2010). https://doi.org/10.1016/j.ecoleng.2009.09.007Article Google Scholar 
  9. Dizabadi, S.; Hakim, S.S.; Azimi, A.H.: Discharge characteristics and structure of flow in labyrinth weirs with a downstream pool. Flow Meas. Instrum. 71, 101683 (2020). https://doi.org/10.1016/j.flowmeasinst.2019.101683Article Google Scholar 
  10. Kim, J.H.: Hydraulic characteristics by weir type in a pool-weir fishway. Ecol. Eng. 16, 425–433 (2001). https://doi.org/10.1016/S0925-8574(00)00125-7Article Google Scholar 
  11. Zhong, Z.; Ruan, T.; Hu, Y.; Liu, J.; Liu, B.; Xu, W.: Experimental and numerical assessment of hydraulic characteristic of a new semi-frustum weir in the pool-weir fishway. Ecol. Eng. 170, 106362 (2021). https://doi.org/10.1016/j.ecoleng.2021.106362Article Google Scholar 
  12. Hirt, C.W.; Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225 (1981). https://doi.org/10.1016/0021-9991(81)90145-5Article Google Scholar 
  13. Roache, P.J.: Perspective: a method for uniform reporting of grid refinement studies. J. Fluids Eng. 1994(116), 405–413 (1994)Article Google Scholar 
  14. Guo, S.; Chen, S.; Huang, X.; Zhang, Y.; Jin, S.: CFD and experimental investigations of drag force on spherical leak detector in pipe flows at high Reynolds number. Comput. Model. Eng. Sci. 101(1), 59–80 (2014)Google Scholar 
  15. Ahmadi, M.; Kuriqi, A.; Nezhad, H.M.; Ghaderi, A.; Mohammadi, M.: Innovative configuration of vertical slot fishway to enhance fish swimming conditions. J. Hydrodyn. 34, 917–933 (2022). https://doi.org/10.1007/s42241-022-0071-yArticle Google Scholar 
  16. Ahmadi, M.; Ghaderi, A.; MohammadNezhad, H.; Kuriqi, A.; Di Francesco, S.J.W.: Numerical investigation of hydraulics in a vertical slot fishway with upgraded configurations. Water 13, 2711 (2021)Article Google Scholar 
  17. Celik, I.B.; Ghia, U.; Roache, P.J.; Freitas, C.J.J.: Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J. Fluids Eng. Trans. ASME (2008). https://doi.org/10.1115/1.2960953Article Google Scholar 
  18. Li, S.; Yang, J.; Ansell, A.: Evaluation of pool-type fish passage with labyrinth weirs. Sustainability (2022). https://doi.org/10.3390/su14031098Article Google Scholar 
  19. Ghaderi, A.; Dasineh, M.; Aristodemo, F.; Aricò, C.: Numerical simulations of the flow field of a submerged hydraulic jump over triangular macroroughnesses. Water 13(5), 674 (2021)Article Google Scholar 
  20. Branco, P.; Santos, J.M.; Katopodis, C.; Pinheiro, A.; Ferreira, M.T.: Pool-type fishways: two different morpho-ecological cyprinid species facing plunging and streaming flows. PLoS ONE 8, e65089 (2013). https://doi.org/10.1371/journal.pone.0065089Article Google Scholar 
  21. Baki, A.B.M.; Zhu, D.Z.; Harwood, A.; Lewis, A.; Healey, K.: Rock-weir fishway I: flow regimes and hydraulic characteristics. J. Ecohydraulics 2, 122–141 (2017). https://doi.org/10.1080/24705357.2017.1369182Article Google Scholar 
  22. Dizabadi, S.; Azimi, A.H.: Hydraulic and turbulence structure of triangular labyrinth weir-pool fishways. River Res. Appl. 36, 280–295 (2020). https://doi.org/10.1002/rra.3581Article Google Scholar 
  23. Faizal, W.M.; Ghazali, N.N.N.; Khor, C.Y.; Zainon, M.Z.; Ibrahim, N.B.; Razif, R.M.: Turbulent kinetic energy of flow during inhale and exhale to characterize the severity of obstructive sleep apnea patient. Comput. Model. Eng. Sci. 136(1), 43–61 (2023)Google Scholar 
  24. Cotel, A.J.; Webb, P.W.; Tritico, H.: Do brown trout choose locations with reduced turbulence? Trans. Am. Fish. Soc. 135, 610–619 (2006). https://doi.org/10.1577/T04-196.1Article Google Scholar 
  25. Hargreaves, D.M.; Wright, N.G.: On the use of the k–ε model in commercial CFD software to model the neutral atmospheric boundary layer. J. Wind Eng. Ind. Aerodyn. 95, 355–369 (2007). https://doi.org/10.1016/j.jweia.2006.08.002Article Google Scholar 
  26. Kupferschmidt, C.; Zhu, D.Z.: Physical modelling of pool and weir fishways with rock weirs. River Res. Appl. 33, 1130–1142 (2017). https://doi.org/10.1002/rra.3157Article Google Scholar 
  27. Romão, F.; Quaresma, A.L.; Santos, J.M.; Amaral, S.D.; Branco, P.; Pinheiro, A.N.: Multislot fishway improves entrance performance and fish transit time over vertical slots. Water (2021). https://doi.org/10.3390/w13030275Article Google Scholar 

Download references

Figura 1 – Mapa de localização da PCH Salto Paraopeba

하천 저수지 물리적 모델의 침적 과정에 대한 전산 유체 역학 모델링(CFD) 기준

Natália Melo da Silva1 1; Jorge Luis Zegarra Tarqui2,Edna Maria de Faria Viana 3

Abstract

저수지 침전은 수력 발전의 지속 가능한 발전을 위한 주요 문제 중 하나이며 브라질에 매우 중요합니다. 브라질의 주요 에너지원은 수력발전소에서 나옵니다. 소규모 수력 발전소(SHP)는 재생 에너지의 보완적 발전을 위한 중요한 대안입니다.

이들의 설계, 건설, 운영 및 재동력을 최적화하기 위해 저수지 내 퇴적물의 유체 역학 및 이동을 연구하는 것이 매우 중요합니다.

3차원 전산유체역학 – CFD 3D 모델링은 복잡한 흐름 문제에 가장 적합한 방법입니다. 제안된 방법은 MG Jeceaba 자치구에 위치한 PCH Salto Paraopeba의 유체 역학 및 퇴적물 이동 현상을 재현하고 평가하는 것을 목표로 하며, 취수구의 완전한 침전으로 인해 작동이 중단되었습니다.

모델의 검증은 미나스제라이스 연방대학교의 수력학 연구 센터(CPH)에 구축된 축소된 물리적 모델의 실험 데이터를 사용하여 수행됩니다.

Abstract: The reservoir silting is one of the main problems for sustainable development in the
generation of hydroelectric energy and it is of great significance for Brazil. The main source of energy
in Brazil comes from hydroelectric power plant. The Small Hydroelectric Power Plant (SHP) are an
important alternative for complementary generation of renewable energy.
Seeking to optimize the design, construction, operation, and repowering of these, it is extremely
important to study the hydrodynamics and transport of sediments in their reservoirs. Threedimensional Computational Fluid Dynamics – CFD 3D modeling is the most appropriate method for
complex flow problems. The proposed method aims to reproduce and evaluate the hydrodynamic and
sediment transport phenomena of the PCH Salto Paraopeba, located in the municipality of Jeceaba,
MG, which stopped working due to the complete silting up of its water intake. The validation of the
model will be done using experimental data from the reduced physical model, built at the Hydraulic
Research Center (CPH) at the Federal University of Minas Gerais.

Keywords

퇴적물 수송, 물리적 모델, 소규모 수력 발전소, Sediment transport, physical model, Small Hydroelectric Power Plant.

Figura 1 – Mapa de localização da PCH Salto Paraopeba
Figura 1 – Mapa de localização da PCH Salto Paraopeba
Figura 2 – PCH Salto Paraopeba e modelo reduzido.
Figura 2 – PCH Salto Paraopeba e modelo reduzido.

REFERÊNCIAS

ALBARELLO, L. “Guia para implantação de pequenas centrais hidrelétricas- PCHs”. Dissertação de Mestrado. Trabalho de Conclusão de Curso de Especialista. Programa de Pós-Graduação em Eficiência Energética Aplicada aos Processos Produtivos. UFSM, Panambi /RS, 2014.

ANEEL, SIGA – Sistema de Informações de Geração da ANEEL. Disponível em: . Acesso em 10 de maio de 2023.

CAMPELLO, B.S.C. “Estudo Da Velocidade de Queda e do Início do Movimento das Partículas de Borracha e Areia”. Dissertação de Mestrado. Programa de Pós-Graduação em Saneamento, Meio Ambiente e Recursos Hídricos. UFMG, Belo Horizonte /MG, 2017.

CAMPOS, A.S. “A Importância do Coeficiente de Rugosidade de Manning na Avaliação Numérica
do Assoreamento de Reservatórios A Fio D’água”. Dissertação de Mestrado. Programa de PósGraduação em Saneamento, Meio Ambiente e Recursos Hídricos. UFMG, Belo Horizonte /MG,
2018.

CARVALHO, N. O. et al. Guia de avaliação de assoreamento de reservatórios, ANEEL, Brasília,
2000.

CARVALHO, N. O. Hidrossedimentologia prática, CPRM, Rio de Janeiro, 1994.

CARVALHO, N. O. Hidrossedimentologia prática, CPRM, Rio de Janeiro, 2008.

EMIG, PCH Salto do Paraopeba. Disponível em: < https://www.cemig.com.br/usina/pch-salto-doparaopeba/>. Acesso em 12 de maio de 2023.

ELETROBRÁS; Instituto de Pesquisas Hidráulicas – IPH. Diagnóstico das Condições sedimentológicas dos Principais Rios Brasileiros. UFRGS, Rio de Janeiro, 1992.

FLOW-3D®. FLOW-3D® 2022R2 – User Manual. Disponível em: < https://users.flow3d.com/flow3d/> FORTUNA, A.O. (2000). Técnicas Computacionais para Dinâmica dos Fluidos – Conceitos Básicos e Aplicações. São Paulo – SP.

GONÇALVES, M.O. “Análise Comparativa Entre Modelo Reduzido e Modelos Computacionais Uni
e Bidimensionais”. Dissertação de Mestrado. Programa de Pós-Graduação em Engenharia de
Recursos Hídricos e Ambiental. UFRP, Curitiba/PR, 2017.

HILLEBRAND, G.; KLASSEN, I.; OLSEN, N. R. B. (2017). “3D CFD modelling of velocities and
sediment transport in the Iffezheim hydropower reservoir”. Hydrology Research 48 (1), pp. 147–159.
JULIEN, P. Y. (2010). Erosion and sedimentation, Cambridge University Press, Cambridge, UK, 2nd
edn.

MAHMOOD, K. (1987). Reservoir sedimentation – impact, extent and mitigation. World Bank Tech.
Paper No. 71. Washington, DC.

MIRANDA, R.B. “A influência do assoreamento na geração de energia hidrelétrica: estudo de caso
na Usina de Três Irmãos – SP”. Dissertação de Mestrado. Programa de Pós-Graduação em Ciências
da Engenharia Ambiental. USP, São Carlos/SP, 2011.

MOHAMMAD, M.E.; AL-ANSARI, N.; KNUTSSON, S.; LAUE, J. (2020). “A Computational
Fluid Dynamics Simulation Model of Sediment Deposition in a Storage Reservoir Subject to Water
Withdrawal”. Water, 12, 959.

OLIVEIRA, M. A.“Repotenciação de pequenas centrais hidrelétricas: Avaliação técnica e
econômica”. Dissertação de Mestrado. Programa de Pós-Graduação em Engenharia de Energia.
UNIFEI, Itajubá/MG, 2012.

SALIBA, A.P.M. Notas de aula, Modelos fundo móvel, Disciplina Introdução a Modelagem Física
em Engenharia, Universidade Federal de Minas Gerais. Belo Horizonte, 2020.

SOARES, W.S. “Taxa de Assoreamento no Reservatório da Usina Hidrelétrica do Funil, MG”.
Dissertação de Mestrado. Programa de Pós-Graduação em Tecnologias e Inovações Ambientais.
UFLA, Lavras/MG, 2015.

비선형 파력의 영향에 따른 잔해 언덕 방파제 형상의 효과에 대한 수치 분석

비선형 파력의 영향에 따른 잔해 언덕 방파제 형상의 효과에 대한 수치 분석

Numerical Analysis of the Effects of Rubble Mound Breakwater Geometry Under the Effect of Nonlinear Wave Force

Arabian Journal for Science and EngineeringAims and scopeSubmit manuscript

Cite this article

Abstract

Assessing the interaction of waves and porous offshore structures such as rubble mound breakwaters plays a critical role in designing such structures optimally. This study focused on the effect of the geometric parameters of a sloped rubble mound breakwater, including the shape of the armour, method of its arrangement, and the breakwater slope. Thus, three main design criteria, including the wave reflection coefficient (Kr), transmission coefficient (Kt), and depreciation wave energy coefficient (Kd), are discussed. Based on the results, a decrease in wavelength reduced the Kr and increased the Kt and Kd. The rubble mound breakwater with the Coreloc armour layer could exhibit the lowest Kr compared to other armour geometries. In addition, a decrease in the breakwater slope reduced the Kr and Kd by 3.4 and 1.25%, respectively. In addition, a decrease in the breakwater slope from 33 to 25° increased the wave breaking height by 6.1% on average. Further, a decrease in the breakwater slope reduced the intensity of turbulence depreciation. Finally, the armour geometry and arrangement of armour layers on the breakwater with its different slopes affect the wave behaviour and interaction between the wave and breakwater. Thus, layering on the breakwater and the correct use of the geometric shapes of the armour should be considered when designing such structures.

파도와 잔해 더미 방파제와 같은 다공성 해양 구조물의 상호 작용을 평가하는 것은 이러한 구조물을 최적으로 설계하는 데 중요한 역할을 합니다. 본 연구는 경사진 잔해 둔덕 방파제의 기하학적 매개변수의 효과에 초점을 맞추었는데, 여기에는 갑옷의 형태, 배치 방법, 방파제 경사 등이 포함된다. 따라서 파동 반사 계수(Kr), 투과 계수(Kt) 및 감가상각파 에너지 계수(Kd)에 대해 논의합니다. 결과에 따르면 파장이 감소하면 K가 감소합니다.r그리고 K를 증가시켰습니다t 및 Kd. Coreloc 장갑 층이 있는 잔해 언덕 방파제는 가장 낮은 K를 나타낼 수 있습니다.r 다른 갑옷 형상과 비교했습니다. 또한 방파제 경사가 감소하여 K가 감소했습니다.r 및 Kd 각각 3.4%, 1.25% 증가했다. 또한 방파제 경사가 33°에서 25°로 감소하여 파도 파쇄 높이가 평균 6.1% 증가했습니다. 또한, 방파제 경사의 감소는 난류 감가상각의 강도를 감소시켰다. 마지막으로, 경사가 다른 방파제의 장갑 형상과 장갑 층의 배열은 파도 거동과 파도와 방파제 사이의 상호 작용에 영향을 미칩니다. 따라서 이러한 구조를 설계 할 때 방파제에 층을 쌓고 갑옷의 기하학적 모양을 올바르게 사용하는 것을 고려해야합니다.

Keywords

  • Rubble mound breakwater
  • Computational fluid dynamics
  • Armour layer
  • Wave reflection coefficient
  • Wave transmission coefficient
  • Wave energy dissipation coefficient

References

  1. Sollitt, C.K.; Cross, R.H.: Wave transmission through permeable breakwaters. In Coastal Engineering. pp. 1827–1846. (1973)
  2. Sulisz, W.: Wave reflection and transmission at permeable breakwaters of arbitrary cross-section. Coast. Eng. 9(4), 371–386 (1985)Article  Google Scholar 
  3. Kobayashi, N.; Wurjanto, A.: Numerical model for waves on rough permeable slopes. J. Coast. Res.149–166. (1990)
  4. Wurjanto, A.; Kobayashi, N.: Irregular wave reflection and runup on permeable slopes. J. Waterw. Port Coast. Ocean Eng. 119(5), 537–557 (1993)Article  Google Scholar 
  5. van Gent, M.R.: Numerical modelling of wave interaction with dynamically stable structures. In Coastal Engineering 1996. pp. 1930–1943. (1997)
  6. Liu, P.L.F.; Wen, J.: Nonlinear diffusive surface waves in porous media. J. Fluid Mech. 347, 119–139 (1997)Article  MathSciNet  MATH  Google Scholar 
  7. Troch, P.; De Rouck, J.: Development of two-dimensional numerical wave flume for wave interaction with rubble mound breakwaters. In Coastal Engineering. pp. 1638–1649. (1999)
  8. Liu, P.L.F.; Lin, P.; Chang, K.A.; Sakakiyama, T.: Numerical modeling of wave interaction with porous structures. J. Waterw. Port Coast. Ocean Eng. 125(6), 322–330 (1999)Article  Google Scholar 
  9. Abdolmaleki, K.; Thiagarajan, K.P.; Morris-Thomas, M.T.: Simulation of the dam break problem and impact flows using a Navier-Stokes solver. Simulation 13, 17 (2004)Google Scholar 
  10. Higuera, P.; Lara, J.L.; Losada, I.J.: Realistic wave generation and active wave absorption for Navier-Stokes models: application to OpenFOAM®. Coast. Eng. 71, 102–118 (2013)Article  Google Scholar 
  11. Higuera, P.; Lara, J.L.; Losada, I.J.: Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part II: application. Coast. Eng. 83, 259–270 (2014)Article  Google Scholar 
  12. Gui, Q.; Dong, P.; Shao, S.; Chen, Y.: Incompressible SPH simulation of wave interaction with porous structure. Ocean Eng. 110, 126–139 (2015)Article  Google Scholar 
  13. Dentale, F.; Donnarumma, G.; Carratelli, E.P.; Reale, F.: A numerical method to analyze the interaction between sea waves and rubble mound emerged breakwaters. WSEAS Trans. Fluid Mech 10, 106–116 (2015)Google Scholar 
  14. Dentale, F.; Reale, F.; Di Leo, A.; Carratelli, E.P.: A CFD approach to rubble mound breakwater design. Int. J. Naval Archit. Ocean Eng. 10(5), 644–650 (2018)Article  Google Scholar 
  15. Koley, S.: Wave transmission through multilayered porous breakwater under regular and irregular incident waves. Eng. Anal. Bound. Elem. 108, 393–401 (2019)Article  MathSciNet  MATH  Google Scholar 
  16. Koley, S.; Panduranga, K.; Almashan, N.; Neelamani, S.; Al-Ragum, A.: Numerical and experimental modeling of water wave interaction with rubble mound offshore porous breakwaters. Ocean Eng. 218, 108218 (2020)Article  Google Scholar 
  17. Pourteimouri, P.; Hejazi, K.: Development of an integrated numerical model for simulating wave interaction with permeable submerged breakwaters using extended Navier-Stokes equations. J. Mar. Sci. Eng. 8(2), 87 (2020)Article  Google Scholar 
  18. Cao, D.; Yuan, J.; Chen, H.: Towards modelling wave-induced forces on an armour layer unit of rubble mound coastal revetments. Ocean Eng. 239, 109811 (2021)Article  Google Scholar 
  19. Díaz-Carrasco, P.; Eldrup, M.R.; Andersen, T.L.: Advance in wave reflection estimation for rubble mound breakwaters: the importance of the relative water depth. Coast. Eng. 168, 103921 (2021)Article  Google Scholar 
  20. Vieira, F.; Taveira-Pinto, F.; Rosa-Santos, P.: Damage evolution in single-layer cube armoured breakwaters with a regular placement pattern. Coast. Eng. 169, 103943 (2021)Article  Google Scholar 
  21. Booshi, S.; Ketabdari, M.J.: Modeling of solitary wave interaction with emerged porous breakwater using PLIC-VOF method. Ocean Eng. 241, 110041 (2021)Article  Google Scholar 
  22. Aristodemo, F.; Filianoti, P.; Tripepi, G.; Gurnari, L.; Ghaderi, A.: On the energy transmission by a submerged barrier interacting with a solitary wave. Appl. Ocean Res. 122, 103123 (2022)Article  Google Scholar 
  23. Teixeira, P.R.; Didier, E.: Numerical analysis of performance of an oscillating water column wave energy converter inserted into a composite breakwater with rubble mound foundation. Ocean Eng. 278, 114421 (2023)Article  Google Scholar 
  24. Burgan, H.I.: Numerical modeling of structural irregularities on unsymmetrical buildings. Tehnički vjesnik 28(3), 856–861 (2021)Google Scholar 
  25. Jones, I.P.: CFDS-Flow3D user guide. (1994)
  26. Al Shaikhli, H.I.; Khassaf, S.I.: Stepped mound breakwater simulation by using flow 3D. Eurasian J. Eng. Technol. 6, 60–68 (2022)Google Scholar 
  27. Hirt, C.W.; Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201–225 (1981)Article  MATH  Google Scholar 
  28. Ghaderi, A.; Dasineh, M.; Aristodemo, F.; Aricò, C.: Numerical simulations of the flow field of a submerged hydraulic jump over triangular macroroughnesses. Water 13(5), 674 (2021)Article  Google Scholar 
  29. Yakhot, V.; Orszag, S.A.; Thangam, S.; Gatski, T.B.; Speziale, C.G.: Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids A 4(7), 1510–1520 (1992)Article  MathSciNet  MATH  Google Scholar 
  30. Van der Meer, J.W.; Stam, C.J.M.: Wave runup on smooth and rock slopes of coastal structures. J. Waterw. Port Coast. Ocean Eng. 118(5), 534–550 (1992)Article  Google Scholar 
  31. Goda, Y.; Suzuki, Y. Estimation of incident and reflected waves in random wave experiments. In: ASCE, Proceedings of 15th International Conference on Coastal Engineering, (Honolulu, Hawaii). vol. 1, pp. 828–845. (1976)
  32. Zanuttigh, B.; Van der Meer, J.W.: Wave reflection from coastal structures. In: AA.VV., Proceedings of the XXX International Conference on Coastal Engineering, World Scientific, (San Diego, CA, USA, September 2006). pp. 4337–4349. (2006)
  33. Seelig W.N.; Ahrens J.P.: Estimation of wave reflection and energy dissipation coefficients for beaches, revetments, and breakwaters. CERC, Technical Paper, Fort Belvoir. vol. 81, p. 41 (1981)
  34. Mase, H.: Random wave runup height on gentle slope. J. Waterw. Port Coast. Ocean Eng. 115(5), 649–661 (1989)Article  Google Scholar 
Predicting solid-state phase transformations during metal additive manufacturing: A case study on electron-beam powder bed fusion of Inconel-738

Predicting solid-state phase transformations during metal additive manufacturing: A case study on electron-beam powder bed fusion of Inconel-738

금속 적층 제조 중 고체 상 변형 예측: Inconel-738의 전자빔 분말층 융합에 대한 사례 연구

Nana Kwabena Adomako a, Nima Haghdadi a, James F.L. Dingle bc, Ernst Kozeschnik d, Xiaozhou Liao bc, Simon P. Ringer bc, Sophie Primig a

Abstract

Metal additive manufacturing (AM) has now become the perhaps most desirable technique for producing complex shaped engineering parts. However, to truly take advantage of its capabilities, advanced control of AM microstructures and properties is required, and this is often enabled via modeling. The current work presents a computational modeling approach to studying the solid-state phase transformation kinetics and the microstructural evolution during AM. Our approach combines thermal and thermo-kinetic modelling. A semi-analytical heat transfer model is employed to simulate the thermal history throughout AM builds. Thermal profiles of individual layers are then used as input for the MatCalc thermo-kinetic software. The microstructural evolution (e.g., fractions, morphology, and composition of individual phases) for any region of interest throughout the build is predicted by MatCalc. The simulation is applied to an IN738 part produced by electron beam powder bed fusion to provide insights into how γ′ precipitates evolve during thermal cycling. Our simulations show qualitative agreement with our experimental results in predicting the size distribution of γ′ along the build height, its multimodal size character, as well as the volume fraction of MC carbides. Our findings indicate that our method is suitable for a range of AM processes and alloys, to predict and engineer their microstructures and properties.

Graphical Abstract

ga1

Keywords

Additive manufacturing, Simulation, Thermal cycles, γ′ phase, IN738

1. Introduction

Additive manufacturing (AM) is an advanced manufacturing method that enables engineering parts with intricate shapes to be fabricated with high efficiency and minimal materials waste. AM involves building up 3D components layer-by-layer from feedstocks such as powder [1]. Various alloys, including steel, Ti, Al, and Ni-based superalloys, have been produced using different AM techniques. These techniques include directed energy deposition (DED), electron- and laser powder bed fusion (E-PBF and L-PBF), and have found applications in a variety of industries such as aerospace and power generation [2][3][4]. Despite the growing interest, certain challenges limit broader applications of AM fabricated components in these industries and others. One of such limitations is obtaining a suitable and reproducible microstructure that offers the desired mechanical properties consistently. In fact, the AM as-built microstructure is highly complex and considerably distinctive from its conventionally processed counterparts owing to the complicated thermal cycles arising from the deposition of several layers upon each other [5][6].

Several studies have reported that the solid-state phases and solidification microstructure of AM processed alloys such as CMSX-4, CoCr [7][8], Ti-6Al-4V [9][10][11]IN738 [6]304L stainless steel [12], and IN718 [13][14] exhibit considerable variations along the build direction. For instance, references [9][10] have reported that there is a variation in the distribution of α and β phases along the build direction in Ti-alloys. Similarly, the microstructure of an L-PBF fabricated martensitic steel exhibits variations in the fraction of martensite [15]. Furthermore, some of the present authors and others [6][16][17][18][19][20] have recently reviewed and reported that there is a difference in the morphology and fraction of nanoscale precipitates as a function of build height in Ni-based superalloys. These non-uniformities in the as-built microstructure result in an undesired heterogeneity in mechanical and other important properties such as corrosion and oxidation [19][21][22][23]. To obtain the desired microstructure and properties, additional processing treatments are utilized, but this incurs extra costs and may lead to precipitation of detrimental phases and grain coarsening. Therefore, a through-process understanding of the microstructure evolution under repeated heating and cooling is now needed to further advance 3D printed microstructure and property control.

It is now commonly understood that the microstructure evolution during printing is complex, and most AM studies concentrate on the microstructure and mechanical properties of the final build only. Post-printing studies of microstructure characteristics at room temperature miss crucial information on how they evolve. In-situ measurements and modelling approaches are required to better understand the complex microstructural evolution under repeated heating and cooling. Most in-situ measurements in AM focus on monitoring the microstructural changes, such as phase transformations and melt pool dynamics during fabrication using X-ray scattering and high-speed X-ray imaging [24][25][26][27]. For example, Zhao et al. [25] measured the rate of solidification and described the α/β phase transformation during L-PBF of Ti-6Al-4V in-situ. Also, Wahlmann et al. [21] recently used an L-PBF machine coupled with X-ray scattering to investigate the changes in CMSX-4 phase during successive melting processes. Although these techniques provide significant understanding of the basic principles of AM, they are not widely accessible. This is due to the great cost of the instrument, competitive application process, and complexities in terms of the experimental set-up, data collection, and analysis [26][28].

Computational modeling techniques are promising and more widely accessible tools that enable advanced understanding, prediction, and engineering of microstructures and properties during AM. So far, the majority of computational studies have concentrated on physics based process models for metal AM, with the goal of predicting the temperature profile, heat transfer, powder dynamics, and defect formation (e.g., porosity) [29][30]. In recent times, there have been efforts in modeling of the AM microstructure evolution using approaches such as phase-field [31], Monte Carlo (MC) [32], and cellular automata (CA) [33], coupled with finite element simulations for temperature profiles. However, these techniques are often restricted to simulating the evolution of solidification microstructures (e.g., grain and dendrite structure) and defects (e.g., porosity). For example, Zinovieva et al. [33] predicted the grain structure of L-PBF Ti-6Al-4V using finite difference and cellular automata methods. However, studies on the computational modelling of the solid-state phase transformations, which largely determine the resulting properties, remain limited. This can be attributed to the multi-component and multi-phase nature of most engineering alloys in AM, along with the complex transformation kinetics during thermal cycling. This kind of research involves predictions of the thermal cycle in AM builds, and connecting it to essential thermodynamic and kinetic data as inputs for the model. Based on the information provided, the thermokinetic model predicts the history of solid-state phase microstructure evolution during deposition as output. For example, a multi-phase, multi-component mean-field model has been developed to simulate the intermetallic precipitation kinetics in IN718 [34] and IN625 [35] during AM. Also, Basoalto et al. [36] employed a computational framework to examine the contrasting distributions of process-induced microvoids and precipitates in two Ni-based superalloys, namely IN718 and CM247LC. Furthermore, McNamara et al. [37] established a computational model based on the Johnson-Mehl-Avrami model for non-isothermal conditions to predict solid-state phase transformation kinetics in L-PBF IN718 and DED Ti-6Al-4V. These models successfully predicted the size and volume fraction of individual phases and captured the repeated nucleation and dissolution of precipitates that occur during AM.

In the current study, we propose a modeling approach with appreciably short computational time to investigate the detailed microstructural evolution during metal AM. This may include obtaining more detailed information on the morphologies of phases, such as size distribution, phase fraction, dissolution and nucleation kinetics, as well as chemistry during thermal cycling and final cooling to room temperature. We utilize the combination of the MatCalc thermo-kinetic simulator and a semi-analytical heat conduction model. MatCalc is a software suite for simulation of phase transformations, microstructure evolution and certain mechanical properties in engineering alloys. It has successfully been employed to simulate solid-state phase transformations in Ni-based superalloys [38][39], steels [40], and Al alloys [41] during complex thermo-mechanical processes. MatCalc uses the classical nucleation theory as well as the so-called Svoboda-Fischer-Fratzl-Kozeschnik (SFFK) growth model as the basis for simulating precipitation kinetics [42]. Although MatCalc was originally developed for conventional thermo-mechanical processes, we will show that it is also applicable for AM if the detailed time-temperature profile of the AM build is known. The semi-analytical heat transfer code developed by Stump and Plotkowski [43] is used to simulate these profile throughout the AM build.

1.1. Application to IN738

Inconel-738 (IN738) is a precipitation hardening Ni-based superalloy mainly employed in high-temperature components, e.g. in gas turbines and aero-engines owing to its exceptional mechanical properties at temperatures up to 980 °C, coupled with high resistance to oxidation and corrosion [44]. Its superior high-temperature strength (∼1090 MPa tensile strength) is provided by the L12 ordered Ni3(Al,Ti) γ′ phase that precipitates in a face-centered cubic (FCC) γ matrix [45][46]. Despite offering great properties, IN738, like most superalloys with high γ′ fractions, is challenging to process owing to its propensity to hot cracking [47][48]. Further, machining of such alloys is challenging because of their high strength and work-hardening rates. It is therefore difficult to fabricate complex INC738 parts using traditional manufacturing techniques like casting, welding, and forging.

The emergence of AM has now made it possible to fabricate such parts from IN738 and other superalloys. Some of the current authors’ recent research successfully applied E-PBF to fabricate defect-free IN738 containing γ′ throughout the build [16][17]. The precipitated γ′ were heterogeneously distributed. In particular, Haghdadi et al. [16] studied the origin of the multimodal size distribution of γ′, while Lim et al. [17] investigated the gradient in γ′ character with build height and its correlation to mechanical properties. Based on these results, the present study aims to extend the understanding of the complex and site-specific microstructural evolution in E-PBF IN738 by using a computational modelling approach. New experimental evidence (e.g., micrographs not published previously) is presented here to support the computational results.

2. Materials and Methods

2.1. Materials preparation

IN738 Ni-based superalloy (59.61Ni-8.48Co-7.00Al-17.47Cr-3.96Ti-1.01Mo-0.81W-0.56Ta-0.49Nb-0.47C-0.09Zr-0.05B, at%) gas-atomized powder was used as feedstock. The powders, with average size of 60 ± 7 µm, were manufactured by Praxair and distributed by Astro Alloys Inc. An Arcam Q10 machine by GE Additive with an acceleration voltage of 60 kV was used to fabricate a 15 × 15 × 25 mm3 block (XYZ, Z: build direction) on a 316 stainless steel substrate. The block was 3D-printed using a ‘random’ spot melt pattern. The random spot melt pattern involves randomly selecting points in any given layer, with an equal chance of each point being melted. Each spot melt experienced a dwell time of 0.3 ms, and the layer thickness was 50 µm. Some of the current authors have previously characterized the microstructure of the very same and similar builds in more detail [16][17]. A preheat temperature of ∼1000 °C was set and kept during printing to reduce temperature gradients and, in turn, thermal stresses [49][50][51]. Following printing, the build was separated from the substrate through electrical discharge machining. It should be noted that this sample was simultaneously printed with the one used in [17] during the same build process and on the same build plate, under identical conditions.

2.2. Microstructural characterization

The printed sample was longitudinally cut in the direction of the build using a Struers Accutom-50, ground, and then polished to 0.25 µm suspension via standard techniques. The polished x-z surface was electropolished and etched using Struers A2 solution (perchloric acid in ethanol). Specimens for image analysis were polished using a 0.06 µm colloidal silica. Microstructure analyses were carried out across the height of the build using optical microscopy (OM) and scanning electron microscopy (SEM) with focus on the microstructure evolution (γ′ precipitates) in individual layers. The position of each layer being analyzed was determined by multiplying the layer number by the layer thickness (50 µm). It should be noted that the position of the first layer starts where the thermal profile is tracked (in this case, 2 mm from the bottom). SEM images were acquired using a JEOL 7001 field emission microscope. The brightness and contrast settings, acceleration voltage of 15 kV, working distance of 10 mm, and other SEM imaging parameters were all held constant for analysis of the entire build. The ImageJ software was used for automated image analysis to determine the phase fraction and size of γ′ precipitates and carbides. A 2-pixel radius Gaussian blur, following a greyscale thresholding and watershed segmentation was used [52]. Primary γ′ sizes (>50 nm), were measured using equivalent spherical diameters. The phase fractions were considered equal to the measured area fraction. Secondary γ′ particles (<50 nm) were not considered here. The γ′ size in the following refers to the diameter of a precipitate.

2.3. Hardness testing

A Struers DuraScan tester was utilized for Vickers hardness mapping on a polished x-z surface, from top to bottom under a maximum load of 100 mN and 10 s dwell time. 30 micro-indentations were performed per row. According to the ASTM standard [53], the indentations were sufficiently distant (∼500 µm) to assure that strain-hardened areas did not interfere with one another.

2.4. Computational simulation of E-PBF IN738 build

2.4.1. Thermal profile modeling

The thermal history was generated using the semi-analytical heat transfer code (also known as the 3DThesis code) developed by Stump and Plotkowski [43]. This code is an open-source C++ program which provides a way to quickly simulate the conductive heat transfer found in welding and AM. The key use case for the code is the simulation of larger domains than is practicable with Computational Fluid Dynamics/Finite Element Analysis programs like FLOW-3D AM. Although simulating conductive heat transfer will not be an appropriate simplification for some investigations (for example the modelling of keyholding or pore formation), the 3DThesis code does provide fast estimates of temperature, thermal gradient, and solidification rate which can be useful for elucidating microstructure formation across entire layers of an AM build. The mathematics involved in the code is as follows:

In transient thermal conduction during welding and AM, with uniform and constant thermophysical properties and without considering fluid convection and latent heat effects, energy conservation can be expressed as:(1)��∂�∂�=�∇2�+�̇where � is density, � specific heat, � temperature, � time, � thermal conductivity, and �̇ a volumetric heat source. By assuming a semi-infinite domain, Eq. 1 can be analytically solved. The solution for temperature at a given time (t) using a volumetric Gaussian heat source is presented as:(2)��,�,�,�−�0=33�����32∫0�1������exp−3�′�′2��+�′�′2��+�′�′2����′(3)and��=12��−�′+��2for�=�,�,�(4)and�′�′=�−���′Where � is the vector �,�,� and �� is the location of the heat source.

The numerical integration scheme used is an adaptive Gaussian quadrature method based on the following nondimensionalization:(5)�=��xy2�,�′=��xy2�′,�=��xy,�=��xy,�=��xy,�=���xy

A more detailed explanation of the mathematics can be found in reference [43].

The main source of the thermal cycling present within a powder-bed fusion process is the fusion of subsequent layers. Therefore, regions near the top of a build are expected to undergo fewer thermal cycles than those closer to the bottom. For this purpose, data from the single scan’s thermal influence on multiple layers was spliced to represent the thermal cycles experienced at a single location caused by multiple subsequent layers being fused.

The cross-sectional area simulated by this model was kept constant at 1 × 1 mm2, and the depth was dependent on the build location modelled with MatCalc. For a build location 2 mm from the bottom, the maximum number of layers to simulate is 460. Fig. 1a shows a stitched overview OM image of the entire build indicating the region where this thermal cycle is simulated and tracked. To increase similarity with the conditions of the physical build, each thermal history was constructed from the results of two simulations generated with different versions of a random scan path. The parameters used for these thermal simulations can be found in Table 1. It should be noted that the main purpose of the thermal profile modelling was to demonstrate how the conditions at different locations of the build change relative to each other. Accurately predicting the absolute temperature during the build would require validation via a temperature sensor measurement during the build process which is beyond the scope of the study. Nonetheless, to establish the viability of the heat source as a suitable approximation for this study, an additional sensitivity analysis was conducted. This analysis focused on the influence of energy input on γ′ precipitation behavior, the central aim of this paper. This was achieved by employing varying beam absorption energies (0.76, 0.82 – the values utilized in the simulation, and 0.9). The direct impact of beam absorption efficiency on energy input into the material was investigated. Specifically, the initial 20 layers of the build were simulated and subsequently compared to experimental data derived from SEM. While phase fractions were found to be consistent across all conditions, disparities emerged in the mean size of γ′ precipitates. An absorption efficiency of 0.76 yielded a mean size of approximately 70 nm. Conversely, absorption efficiencies of 0.82 and 0.9 exhibited remarkably similar mean sizes of around 130 nm, aligning closely with the outcomes of the experiments.

Fig. 1

Table 1. A list of parameters used in thermal simulation of E-PBF.

ParameterValue
Spatial resolution5 µm
Time step0.5 s
Beam diameter200 µm
Beam penetration depth1 µm
Beam power1200 W
Beam absorption efficiency0.82
Thermal conductivity25.37 W/(m⋅K)
Chamber temperature1000 °C
Specific heat711.756 J/(kg⋅K)
Density8110 kg/m3

2.4.2. Thermo-kinetic simulation

The numerical analyses of the evolution of precipitates was performed using MatCalc version 6.04 (rel 0.011). The thermodynamic (‘mc_ni.tdb’, version 2.034) and diffusion (‘mc_ni.ddb’, version 2.007) databases were used. MatCalc’s basic principles are elaborated as follows:

The nucleation kinetics of precipitates are computed using a computational technique based on a classical nucleation theory [54] that has been modified for systems with multiple components [42][55]. Accordingly, the transient nucleation rate (�), which expresses the rate at which nuclei are formed per unit volume and time, is calculated as:(6)�=�0��*∙�xp−�*�∙�∙exp−��where �0 denotes the number of active nucleation sites, �* the rate of atomic attachment, � the Boltzmann constant, � the temperature, �* the critical energy for nucleus formation, τ the incubation time, and t the time. � (Zeldovich factor) takes into consideration that thermal excitation destabilizes the nucleus as opposed to its inactive state [54]. Z is defined as follows:(7)�=−12�kT∂2∆�∂�2�*12where ∆� is the overall change in free energy due to the formation of a nucleus and n is the nucleus’ number of atoms. ∆�’s derivative is evaluated at n* (critical nucleus size). �* accounts for the long-range diffusion of atoms required for nucleation, provided that the matrix’ and precipitates’ composition differ. Svoboda et al. [42] developed an appropriate multi-component equation for �*, which is given by:(8)�*=4��*2�4�∑�=1��ki−�0�2�0��0�−1where �* denotes the critical radius for nucleation, � represents atomic distance, and � is the molar volume. �ki and �0� represent the concentration of elements in the precipitate and matrix, respectively. The parameter �0� denotes the rate of diffusion of the ith element within the matrix. The expression for the incubation time � is expressed as [54]:(9)�=12�*�2

and �*, which represents the critical energy for nucleation:(10)�*=16�3�3∆�vol2where � is the interfacial energy, and ∆Gvol the change in the volume free energy. The critical nucleus’ composition is similar to the γ′ phase’s equilibrium composition at the same temperature. � is computed based on the precipitate and matrix compositions, using a generalized nearest neighbor broken bond model, with the assumption of interfaces being planar, sharp, and coherent [56][57][58].

In Eq. 7, it is worth noting that �* represents the fundamental variable in the nucleation theory. It contains �3/∆�vol2 and is in the exponent of the nucleation rate. Therefore, even small variations in γ and/or ∆�vol can result in notable changes in �, especially if �* is in the order of �∙�. This is demonstrated in [38] for UDIMET 720 Li during continuous cooling, where these quantities change steadily during precipitation due to their dependence on matrix’ and precipitate’s temperature and composition. In the current work, these changes will be even more significant as the system is exposed to multiple cycles of rapid cooling and heating.

Once nucleated, the growth of a precipitate is assessed using the radius and composition evolution equations developed by Svoboda et al. [42] with a mean-field method that employs the thermodynamic extremal principle. The expression for the total Gibbs free energy of a thermodynamic system G, which consists of n components and m precipitates, is given as follows:(11)�=∑���0��0�+∑�=1�4���33��+∑�=1��ki�ki+∑�=1�4���2��.

The chemical potential of component � in the matrix is denoted as �0�(�=1,…,�), while the chemical potential of component � in the precipitate is represented by �ki(�=1,…,�,�=1,…,�). These chemical potentials are defined as functions of the concentrations �ki(�=1,…,�,�=1,…,�). The interface energy density is denoted as �, and �� incorporates the effects of elastic energy and plastic work resulting from the volume change of each precipitate.

Eq. (12) establishes that the total free energy of the system in its current state relies on the independent state variables: the sizes (radii) of the precipitates �� and the concentrations of each component �ki. The remaining variables can be determined by applying the law of mass conservation to each component �. This can be represented by the equation:(12)��=�0�+∑�=1�4���33�ki,

Furthermore, the global mass conservation can be expressed by equation:(13)�=∑�=1���When a thermodynamic system transitions to a more stable state, the energy difference between the initial and final stages is dissipated. This model considers three distinct forms of dissipation effects [42]. These include dissipations caused by the movement of interfaces, diffusion within the precipitate and diffusion within the matrix.

Consequently, �̇� (growth rate) and �̇ki (chemical composition’s rate of change) of the precipitate with index � are derived from the linear system of equation system:(14)�ij��=��where �� symbolizes the rates �̇� and �̇ki [42]. Index i contains variables for precipitate radius, chemical composition, and stoichiometric boundary conditions suggested by the precipitate’s crystal structure. Eq. (10) is computed separately for every precipitate �. For a more detailed description of the formulae for the coefficients �ij and �� employed in this work please refer to [59].

The MatCalc software was used to perform the numerical time integration of �̇� and �̇ki of precipitates based on the classical numerical method by Kampmann and Wagner [60]. Detailed information on this method can be found in [61]. Using this computational method, calculations for E-PBF thermal cycles (cyclic heating and cooling) were computed and compared to experimental data. The simulation took approximately 2–4 hrs to complete on a standard laptop.

3. Results

3.1. Microstructure

Fig. 1 displays a stitched overview image and selected SEM micrographs of various γ′ morphologies and carbides after observations of the X-Z surface of the build from the top to 2 mm above the bottom. Fig. 2 depicts a graph that charts the average size and phase fraction of the primary γ′, as it changes with distance from the top to the bottom of the build. The SEM micrographs show widespread primary γ′ precipitation throughout the entire build, with the size increasing in the top to bottom direction. Particularly, at the topmost height, representing the 460th layer (Z = 22.95 mm), as seen in Fig. 1b, the average size of γ′ is 110 ± 4 nm, exhibiting spherical shapes. This is representative of the microstructure after it solidifies and cools to room temperature, without experiencing additional thermal cycles. The γ′ size slightly increases to 147 ± 6 nm below this layer and remains constant until 0.4 mm (∼453rd layer) from the top. At this position, the microstructure still closely resembles that of the 460th layer. After the 453rd layer, the γ′ size grows rapidly to ∼503 ± 19 nm until reaching the 437th layer (1.2 mm from top). The γ′ particles here have a cuboidal shape, and a small fraction is coarser than 600 nm. γ′ continue to grow steadily from this position to the bottom (23 mm from the top). A small fraction of γ′ is > 800 nm.

Fig. 2

Besides primary γ′, secondary γ′ with sizes ranging from 5 to 50 nm were also found. These secondary γ′ precipitates, as seen in Fig. 1f, were present only in the bottom and middle regions. A detailed analysis of the multimodal size distribution of γ′ can be found in [16]. There is no significant variation in the phase fraction of the γ′ along the build. The phase fraction is ∼ 52%, as displayed in Fig. 2. It is worth mentioning that the total phase fraction of γ′ was estimated based on the primary γ′ phase fraction because of the small size of secondary γ′. Spherical MC carbides with sizes ranging from 50 to 400 nm and a phase fraction of 0.8% were also observed throughout the build. The carbides are the light grey precipitates in Fig. 1g. The light grey shade of carbides in the SEM images is due to their composition and crystal structure [52]. These carbides are not visible in Fig. 1b-e because they were dissolved during electro-etching carried out after electropolishing. In Fig. 1g, however, the sample was examined directly after electropolishing, without electro-etching.

Table 2 shows the nominal and measured composition of γ′ precipitates throughout the build by atom probe microscopy as determined in our previous study [17]. No build height-dependent composition difference was observed in either of the γ′ precipitate populations. However, there was a slight disparity between the composition of primary and secondary γ′. Among the main γ′ forming elements, the primary γ′ has a high Ti concentration while secondary γ′ has a high Al concentration. A detailed description of the atom distribution maps and the proxigrams of the constituent elements of γ′ throughout the build can be found in [17].

Table 2. Bulk IN738 composition determined using inductively coupled plasma atomic emission spectroscopy (ICP-AES). Compositions of γ, primary γ′, and secondary γ′ at various locations in the build measured by APT. This information is reproduced from data in Ref. [17] with permission.

at%NiCrCoAlMoWTiNbCBZrTaOthers
Bulk59.1217.478.487.001.010.813.960.490.470.050.090.560.46
γ matrix
Top50.4832.9111.591.941.390.820.440.80.030.030.020.24
Mid50.3732.6111.931.791.540.890.440.10.030.020.020.010.23
Bot48.1034.5712.082.141.430.880.480.080.040.030.010.12
Primary γ′
Top72.172.513.4412.710.250.397.780.560.030.020.050.08
Mid71.602.573.2813.550.420.687.040.730.010.030.040.04
Bot72.342.473.8612.500.260.447.460.500.050.020.020.030.04
Secondary γ′
Mid70.424.203.2314.190.631.035.340.790.030.040.040.05
Bot69.914.063.6814.320.811.045.220.650.050.100.020.11

3.2. Hardness

Fig. 3a shows the Vickers hardness mapping performed along the entire X-Z surface, while Fig. 3b shows the plot of average hardness at different build heights. This hardness distribution is consistent with the γ′ precipitate size gradient across the build direction in Fig. 1Fig. 2. The maximum hardness of ∼530 HV1 is found at ∼0.5 mm away from the top surface (Z = 22.5), where γ′ particles exhibit the smallest observed size in Fig. 2b. Further down the build (∼ 2 mm from the top), the hardness drops to the 440–490 HV1 range. This represents the region where γ′ begins to coarsen. The hardness drops further to 380–430 HV1 at the bottom of the build.

Fig. 3

3.3. Modeling of the microstructural evolution during E-PBF

3.3.1. Thermal profile modeling

Fig. 4 shows the simulated thermal profile of the E-PBF build at a location of 23 mm from the top of the build, using a semi-analytical heat conduction model. This profile consists of the time taken to deposit 460 layers until final cooling, as shown in Fig. 4a. Fig. 4b-d show the magnified regions of Fig. 4a and reveal the first 20 layers from the top, a single layer (first layer from the top), and the time taken for the build to cool after the last layer deposition, respectively.

Fig. 4

The peak temperatures experienced by previous layers decrease progressively as the number of layers increases but never fall below the build preheat temperature (1000 °C). Our simulated thermal cycle may not completely capture the complexity of the actual thermal cycle utilized in the E-PBF build. For instance, the top layer (Fig. 4c), also representing the first deposit’s thermal profile without additional cycles (from powder heating, melting, to solidification), recorded the highest peak temperature of 1390 °C. Although this temperature is above the melting range of the alloy (1230–1360 °C) [62], we believe a much higher temperature was produced by the electron beam to melt the powder. Nevertheless, the solidification temperature and dynamics are outside the scope of this study as our focus is on the solid-state phase transformations during deposition. It takes ∼25 s for each layer to be deposited and cooled to the build temperature. The interlayer dwell time is 125 s. The time taken for the build to cool to room temperature (RT) after final layer deposition is ∼4.7 hrs (17,000 s).

3.3.2. MatCalc simulation

During the MatCalc simulation, the matrix phase is defined as γ. γ′, and MC carbide are included as possible precipitates. The domain of these precipitates is set to be the matrix (γ), and nucleation is assumed to be homogenous. In homogeneous nucleation, all atoms of the unit volume are assumed to be potential nucleation sitesTable 3 shows the computational parameters used in the simulation. All other parameters were set at default values as recommended in the version 6.04.0011 of MatCalc. The values for the interfacial energies are automatically calculated according to the generalized nearest neighbor broken bond model and is one of the most outstanding features in MatCalc [56][57][58]. It should be noted that the elastic misfit strain was not included in the calculation. The output of MatCalc includes phase fraction, size, nucleation rate, and composition of the precipitates. The phase fraction in MatCalc is the volume fraction. Although the experimental phase fraction is the measured area fraction, it is relatively similar to the volume fraction. This is because of the generally larger precipitate size and similar morphology at the various locations along the build [63]. A reliable phase fraction comparison between experiment and simulation can therefore be made.

Table 3. Computational parameters used in the simulation.

Precipitation domainγ
Nucleation site γ′Bulk (homogenous)
Nucleation site MC carbideBulk (Homogenous)
Precipitates class size250
Regular solution critical temperature γ′2500 K[64]
Calculated interfacial energyγ′ = 0.080–0.140 J/m2 and MC carbide = 0.410–0.430 J/m2
3.3.2.1. Precipitate phase fraction

Fig. 5a shows the simulated phase fraction of γ′ and MC carbide during thermal cycling. Fig. 5b is a magnified view of 5a showing the simulated phase fraction at the center points of the top 70 layers, whereas Fig. 5c corresponds to the first two layers from the top. As mentioned earlier, the top layer (460th layer) represents the microstructure after solidification. The microstructure of the layers below is determined by the number of thermal cycles, which increases with distance to the top. For example, layers 459, 458, 457, up to layer 1 (region of interest) experience 1, 2, 3 and 459 thermal cycles, respectively. In the top layer in Fig. 5c, the volume fraction of γ′ and carbides increases with temperature. For γ′, it decreases to zero when the temperature is above the solvus temperature after a few seconds. Carbides, however, remain constant in their volume fraction reaching equilibrium (phase fraction ∼ 0.9%) in a short time. The topmost layer can be compared to the first deposit, and the peak in temperature symbolizes the stage where the electron beam heats the powder until melting. This means γ′ and carbide precipitation might have started in the powder particles during heating from the build temperature and electron beam until the onset of melting, where γ′ dissolves, but carbides remain stable [28].

Fig. 5

During cooling after deposition, γ′ reprecipitates at a temperature of 1085 °C, which is below its solvus temperature. As cooling progresses, the phase fraction increases steadily to ∼27% and remains constant at 1000 °C (elevated build temperature). The calculated equilibrium fraction of phases by MatCalc is used to show the complex precipitation characteristics in this alloy. Fig. 6 shows that MC carbides form during solidification at 1320 °C, followed by γ′, which precipitate when the solidified layer cools to 1140 °C. This indicates that all deposited layers might contain a negligible amount of these precipitates before subsequent layer deposition, while being at the 1000 °C build temperature or during cooling to RT. The phase diagram also shows that the equilibrium fraction of the γ′ increases as temperature decreases. For instance, at 1000, 900, and 800 °C, the phase fractions are ∼30%, 38%, and 42%, respectively.

Fig. 6

Deposition of subsequent layers causes previous layers to undergo phase transformations as they are exposed to several thermal cycles with different peak temperatures. In Fig. 5c, as the subsequent layer is being deposited, γ′ in the previous layer (459th layer) begins to dissolve as the temperature crosses the solvus temperature. This is witnessed by the reduction of the γ′ phase fraction. This graph also shows how this phase dissolves during heating. However, the phase fraction of MC carbide remains stable at high temperatures and no dissolution is seen during thermal cycling. Upon cooling, the γ′ that was dissolved during heating reprecipitates with a surge in the phase fraction until 1000 °C, after which it remains constant. This microstructure is similar to the solidification microstructure (layer 460), with a similar γ′ phase fraction (∼27%).

The complete dissolution and reprecipitation of γ′ continue for several cycles until the 50th layer from the top (layer 411), where the phase fraction does not reach zero during heating to the peak temperature (see Fig. 5d). This indicates the ‘partial’ dissolution of γ′, which continues progressively with additional layers. It should be noted that the peak temperatures for layers that underwent complete dissolution were much higher (1170–1300 °C) than the γ′ solvus.

The dissolution and reprecipitation of γ′ during thermal cycling are further confirmed in Fig. 7, which summarizes the nucleation rate, phase fraction, and concentration of major elements that form γ′ in the matrix. Fig. 7b magnifies a single layer (3rd layer from top) within the full dissolution region in Fig. 7a to help identify the nucleation and growth mechanisms. From Fig. 7b, γ′ nucleation begins during cooling whereby the nucleation rate increases to reach a maximum value of approximately 1 × 1020 m−3s−1. This fast kinetics implies that some rearrangement of atoms is required for γ′ precipitates to form in the matrix [65][66]. The matrix at this stage is in a non-equilibrium condition. Its composition is similar to the nominal composition and remains unchanged. The phase fraction remains insignificant at this stage although nucleation has started. The nucleation rate starts declining upon reaching the peak value. Simultaneously, diffusion-controlled growth of existing nuclei occurs, depleting the matrix of γ′ forming elements (Al and Ti). Thus, from (7)(11), ∆�vol continuously decreases until nucleation ceases. The growth of nuclei is witnessed by the increase in phase fraction until a constant level is reached at 27% upon cooling to and holding at build temperature. This nucleation event is repeated several times.

Fig. 7

At the onset of partial dissolution, the nucleation rate jumps to 1 × 1021 m−3s−1, and then reduces sharply at the middle stage of partial dissolution. The nucleation rate reaches 0 at a later stage. Supplementary Fig. S1 shows a magnified view of the nucleation rate, phase fraction, and thermal profile, underpinning this trend. The jump in nucleation rate at the onset is followed by a progressive reduction in the solute content of the matrix. The peak temperatures (∼1130–1160 °C) are lower than those in complete dissolution regions but still above or close to the γ′ solvus. The maximum phase fraction (∼27%) is similar to that of the complete dissolution regions. At the middle stage, the reduction in nucleation rate is accompanied by a sharp drop in the matrix composition. The γ′ fraction drops to ∼24%, where the peak temperatures of the layers are just below or at γ′ solvus. The phase fraction then increases progressively through the later stage of partial dissolution to ∼30% towards the end of thermal cycling. The matrix solute content continues to drop although no nucleation event is seen. The peak temperatures are then far below the γ′ solvus. It should be noted that the matrix concentration after complete dissolution remains constant. Upon cooling to RT after final layer deposition, the nucleation rate increases again, indicating new nucleation events. The phase fraction reaches ∼40%, with a further depletion of the matrix in major γ′ forming elements.

3.3.2.2. γ′ size distribution

Fig. 8 shows histograms of the γ′ precipitate size distributions (PSD) along the build height during deposition. These PSDs are predicted at the end of each layer of interest just before final cooling to room temperature, to separate the role of thermal cycles from final cooling on the evolution of γ′. The PSD for the top layer (layer 460) is shown in Fig. 8a (last solidified region with solidification microstructure). The γ′ size ranges from 120 to 230 nm and is similar to the 44 layers below (2.2 mm from the top).

Fig. 8

Further down the build, γ′ begins to coarsen after layer 417 (44th layer from top). Fig. 8c shows the PSD after the 44th layer, where the γ′ size exhibits two peaks at ∼120–230 and ∼300 nm, with most of the population being in the former range. This is the onset of partial dissolution where simultaneously with the reprecipitation and growth of fresh γ′, the undissolved γ′ grows rapidly through diffusive transport of atoms to the precipitates. This is shown in Fig. 8c, where the precipitate class sizes between 250 and 350 represent the growth of undissolved γ′. Although this continues in the 416th layer, the phase fractions plot indicates that the onset of partial dissolution begins after the 411th layer. This implies that partial dissolution started early, but the fraction of undissolved γ′ was too low to impact the phase fraction. The reprecipitated γ′ are mostly in the 100–220 nm class range and similar to those observed during full dissolution.

As the number of layers increases, coarsening intensifies with continued growth of more undissolved γ′, and reprecipitation and growth of partially dissolved ones. Fig. 8d, e, and f show this sequence. Further down the build, coarsening progresses rapidly, as shown in Figs. 8d, 8e, and 8f. The γ′ size ranges from 120 to 1100 nm, with the peaks at 160, 180, and 220 nm in Figs. 8d, 8e, and 8f, respectively. Coarsening continues until nucleation ends during dissolution, where only the already formed γ′ precipitates continue to grow during further thermal cycling. The γ′ size at this point is much larger, as observed in layers 361 and 261, and continues to increase steadily towards the bottom (layer 1). Two populations in the ranges of ∼380–700 and ∼750–1100 nm, respectively, can be seen. The steady growth of γ′ towards the bottom is confirmed by the gradual decrease in the concentration of solute elements in the matrix (Fig. 7a). It should be noted that for each layer, the γ′ class with the largest size originates from continuous growth of the earliest set of the undissolved precipitates.

Fig. 9Fig. 10 and supplementary Figs. S2 and S3 show the γ′ size evolution during heating and cooling of a single layer in the full dissolution region, and early, middle stages, and later stages of partial dissolution, respectively. In all, the size of γ′ reduces during layer heating. Depending on the peak temperature of the layer which varies with build height, γ′ are either fully or partially dissolved as mentioned earlier. Upon cooling, the dissolved γ′ reprecipitate.

Fig. 9
Fig. 10

In Fig. 9, those layers that underwent complete dissolution (top layers) were held above γ′ solvus temperature for longer. In Fig. 10, layers at the early stage of partial dissolution spend less time in the γ′ solvus temperature region during heating, leading to incomplete dissolution. In such conditions, smaller precipitates are fully dissolved while larger ones shrink [67]. Layers in the middle stages of partial dissolution have peak temperatures just below or at γ′ solvus, not sufficient to achieve significant γ′ dissolution. As seen in supplementary Fig. S2, only a few smaller γ′ are dissolved back into the matrix during heating, i.e., growth of precipitates is more significant than dissolution. This explains the sharp decrease in concentration of Al and Ti in the matrix in this layer.

The previous sections indicate various phenomena such as an increase in phase fraction, further depletion of matrix composition, and new nucleation bursts during cooling. Analysis of the PSD after the final cooling of the build to room temperature allows a direct comparison to post-printing microstructural characterization. Fig. 11 shows the γ′ size distribution of layer 1 (460th layer from the top) after final cooling to room temperature. Precipitation of secondary γ′ is observed, leading to the multimodal size distribution of secondary and primary γ′. The secondary γ′ size falls within the 10–80 nm range. As expected, a further growth of the existing primary γ′ is also observed during cooling.

Fig. 11
3.3.2.3. γ′ chemistry after deposition

Fig. 12 shows the concentration of the major elements that form γ′ (Al, Ti, and Ni) in the primary and secondary γ′ at the bottom of the build, as calculated by MatCalc. The secondary γ′ has a higher Al content (13.5–14.5 at% Al), compared to 13 at% Al in the primary γ′. Additionally, within the secondary γ′, the smallest particles (∼10 nm) have higher Al contents than larger ones (∼70 nm). In contrast, for the primary γ′, there is no significant variation in the Al content as a function of their size. The Ni concentration in secondary γ′ (71.1–72 at%) is also higher in comparison to the primary γ′ (70 at%). The smallest secondary γ′ (∼10 nm) have higher Ni contents than larger ones (∼70 nm), whereas there is no substantial change in the Ni content of primary γ′, based on their size. As expected, Ti shows an opposite size-dependent variation. It ranges from ∼ 7.7–8.7 at% Ti in secondary γ′ to ∼9.2 at% in primary γ′. Similarly, within the secondary γ′, the smallest (∼10 nm) have lower Al contents than the larger ones (∼70 nm). No significant variation is observed for Ti content in primary γ′.

Fig. 12

4. Discussion

A combined modelling method is utilized to study the microstructural evolution during E-PBF of IN738. The presented results are discussed by examining the precipitation and dissolution mechanism of γ′ during thermal cycling. This is followed by a discussion on the phase fraction and size evolution of γ′ during thermal cycling and after final cooling. A brief discussion on carbide morphology is also made. Finally, a comparison is made between the simulation and experimental results to assess their agreement.

4.1. γ′ morphology as a function of build height

4.1.1. Nucleation of γ′

The fast precipitation kinetics of the γ′ phase enables formation of γ′ upon quenching from higher temperatures (above solvus) during thermal cycling [66]. In Fig. 7b, for a single layer in the full dissolution region, during cooling, the initial increase in nucleation rate signifies the first formation of nuclei. The slight increase in nucleation rate during partial dissolution, despite a decrease in the concentration of γ′ forming elements, may be explained by the nucleation kinetics. During partial dissolution and as the precipitates shrink, it is assumed that the regions at the vicinity of partially dissolved precipitates are enriched in γ′ forming elements [68][69]. This differs from the full dissolution region, in which case the chemical composition is evenly distributed in the matrix. Several authors have attributed the solute supersaturation of the matrix around primary γ′ to partial dissolution during isothermal ageing [69][70][71][72]. The enhanced supersaturation in the regions close to the precipitates results in a much higher driving force for nucleation, leading to a higher nucleation rate upon cooling. This phenomenon can be closely related to the several nucleation bursts upon continuous cooling of Ni-based superalloys, where second nucleation bursts exhibit higher nucleation rates [38][68][73][74].

At middle stages of partial dissolution, the reduction in the nucleation rate indicates that the existing composition and low supersaturation did not trigger nucleation as the matrix was closer to the equilibrium state. The end of a nucleation burst means that the supersaturation of Al and Ti has reached a low level, incapable of providing sufficient driving force during cooling to or holding at 1000 °C for further nucleation [73]. Earlier studies on Ni-based superalloys have reported the same phenomenon during ageing or continuous cooling from the solvus temperature to RT [38][73][74].

4.1.2. Dissolution of γ′ during thermal cycling

γ′ dissolution kinetics during heating are fast when compared to nucleation due to exponential increase in phase transformation and diffusion activities with temperature [65]. As shown in Fig. 9Fig. 10, and supplementary Figs. S2 and S3, the reduction in γ′ phase fraction and size during heating indicates γ′ dissolution. This is also revealed in Fig. 5 where phase fraction decreases upon heating. The extent of γ′ dissolution mostly depends on the temperature, time spent above γ′ solvus, and precipitate size [75][76][77]. Smaller γ′ precipitates are first to be dissolved [67][77][78]. This is mainly because more solute elements need to be transported away from large γ′ precipitates than from smaller ones [79]. Also, a high temperature above γ′ solvus temperature leads to a faster dissolution rate [80]. The equilibrium solvus temperature of γ′ in IN738 in our MatCalc simulation (Fig. 6) and as reported by Ojo et al. [47] is 1140 °C and 1130–1180 °C, respectively. This means the peak temperature experienced by previous layers decreases progressively from γ′ supersolvus to subsolvus, near-solvus, and far from solvus as the number of subsequent layers increases. Based on the above, it can be inferred that the degree of dissolution of γ′ contributes to the gradient in precipitate distribution.

Although the peak temperatures during later stages of partial dissolution are much lower than the equilibrium γ′ solvus, γ′ dissolution still occurs but at a significantly lower rate (supplementary Fig. S3). Wahlmann et al. [28] also reported a similar case where they observed the rapid dissolution of γ′ in CMSX-4 during fast heating and cooling cycles at temperatures below the γ′ solvus. They attributed this to the γ′ phase transformation process taking place in conditions far from the equilibrium. While the same reasoning may be valid for our study, we further believe that the greater surface area to volume ratio of the small γ′ precipitates contributed to this. This ratio means a larger area is available for solute atoms to diffuse into the matrix even at temperatures much below the solvus [81].

4.2. γ′ phase fraction and size evolution

4.2.1. During thermal cycling

In the first layer, the steep increase in γ′ phase fraction during heating (Fig. 5), which also represents γ′ precipitation in the powder before melting, has qualitatively been validated in [28]. The maximum phase fraction of 27% during the first few layers of thermal cycling indicates that IN738 theoretically could reach the equilibrium state (∼30%), but the short interlayer time at the build temperature counteracts this. The drop in phase fraction at middle stages of partial dissolution is due to the low number of γ′ nucleation sites [73]. It has been reported that a reduction of γ′ nucleation sites leads to a delay in obtaining the final volume fraction as more time is required for γ′ precipitates to grow and reach equilibrium [82]. This explains why even upon holding for 150 s before subsequent layer deposition, the phase fraction does not increase to those values that were observed in the previous full γ′ dissolution regions. Towards the end of deposition, the increase in phase fraction to the equilibrium value of 30% is as a result of the longer holding at build temperature or close to it [83].

During thermal cycling, γ′ particles begin to grow immediately after they first precipitate upon cooling. This is reflected in the rapid increase in phase fraction and size during cooling in Fig. 5 and supplementary Fig. S2, respectively. The rapid growth is due to the fast diffusion of solute elements at high temperatures [84]. The similar size of γ′ for the first 44 layers from the top can be attributed to the fact that all layers underwent complete dissolution and hence, experienced the same nucleation event and growth during deposition. This corresponds with the findings by Balikci et al. [85], who reported that the degree of γ′ precipitation in IN738LC does not change when a solution heat treatment is conducted above a certain critical temperature.

The increase in coarsening rate (Fig. 8) during thermal cycling can first be ascribed to the high peak temperature of the layers [86]. The coarsening rate of γ′ is known to increase rapidly with temperature due to the exponential growth of diffusion activity. Also, the simultaneous dissolution with coarsening could be another reason for the high coarsening rate, as γ′ coarsening is a diffusion-driven process where large particles grow by consuming smaller ones [78][84][86][87]. The steady growth of γ′ towards the bottom of the build is due to the much lower layer peak temperature, which is almost close to the build temperature, and reduced dissolution activity, as is seen in the much lower solute concentration in γ′ compared to those in the full and partial dissolution regions.

4.2.2. During cooling

The much higher phase fraction of ∼40% upon cooling signifies the tendency of γ′ to reach equilibrium at lower temperatures (Fig. 4). This is due to the precipitation of secondary γ′ and a further increase in the size of existing primary γ′, which leads to a multimodal size distribution of γ′ after cooling [38][73][88][89][90]. The reason for secondary γ′ formation during cooling is as follows: As cooling progresses, it becomes increasingly challenging to redistribute solute elements in the matrix owing to their lower mobility [38][73]. A higher supersaturation level in regions away from or free of the existing γ′ precipitates is achieved, making them suitable sites for additional nucleation bursts. More cooling leads to the growth of these secondary γ′ precipitates, but as the temperature and in turn, the solute diffusivity is low, growth remains slow.

4.3. Carbides

MC carbides in IN738 are known to have a significant impact on the high-temperature strength. They can also act as effective hardening particles and improve the creep resistance [91]. Precipitation of MC carbides in IN738 and several other superalloys is known to occur during solidification or thermal treatments (e.g., hot isostatic pressing) [92]. In our case, this means that the MC carbides within the E-PBF build formed because of the thermal exposure from the E-PBF thermal cycle in addition to initial solidification. Our simulation confirms this as MC carbides appear during layer heating (Fig. 5). The constant and stable phase fraction of MC carbides during thermal cycling can be attributed to their high melting point (∼1360 °C) and the short holding time at peak temperatures [75][93][94]. The solvus temperature for most MC carbides exceeds most of the peak temperatures observed in our simulation, and carbide dissolution kinetics at temperatures above the solvus are known to be comparably slow [95]. The stable phase fraction and random distribution of MC carbides signifies the slight influence on the gradient in hardness.

4.4. Comparison of simulations and experiments

4.4.1. Precipitate phase fraction and morphology as a function of build height

A qualitative agreement is observed for the phase fraction of carbides, i.e. ∼0.8% in the experiment and ∼0.9% in the simulation. The phase fraction of γ′ differs, with the experiment reporting a value of ∼51% and the simulation, 40%. Despite this, the size distribution of primary γ′ along the build shows remarkable consistency between experimental and computational analyses. It is worth noting that the primary γ′ morphology in the experimental analysis is observed in the as-fabricated state, whereas the simulation (Fig. 8) captures it during deposition process. The primary γ′ size in the experiment is expected to experience additional growth during the cooling phase. Regardless, both show similar trends in primary γ′ size increments from the top to the bottom of the build. The larger primary γ’ size in the simulation versus the experiment can be attributed to the fact that experimental and simulation results are based on 2D and 3D data, respectively. The absence of stereological considerations [96] in our analysis could have led to an underestimation of the precipitate sizes from SEM measurements. The early starts of coarsening (8th layer) in the experiment compared to the simulation (45th layer) can be attributed to a higher actual γ′ solvus temperature than considered in our simulation [47]. The solvus temperature of γ′ in a Ni-based superalloy is mainly determined by the detailed composition. A high amount of Cr and Co are known to reduce the solvus temperature, whereas Ta and Mo will increase it [97][98][99]. The elemental composition from our experimental work was used for the simulation except for Ta. It should be noted that Ta is not included in the thermodynamic database in MatCalc used, and this may have reduced the solvus temperature. This could also explain the relatively higher γ′ phase fraction in the experiment than in simulation, as a higher γ′ solvus temperature will cause more γ′ to precipitate and grow early during cooling [99][100].

Another possible cause of this deviation can be attributed to the extent of γ′ dissolution, which is mainly determined by the peak temperature. It can be speculated that individual peak temperatures at different layers in the simulation may have been over-predicted. However, one needs to consider that the true thermal profile is likely more complicated in the actual E-PBF process [101]. For example, the current model assumes that the thermophysical properties of the material are temperature-independent, which is not realistic. Many materials, including IN738, exhibit temperature-dependent properties such as thermal conductivityspecific heat capacity, and density [102]. This means that heat transfer simulations may underestimate or overestimate the temperature gradients and cooling rates within the powder bed and the solidified part. Additionally, the model does not account for the reduced thermal diffusivity through unmelted powder, where gas separating the powder acts as insulation, impeding the heat flow [1]. In E-PBF, the unmelted powder regions with trapped gas have lower thermal diffusivity compared to the fully melted regions, leading to localized temperature variations, and altered solidification behavior. These limitations can impact the predictions, particularly in relation to the carbide dissolution, as the peak temperatures may be underestimated.

While acknowledging these limitations, it is worth emphasizing that achieving a detailed and accurate representation of each layer’s heat source would impose tough computational challenges. Given the substantial layer count in E-PBF, our decision to employ a semi-analytical approximation strikes a balance between computational feasibility and the capture of essential trends in thermal profiles across diverse build layers. In future work, a dual-calibration strategy is proposed to further reduce simulation-experiment disparities. By refining temperature-independent thermophysical property approximations and absorptivity in the heat source model, and by optimizing interfacial energy descriptions in the kinetic model, the predictive precision could be enhanced. Further refining the simulation controls, such as adjusting the precipitate class size may enhance quantitative comparisons between modeling outcomes and experimental data in future work.

4.4.2. Multimodal size distribution of γ′ and concentration

Another interesting feature that sees qualitative agreement between the simulation and the experiment is the multimodal size distribution of γ′. The formation of secondary γ′ particles in the experiment and most E-PBF Ni-based superalloys is suggested to occur at low temperatures, during final cooling to RT [16][73][90]. However, so far, this conclusion has been based on findings from various continuous cooling experiments, as the study of the evolution during AM would require an in-situ approach. Our simulation unambiguously confirms this in an AM context by providing evidence for secondary γ′ precipitation during slow cooling to RT. Additionally, it is possible to speculate that the chemical segregation occurring during solidification, due to the preferential partitioning of certain elements between the solid and liquid phases, can contribute to the multimodal size distribution during deposition [51]. This is because chemical segregation can result in variations in the local composition of superalloys, which subsequently affects the nucleation and growth of γ′. Regions with higher concentrations of alloying elements will encourage the formation of larger γ′ particles, while regions with lower concentrations may favor the nucleation of smaller precipitates. However, it is important to acknowledge that the elevated temperature during the E-PBF process will largely homogenize these compositional differences [103][104].

A good correlation is also shown in the composition of major γ′ forming elements (Al and Ti) in primary and secondary γ′. Both experiment and simulation show an increasing trend for Al content and a decreasing trend for Ti content from primary to secondary γ′. The slight composition differences between primary and secondary γ′ particles are due to the different diffusivity of γ′ stabilizers at different thermal conditions [105][106]. As the formation of multimodal γ′ particles with different sizes occurs over a broad temperature range, the phase chemistry of γ′ will be highly size dependent. The changes in the chemistry of various γ′ (primary, secondary, and tertiary) have received significant attention since they have a direct influence on the performance [68][105][107][108][109]. Chen et al. [108][109], reported a high Al content in the smallest γ′ precipitates compared to the largest, while Ti showed an opposite trend during continuous cooling in a RR1000 Ni-based superalloy. This was attributed to the temperature and cooling rate at which the γ′ precipitates were formed. The smallest precipitates formed last, at the lowest temperature and cooling rate. A comparable observation is evident in the present investigation, where the secondary γ′ forms at a low temperature and cooling rate in comparison to the primary. The temperature dependence of γ′ chemical composition is further evidenced in supplementary Fig. S4, which shows the equilibrium chemical composition of γ′ as a function of temperature.

5. Conclusions

A correlative modelling approach capable of predicting solid-state phase transformations kinetics in metal AM was developed. This approach involves computational simulations with a semi-analytical heat transfer model and the MatCalc thermo-kinetic software. The method was used to predict the phase transformation kinetics and detailed morphology and chemistry of γ′ and MC during E-PBF of IN738 Ni-based superalloy. The main conclusions are:

  • 1.The computational simulations are in qualitative agreement with the experimental observations. This is particularly true for the γ′ size distribution along the build height, the multimodal size distribution of particles, and the phase fraction of MC carbides.
  • 2.The deviations between simulation and experiment in terms of γ′ phase fraction and location in the build are most likely attributed to a higher γ′ solvus temperature during the experiment than in the simulation, which is argued to be related to the absence of Ta in the MatCalc database.
  • 3.The dissolution and precipitation of γ′ occur fast and under non-equilibrium conditions. The level of γ′ dissolution determines the gradient in γ′ size distribution along the build. After thermal cycling, the final cooling to room temperature has further significant impacts on the final γ′ size, morphology, and distribution.
  • 4.A negligible amount of γ′ forms in the first deposited layer before subsequent layer deposition, and a small amount of γ′ may also form in the powder induced by the 1000 °C elevated build temperature before melting.

Our findings confirm the suitability of MatCalc to predict the microstructural evolution at various positions throughout a build in a Ni-based superalloy during E-PBF. It also showcases the suitability of a tool which was originally developed for traditional thermo-mechanical processing of alloys to the new additive manufacturing context. Our simulation capabilities are likely extendable to other alloy systems that undergo solid-state phase transformations implemented in MatCalc (various steels, Ni-based superalloys, and Al-alloys amongst others) as well as other AM processes such as L-DED and L-PBF which have different thermal cycle characteristics. New tools to predict the microstructural evolution and properties during metal AM are important as they provide new insights into the complexities of AM. This will enable control and design of AM microstructures towards advanced materials properties and performances.

CRediT authorship contribution statement

Primig Sophie: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. Adomako Nana Kwabena: Writing – original draft, Writing – review & editing, Visualization, Software, Investigation, Formal analysis, Conceptualization. Haghdadi Nima: Writing – review & editing, Supervision, Project administration, Methodology, Conceptualization. Dingle James F.L.: Methodology, Conceptualization, Software, Writing – review & editing, Visualization. Kozeschnik Ernst: Writing – review & editing, Software, Methodology. Liao Xiaozhou: Writing – review & editing, Project administration, Funding acquisition. Ringer Simon P: Writing – review & editing, Project administration, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was sponsored by the Department of Industry, Innovation, and Science under the auspices of the AUSMURI program – which is a part of the Commonwealth’s Next Generation Technologies Fund. The authors acknowledge the facilities and the scientific and technical assistance at the Electron Microscope Unit (EMU) within the Mark Wainwright Analytical Centre (MWAC) at UNSW Sydney and Microscopy Australia. Nana Adomako is supported by a UNSW Scientia PhD scholarship. Michael Haines’ (UNSW Sydney) contribution to the revised version of the original manuscript is thankfully acknowledged.

Appendix A. Supplementary material

Download : Download Word document (462KB)

Supplementary material.

Data Availability

Data will be made available on request.

References

Figure 1. Three-dimensional finite element model of local scouring of semi-exposed submarine cable.

반노출 해저케이블의 국부 정련과정 및 영향인자에 대한 수치적 연구

Numerical Study of the Local Scouring Process and Influencing Factors of Semi-Exposed Submarine Cables

by Qishun Li,Yanpeng Hao *,Peng Zhang,Haotian Tan,Wanxing Tian,Linhao Chen andLin Yang

School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China

*Author to whom correspondence should be addressed.J. Mar. Sci. Eng.202311(7), 1349; https://doi.org/10.3390/jmse11071349

Received: 10 June 2023 / Revised: 19 June 2023 / Accepted: 27 June 2023 / Published: 1 July 2023(This article belongs to the Section Ocean Engineering)

일부 수식이 손상되어 표시될 수 있습니다. 이 경우 원문을 참조하시기 바랍니다.

Abstract

Local scouring might result in the spanning of submarine cables, endangering their mechanical and electrical properties. In this contribution, a three-dimensional computational fluid dynamics simulation model is developed using FLOW-3D, and the scouring process of semi-exposed submarine cables is investigated. The effects of the sediment critical Shields number, sediment density, and ocean current velocity on local scouring are discussed, and variation rules for the submarine cables’ spanning time are provided. The results indicate that three scouring holes are formed around the submarine cables. The location of the bottom of the holes corresponds to that of the maximum shear velocity. The continuous development of scouring holes at the wake position leads to the spanning of the submarine cables. The increase in the sediment’s critical Shields number and sediment density, as well as the decrease in the ocean current velocity, will extend the time for maintaining the stability of the upstream scouring hole and retard the development velocity of the wake position and downstream scouring holes. The spanning time has a cubic relationship with the sediment’s critical Shields number, a linear relationship with the sediment density, and an exponential relationship with the ocean current velocity. In this paper, the local scouring process of semi-exposed submarine cables is studied, which provides a theoretical basis for the operation and maintenance of submarine cables.

Keywords: 

submarine cablelocal scouringnumerical simulationcomputational fluid dynamics

1. Introduction

As a key piece of equipment in cross-sea power grids, submarine cables are widely used to connect autonomous power grids, supply power to islands or offshore platforms, and transmit electric power generated by marine renewable energy installations to onshore substations [1]. Once submarine cables break down due to natural disasters or human-made damage, the normal operation of other marine electric power equipment connected to them may be affected. These chain reactions will cause great economic losses and serious social impacts [2].

To protect submarine cables, they are usually buried 1 to 3 m below the seabed [3]. However, submarine cables are still confronted with potential threats from the complex subsea environment. Under the influence of fishing, anchor damage, ocean current scouring, and other factors, the sediment above submarine cables will always inevitably migrate. When a submarine cable is partially exposed, the scouring at this position will be exacerbated; eventually, it will cause the submarine cable to span. According to a field investigation of the 500 kV oil-filled submarine cable that is part of the Hainan networking system, the total length of the span is 49 m [4]. Under strong ocean currents, spanning submarine cables may experience vortex-induced vibrations. Fatigue stress caused by vortex-induced vibrations may lead to metal sheath rupture [5], which endangers the mechanical and electrical properties of submarine cables. Therefore, understanding the local scouring processes of partially exposed submarine cables is crucial for predicting scouring patterns. This is the basis for developing effective operation and maintenance strategies for submarine cables.

The mechanism and influencing factors of sediment erosion have been examined by researchers around the world. In 1988, Sumer [6] conducted experiments to show that the shedding vortex in the wake of a pipeline would increase the Shields parameter by 3–4 times, which would result in severe scouring. In 1991, Chiew [7] performed experiments to prove that the maximum scouring depth could be obtained when the pipeline was located on a flat bed and was scoured by a unidirectional water flow. Based on the test results, they provided a prediction formula for the maximum scouring depth. In 2003, Mastbergen [8] proposed a one-dimensional, steady-state numerical model of turbidity currents, which considered the negative pore pressures in the seabed. The calculated results of this model were basically consistent with the actual scouring of a submarine canyon. In 2007, Dey [9] presented a semitheoretical model for the computation of the maximum clear-water scour depth below underwater pipelines in uniform sediments under a steady flow, and the predicted scour depth in clear water satisfactorily agreed with the observed values. In 2008, Dey [10] conducted experiments on clear-water scour below underwater pipelines under a steady flow and obtained a variation pattern of the depth of the scouring hole. In 2008, Liang [11] used a two-dimensional numerical simulation to study the scouring process of a tube bundle under the action of currents and waves. They discovered that, compared with the scouring of a single tube, the scouring depth of the tube bundle was deeper, and the scouring time was longer. In 2012, Yang [12] found that placing rubber sheets under pipes can greatly accelerate their self-burial. The rubber sheets had the best performance when their length was about 1.5 times the size of the pipe. In 2020, Li [13] investigated the two-dimensional local scour beneath two submarine pipelines in tandem under wave-plus-current conditions via numerical simulation. They found that for conditions involving waves plus a low-strength current, the scour pattern beneath the two pipelines behaved like that in the pure-wave condition. Conversely, when the current had equal strength to the wave-induced flow, the scour pattern beneath the two pipelines resembled that in the pure-current condition. In 2020, Guan [14] studied and discussed the interactive coupling effects among a vibrating pipeline, flow field, and scour process through experiments, and the experimental data showed that the evolution of the scour hole had significant influences on the pipeline vibrations. In 2021, Liu [15] developed a two-dimensional finite element numerical model and researched the local scour around a vibrating pipeline. The numerical results showed that the maximum vibration amplitude of the pipeline could reach about 1.2 times diameter, and the maximum scour depth occurred on the wake side of the vibrating pipeline. In 2021, Huang [16] carried out two-dimensional numerical simulations to investigate the scour beneath a single pipeline and piggyback pipelines subjected to an oscillatory flow condition at a KC number of 11 and captured typical steady-streaming structures around the pipelines due to the oscillatory flow condition. In 2021, Cui [17] investigated the characteristics of the riverbed scour profile for a pipeline buried at different depths under the condition of riverbed sediments with different particle sizes. The results indicated that, in general, the equilibrium scour depth changed in a spoon shape with the gradual increase in the embedment ratio. In 2022, Li [18] used numerical simulation to study the influence of the burial depth of partially buried pipelines on the surrounding flow field, but they did not investigate the scour depth. In 2022, Zhu [19] performed experiments to prove that the scour hole propagation rate under a pipeline decreases with an increasing pipeline embedment ratio and rises with the KC number. In 2022, Najafzadeh [20] proposed equations for the prediction of the scouring propagation rate around pipelines due to currents based on a machine learning model, and the prediction results were consistent with the experimental data. In 2023, Ma [21] used the computational fluid dynamics coarse-grained discrete element method to simulate the scour process around a pipeline. The results showed that this method can effectively reduce the considerable need for computing resources and excessive computation time. In 2023, through numerical simulations, Hu [22] discovered that the water velocity and the pipeline diameter had a significant effect on the depth of scouring.

In the preceding works, the researchers investigated the mechanism of sediment scouring and the effect of various factors on the local scouring of submarine pipelines. However, submarine cables are buried beneath the seabed, while submarine pipelines are erected above the seabed. The difference in laying methods leads to a large discrepancy between their local scouring processes. Therefore, the conclusions of the above investigations are not applicable to the local scouring of submarine cables. Currently, there is no report on the research of the local scouring of partially exposed submarine cables.

In this paper, a three-dimensional computational fluid dynamics (CFD) finite element model, based on two-phase flow, is established using FLOW-3D. The local scouring process of semi-exposed submarine cables under steady-state ocean currents is studied, and the variation rules of the depth and the shape of the scouring holes, as well as the shear velocity with time, are obtained. By setting different critical Shields numbers of the sediment, different sediment densities, and different ocean current velocities, the change rule of the scouring holes’ development rate and the time required for the spanning of submarine cables are explored.

2. Sediment Scouring Model

In the sediment scouring model, the sediment is set as the dispersed particle, which is regarded as a kind of quasifluid. In this context, sediment scouring is considered as a two-phase flow process between the liquid phase and solid particle phase. The sediment in this process is further divided into two categories: one is suspended in the fluid, and the other is deposited on the bottom.When the local Shields number of sediment is greater than the critical Shields number, the deposited sediment will be transformed into the suspended sediment under the action of ocean currents. The calculation formulae of the local Shields numbers θ and the critical Shields numbers 

θcr of sediment is given as [23,24

]

𝜃=𝑈2𝑓(𝜌𝑠/𝜌𝑓−1)𝑔𝑑50,�=��2(��/��−1)��50,(1)

𝜃𝑐𝑟=0.31+1.2𝐷∗+0.055(1−𝑒−0.02𝐷∗),���=0.31+1.2�*+0.055(1−�−0.02�*),(2)

𝐷∗=𝑑50𝜌𝑓(𝜌𝑠−𝜌𝑓)𝑔/𝜇2−−−−−−−−−−−−−−√3,�*=�50��(��−��)�/�23,(3)where 

Uf is the shearing velocity of bed surface, 

ρs is the density of the sediment particle, 

ρf is the fluid density, g is the acceleration of gravity, d

50 is the median size of sediment, and μ is the dynamic viscosity of sediment.And each sediment particle suspended in the fluid obeys the equations for mass conservation and energy conservation

∂𝑐𝑠∂𝑡+∇⋅(𝑢𝑐𝑠)=0,∂��∂�+∇⋅(�¯��)=0,(4)

∂𝑢𝑠∂𝑡+𝑢⋅∇𝑢𝑠=−1𝜌𝑠∇𝑃+𝐹−𝐾𝑓𝑠𝜌𝑠𝑢𝑟,∂��∂�+�¯⋅∇��=−1��∇�+�−�������,(5)where 

cs is the concentration of the sediment particle, 

𝑢�¯ is the mean velocity vector of the fluid and the sediment particle, 

us is the velocity of the sediment particle, 

fs is the volume fraction of the sediment particle, P is the pressure, F is the volumetric and viscous force, K is the drag force, and 

ur is the relative velocity.

3. Numerical Setup and Modeling

In this paper, a three-dimensional submarine cable local scouring simulation model is established by FLOW-3D. Based on the numerical simulation, the process of the submarine cable, which gradually changes from semi-exposed to the spanning state under the steady-state ocean current, is studied. The geometric modeling, the mesh division, the physical field setup, and the grid independent test of CFD numerical model are as follows.

3.1. Geometric Modeling and Mesh Division

A three-dimensional (3D) numerical model of the local scouring of a semi-exposed submarine cable is established, which is shown in Figure 1. The dimensions of the model are marked in Figure 1. The inlet direction of the ocean current is defined as the upstream of the submarine cable (referred to as upstream), and the outlet direction of the ocean current is defined as the downstream of the submarine cable (referred to as downstream).

Jmse 11 01349 g001 550

Figure 1. Three-dimensional finite element model of local scouring of semi-exposed submarine cable.

The submarine cable with a diameter of 0.2 m is positioned on sediment that is initially in a semi-exposed state. When the length of the span is short, the submarine cable will not show obvious deformation due to gravity or scouring from the ocean current. Therefore, the submarine cable surface is set as the fixed boundary. The model’s left boundary is set as the inlet, the right boundary is set as the outlet, the front and rear boundaries are set as symmetry, and the bottom boundary is set as the non-slip wall. Since the water depth above the submarine cable is more than 0.6 m in practice, the top boundary of the model is also set as symmetry. The sediment near the inlet and the outlet will be carried by ocean currents, which leads to the abnormal scouring terrain. At each end of the sediment, a baffle (thickness of 3 cm) is installed to ensure that the simulation results can reflect the real situation.

Due to the fact that the flow field around the semi-exposed submarine cable is not a simple two-dimensional symmetrical distribution, it should be solved by three-dimensional numerical simulation. Considering the accuracy and efficiency of the calculation, the size of mesh is set to 0.02 m. The total number of meshes after the dissection is 133,254.

3.2. Physical Field Setup

The CFD finite element model contains four physical field modules: sediment scouring module, gravity and non-inertial reference frame module, density evaluation module, and viscosity and turbulence module. In this paper, the renormalization group (RNG) kε turbulence model is used, which has high computational accuracy for turbulent vortices. Therefore, this turbulence model is suitable for calculating the sediment scouring process around the semi-exposed submarine cable [25]. The key parameters of the numerical simulation are referring to the survey results of submarine sediments in the Korean Peninsula [26], as listed in Table 1.Table 1. Key parameters of numerical simulation.

Table

3.3. Mesh Independent Test

In order to eliminate errors caused by the quantity of grids in the calculation process, two sizes of mesh are set on the validation model, and the scour profiles under different mesh sizes are compared. The validation model is shown in Figure 2, and the scouring terrain under different mesh size is given in Figure 3.

Jmse 11 01349 g002 550

Figure 2. Validation model.

Jmse 11 01349 g003 550

Figure 3. Scouring terrain under different mesh sizes.

It can be seen from Figure 3 that with the increase in the number of meshes, the scouring terrain of the verification model changes slightly, and the scouring depth is basically unchanged. Considering the accuracy of the numerical simulation and the calculation’s time cost, it is reasonable to consider setting the mesh size to 0.02 m.

4. Results and Analysis

4.1. Analysis of Local Scouring Process

Based on the CFD finite element numerical simulation, the local scouring process of the submarine cable under the steady-state ocean current is analyzed. The end time of the simulation is 9 h, the initial time step is 0.01 s, and the fluid velocity is 0.40 m/s. Simulation results are saved every minute. Figure 4 illustrates the scouring terrain around the semi-exposed submarine cable, which has been scoured by the steady-state current for 5 h.

Jmse 11 01349 g004 550

Figure 4. Scouring terrain around semi-exposed submarine cable (scour for 5 h).

As can be seen from Figure 4, three scouring holes were separately formed in the upstream wake position and downstream of the semi-exposed submarine cable. The scouring holes are labeled according to their locations. The variation of the scouring terrain around the semi-exposed submarine cable over time is given in Figure 5. The red circle in the picture corresponds to the position of the submarine cable, and the red box in the legend marks the time when the submarine cable is spanning.

Jmse 11 01349 g005 550

Figure 5. Variation of scouring terrain around semi-exposed submarine cable adapted to time.

From Figure 5, in the first hour of scouring, the upstream (−0.5 m to −0.1 m) and downstream (0.43 m to 1.5 m) scouring holes appeared. The upstream scouring hole was relatively flat with depth of 0.04 m. The depth of the downstream scouring hole increased with the increase in distance, and the maximum depth was 0.13 m. The scouring hole that developed at the wake position was very shallow, and its depth was only 0.007 m.

In the second hour of scouring, the upstream scouring hole’s depth remained nearly constant. The depth of the downstream scouring hole only increased by 0.002 m. The scouring hole at the wake position developed steadily, and its depth increased from 0.007 m to 0.014 m.

The upstream and downstream scouring holes did not continue to develop during the third to the sixth hour. Compared to the first two hours, the development of scouring holes at the wake position accelerated significantly, with an average growth rate of 0.028 m/h. The growth rate in the fifth hour of the scouring hole at the wake position was slightly faster than the other times. After 6 h of scouring, the sediment on the right side of the submarine cable had been hollowed out.

In the seventh and the eighth hour of scouring, the upstream scouring hole’s depth increased slightly, the downstream scouring hole still remained stable, and the depth of the scouring hole at wake position increased by 0.019 m. The sediment under the submarine cable was gradually eroded as well. By the end of the eighth hour, the lower right part of the submarine cable had been exposed to water as well.

At 8 h 21 min of the scouring, the submarine cable was completely spanned, and the scouring holes were connected to each other. Within the next 10 min, the development of the scouring holes sped up significantly, and the maximum depth of scouring holes increased greatly to 0.27 m.

In reference [17], researchers have studied the local scouring process of semi-buried pipelines in sandy riverbeds through experiments. The test results show that the scouring process can be divided into a start-up stage, micropore formation stage, extension stage, and equilibrium stage. In this paper, the first three stages are simulated, and the results are in good agreement with the experiment, which proves the accuracy of the present numerical model.

In this research, the velocity of ocean currents at the sediment surface is defined as the shear velocity, which plays an important role in the process of local scouring. Figure 6 provides visual data on how the shear velocity varies over time.

Jmse 11 01349 g006 550

Figure 6. Shear velocity changes in the scouring process.

The semi-exposed submarine cable protrudes from the seabed, which makes the shear velocity of its surface much higher than other locations. After the submarine cable is spanned, the shear velocity of the scouring hole surface below it is taken. This is the reason for the sudden change of shear velocity at the submarine cable’s location in Figure 6.The shear velocity in the initial state of the upstream scouring hole is obviously greater than in subsequent times. After 1 h of scouring, the shear velocity in the upstream scouring hole rapidly decreased from 1.1 × 10

−2 m/s to 3.98 × 10

−3 m/s and remained stable until the end of the sixth hour. This phenomenon explains why the upstream scouring hole developed rapidly in the first hour but remained stable for the following 5 h.The shear velocity in the downstream scouring hole reduced at first and then increased; its initial value was 1.41 × 10

−2 m/s. It took approximately 5 h for the shear velocity to stabilize, and the stable shear velocity was 2.26 × 10

−3 m/s. Therefore, compared with the upstream scouring hole, the downstream scouring hole was deeper and required more time to reach stability.The initial shear velocity in the scouring hole at the wake position was only 7.1 × 10

−3 m/s, which almost does not change in the first hour. This leads to a very slow development of the scouring hole at the wake position in the early stages. The maximum shear velocity in this scouring hole gradually increased to 1.05 × 10

−2 m/s from the second to the fifth hour, and then decreased to 6.61 × 10

−3 m/s by the end of the eighth hour. This is why the scouring hole at the wake position grows fastest around the fifth hour. Consistent with the pattern of change in the scouring hole’s terrain, the location of the maximal shear velocity also shifted to the right with time.

The shear velocity of all three scouring holes rose dramatically in the last hour. Combined with the terrain in Figure 5, this can be attributed to the complete spanning of the submarine cable.

From Equations (3)–(5), one can see the movement of the sediment is related directly with the sediment’s critical Shields number, sediment density, and ocean current velocity. Based on the parameters in Table 1, the influence of the above parameters on the local scouring process of semi-exposed submarine cables will be discussed.

4.2. Influence Factors

4.2.1. Sediment’s Critical Shields Number

The sediment’s critical Shields number 

θcr is set as 0.02, 0.03, 0.04, 0.05, 0.06, and 0.07, and the variations of scouring terrain over time under each 

θcr are displayed in Figure 7.

Jmse 11 01349 g007 550

Figure 7. Influence of sediment’s critical Shields number 

θcr on local scouring around semi-exposed submarine cable: (a

θcr = 0.02; (b

θcr = 0.03; (c

θcr = 0.04; (d

θcr = 0.05; (e

θcr = 0.06; and (f

θcr = 0.07.From Figure 7, one can see that a change in 

θcr will affect the depth of the upstream scouring hole and the development speed of the scouring hole at the wake position, but it will have no significant impact on the expansion of the downstream scouring hole.Under conditions of different 

θcr, the upstream scouring hole will reach a temporary plateau within 1 h, at which time the stable depth will be about 0.04 m. When 

θcr ≤ 0.05, the upstream scouring hole will continue to expand after a few hours. The stable time is obviously affected by 

θcr, which will gradually increase from 1 h to 11 h with the increase in 

θcr. The terrain of the upstream scouring hole will gradually convert to deep on the left and to shallow on the right. Since the scouring hole at the wake position has not been stable, its state at the time of submarine cable spanning is studied emphatically. In the whole process of scouring, the scouring hole at the wake position continues to develop and does not reach a stable state. With the increase in 

θcr, the development velocity of the scouring hole at the wake position will decrease considerably. Its average evolution velocity decreases from 3.88 cm/h to 1.62 cm/h, and its depth decreases from 21.9 cm to 18.8 cm. Under the condition of each 

θcr, the downstream scouring hole will stabilize within 1 h, and the stable depth will be basically unchanged (all about 13.5 cm).As 

θcr increases, so does the sediment’s ability to withstand shearing forces, which will cause it to become increasingly difficult to be eroded or carried away by ocean currents. This effect has been directly reflected in the depth of scouring holes (upstream and wake position). Due to the blocking effect of semi-exposed submarine cables, the wake is elongated, which is why the downstream scouring hole develops before the scouring hole at the wake position and quickly reaches a stable state. However, due to the high wake intensity, this process is not significantly affected by the change of 

θcr.

4.2.2. Sediment Density

The density of sediment 

ρs is set as 1550 kg/m

3, 1600 kg/m

3, 1650 kg/m

3, 1700 kg/m

3, 1750 kg/m

3, and 1800 kg/m

3, and the variation of scouring terrain over time under each 

ρs are displayed in Figure 8.

Jmse 11 01349 g008 550

Figure 8. Influence of sediment density 

ρs on local scouring around semi-exposed submarine cable: (a

ρs = 1550 kg/m

3; (bρs = 1600 kg/m

3; (cρs = 1650 kg/m

3; (dρs = 1700 kg/m

3; (eρs = 1750 kg/m

3; and (f

ρs = 1800 kg/m

3.From Figure 8, one can see that a change in 

ρs will also affect the depth of the upstream scouring hole and the development speed of the scouring hole at the wake position. In addition, it can even have an impact on the downstream scouring hole depth.Under different 

ρs conditions, the upstream scouring hole will always reach a temporary stable state in 1 h, at which time the stable depth will be 0.04 m. When 

ρs ≤ 1750 kg/m

3, the upstream scouring hole will continue to expand after a few hours. The stabilization time of upstream scouring hole is more clearly affected by 

ρs, which will gradually increase from 3 h to 13 h with the increase in 

ρs. The terrain of the upstream scouring hole will gradually change to deep on the left and to shallow on the right. Since the scouring hole at the wake position has not been stable, its state at the time of the submarine cable spanning is studied emphatically, too. In the whole process of scouring, the scouring hole at the wake position continues to develop and does not reach a stable state. When 

ρs is large, the development rate of scouring hole obviously decreased with time. With the increase in 

ρs, the development velocity of the scouring hole at the wake position reduces from 3.38 cm/h to 1.14 cm/h, and the depth of this scouring hole declines from 20 cm to 15 cm. As 

ρs increases, the stabilization time of the downstream scouring hole increases from less than 1 h to about 2 h, but the stabilization depth of the downstream scouring hole remains essentially the same (all around 13.5 cm).As can be seen from Equation (1), the increase in 

ρs will reduce the Shields number, thus weakening the shear action of the sediment by the ocean current, which explains the extension of the stability time of the upstream scouring hole. At the same time, with the increase in the depth of scouring hole at the wake position, its shear velocity will decreases. Therefore, under a larger 

ρs value, the development speed of scouring hole at the wake position will decrease significantly with time. Possibly for the same reason, 

ρs can affect the development rate of downstream scouring hole.

4.2.3. Ocean Current Velocity

The ocean current velocity v is set as 0.35 m/s, 0.40 m/s, 0.45 m/s, 0.50 m/s, 0.55 m/s, and 0.60 m/s. Figure 9 presents the variation in scouring terrain with time for each v.

Jmse 11 01349 g009 550

Figure 9. Influence of ocean current velocity v on local scouring around semi-exposed submarine cable: (av = 0.35 m/s; (bv = 0.40 m/s; (cv = 0.45 m/s; (dv = 0.50 m/s; (ev = 0.55 m/s; and (fv = 0.60 m/s.

Changes in v affect the depth of the upstream and downstream scouring holes, as well as the development velocity of the wake position and downstream scouring holes.

When v ≤ 0.45 m/s, the upstream scouring hole will reach a temporary stable state within 1 h, at which point the stable depth will be 0.04 m. The stabilization time of the upstream scouring hole is affected by v, which will gradually decrease from 15 h to 3 h with the increase in v. When v > 0.45 m/s, the upstream scouring hole is going to expand continuously. With the increase in v, its average development velocity increases from 6.68 cm/h to 8.66 cm/h, and its terrain changes to deep on the left and to shallow on the right. When the submarine cable is spanning, special attention should be paid to the depth of the scouring hole at the wake position. Throughout whole scouring process, the scouring hole at the wake position continues to develop and does not reach a stable state. With the increase in v, the depth of scouring hole at the wake position will increase from 14 cm to 20 cm, and the average development velocity will increase from 0.91 cm/h to 10.43 cm/h. As v increases, the time required to stabilize the downstream scouring hole is shortened from 1to 2 h to less than 1 h, but the stable depth is remains nearly constant at 13.5 cm.

An increase in v will increase the shear velocity. Therefore, when the depth of the scouring hole increases, the shear velocity in the hole will also increase, which can deepen both the upstream and downstream scouring hole. According to Equation (1), the Shields number is proportional to the square of the shear velocity. The increase in shear velocity significantly intensifies local scouring, which increases the development rate of scouring holes at the wake position and downstream.

4.3. Variation Rule of Spanning Time

In this paper, the spanning time is defined as the time taken for a semi-exposed submarine cable (initial state) to become a spanning submarine cable. Figure 10 illustrates the effect of the above parameters on the spanning time of the semi-exposed submarine cable.

Jmse 11 01349 g010 550

Figure 10. Influence of different parameters on spanning time of the semi-exposed submarine cable: (a) Sediment critical Shields number; (b) Sediment density; and (c) Ocean current velocity.From Figure 10a, the spanning time monotonically increases with the increase in the critical Shields number of sediment. However, the slope of the curve decreases first and then increases, and the inflection point is at 

θcr = 4.59 × 10

−2. The relationship between spanning time t and sediment’s critical Shields number 

θcr can be formulated by a cubic function as shown in Equation (6):

𝑡=−2.98+6.76𝜃𝑐𝑟−1.45𝜃2𝑐𝑟+0.11𝜃3𝑐𝑟.�=−2.98+6.76���−1.45���2+0.11���3.(6)It can be seen from Figure 10b that with the increase in the sediment density, the spanning time increases monotonically and linearly. The relationship between the spanning time t and the sediment’s density 

ρs can be formulated by the first order function as shown in Equation (7):

𝑡=−41.59+30.54𝜌𝑠.�=−41.59+30.54��.(7)Figure 10c shows that with the increase in the ocean current velocity, the spanning time decreases monotonically. The slope of the curve increases with the increase in the ocean current velocity, so it can be considered that there is saturation of the ocean current velocity effect. The relationship between the spanning time t and the ocean current velocity v can be formulated by the exponential function

𝑡=0.15𝑣−4.38.�=0.15�−4.38.(8)

5. Conclusions

In this paper, a three-dimensional CFD finite element numerical simulation model is established, which is used to research the local scouring process of the semi-exposed submarine cable under the steady-state ocean current. The relationship between shear velocity and scouring terrain is discussed, the influence of sediment critical Shields number, sediment density and ocean current velocity on the local scouring process is analyzed, and the variation rules of the spanning time of the semi-exposed submarine cable is given. The conclusions are as follows:

  • Under the steady-state ocean currents, scouring holes will be formed at the upstream, wake position and downstream of the semi-exposed submarine cable. The upstream and downstream scouring holes develop faster, which will reach a temporary stable state at about 1 h after the start of the scouring. The scouring hole at the wake position will continue to expand at a slower rate and eventually lead to the spanning of the submarine cable.
  • There is a close relationship between the distribution of shear velocity and the scouring terrain. As the local scouring process occurs, the location of the maximum shear velocity within the scouring hole shifts and causes the bottom of the hole to move as well.
  • When the sediment’s critical Shields number and density are significantly large and ocean current velocity is sufficiently low, the duration of the stable state of the upstream scouring hole will be prolonged, and the average development velocity of the scouring holes at the wake position and downstream will be reduced.
  • The relationship between the spanning time and the critical Shields number θcr can be formulated as a cubic function, in which the curve’s inflection point is θcr = 4.59 × 10−2. The relationship between spanning time and sediment density can be formulated as a linear function. The relationship between spanning time and ocean current velocity can be formulated by exponential function.

Based on the conclusions of this paper, even when it is too late to take measures or when the exposed position of the submarine cable cannot be located, the degree of burial depth development still can be predicted. This prediction is important for the operation and maintenance of the submarine cable. However, the study still leaves something to be desired. Only the local scouring process under the steady-state ocean current was studied, which is an extreme condition. In practice, exposed submarine cables are more likely to be scoured by reciprocating ocean currents. In the future, we will investigate the local scouring of submarine cables under the reciprocating ocean current.

Author Contributions

Conceptualization, Y.H. and Q.L.; methodology, Q.L., P.Z. and H.T.; software, Q.L.; validation, Q.L., L.C. and W.T.; writing—original draft preparation, Q.L.; writing—review and editing, Y.H. and Q.L.; supervision, Y.H. and L.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the [Smart Grid Joint Fund Key Project between National Natural Science Foundation of China and State Grid Corporation] grant number [U1766220].

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data supporting the reported results cannot be shared at this time, as they have been used in producing more publications on this research.

Acknowledgments

This work is supported by the Smart Grid Joint Fund Key Project of the National Natural Science Foundation of China and State Grid Corporation (Grant No. U1766220).

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Taormina, B.; Bald, J.; Want, A.; Thouzeau, G.; Lejart, M.; Desroy, N.; Carlier, A. A review of potential impacts of submarine power cables on the marine environment: Knowledge gaps, recommendations and future directions. Renew. Sust. Energ. Rev. 201896, 380–391. [Google Scholar] [CrossRef]
  2. Gulski, E.; Anders, G.J.; Jogen, R.A.; Parciak, J.; Siemiński, J.; Piesowicz, E.; Paszkiewicz, S.; Irska, I. Discussion of electrical and thermal aspects of offshore wind farms’ power cables reliability. Renew. Sust. Energ. Rev. 2021151, 111580. [Google Scholar] [CrossRef]
  3. Wang, W.; Yan, X.; Li, S.; Zhang, L.; Ouyang, J.; Ni, X. Failure of submarine cables used in high-voltage power transmission: Characteristics, mechanisms, key issues and prospects. IET Gener. Transm. Distrib. 202115, 1387–1402. [Google Scholar] [CrossRef]
  4. Chen, H.; Chen, Z.; Lu, H.; Wu, C.; Liang, J. Protection method for submarine cable detection and exposed suspension problem in Qiongzhou straits. Telecom Pow. Technol. 201936, 60–61+63. [Google Scholar]
  5. Zhu, J.; Ren, B.; Dong, P.; Chen, W. Vortex-induced vibrations of a free spanning submarine power cable. Ocean Eng. 2023272, 113792. [Google Scholar] [CrossRef]
  6. Sumer, B.M.; Jensen, H.R.; Mao, Y.; Fredsøe, J. Effect of lee-wake on scour below pipelines in current. J. Waterw. Port Coast. Ocean. Eng. 1988114, 599–614. [Google Scholar] [CrossRef]
  7. Chiew, Y.M. Prediction of maximum scour depth at submarine pipelines. J. Hydraul. Eng. 1991117, 452–466. [Google Scholar] [CrossRef]
  8. Mastbergen, D.R.; Vandenberg, J.H. Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology 200350, 625–637. [Google Scholar] [CrossRef]
  9. Dey, S.; Singh, N.P. Clear-water scour depth below underwater pipelines. J. Hydro-Env. Res. 20071, 157–162. [Google Scholar] [CrossRef]
  10. Dey, S.; Singh, N.P. Clear-water scour below underwater pipelines under steady flow. J. Hydraul. Eng. 2008134, 588–600. [Google Scholar] [CrossRef]
  11. Liang, D.; Cheng, L. Numerical study of scour around a pipeline bundle. Proc. Inst. Civil Eng. Mar. Eng. 2008161, 89–95. [Google Scholar] [CrossRef]
  12. Yang, L.; Guo, Y.; Shi, B.; Kuang, C.; Xu, W.; Cao, S. Study of scour around submarine pipeline with a rubber plate or rigid spoiler in wave conditions. J. Waterw. Port Coast. Ocean Eng. 2012138, 484–490. [Google Scholar] [CrossRef]
  13. Li, Y.; Ong, M.C.; Fuhrman, D.R.; Larsen, B.E. Numerical investigation of wave-plus-current induced scour beneath two submarine pipelines in tandem. Coast. Eng. 2020156, 103619. [Google Scholar] [CrossRef]
  14. Guan, D.; Hsieh, S.C.; Chiew, Y.M.; Low, Y.M.; Wei, M. Local scour and flow characteristics around pipeline subjected to vortex-induced vibrations. J. Hydraul. Eng. 2020146, 04019048. [Google Scholar] [CrossRef]
  15. Liu, M.M.; Jin, X.; Wang, L.; Yang, F.; Tang, J. Numerical investigation of local scour around a vibrating pipeline under steady currents. Ocean Eng. 2021221, 108546. [Google Scholar] [CrossRef]
  16. Huang, J.; Yin, G.; Ong, M.C.; Myrhaug, D.; Jia, X. Numerical investigation of scour beneath pipelines subjected to an oscillatory flow condition. J. Mar. Sci. Eng. 20219, 1102. [Google Scholar] [CrossRef]
  17. Cui, F.; Du, Y.; Hao, X.; Peng, S.; Bao, Z.; Peng, S. Experimental study on local scour and related mechanical effects at river-crossing underwater oil and gas pipelines. Adv. Civ. Eng. 20212021, 6689212. [Google Scholar] [CrossRef]
  18. Li, B.; Ma, H. Scouring mechanism of suspended and partially-buried pipelines under steady flow. Coast. Eng. 2022177, 104201. [Google Scholar] [CrossRef]
  19. Najafzadeh, M.; Oliveto, G. Scour propagation rates around offshore pipelines exposed to currents by applying data-driven models. Water 202214, 493. [Google Scholar] [CrossRef]
  20. Zhu, Y.; Xie, L.; Wong, T.; Su, T. Development of three-dimensional scour below pipelines in regular waves. J. Mar. Sci. Eng. 202210, 124. [Google Scholar] [CrossRef]
  21. Ma, H.; Li, B. CFD-CGDEM coupling model for scour process simulation of submarine pipelines. Ocean Eng. 2023271, 113789. [Google Scholar] [CrossRef]
  22. Hu, K.; Bai, X.; Vaz, M.A. Numerical simulation on the local scour processing and influencing factors of submarine pipeline. J. Mar. Sci. Eng. 202311, 234. [Google Scholar] [CrossRef]
  23. Yang, B.; Gao, F.; Wu, Y. Experimental study on local scour of sandy seabed under submarine pipeline in unidirectional currents. Eng. Mech. 200825, 206–210. [Google Scholar]
  24. Cheng, Y.; Wang, X.; Luo, W.; Huang, X.; Lyu, X. Experimental study of local scour around a downstream inclined pile under combined waves and current. Adv. Eng. Sci. 202153, 64–71. [Google Scholar]
  25. Lu, Y.; Zhou, L.; Shen, X. Different turbulence models for simulating a liquid-liquid hydro cyclone. J. Tsinghua Univ. 200141, 105–109. [Google Scholar]
  26. Yun, D.H.; Kim, Y.T. Experimental study on settlement and scour characteristics of artificial reef with different reinforcement type and soil type. Geotext. Geomembr. 201846, 448–454. [Google Scholar] [CrossRef]
The distribution of the computed maximum current speed during the entire duration of the NAMI DANCE and FLOW-3D simulations. The resolution of computational domain is 10 m

Performance Comparison of NAMI DANCE and FLOW-3D® Models in Tsunami Propagation, Inundation and Currents using NTHMP Benchmark Problems

NTHMP 벤치마크 문제를 사용하여 쓰나미 전파, 침수 및 해류에서 NAMI DANCE 및 FLOW-3D® 모델의 성능 비교

Pure and Applied Geophysics volume 176, pages3115–3153 (2019)Cite this article

Abstract

Field observations provide valuable data regarding nearshore tsunami impact, yet only in inundation areas where tsunami waves have already flooded. Therefore, tsunami modeling is essential to understand tsunami behavior and prepare for tsunami inundation. It is necessary that all numerical models used in tsunami emergency planning be subject to benchmark tests for validation and verification. This study focuses on two numerical codes, NAMI DANCE and FLOW-3D®, for validation and performance comparison. NAMI DANCE is an in-house tsunami numerical model developed by the Ocean Engineering Research Center of Middle East Technical University, Turkey and Laboratory of Special Research Bureau for Automation of Marine Research, Russia. FLOW-3D® is a general purpose computational fluid dynamics software, which was developed by scientists who pioneered in the design of the Volume-of-Fluid technique. The codes are validated and their performances are compared via analytical, experimental and field benchmark problems, which are documented in the ‘‘Proceedings and Results of the 2011 National Tsunami Hazard Mitigation Program (NTHMP) Model Benchmarking Workshop’’ and the ‘‘Proceedings and Results of the NTHMP 2015 Tsunami Current Modeling Workshop”. The variations between the numerical solutions of these two models are evaluated through statistical error analysis.

현장 관찰은 연안 쓰나미 영향에 관한 귀중한 데이터를 제공하지만 쓰나미 파도가 이미 범람한 침수 지역에서만 가능합니다. 따라서 쓰나미 모델링은 쓰나미 행동을 이해하고 쓰나미 범람에 대비하는 데 필수적입니다.

쓰나미 비상 계획에 사용되는 모든 수치 모델은 검증 및 검증을 위한 벤치마크 테스트를 받아야 합니다. 이 연구는 검증 및 성능 비교를 위해 NAMI DANCE 및 FLOW-3D®의 두 가지 숫자 코드에 중점을 둡니다.

NAMI DANCE는 터키 중동 기술 대학의 해양 공학 연구 센터와 러시아 해양 연구 자동화를 위한 특별 조사국 연구소에서 개발한 사내 쓰나미 수치 모델입니다. FLOW-3D®는 Volume-of-Fluid 기술의 설계를 개척한 과학자들이 개발한 범용 전산 유체 역학 소프트웨어입니다.

코드의 유효성이 검증되고 분석, 실험 및 현장 벤치마크 문제를 통해 코드의 성능이 비교되며, 이는 ‘2011년 NTHMP(National Tsunami Hazard Mitigation Program) 모델 벤치마킹 워크숍의 절차 및 결과’와 ”절차 및 NTHMP 2015 쓰나미 현재 모델링 워크숍 결과”. 이 두 모델의 수치 해 사이의 변동은 통계적 오류 분석을 통해 평가됩니다.

The distribution of the computed maximum current speed during the entire duration of the NAMI DANCE and FLOW-3D simulations. The resolution of computational domain is 10 m
The distribution of the computed maximum current speed during the entire duration of the NAMI DANCE and FLOW-3D simulations. The resolution of computational domain is 10 m

References

  • Allan, J. C., Komar, P. D., Ruggiero, P., & Witter, R. (2012). The March 2011 Tohoku tsunami and its impacts along the U.S. West Coast. Journal of Coastal Research, 28(5), 1142–1153. https://doi.org/10.2112/jcoastres-d-11-00115.1.Article Google Scholar 
  • Apotsos, A., Buckley, M., Gelfenbaum, G., Jafe, B., & Vatvani, D. (2011). Nearshore tsunami inundation and sediment transport modeling: towards model validation and application. Pure and Applied Geophysics, 168(11), 2097–2119. https://doi.org/10.1007/s00024-011-0291-5.Article Google Scholar 
  • Barberopoulou, A., Legg, M. R., & Gica, E. (2015). Time evolution of man-made harbor modifications in San Diego: effects on Tsunamis. Journal of Marine Science and Engineering, 3, 1382–1403.Article Google Scholar 
  • Basu, D., Green, S., Das, K., Janetzke, R. and Stamatakos, J. (2009). Numerical Simulation of Surface Waves Generated by a Subaerial Landslide at Lituya Bay, Alaska. Proceedings of 28th International Conference on Ocean, Offshore and Arctic Engineering. Honolulu, Hawaii, USA.
  • Briggs, M. J., Synolakis, C. E., Harkins, G. S., & Green, D. R. (1995). Laboratory experiments of tsunami run-up on a circular island. Pure and Applied Geophysics, 144(3/4), 569–593.Article Google Scholar 
  • Cheung, K. F., Bai, Y., & Yamazaki, Y. (2013). Surges around the Hawaiian Islands from the 2011 Tohoku Tsunami. Journal of Geophysical Research: Oceans, 118, 5703–5719. https://doi.org/10.1002/jgrc.20413.Google Scholar 
  • Choi, B. H., Dong, C. K., Pelinovsky, E., & Woo, S. B. (2007). Three-dimensional Simulation of Tsunami Run-up Around Conical Island. Coastal Engineering, 54, 618–629.Article Google Scholar 
  • Cox, D., T. Tomita, P. Lynett, R.A., Holman. (2008). Tsunami Inundation with Macroroughness in the Constructed Environment. Proceedings of 31st International Conference on Coastal Engineering, ASCE, pp. 1421–1432.
  • Flow Science. (2002). FLOW-3D User’s Manual.
  • Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39, 201–225.Article Google Scholar 
  • Horrillo, J., Grilli, S. T., Nicolsky, D., Roeber, V., & Zang, J. (2015). Performance benchmarking Tsunami models for NTHMP’s inundation mapping activities. Pure and Applied Geophysics, 172, 869–884.Article Google Scholar 
  • http://nws.weather.gov/nthmp/documents/nthmpWorkshopProcMerged.pdf.
  • http://nws.weather.gov/nthmp/documents/NTHMP_Currents_Workshop_Report.pdf.
  • Kim, K. O., Kim, D. C., Choi, B.-H., Jung, T. K., Yuk, J. H., & Pelinovsky, E. (2015). The role of diffraction effects in extreme run-up inundation at Okushiri Island due to 1993 Tsunami. Natural Hazards and Earth Systems Sciences, 15, 747–755.Article Google Scholar 
  • Liu, P. L.-F. (1994). Model equations for wave propagations from deep to shallow water. (P.-F. Liu, Ed.) Advances in Coastal and Ocean Engineering, 1, 125–158.
  • Liu, P. L.-F., Yeh, H., & Synolakis, C. E. (2008). Advanced numerical models for simulating Tsunami waves and run-up. Advances in Coastal and Ocean Engineering, 10, 344.Google Scholar 
  • Lynett, P. J., Borrero, J., Son, S., Wilson, R., & Miller, K. (2014). Assessment of the tsunami-induced current hazard. Geophysical Research Letters, 41, 2048–2055. https://doi.org/10.1002/2013GL058680.Article Google Scholar 
  • Lynett, P. J., Gately, K., Wilson, R., Montoya, L., Arcas, D., Aytore, B., et al. (2017). Inter-model analysis of Tsunami-induced coastal currents. Ocean Modelling, 114, 14–32.Article Google Scholar 
  • Lynett, P. J., Wu, T.-R., & Liu, P. L.-F. (2002). Modeling wave run-up with depth-integrated equations. Coastal Engineering, 46(2), 89–107.Article Google Scholar 
  • Macias, J., Castro, M. J., Ortega, S., Escalante, C., & Gonzalez-Vida, J. M. (2017). Performance benchmarking of Tsunami-HySEA model for nthmp’s inundation mapping activities. Pure and Applied Geophysics, 174, 3147–3183.Article Google Scholar 
  • Matsuyama, M., & Tanaka, H. (2001). An experimental study of the highest run-up height in the 1993 Hokkaidō Nansei-Oki Earthquake Tsunami. Proceedings of ITS, 2001, 879–889.Google Scholar 
  • National Tsunami Hazard Mitigation Program. 2012. Proceedings and Results of the 2011 NTHMP Model Benchmarking Workshop. Boulder: U.S. Department of Commerce/NOAA/NTHMP; (NOAA Special Report). p. 436.
  • National Tsunami Hazard Mitigation Program. (2017). Proceedings and Results of the National Tsunami Hazard Mitigation Program 2015 Tsunami Current Modeling Workshop, February 9-10, 2015, Portland, Oregon: compiled by Patrick Lynett and Rick Wilson, p 194.
  • Necmioglu, O., & Ozel, N. M. (2014). An earthquake source sensitivity analysis for Tsunami propagation in the Eastern Mediterranean. Oceanography, 27(2), 76–85.Article Google Scholar 
  • Nichols, B.D. and Hirt, C.W. (1975). Methods for Calculating Multi-Dimensional, Transient Free Surface Flows Past Bodies. Proceedings of 1st International Conference Num. Ship Hydrodynamics. Gaithersburg.
  • Nicolsky, D. J., Suleimani, E. N., & Hansen, R. A. (2011). Validation and verification of a numerical model for Tsunami propagation and run-up. Pure and Applied Geophysics, 168(6), 1199–1222.Article Google Scholar 
  • NOAA Center for Tsunami Research: Tsunami Run-up onto a Complex Three-dimensional Beach; Monai Valley. (n.d). Retrieved from: https://nctr.pmel.noaa.gov/benchmark/Laboratory/Laboratory_MonaiValley/.
  • Park, H., Cox, D. T., Lynett, P. J., Wiebe, D. M., & Shin, S. (2013). Tsunami inundation modeling in constructed environments: a physical and numerical comparison of free-surface elevation, velocity, and momentum flux. Coastal Engineering, 79, 9–21.Article Google Scholar 
  • Patel, V. M., Dholakia, M. B., & Singh, A. P. (2016). Emergency preparedness in the case of Makran Tsunami: a case study on Tsunami risk visualization for the Western Parts of Gujarat, India. Geomatics Natural Hazard and Risk, 7(2), 826–842.Article Google Scholar 
  • Pelinovsky, E., Kim, D.-C., Kim, K.-O., & Choi, B.-H. (2013). Three-dimensional simulation of extreme run-up heights during the 2004 Indonesian and 2011 Japanese Tsunamis. Vienna: EGU General Assembly.Google Scholar 
  • Rueben, M., Holman, R., Cox, D., Shin, S., Killian, J., & Stanley, J. (2011). Optical measurements of Tsunami inundation through an urban waterfront modeled in a large-scale laboratory basin. Coastal Engineering, 58, 229–238.Article Google Scholar 
  • Shuto, N. (1991). Numerical simulation of Tsunamis—its present and near future. Natural Hazards, 4, 171–191.Article Google Scholar 
  • Synolakis, C. E. (1986). The run-up of long waves. Ph.D. Thesis. California Institute of Technology, Pasadena, California.
  • Synolakis, C. E., Bernard, E. N., Titov, V. V., Kanoglu, U. & Gonzalez, F. (2007). Standards, criteria, and procedures for NOAA evaluation of Tsunami Numerical Models. 55 p. Seattle, Washington: NOAA OAR Special Report, Contribution No 3053, NOAA/OAR/PMEL.
  • Synolakis, C. E., Bernard, E. N., Titov, V. V., Kanoglu, U., & Gonzalez, F. I. (2008). Validation and verification of Tsunami numerical models. Pure and Applied Geophysics, 165, 2197–2228.Article Google Scholar 
  • Tolkova, E. (2014). Land-water boundary treatment for a tsunami model with dimensional splitting. Pure and Applied Geophysics, 171(9), 2289–2314.Article Google Scholar 
  • Velioglu, D. (2017). Advanced two- and three-dimensional Tsunami models: benchmarking and validation. Ph.D. Thesis. Middle East Technical University, Ankara.
  • Velioglu, D., Kian, R., Yalciner, A.C. and Zaytsev, A. (2016). Performance assessment of NAMI DANCE in Tsunami evolution and currents using a benchmark problem. (R. Signell, Ed.) J. Mar. Sci. Eng., 4(3), 49.
  • Wu, T. (2001). A unified theory for modeling water waves. Advances in Applied Mechanics, 37, 1–88.Article Google Scholar 
  • Wu, N.-J., Hsiao, S.-C., Chen, H.-H., & Yang, R.-Y. (2016). The study on solitary waves generated by a piston-type wave maker. Ocean Engineering, 117, 114–129.Article Google Scholar 
  • Yalciner, A. C., Dogan, P. and Sukru. E. (2005). December 26 2004, Indian Ocean Tsunami Field Survey, North of Sumatra Island. UNESCO.
  • Yalciner, A. C., Gülkan, P., Dilmen, I., Aytore, B., Ayca, A., Insel, I., et al. (2014). Evaluation of Tsunami scenarios For Western Peloponnese, Greece. Bollettino di Geofisica Teorica ed Applicata, 55, 485–500.Google Scholar 
  • Yen, B. C. (1991). Hydraulic resistance in open channels. In B. C. Yen (Ed.), Channel flow resistance: centennial of manning’s formula (pp. 1–135). Highlands Ranch: Water Resource Publications.Google Scholar 
  • Zaitsev, A. I., Kovalev, D. P., Kurkin, A. A., Levin, B. V., Pelinovskii, E. N., Chernov, A. G., et al. (2009). The Tsunami on Sakhalin on August 2, 2007: mareograph evidence and numerical simulation. Tikhookeanskaya Geologiya, 28, 30–35.Google Scholar 

Download references

Acknowledgements

The authors wish to thank Dr. Andrey Zaytsev due to his undeniable contributions to the development of in-house numerical model, NAMI DANCE. The Turkish branch of Flow Science, Inc. is also acknowledged. Finally, the National Tsunami Hazard Mitigation Program (NTHMP), who provided most of the benchmark data, is appreciated. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Author information

Author notes

  1. Deniz Velioglu SogutPresent address: 1212 Computer Science, Department of Civil Engineering, Stony Brook University, Stony Brook, NY, 11794, USA

Authors and Affiliations

  1. Middle East Technical University, 06800, Ankara, TurkeyDeniz Velioglu Sogut & Ahmet Cevdet Yalciner

Corresponding author

Correspondence to Deniz Velioglu Sogut.

Ethics declarations

Conflicts of Interest

The authors declare no conflict of interest.

Reprints and Permissions

About this article

Cite this article

Velioglu Sogut, D., Yalciner, A.C. Performance Comparison of NAMI DANCE and FLOW-3D® Models in Tsunami Propagation, Inundation and Currents using NTHMP Benchmark Problems. Pure Appl. Geophys. 176, 3115–3153 (2019). https://doi.org/10.1007/s00024-018-1907-9

Download citation

  • Received22 December 2017
  • Revised16 May 2018
  • Accepted24 May 2018
  • Published07 June 2018
  • Issue Date01 July 2019
  • DOIhttps://doi.org/10.1007/s00024-018-1907-9

Keywords

  • Tsunami
  • depth-averaged shallow water
  • Reynolds-averaged Navier–Stokes
  • benchmarking
  • NAMI DANCE
  • FLOW-3D®
Figure 4.2 Protrusion length investigation under R1 regime Q=1 m³/s with non-constrained BC elevation, 3 cm, 4 cm, 5 cm, 6cm & 7 cm from up to down respectively (grid M3 is employed).

Mathematical Modelling of Air-water flow Structure in Circular Dropshafts

Alternate title: Dairesel Düşülü Bacalarda Hava-Su Karışımının Matematiksel Modellemesi
Uçar, Muhammed.   Necmettin Erbakan University (Turkey) ProQuest Dissertations Publishing,  2021. 28840631.

Abstract

Citizens’ daily needs such as; transportation, communication, clean water and sewage are supplied with infrastructure systems. Horizontal and vertical expansion in the cities due to the increase in population leads to serious demand for infrastructural improvements. The infrastructure systems in developing cities are required to be designed in a satisfactory capacity to supply the increasing demand for residential and industrial constructions. The districts having insufficient infrastructure systems inevitably confront heavy traffic, flood, air pollution problems, and also having difficulties with the inadequacy of parking area, clear and potable water, communication. The problems may cause social and health problems over time. At this point, it is wished to emphasize that the primary factor of citycivilization development depends on infrastructural systems and it is meaningful to name the engineering field like civil engineering, literally leads civilization. Dropshafts, commonly used in the urban storm and sewage water systems produced generally circular are used for energy dissipation and flow direction control. Aeration is significant for the working principle of the flow in dropshaft and this study is made mainly for this two-phase (air-water) physics of dropshafts. Chanson showed that aeration and energy dissipation is directly linked to each other (2002), but the influencing factors and the action mechanisms of the factors on the phenomena are not discovered entirely. By the comprehension of the factors, more effective dropshafts will be able to design. This study aims to guide the more comprehensive investigation of design factors using Computational Fluid Dynamics-CFD programs. The reasons for the preference of the programs are the cost-effectiveness of material, workmanship and duration relative to hydraulic modelling. The competence of the inputs, outputs and solution system of the CFD code is validated by the comparison of previous hydraulic modelling results.

Keywords

CFD, Dropshaft, Sewer system, Storm Water System, Two-Phase Flow

Influence of crest geometric on discharge coefficient efficiency of labyrinth weirs

Influence of crest geometric on discharge coefficient efficiency of labyrinth weirs

Erick Mattos-Villarroel a, Jorge Flores-Velázquez b, Waldo Ojeda-Bustamante c, Carlos Díaz-Delgado d, Humberto Salinas-Tapia dShow moreAdd to MendeleyShareCite

aMexican Institute of Water Technology, Mexico
bPostgraduate College, Hydrosciences, Carr. Mex-Tex Km 36.5, Texcoco, Mexico State, 56230, Mexico
cAgricultural Engineering Graduate Program, University of Chapingo, Mexicod
Inter-American Institute of Water Science and Technology, Mexico

https://doi.org/10.1016/j.flowmeasinst.2021.102031Get rights and content

Highlights

  • •Optimizing the geometric design of weirs can improve hydraulic performance.
  • •Labyrinth type weirs allow the discharge capacity to be increased compared to linear weirs.
  • •Hydraulic heads with ratio HT/P > 0.5 generated sub-atmospheric pressures on the side walls of the weir.
  • •Numerical simulation it is a strong tool to analyze and get optimized the weir function.

Abstract

Labyrinth type weirs are structures that, due to their geometry, allow the discharge capacity to be increased compared to linear weirs. They are a favorable option for dam rehabilitation and upstream level control. There are various geometries of labyrinth type weirs such as trapezoidal, triangular or piano key as well as different types of crest profiles. Geometric changes are directly related to hydraulic efficiency. The objective of this work was to analyze the hydraulic performance of a labyrinth type weir, by simulating several geometries of the apex and of the crest using Computational Fluid Dynamics (CFD). For model validation, experimental studies reported in the literature were used. Tests were carried out with trapezoidal and circular apexes and four types of crest profiles: sharp-crest, half-round, quarter-round and Waterways Experiment Station (WES). The results revealed a determination coefficient of R2 = 0.984 between experimental and simulated data with CFD, which provides statistical agreement. Simulations showed that circular-apex weirs are more efficient than those with trapezoidal apex, because they have a higher discharge coefficient (4.7% higher). Of the four types of crest profiles analyzed, the half-round and the WES crest profiles had similar discharge coefficients and were generally greater than those of the sharp-crest and the quarter-round (5.26% y 8.5% higher) profiles. Nevertheless, to facilitate a practical construction process, it is recommended to use a half-round profile. For hydraulic heads with HT/P > 0.5 ratio, all profiles generated sub-atmospheric pressures on the side walls of the weir. However, when HT/P ≈ 0.8 ratio the half-round crest generated a higher negative pressure (−1500 Pa), while the sharp-crest profile managed to increase the pressure by 76% (−350 Pa), but with a greater area of negative pressure. On the other hand, the WES profile reduced the negative-pressure area by 50%.

Keywords

Labyrinth weir

Computational fluids dynamics (CFD)

Discharge coefficient

Apex shape

Crest profile

Figures (12)

  1. Fig. 1. Geometric parameters of a labyrinth weir
  2. Fig. 2. Crest profiles: (A) sharp-crest, (B) half-round, (C) quarter-round, (D) WES
  3. Fig. 3. Apex shapes
  4. Fig. 4. Weir and boundary conditions
  5. Fig. 5. Hydraulic head approach an asymptotic zero-grid spacing value
  6. Fig. 6. Percentage relative error of the discharge coefficient as a function of HT/P
  7. Fig. 7. Comparison of the discharge coefficients obtained numerically against the…
  8. Fig. 8. Pressure distribution in the downstream side walls of the labyrinth weir
  9. Fig. 9. Comparison of the discharge coefficient in trapezoidal apex labyrinth weirs
  10. Fig. 10. Comparison of the discharge coefficient in circular apex labyrinth weirs
  11. Fig. 11. Local drowning at the upstream apex
  12. Fig. 12. Ratio of the discharge coefficient of the circular apex weir with the…
Figure 1. Photorealistic view of an inclined axis TAST (photo A. Stergiopoulou).

CFD Simulations of Tubular Archimedean Screw Turbines Harnessing the Small Hydropotential of Greek Watercourses

Alkistis Stergiopoulou1, Vassilios Stergiopoulos2
1Institut für Wasserwirtschaft, Hydrologie und Konstruktiven Wasserbau, B.O.K.U. University,
Muthgasse 18, 1190 Vienna, (actually Senior Process Engineer at the VTU Engineering in Vienna,
Zieglergasse 53/1/24, 1070 Vienna, Austria).
2 School of Pedagogical and Technological Education, Department of Civil Engineering Educators,
ASPETE Campus, Eirini Station, 15122 Amarousio, Athens, Greece.
Received 4 Jan. 2021; Received in revised form 8 Aug. 2021; Accepted 8 Aug. 2021; Available online 14 Aug. 2021

Abstract

This paper presents a short view of the first Archimedean Screw Turbines CFD modelling results, which
were carried out within the recent research entitled “Rebirth of Archimedes in Greece: contribution to the
study of hydraulic mechanics and hydrodynamic behavior of Archimedean cochlear waterwheels, for
recovering the hydraulic potential of Greek natural and technical watercourses”. This CFD analysis, based
to the Flow-3D code, concerns typical Tubular Archimedean Screw Turbines (TASTs) and shows some
promising performances for such small hydropower systems harnessing the important unexploited
hydraulic potential of natural and technical watercourses of Greece, of the order of several TWh / year and of a total installed capacity in the range of thousands MWs.

이 논문은 최초의 아르키메데스 나사 터빈 CFD 모델링 결과에 대한 간략한 견해를 제시하며, 이는 “그리스에서 아르키메데스의 부활: 수리 역학 및 아르키메데스 달팽이관 물레방아의 유체역학적 거동 연구에 대한 기여”라는 제목의 최근 연구에서 수행되었습니다. 그리스 자연 및 기술 수로의 수력 잠재력”. Flow-3D 코드를 기반으로 하는 이 CFD 분석은 일반적인 TAST(Tubular Archimedean Screw Turbines)에 관한 것이며 그리스의 자연 및 기술 수로의 중요한 미개발 수력 잠재력을 활용하는 이러한 TWh/년 및 수천 MW 범위의 총 설치 용량인 소규모 수력 발전 시스템에 대한 몇 가지 유망한 성능을 보여줍니다.
Copyright © 2021 International Energy and Environment Foundation – All rights reserved.

Keywords

CFD; Flow-3D; TAST; Small Hydro; Renewable Energy; Greek Watercourses.

Figure 1. Photorealistic view of an inclined axis TAST (photo A. Stergiopoulou).
Figure 1. Photorealistic view of an inclined axis TAST (photo A. Stergiopoulou).

References.

[1] A. Stergiopoulou, Computational and experimental investigation of the hydrodynamic behaviour of
screw hydro turbine, Ph.D. Thesis, NTUA, 2017.
[2] B. Pelikan, A. Lashofer, Verbesserung der Strömungseigenschaften sowie Planungs-und
Betriebsoptimierung von Wasserkraftschnecken, Research Project, BOKU University, Vienna,
2012.
[3] G. Müller, J. Senior, Simplified theory of Archimedean screws, Journal of Hydraulic Research 47
(5) (2009) 666-669.
[4] C. Rorres, The turn of the screw: Optimal design of an Archimedes screw, Journal of Hydraulic
Engineering, 80 (2000) 72-80.
[5] A. Stergiopoulou, V. Stergiopoulos, Return of Archimedes: Harnessing with new Archimedean
spirals the hydraulic potential of the Greek watercourses, in: Proceedings of the Conference for
Climate Change, Thessaloniki, 2009.
[6] A. Stergiopoulou, V. Stergiopoulos, from the old Archimedean screw pumps to the new
Archimedean screw turbines for hydropower production in Greece, in: Proceedings of CEMEPE
Conference, Mykonos, June 21-26, 2009.
International Journal of Energy and Environment (IJEE), Volume 12, Issue 1, 2021, pp.19-30
[7] V. Stergiopoulos, A. Stergiopoulou, E. Kalkani, Quo Vadis Archimedes Nowadays in Greece?
Towards Modern Archimedean Turbines for Recovering Greek Small Hydropower Potential, in:
Proceedings of 3rd International Scientific “Energy and Climate Change” Conference, Athens, 2010.
[8] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Greece beyond the horizon of the era of transition:
Archimedean screw hydropower development terra incognita, International Journal of Energy and
Development, v.6, Issue 6, pp. 627-536, 2015.
[9] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Experimental and theoretical research of zero head
innovative horizontal axis Archimedean screw turbines, Journal of Energy and Development, v.6,
Issue 5, pp. 471-478, 2015.
[10] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Back to the Future: Rediscovering the Archimedean
screws as modern turbines for harnessing Greek small hydropower potential, in: Proceedings of the
Third International Conference CEMEPE 2011 & SECOTOX, Skiathos, 2011.
[11] A. Stergiopoulou, V. Stergiopoulos, Educational Renewable Energy Screw Wheel Technologies for
Pico Hydropower Generation, Modern Environmental Science and Engineering, v.4, No.5, pp. 439-
445, May 2018.
[12] A. Stergiopoulou, V. Stergiopoulos, Educational Renewable Energy Screw Wheel Technologies for
Pico Hydropower Generation, Modern Environmental Science and Engineering, v.4, No.5, pp. 439-
445, May 2018.
[13] A. Stergiopoulou, V. Stergiopoulos, Towards an inventory of the archimedean small hydropower
potential of Greece, INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT
Volume 11, Issue 2, 2020 pp.137-144.
[14] Flow Science, FLOW-3D Manual, 2013.
[15] K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics, Pearson,
2007.
[16] C. Hirsch, Numerical Computation of internal and external flows: The fundamentals of
Computational Fluid dynamics, John Wiley & Sons, 2007.
[17] A. Stergiopoulou, V. Stergiopoulos and E. Kalkani, An eagle’s CFD view of Studying Innovative
Archimedean Screw Renewable Hydraulic Energy Systems, Proceedings of the 4th International
Conference on Environmental Management, Engineering, Planning and Economics (CEMEPE) and
SECOTOX Conference, Mykonos island, Greece, pp.454-460 June 24-28, 2013.
[18] A. Stergiopoulou, V. Stergiopoulos, A., E. Kalkani, Computational Fluid Dynamics Study on a 3D
Graphic Solid Model of Archimedean Screw Turbines, Fresenius Environmental Bulletin, vol.23-
No1, 2014.
[19] Α. Stergiopoulou, Kalkani E., “Towards a First C.F.D. Study of Innovative Archimedean Inclined
Axis Hydropower Turbines”, International Journal of Engineering Research & Technology (IJERT),
Vol. 2 Issue 9, September – 2013, pp. 193-199.
[20] A. Stergiopoulou, V. Stergiopoulos, A first CFD study of small hydro energy recovery from the
Attica water supply network, INTERNATIONAL JOURNAL OF ENERGY AND
ENVIRONMENT, Volume 11, Issue 3, 2020 pp.157-166.

Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

레이저 보조 분말 기반 직접 에너지 증착에서 용융 풀 거동에 대한 감쇠 레이저 빔 강도 프로파일의 영향에 대한 열유체 모델링

Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

Mohammad Sattari, Amin Ebrahimi, Martin Luckabauer, Gert-willem R.B.E. Römer

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Professional

5Downloads (Pure)

Abstract

A numerical framework based on computational fluid dynamics (CFD), using the finite volume method (FVM) and volume of fluid (VOF) technique is presented to investigate the effect of the laser beam intensity profile on melt pool behavior in laser-assisted powder-based directed energy deposition (L-DED). L-DED is an additive manufacturing (AM) process that utilizes a laser beam to fuse metal powder particles. To assure high-fidelity modeling, it was found that it is crucial to accurately model the interaction between the powder stream and the laser beam in the gas region above the substrate. The proposed model considers various phenomena including laser energy attenuation and absorption, multiple reflections of the laser rays, powder particle stream, particle-fluid interaction, temperature-dependent properties, buoyancy effects, thermal expansion, solidification shrinkage and drag, and Marangoni flow. The latter is induced by temperature and element-dependent surface tension. The model is validated using experimental results and highlights the importance of considering laser energy attenuation. Furthermore, the study investigates how the laser beam intensity profile affects melt pool size and shape, influencing the solidification microstructure and mechanical properties of the deposited material. The proposed model has the potential to optimize the L-DED process for a variety of materials and provides insights into the capability of numerical modeling for additive manufacturing optimization.

Original languageEnglish
Title of host publicationFlow-3D World Users Conference
Publication statusPublished – 2023
EventFlow-3D World User Conference – Strasbourg, France
Duration: 5 Jun 2023 → 7 Jun 2023

Conference

ConferenceFlow-3D World User Conference
Country/TerritoryFrance
CityStrasbourg
Period5/06/23 → 7/06/23
Figure 2 Modeling the plant with cylindrical tubes at the bottom of the canal.

Optimized Vegetation Density to Dissipate Energy of Flood Flow in Open Canals

열린 운하에서 홍수 흐름의 에너지를 분산시키기 위해 최적화된 식생 밀도

Mahdi Feizbahr,1Navid Tonekaboni,2Guang-Jun Jiang,3,4and Hong-Xia Chen3,4
Academic Editor: Mohammad Yazdi

Abstract

강을 따라 식생은 조도를 증가시키고 평균 유속을 감소시키며, 유동 에너지를 감소시키고 강 횡단면의 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받기 때문에 홍수시 유동저항에 큰 영향을 미친다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건과 식물에 따라 달라지므로 모델은 유속, 유속 깊이 및 수로를 따라 식생 유형의 영향을 고려하여 유속을 시뮬레이션해야 합니다. 총 48개의 모델을 시뮬레이션하여 근관의 거칠기 효과를 조사했습니다. 결과는 속도를 높임으로써 베드 속도를 감소시키는 식생의 영향이 무시할만하다는 것을 나타냅니다.

Abstract

Vegetation along the river increases the roughness and reduces the average flow velocity, reduces flow energy, and changes the flow velocity profile in the cross section of the river. Many canals and rivers in nature are covered with vegetation during the floods. Canal’s roughness is strongly affected by plants and therefore it has a great effect on flow resistance during flood. Roughness resistance against the flow due to the plants depends on the flow conditions and plant, so the model should simulate the current velocity by considering the effects of velocity, depth of flow, and type of vegetation along the canal. Total of 48 models have been simulated to investigate the effect of roughness in the canal. The results indicated that, by enhancing the velocity, the effect of vegetation in decreasing the bed velocity is negligible, while when the current has lower speed, the effect of vegetation on decreasing the bed velocity is obviously considerable.

1. Introduction

Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [114]. This can help research for better modeling considering the relation of variables or interaction of them toward reaching a better condition for the objective function in control and engineering [1527]. Consequently, it is necessary to study the effects of the passive factors on the active domain [2836]. Because of the effect of vegetation on reducing the discharge capacity of rivers [37], pruning plants was necessary to improve the condition of rivers. One of the important effects of vegetation in river protection is the action of roots, which cause soil consolidation and soil structure improvement and, by enhancing the shear strength of soil, increase the resistance of canal walls against the erosive force of water. The outer limbs of the plant increase the roughness of the canal walls and reduce the flow velocity and deplete the flow energy in vicinity of the walls. Vegetation by reducing the shear stress of the canal bed reduces flood discharge and sedimentation in the intervals between vegetation and increases the stability of the walls [3841].

One of the main factors influencing the speed, depth, and extent of flood in this method is Manning’s roughness coefficient. On the other hand, soil cover [42], especially vegetation, is one of the most determining factors in Manning’s roughness coefficient. Therefore, it is expected that those seasonal changes in the vegetation of the region will play an important role in the calculated value of Manning’s roughness coefficient and ultimately in predicting the flood wave behavior [4345]. The roughness caused by plants’ resistance to flood current depends on the flow and plant conditions. Flow conditions include depth and velocity of the plant, and plant conditions include plant type, hardness or flexibility, dimensions, density, and shape of the plant [46]. In general, the issue discussed in this research is the optimization of flood-induced flow in canals by considering the effect of vegetation-induced roughness. Therefore, the effect of plants on the roughness coefficient and canal transmission coefficient and in consequence the flow depth should be evaluated [4748].

Current resistance is generally known by its roughness coefficient. The equation that is mainly used in this field is Manning equation. The ratio of shear velocity to average current velocity  is another form of current resistance. The reason for using the  ratio is that it is dimensionless and has a strong theoretical basis. The reason for using Manning roughness coefficient is its pervasiveness. According to Freeman et al. [49], the Manning roughness coefficient for plants was calculated according to the Kouwen and Unny [50] method for incremental resistance. This method involves increasing the roughness for various surface and plant irregularities. Manning’s roughness coefficient has all the factors affecting the resistance of the canal. Therefore, the appropriate way to more accurately estimate this coefficient is to know the factors affecting this coefficient [51].

To calculate the flow rate, velocity, and depth of flow in canals as well as flood and sediment estimation, it is important to evaluate the flow resistance. To determine the flow resistance in open ducts, Manning, Chézy, and Darcy–Weisbach relations are used [52]. In these relations, there are parameters such as Manning’s roughness coefficient (n), Chézy roughness coefficient (C), and Darcy–Weisbach coefficient (f). All three of these coefficients are a kind of flow resistance coefficient that is widely used in the equations governing flow in rivers [53].

The three relations that express the relationship between the average flow velocity (V) and the resistance and geometric and hydraulic coefficients of the canal are as follows:where nf, and c are Manning, Darcy–Weisbach, and Chézy coefficients, respectively. V = average flow velocity, R = hydraulic radius, Sf = slope of energy line, which in uniform flow is equal to the slope of the canal bed,  = gravitational acceleration, and Kn is a coefficient whose value is equal to 1 in the SI system and 1.486 in the English system. The coefficients of resistance in equations (1) to (3) are related as follows:

Based on the boundary layer theory, the flow resistance for rough substrates is determined from the following general relation:where f = Darcy–Weisbach coefficient of friction, y = flow depth, Ks = bed roughness size, and A = constant coefficient.

On the other hand, the relationship between the Darcy–Weisbach coefficient of friction and the shear velocity of the flow is as follows:

By using equation (6), equation (5) is converted as follows:

Investigation on the effect of vegetation arrangement on shear velocity of flow in laboratory conditions showed that, with increasing the shear Reynolds number (), the numerical value of the  ratio also increases; in other words the amount of roughness coefficient increases with a slight difference in the cases without vegetation, checkered arrangement, and cross arrangement, respectively [54].

Roughness in river vegetation is simulated in mathematical models with a variable floor slope flume by different densities and discharges. The vegetation considered submerged in the bed of the flume. Results showed that, with increasing vegetation density, canal roughness and flow shear speed increase and with increasing flow rate and depth, Manning’s roughness coefficient decreases. Factors affecting the roughness caused by vegetation include the effect of plant density and arrangement on flow resistance, the effect of flow velocity on flow resistance, and the effect of depth [4555].

One of the works that has been done on the effect of vegetation on the roughness coefficient is Darby [56] study, which investigates a flood wave model that considers all the effects of vegetation on the roughness coefficient. There are currently two methods for estimating vegetation roughness. One method is to add the thrust force effect to Manning’s equation [475758] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [455961]. These two methods provide acceptable results in models designed to simulate floodplain flow. Wang et al. [62] simulate the floodplain with submerged vegetation using these two methods and to increase the accuracy of the results, they suggested using the effective height of the plant under running water instead of using the actual height of the plant. Freeman et al. [49] provided equations for determining the coefficient of vegetation roughness under different conditions. Lee et al. [63] proposed a method for calculating the Manning coefficient using the flow velocity ratio at different depths. Much research has been done on the Manning roughness coefficient in rivers, and researchers [496366] sought to obtain a specific number for n to use in river engineering. However, since the depth and geometric conditions of rivers are completely variable in different places, the values of Manning roughness coefficient have changed subsequently, and it has not been possible to choose a fixed number. In river engineering software, the Manning roughness coefficient is determined only for specific and constant conditions or normal flow. Lee et al. [63] stated that seasonal conditions, density, and type of vegetation should also be considered. Hydraulic roughness and Manning roughness coefficient n of the plant were obtained by estimating the total Manning roughness coefficient from the matching of the measured water surface curve and water surface height. The following equation is used for the flow surface curve:where  is the depth of water change, S0 is the slope of the canal floor, Sf is the slope of the energy line, and Fr is the Froude number which is obtained from the following equation:where D is the characteristic length of the canal. Flood flow velocity is one of the important parameters of flood waves, which is very important in calculating the water level profile and energy consumption. In the cases where there are many limitations for researchers due to the wide range of experimental dimensions and the variety of design parameters, the use of numerical methods that are able to estimate the rest of the unknown results with acceptable accuracy is economically justified.

FLOW-3D software uses Finite Difference Method (FDM) for numerical solution of two-dimensional and three-dimensional flow. This software is dedicated to computational fluid dynamics (CFD) and is provided by Flow Science [67]. The flow is divided into networks with tubular cells. For each cell there are values of dependent variables and all variables are calculated in the center of the cell, except for the velocity, which is calculated at the center of the cell. In this software, two numerical techniques have been used for geometric simulation, FAVOR™ (Fractional-Area-Volume-Obstacle-Representation) and the VOF (Volume-of-Fluid) method. The equations used at this model for this research include the principle of mass survival and the magnitude of motion as follows. The fluid motion equations in three dimensions, including the Navier–Stokes equations with some additional terms, are as follows:where  are mass accelerations in the directions xyz and  are viscosity accelerations in the directions xyz and are obtained from the following equations:

Shear stresses  in equation (11) are obtained from the following equations:

The standard model is used for high Reynolds currents, but in this model, RNG theory allows the analytical differential formula to be used for the effective viscosity that occurs at low Reynolds numbers. Therefore, the RNG model can be used for low and high Reynolds currents.

Weather changes are high and this affects many factors continuously. The presence of vegetation in any area reduces the velocity of surface flows and prevents soil erosion, so vegetation will have a significant impact on reducing destructive floods. One of the methods of erosion protection in floodplain watersheds is the use of biological methods. The presence of vegetation in watersheds reduces the flow rate during floods and prevents soil erosion. The external organs of plants increase the roughness and decrease the velocity of water flow and thus reduce its shear stress energy. One of the important factors with which the hydraulic resistance of plants is expressed is the roughness coefficient. Measuring the roughness coefficient of plants and investigating their effect on reducing velocity and shear stress of flow is of special importance.

Roughness coefficients in canals are affected by two main factors, namely, flow conditions and vegetation characteristics [68]. So far, much research has been done on the effect of the roughness factor created by vegetation, but the issue of plant density has received less attention. For this purpose, this study was conducted to investigate the effect of vegetation density on flow velocity changes.

In a study conducted using a software model on three density modes in the submerged state effect on flow velocity changes in 48 different modes was investigated (Table 1).

Table 1 

The studied models.

The number of cells used in this simulation is equal to 1955888 cells. The boundary conditions were introduced to the model as a constant speed and depth (Figure 1). At the output boundary, due to the presence of supercritical current, no parameter for the current is considered. Absolute roughness for floors and walls was introduced to the model (Figure 1). In this case, the flow was assumed to be nonviscous and air entry into the flow was not considered. After  seconds, this model reached a convergence accuracy of .

Figure 1 

The simulated model and its boundary conditions.

Due to the fact that it is not possible to model the vegetation in FLOW-3D software, in this research, the vegetation of small soft plants was studied so that Manning’s coefficients can be entered into the canal bed in the form of roughness coefficients obtained from the studies of Chow [69] in similar conditions. In practice, in such modeling, the effect of plant height is eliminated due to the small height of herbaceous plants, and modeling can provide relatively acceptable results in these conditions.

48 models with input velocities proportional to the height of the regular semihexagonal canal were considered to create supercritical conditions. Manning coefficients were applied based on Chow [69] studies in order to control the canal bed. Speed profiles were drawn and discussed.

Any control and simulation system has some inputs that we should determine to test any technology [7077]. Determination and true implementation of such parameters is one of the key steps of any simulation [237881] and computing procedure [8286]. The input current is created by applying the flow rate through the VFR (Volume Flow Rate) option and the output flow is considered Output and for other borders the Symmetry option is considered.

Simulation of the models and checking their action and responses and observing how a process behaves is one of the accepted methods in engineering and science [8788]. For verification of FLOW-3D software, the results of computer simulations are compared with laboratory measurements and according to the values of computational error, convergence error, and the time required for convergence, the most appropriate option for real-time simulation is selected (Figures 2 and 3 ).

Figure 2 

Modeling the plant with cylindrical tubes at the bottom of the canal.

Figure 3 

Velocity profiles in positions 2 and 5.

The canal is 7 meters long, 0.5 meters wide, and 0.8 meters deep. This test was used to validate the application of the software to predict the flow rate parameters. In this experiment, instead of using the plant, cylindrical pipes were used in the bottom of the canal.

The conditions of this modeling are similar to the laboratory conditions and the boundary conditions used in the laboratory were used for numerical modeling. The critical flow enters the simulation model from the upstream boundary, so in the upstream boundary conditions, critical velocity and depth are considered. The flow at the downstream boundary is supercritical, so no parameters are applied to the downstream boundary.

The software well predicts the process of changing the speed profile in the open canal along with the considered obstacles. The error in the calculated speed values can be due to the complexity of the flow and the interaction of the turbulence caused by the roughness of the floor with the turbulence caused by the three-dimensional cycles in the hydraulic jump. As a result, the software is able to predict the speed distribution in open canals.

2. Modeling Results

After analyzing the models, the results were shown in graphs (Figures 414 ). The total number of experiments in this study was 48 due to the limitations of modeling.


(d)


(a)


(b)


(c)


(d)


(a)


(b)


(c)


(d)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)
  • (d)
    (d)

Figure 4 

Flow velocity profiles for canals with a depth of 1 m and flow velocities of 3–3.3 m/s. Canal with a depth of 1 meter and a flow velocity of (a) 3 meters per second, (b) 3.1 meters per second, (c) 3.2 meters per second, and (d) 3.3 meters per second.

Figure 5 

Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.

Figure 6 

Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.

Figure 7 

Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.

Figure 8 

Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second.


(d)


(a)


(b)


(c)


(d)


(a)


(b)


(c)


(d)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)
  • (d)
    (d)

Figure 9 

Flow velocity profiles for canals with a depth of 2 m and flow velocities of 4–4.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

Figure 10 

Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.

Figure 11 

Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.

Figure 12 

Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.

Figure 13 

Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second.


(d)


(a)


(b)


(c)


(d)


(a)


(b)


(c)


(d)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)
  • (d)
    (d)

Figure 14 

Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

To investigate the effects of roughness with flow velocity, the trend of flow velocity changes at different depths and with supercritical flow to a Froude number proportional to the depth of the section has been obtained.

According to the velocity profiles of Figure 5, it can be seen that, with the increasing of Manning’s coefficient, the canal bed speed decreases.

According to Figures 5 to 8, it can be found that, with increasing the Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the models 1 to 12, which can be justified by increasing the speed and of course increasing the Froude number.

According to Figure 10, we see that, with increasing Manning’s coefficient, the canal bed speed decreases.

According to Figure 11, we see that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 510, which can be justified by increasing the speed and, of course, increasing the Froude number.

With increasing Manning’s coefficient, the canal bed speed decreases (Figure 12). But this deceleration is more noticeable than the deceleration of the higher models (Figures 58 and 1011), which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 13, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5 to 12, which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 15, with increasing Manning’s coefficient, the canal bed speed decreases.

Figure 15 

Canal diagram with a depth of 3 meters and a flow rate of 5 meters per second.

According to Figure 16, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher model, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 16 

Canal diagram with a depth of 3 meters and a flow rate of 5.1 meters per second.

According to Figure 17, it is clear that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 17 

Canal diagram with a depth of 3 meters and a flow rate of 5.2 meters per second.

According to Figure 18, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 18 

Canal diagram with a depth of 3 meters and a flow rate of 5.3 meters per second.

According to Figure 19, it can be seen that the vegetation placed in front of the flow input velocity has negligible effect on the reduction of velocity, which of course can be justified due to the flexibility of the vegetation. The only unusual thing is the unexpected decrease in floor speed of 3 m/s compared to higher speeds.


(c)


(a)


(b)


(c)


(a)


(b)


(c)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)

Figure 19 

Comparison of velocity profiles with the same plant densities (depth 1 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 1 m; (b) plant densities of 50%, depth 1 m; and (c) plant densities of 75%, depth 1 m.

According to Figure 20, by increasing the speed of vegetation, the effect of vegetation on reducing the flow rate becomes more noticeable. And the role of input current does not have much effect in reducing speed.


(c)


(a)


(b)


(c)


(a)


(b)


(c)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)

Figure 20 

Comparison of velocity profiles with the same plant densities (depth 2 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 2 m; (b) plant densities of 50%, depth 2 m; and (c) plant densities of 75%, depth 2 m.

According to Figure 21, it can be seen that, with increasing speed, the effect of vegetation on reducing the bed flow rate becomes more noticeable and the role of the input current does not have much effect. In general, it can be seen that, by increasing the speed of the input current, the slope of the profiles increases from the bed to the water surface and due to the fact that, in software, the roughness coefficient applies to the channel floor only in the boundary conditions, this can be perfectly justified. Of course, it can be noted that, due to the flexible conditions of the vegetation of the bed, this modeling can show acceptable results for such grasses in the canal floor. In the next directions, we may try application of swarm-based optimization methods for modeling and finding the most effective factors in this research [27815188994]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [9599].


(c)


(a)


(b)


(c)


(a)


(b)


(c)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)

Figure 21 

Comparison of velocity profiles with the same plant densities (depth 3 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 3 m; (b) plant densities of 50%, depth 3 m; and (c) plant densities of 75%, depth 3 m.

3. Conclusion

The effects of vegetation on the flood canal were investigated by numerical modeling with FLOW-3D software. After analyzing the results, the following conclusions were reached:(i)Increasing the density of vegetation reduces the velocity of the canal floor but has no effect on the velocity of the canal surface.(ii)Increasing the Froude number is directly related to increasing the speed of the canal floor.(iii)In the canal with a depth of one meter, a sudden increase in speed can be observed from the lowest speed and higher speed, which is justified by the sudden increase in Froude number.(iv)As the inlet flow rate increases, the slope of the profiles from the bed to the water surface increases.(v)By reducing the Froude number, the effect of vegetation on reducing the flow bed rate becomes more noticeable. And the input velocity in reducing the velocity of the canal floor does not have much effect.(vi)At a flow rate between 3 and 3.3 meters per second due to the shallow depth of the canal and the higher landing number a more critical area is observed in which the flow bed velocity in this area is between 2.86 and 3.1 m/s.(vii)Due to the critical flow velocity and the slight effect of the roughness of the horseshoe vortex floor, it is not visible and is only partially observed in models 1-2-3 and 21.(viii)As the flow rate increases, the effect of vegetation on the rate of bed reduction decreases.(ix)In conditions where less current intensity is passing, vegetation has a greater effect on reducing current intensity and energy consumption increases.(x)In the case of using the flow rate of 0.8 cubic meters per second, the velocity distribution and flow regime show about 20% more energy consumption than in the case of using the flow rate of 1.3 cubic meters per second.

Nomenclature

n:Manning’s roughness coefficient
C:Chézy roughness coefficient
f:Darcy–Weisbach coefficient
V:Flow velocity
R:Hydraulic radius
g:Gravitational acceleration
y:Flow depth
Ks:Bed roughness
A:Constant coefficient
:Reynolds number
y/∂x:Depth of water change
S0:Slope of the canal floor
Sf:Slope of energy line
Fr:Froude number
D:Characteristic length of the canal
G:Mass acceleration
:Shear stresses.

Data Availability

All data are included within the paper.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.

References

  1. H. Yu, L. Jie, W. Gui et al., “Dynamic Gaussian bare-bones fruit fly optimizers with abandonment mechanism: method and analysis,” Engineering with Computers, vol. 20, pp. 1–29, 2020.View at: Publisher Site | Google Scholar
  2. X. Zhao, D. Li, B. Yang, C. Ma, Y. Zhu, and H. Chen, “Feature selection based on improved ant colony optimization for online detection of foreign fiber in cotton,” Applied Soft Computing, vol. 24, pp. 585–596, 2014.View at: Publisher Site | Google Scholar
  3. J. Hu, H. Chen, A. A. Heidari et al., “Orthogonal learning covariance matrix for defects of grey wolf optimizer: insights, balance, diversity, and feature selection,” Knowledge-Based Systems, vol. 213, Article ID 106684, 2021.View at: Publisher Site | Google Scholar
  4. C. Yu, M. Chen, K. Chen et al., “SGOA: annealing-behaved grasshopper optimizer for global tasks,” Engineering with Computers, vol. 4, pp. 1–28, 2021.View at: Publisher Site | Google Scholar
  5. W. Shan, Z. Qiao, A. A. Heidari, H. Chen, H. Turabieh, and Y. Teng, “Double adaptive weights for stabilization of moth flame optimizer: balance analysis, engineering cases, and medical diagnosis,” Knowledge-Based Systems, vol. 8, Article ID 106728, 2020.View at: Google Scholar
  6. J. Tu, H. Chen, J. Liu et al., “Evolutionary biogeography-based whale optimization methods with communication structure: towards measuring the balance,” Knowledge-Based Systems, vol. 212, Article ID 106642, 2021.View at: Publisher Site | Google Scholar
  7. Y. Zhang, R. Liu, X. Wang et al., “Towards augmented kernel extreme learning models for bankruptcy prediction: algorithmic behavior and comprehensive analysis,” Neurocomputing, vol. 430, 2020.View at: Google Scholar
  8. H.-L. Chen, G. Wang, C. Ma, Z.-N. Cai, W.-B. Liu, and S.-J. Wang, “An efficient hybrid kernel extreme learning machine approach for early diagnosis of Parkinson׳s disease,” Neurocomputing, vol. 184, pp. 131–144, 2016.View at: Publisher Site | Google Scholar
  9. J. Xia, H. Chen, Q. Li et al., “Ultrasound-based differentiation of malignant and benign thyroid Nodules: an extreme learning machine approach,” Computer Methods and Programs in Biomedicine, vol. 147, pp. 37–49, 2017.View at: Publisher Site | Google Scholar
  10. C. Li, L. Hou, B. Y. Sharma et al., “Developing a new intelligent system for the diagnosis of tuberculous pleural effusion,” Computer Methods and Programs in Biomedicine, vol. 153, pp. 211–225, 2018.View at: Publisher Site | Google Scholar
  11. X. Xu and H.-L. Chen, “Adaptive computational chemotaxis based on field in bacterial foraging optimization,” Soft Computing, vol. 18, no. 4, pp. 797–807, 2014.View at: Publisher Site | Google Scholar
  12. M. Wang, H. Chen, B. Yang et al., “Toward an optimal kernel extreme learning machine using a chaotic moth-flame optimization strategy with applications in medical diagnoses,” Neurocomputing, vol. 267, pp. 69–84, 2017.View at: Publisher Site | Google Scholar
  13. L. Chao, K. Zhang, Z. Li, Y. Zhu, J. Wang, and Z. Yu, “Geographically weighted regression based methods for merging satellite and gauge precipitation,” Journal of Hydrology, vol. 558, pp. 275–289, 2018.View at: Publisher Site | Google Scholar
  14. F. J. Golrokh, G. Azeem, and A. Hasan, “Eco-efficiency evaluation in cement industries: DEA malmquist productivity index using optimization models,” ENG Transactions, vol. 1, 2020.View at: Google Scholar
  15. D. Zhao, L. Lei, F. Yu et al., “Chaotic random spare ant colony optimization for multi-threshold image segmentation of 2D Kapur entropy,” Knowledge-Based Systems, vol. 8, Article ID 106510, 2020.View at: Google Scholar
  16. Y. Zhang, R. Liu, X. Wang, H. Chen, and C. Li, “Boosted binary Harris hawks optimizer and feature selection,” Engineering with Computers, vol. 517, pp. 1–30, 2020.View at: Publisher Site | Google Scholar
  17. L. Hu, G. Hong, J. Ma, X. Wang, and H. Chen, “An efficient machine learning approach for diagnosis of paraquat-poisoned patients,” Computers in Biology and Medicine, vol. 59, pp. 116–124, 2015.View at: Publisher Site | Google Scholar
  18. L. Shen, H. Chen, Z. Yu et al., “Evolving support vector machines using fruit fly optimization for medical data classification,” Knowledge-Based Systems, vol. 96, pp. 61–75, 2016.View at: Publisher Site | Google Scholar
  19. X. Zhao, X. Zhang, Z. Cai et al., “Chaos enhanced grey wolf optimization wrapped ELM for diagnosis of paraquat-poisoned patients,” Computational Biology and Chemistry, vol. 78, pp. 481–490, 2019.View at: Publisher Site | Google Scholar
  20. Y. Xu, H. Chen, J. Luo, Q. Zhang, S. Jiao, and X. Zhang, “Enhanced Moth-flame optimizer with mutation strategy for global optimization,” Information Sciences, vol. 492, pp. 181–203, 2019.View at: Publisher Site | Google Scholar
  21. M. Wang and H. Chen, “Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis,” Applied Soft Computing Journal, vol. 88, Article ID 105946, 2020.View at: Publisher Site | Google Scholar
  22. Y. Chen, J. Li, H. Lu, and P. Yan, “Coupling system dynamics analysis and risk aversion programming for optimizing the mixed noise-driven shale gas-water supply chains,” Journal of Cleaner Production, vol. 278, Article ID 123209, 2020.View at: Google Scholar
  23. H. Tang, Y. Xu, A. Lin et al., “Predicting green consumption behaviors of students using efficient firefly grey wolf-assisted K-nearest neighbor classifiers,” IEEE Access, vol. 8, pp. 35546–35562, 2020.View at: Publisher Site | Google Scholar
  24. H.-J. Ma and G.-H. Yang, “Adaptive fault tolerant control of cooperative heterogeneous systems with actuator faults and unreliable interconnections,” IEEE Transactions on Automatic Control, vol. 61, no. 11, pp. 3240–3255, 2015.View at: Google Scholar
  25. H.-J. Ma and L.-X. Xu, “Decentralized adaptive fault-tolerant control for a class of strong interconnected nonlinear systems via graph theory,” IEEE Transactions on Automatic Control, vol. 66, 2020.View at: Google Scholar
  26. H. J. Ma, L. X. Xu, and G. H. Yang, “Multiple environment integral reinforcement learning-based fault-tolerant control for affine nonlinear systems,” IEEE Transactions on Cybernetics, vol. 51, pp. 1–16, 2019.View at: Publisher Site | Google Scholar
  27. J. Hu, M. Wang, C. Zhao, Q. Pan, and C. Du, “Formation control and collision avoidance for multi-UAV systems based on Voronoi partition,” Science China Technological Sciences, vol. 63, no. 1, pp. 65–72, 2020.View at: Publisher Site | Google Scholar
  28. C. Zhang, H. Li, Y. Qian, C. Chen, and X. Zhou, “Locality-constrained discriminative matrix regression for robust face identification,” IEEE Transactions on Neural Networks and Learning Systems, vol. 99, pp. 1–15, 2020.View at: Publisher Site | Google Scholar
  29. X. Zhang, D. Wang, Z. Zhou, and Y. Ma, “Robust low-rank tensor recovery with rectification and alignment,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 43, no. 1, pp. 238–255, 2019.View at: Google Scholar
  30. X. Zhang, J. Wang, T. Wang, R. Jiang, J. Xu, and L. Zhao, “Robust feature learning for adversarial defense via hierarchical feature alignment,” Information Sciences, vol. 560, 2020.View at: Google Scholar
  31. X. Zhang, R. Jiang, T. Wang, and J. Wang, “Recursive neural network for video deblurring,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 03, p. 1, 2020.View at: Publisher Site | Google Scholar
  32. X. Zhang, T. Wang, J. Wang, G. Tang, and L. Zhao, “Pyramid channel-based feature attention network for image dehazing,” Computer Vision and Image Understanding, vol. 197-198, Article ID 103003, 2020.View at: Publisher Site | Google Scholar
  33. X. Zhang, T. Wang, W. Luo, and P. Huang, “Multi-level fusion and attention-guided CNN for image dehazing,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 3, p. 1, 2020.View at: Publisher Site | Google Scholar
  34. L. He, J. Shen, and Y. Zhang, “Ecological vulnerability assessment for ecological conservation and environmental management,” Journal of Environmental Management, vol. 206, pp. 1115–1125, 2018.View at: Publisher Site | Google Scholar
  35. Y. Chen, W. Zheng, W. Li, and Y. Huang, “Large group Activity security risk assessment and risk early warning based on random forest algorithm,” Pattern Recognition Letters, vol. 144, pp. 1–5, 2021.View at: Publisher Site | Google Scholar
  36. J. Hu, H. Zhang, Z. Li, C. Zhao, Z. Xu, and Q. Pan, “Object traversing by monocular UAV in outdoor environment,” Asian Journal of Control, vol. 25, 2020.View at: Google Scholar
  37. P. Tian, H. Lu, W. Feng, Y. Guan, and Y. Xue, “Large decrease in streamflow and sediment load of Qinghai-Tibetan Plateau driven by future climate change: a case study in Lhasa River Basin,” Catena, vol. 187, Article ID 104340, 2020.View at: Publisher Site | Google Scholar
  38. A. Stokes, C. Atger, A. G. Bengough, T. Fourcaud, and R. C. Sidle, “Desirable plant root traits for protecting natural and engineered slopes against landslides,” Plant and Soil, vol. 324, no. 1, pp. 1–30, 2009.View at: Publisher Site | Google Scholar
  39. T. B. Devi, A. Sharma, and B. Kumar, “Studies on emergent flow over vegetative channel bed with downward seepage,” Hydrological Sciences Journal, vol. 62, no. 3, pp. 408–420, 2017.View at: Google Scholar
  40. G. Ireland, M. Volpi, and G. Petropoulos, “Examining the capability of supervised machine learning classifiers in extracting flooded areas from Landsat TM imagery: a case study from a Mediterranean flood,” Remote Sensing, vol. 7, no. 3, pp. 3372–3399, 2015.View at: Publisher Site | Google Scholar
  41. L. Goodarzi and S. Javadi, “Assessment of aquifer vulnerability using the DRASTIC model; a case study of the Dezful-Andimeshk Aquifer,” Computational Research Progress in Applied Science & Engineering, vol. 2, no. 1, pp. 17–22, 2016.View at: Google Scholar
  42. K. Zhang, Q. Wang, L. Chao et al., “Ground observation-based analysis of soil moisture spatiotemporal variability across a humid to semi-humid transitional zone in China,” Journal of Hydrology, vol. 574, pp. 903–914, 2019.View at: Publisher Site | Google Scholar
  43. L. De Doncker, P. Troch, R. Verhoeven, K. Bal, P. Meire, and J. Quintelier, “Determination of the Manning roughness coefficient influenced by vegetation in the river Aa and Biebrza river,” Environmental Fluid Mechanics, vol. 9, no. 5, pp. 549–567, 2009.View at: Publisher Site | Google Scholar
  44. M. Fathi-Moghadam and K. Drikvandi, “Manning roughness coefficient for rivers and flood plains with non-submerged vegetation,” International Journal of Hydraulic Engineering, vol. 1, no. 1, pp. 1–4, 2012.View at: Google Scholar
  45. F.-C. Wu, H. W. Shen, and Y.-J. Chou, “Variation of roughness coefficients for unsubmerged and submerged vegetation,” Journal of Hydraulic Engineering, vol. 125, no. 9, pp. 934–942, 1999.View at: Publisher Site | Google Scholar
  46. M. K. Wood, “Rangeland vegetation-hydrologic interactions,” in Vegetation Science Applications for Rangeland Analysis and Management, vol. 3, pp. 469–491, Springer, 1988.View at: Publisher Site | Google Scholar
  47. C. Wilson, O. Yagci, H.-P. Rauch, and N. Olsen, “3D numerical modelling of a willow vegetated river/floodplain system,” Journal of Hydrology, vol. 327, no. 1-2, pp. 13–21, 2006.View at: Publisher Site | Google Scholar
  48. R. Yazarloo, M. Khamehchian, and M. R. Nikoodel, “Observational-computational 3d engineering geological model and geotechnical characteristics of young sediments of golestan province,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 03, 2017.View at: Google Scholar
  49. G. E. Freeman, W. H. Rahmeyer, and R. R. Copeland, “Determination of resistance due to shrubs and woody vegetation,” International Journal of River Basin Management, vol. 19, 2000.View at: Google Scholar
  50. N. Kouwen and T. E. Unny, “Flexible roughness in open channels,” Journal of the Hydraulics Division, vol. 99, no. 5, pp. 713–728, 1973.View at: Publisher Site | Google Scholar
  51. S. Hosseini and J. Abrishami, Open Channel Hydraulics, Elsevier, Amsterdam, Netherlands, 2007.
  52. C. S. James, A. L. Birkhead, A. A. Jordanova, and J. J. O’Sullivan, “Flow resistance of emergent vegetation,” Journal of Hydraulic Research, vol. 42, no. 4, pp. 390–398, 2004.View at: Publisher Site | Google Scholar
  53. F. Huthoff and D. Augustijn, “Channel roughness in 1D steady uniform flow: Manning or Chézy?,,” NCR-days, vol. 102, 2004.View at: Google Scholar
  54. M. S. Sabegh, M. Saneie, M. Habibi, A. A. Abbasi, and M. Ghadimkhani, “Experimental investigation on the effect of river bank tree planting array, on shear velocity,” Journal of Watershed Engineering and Management, vol. 2, no. 4, 2011.View at: Google Scholar
  55. A. Errico, V. Pasquino, M. Maxwald, G. B. Chirico, L. Solari, and F. Preti, “The effect of flexible vegetation on flow in drainage channels: estimation of roughness coefficients at the real scale,” Ecological Engineering, vol. 120, pp. 411–421, 2018.View at: Publisher Site | Google Scholar
  56. S. E. Darby, “Effect of riparian vegetation on flow resistance and flood potential,” Journal of Hydraulic Engineering, vol. 125, no. 5, pp. 443–454, 1999.View at: Publisher Site | Google Scholar
  57. V. Kutija and H. Thi Minh Hong, “A numerical model for assessing the additional resistance to flow introduced by flexible vegetation,” Journal of Hydraulic Research, vol. 34, no. 1, pp. 99–114, 1996.View at: Publisher Site | Google Scholar
  58. T. Fischer-Antze, T. Stoesser, P. Bates, and N. R. B. Olsen, “3D numerical modelling of open-channel flow with submerged vegetation,” Journal of Hydraulic Research, vol. 39, no. 3, pp. 303–310, 2001.View at: Publisher Site | Google Scholar
  59. U. Stephan and D. Gutknecht, “Hydraulic resistance of submerged flexible vegetation,” Journal of Hydrology, vol. 269, no. 1-2, pp. 27–43, 2002.View at: Publisher Site | Google Scholar
  60. F. G. Carollo, V. Ferro, and D. Termini, “Flow resistance law in channels with flexible submerged vegetation,” Journal of Hydraulic Engineering, vol. 131, no. 7, pp. 554–564, 2005.View at: Publisher Site | Google Scholar
  61. W. Fu-sheng, “Flow resistance of flexible vegetation in open channel,” Journal of Hydraulic Engineering, vol. S1, 2007.View at: Google Scholar
  62. P.-f. Wang, C. Wang, and D. Z. Zhu, “Hydraulic resistance of submerged vegetation related to effective height,” Journal of Hydrodynamics, vol. 22, no. 2, pp. 265–273, 2010.View at: Publisher Site | Google Scholar
  63. J. K. Lee, L. C. Roig, H. L. Jenter, and H. M. Visser, “Drag coefficients for modeling flow through emergent vegetation in the Florida Everglades,” Ecological Engineering, vol. 22, no. 4-5, pp. 237–248, 2004.View at: Publisher Site | Google Scholar
  64. G. J. Arcement and V. R. Schneider, Guide for Selecting Manning’s Roughness Coefficients for Natural Channels and Flood Plains, US Government Printing Office, Washington, DC, USA, 1989.
  65. Y. Ding and S. S. Y. Wang, “Identification of Manning’s roughness coefficients in channel network using adjoint analysis,” International Journal of Computational Fluid Dynamics, vol. 19, no. 1, pp. 3–13, 2005.View at: Publisher Site | Google Scholar
  66. E. T. Engman, “Roughness coefficients for routing surface runoff,” Journal of Irrigation and Drainage Engineering, vol. 112, no. 1, pp. 39–53, 1986.View at: Publisher Site | Google Scholar
  67. M. Feizbahr, C. Kok Keong, F. Rostami, and M. Shahrokhi, “Wave energy dissipation using perforated and non perforated piles,” International Journal of Engineering, vol. 31, no. 2, pp. 212–219, 2018.View at: Publisher Site | Google Scholar
  68. M. Farzadkhoo, A. Keshavarzi, H. Hamidifar, and M. Javan, “Sudden pollutant discharge in vegetated compound meandering rivers,” Catena, vol. 182, Article ID 104155, 2019.View at: Publisher Site | Google Scholar
  69. V. T. Chow, Open-channel Hydraulics, Mcgraw-Hill Civil Engineering Series, Chennai, TN, India, 1959.
  70. X. Zhang, R. Jing, Z. Li, Z. Li, X. Chen, and C.-Y. Su, “Adaptive pseudo inverse control for a class of nonlinear asymmetric and saturated nonlinear hysteretic systems,” IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 4, pp. 916–928, 2020.View at: Google Scholar
  71. C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: the phase space perspective,” Optics and Lasers in Engineering, vol. 71, pp. 20–32, 2015.View at: Publisher Site | Google Scholar
  72. C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Scientific Reports, vol. 7, no. 1, pp. 7654–7722, 2017.View at: Publisher Site | Google Scholar
  73. B.-H. Li, Y. Liu, A.-M. Zhang, W.-H. Wang, and S. Wan, “A survey on blocking technology of entity resolution,” Journal of Computer Science and Technology, vol. 35, no. 4, pp. 769–793, 2020.View at: Publisher Site | Google Scholar
  74. Y. Liu, B. Zhang, Y. Feng et al., “Development of 340-GHz transceiver front end based on GaAs monolithic integration technology for THz active imaging array,” Applied Sciences, vol. 10, no. 21, p. 7924, 2020.View at: Publisher Site | Google Scholar
  75. J. Hu, H. Zhang, L. Liu, X. Zhu, C. Zhao, and Q. Pan, “Convergent multiagent formation control with collision avoidance,” IEEE Transactions on Robotics, vol. 36, no. 6, pp. 1805–1818, 2020.View at: Publisher Site | Google Scholar
  76. M. B. Movahhed, J. Ayoubinejad, F. N. Asl, and M. Feizbahr, “The effect of rain on pedestrians crossing speed,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 6, no. 3, 2020.View at: Google Scholar
  77. A. Li, D. Spano, J. Krivochiza et al., “A tutorial on interference exploitation via symbol-level precoding: overview, state-of-the-art and future directions,” IEEE Communications Surveys & Tutorials, vol. 22, no. 2, pp. 796–839, 2020.View at: Publisher Site | Google Scholar
  78. W. Zhu, C. Ma, X. Zhao et al., “Evaluation of sino foreign cooperative education project using orthogonal sine cosine optimized kernel extreme learning machine,” IEEE Access, vol. 8, pp. 61107–61123, 2020.View at: Publisher Site | Google Scholar
  79. G. Liu, W. Jia, M. Wang et al., “Predicting cervical hyperextension injury: a covariance guided sine cosine support vector machine,” IEEE Access, vol. 8, pp. 46895–46908, 2020.View at: Publisher Site | Google Scholar
  80. Y. Wei, H. Lv, M. Chen et al., “Predicting entrepreneurial intention of students: an extreme learning machine with Gaussian barebone harris hawks optimizer,” IEEE Access, vol. 8, pp. 76841–76855, 2020.View at: Publisher Site | Google Scholar
  81. A. Lin, Q. Wu, A. A. Heidari et al., “Predicting intentions of students for master programs using a chaos-induced sine cosine-based fuzzy K-Nearest neighbor classifier,” Ieee Access, vol. 7, pp. 67235–67248, 2019.View at: Publisher Site | Google Scholar
  82. Y. Fan, P. Wang, A. A. Heidari et al., “Rationalized fruit fly optimization with sine cosine algorithm: a comprehensive analysis,” Expert Systems with Applications, vol. 157, Article ID 113486, 2020.View at: Publisher Site | Google Scholar
  83. E. Rodríguez-Esparza, L. A. Zanella-Calzada, D. Oliva et al., “An efficient Harris hawks-inspired image segmentation method,” Expert Systems with Applications, vol. 155, Article ID 113428, 2020.View at: Publisher Site | Google Scholar
  84. S. Jiao, G. Chong, C. Huang et al., “Orthogonally adapted Harris hawks optimization for parameter estimation of photovoltaic models,” Energy, vol. 203, Article ID 117804, 2020.View at: Publisher Site | Google Scholar
  85. Z. Xu, Z. Hu, A. A. Heidari et al., “Orthogonally-designed adapted grasshopper optimization: a comprehensive analysis,” Expert Systems with Applications, vol. 150, Article ID 113282, 2020.View at: Publisher Site | Google Scholar
  86. A. Abbassi, R. Abbassi, A. A. Heidari et al., “Parameters identification of photovoltaic cell models using enhanced exploratory salp chains-based approach,” Energy, vol. 198, Article ID 117333, 2020.View at: Publisher Site | Google Scholar
  87. M. Mahmoodi and K. K. Aminjan, “Numerical simulation of flow through sukhoi 24 air inlet,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 03, 2017.View at: Google Scholar
  88. F. J. Golrokh and A. Hasan, “A comparison of machine learning clustering algorithms based on the DEA optimization approach for pharmaceutical companies in developing countries,” ENG Transactions, vol. 1, 2020.View at: Google Scholar
  89. H. Chen, A. A. Heidari, H. Chen, M. Wang, Z. Pan, and A. H. Gandomi, “Multi-population differential evolution-assisted Harris hawks optimization: framework and case studies,” Future Generation Computer Systems, vol. 111, pp. 175–198, 2020.View at: Publisher Site | Google Scholar
  90. J. Guo, H. Zheng, B. Li, and G.-Z. Fu, “Bayesian hierarchical model-based information fusion for degradation analysis considering non-competing relationship,” IEEE Access, vol. 7, pp. 175222–175227, 2019.View at: Publisher Site | Google Scholar
  91. J. Guo, H. Zheng, B. Li, and G.-Z. Fu, “A Bayesian approach for degradation analysis with individual differences,” IEEE Access, vol. 7, pp. 175033–175040, 2019.View at: Publisher Site | Google Scholar
  92. M. M. A. Malakoutian, Y. Malakoutian, P. Mostafapour, and S. Z. D. Abed, “Prediction for monthly rainfall of six meteorological regions and TRNC (case study: north Cyprus),” ENG Transactions, vol. 2, no. 2, 2021.View at: Google Scholar
  93. H. Arslan, M. Ranjbar, and Z. Mutlum, “Maximum sound transmission loss in multi-chamber reactive silencers: are two chambers enough?,,” ENG Transactions, vol. 2, no. 1, 2021.View at: Google Scholar
  94. N. Tonekaboni, M. Feizbahr, N. Tonekaboni, G.-J. Jiang, and H.-X. Chen, “Optimization of solar CCHP systems with collector enhanced by porous media and nanofluid,” Mathematical Problems in Engineering, vol. 2021, Article ID 9984840, 12 pages, 2021.View at: Publisher Site | Google Scholar
  95. Z. Niu, B. Zhang, J. Wang et al., “The research on 220GHz multicarrier high-speed communication system,” China Communications, vol. 17, no. 3, pp. 131–139, 2020.View at: Publisher Site | Google Scholar
  96. B. Zhang, Z. Niu, J. Wang et al., “Four‐hundred gigahertz broadband multi‐branch waveguide coupler,” IET Microwaves, Antennas & Propagation, vol. 14, no. 11, pp. 1175–1179, 2020.View at: Publisher Site | Google Scholar
  97. Z.-Q. Niu, L. Yang, B. Zhang et al., “A mechanical reliability study of 3dB waveguide hybrid couplers in the submillimeter and terahertz band,” Journal of Zhejiang University Science, vol. 1, no. 1, 1998.View at: Google Scholar
  98. B. Zhang, D. Ji, D. Fang, S. Liang, Y. Fan, and X. Chen, “A novel 220-GHz GaN diode on-chip tripler with high driven power,” IEEE Electron Device Letters, vol. 40, no. 5, pp. 780–783, 2019.View at: Publisher Site | Google Scholar
  99. M. Taleghani and A. Taleghani, “Identification and ranking of factors affecting the implementation of knowledge management engineering based on TOPSIS technique,” ENG Transactions, vol. 1, no. 1, 2020.View at: Google Scholar
Strain rate magnitude at the free surface, illustrating Kelvin-Helmoltz (KH) shear instabilities.

On the reef scale hydrodynamics at Sodwana Bay, South Africa

Environmental Fluid Mechanics (2022)Cite this article

Abstract

The hydrodynamics of coral reefs strongly influences their biological functioning, impacting processes such as nutrient availability and uptake, recruitment success and bleaching. For example, coral reefs located in oligotrophic regions depend on upwelling for nutrient supply. Coral reefs at Sodwana Bay, located on the east coast of South Africa, are an example of high latitude marginal reefs. These reefs are subjected to complex hydrodynamic forcings due to the interaction between the strong Agulhas current and the highly variable topography of the region. In this study, we explore the reef scale hydrodynamics resulting from the bathymetry for two steady current scenarios at Two-Mile Reef (TMR) using a combination of field data and numerical simulations. The influence of tides or waves was not considered for this study as well as reef-scale roughness. Tilt current meters with onboard temperature sensors were deployed at selected locations within TMR. We used field observations to identify the dominant flow conditions on the reef for numerical simulations that focused on the hydrodynamics driven by mean currents. During the field campaign, southerly currents were the predominant flow feature with occasional flow reversals to the north. Northerly currents were associated with greater variability towards the southern end of TMR. Numerical simulations showed that Jesser Point was central to the development of flow features for both the northerly and southerly current scenarios. High current variability in the south of TMR during reverse currents is related to the formation of Kelvin-Helmholtz type shear instabilities along the outer edge of an eddy formed north of Jesser Point. Furthermore, downward vertical velocities were computed along the offshore shelf at TMR during southerly currents. Current reversals caused a change in vertical velocities to an upward direction due to the orientation of the bathymetry relative to flow directions.

Highlights

  • A predominant southerly current was measured at Two-Mile Reef with occasional reversals towards the north.
  • Field observations indicated that northerly currents are spatially varied along Two-Mile Reef.
  • Simulation of reverse currents show the formation of a separated flow due to interaction with Jesser Point with Kelvin–Helmholtz type shear instabilities along the seaward edge.

지금까지 Sodwana Bay에서 자세한 암초 규모 유체 역학을 모델링하려는 시도는 없었습니다. 이러한 모델의 결과는 규모가 있는 산호초 사이의 흐름이 산호초 건강에 어떤 영향을 미치는지 탐색하는 데 사용할 수 있습니다. 이 연구에서는 Sodwana Bay의 유체역학을 탐색하는 데 사용할 수 있는 LES 모델을 개발하기 위한 단계별 접근 방식을 구현합니다. 여기서 우리는 이 초기 단계에서 파도와 조수의 영향을 배제하면서 Agulhas 해류의 유체역학에 초점을 맞춥니다. 이 접근법은 흐름의 첫 번째 LES를 제시하고 Sodwana Bay의 산호초에서 혼합함으로써 향후 연구의 기초를 제공합니다.

This is a preview of subscription content, access via your institution.

References

  1. Anarde K, Myres H, Figlus J (2016) Tilt current meter field validation in the surf zone. In: AGU fall meeting abstracts, vol 2016, pp EP23A—-0950
  2. Blocken B (2018) LES over RANS in building simulation for outdoor and indoor applications: A foregone conclusion? Build Simul 11(5):821–870. https://doi.org/10.1007/s12273-018-0459-3Article Google Scholar 
  3. Booij N, Ris RC, Holthuijsen LH (1999) A third-generation wave model for coastal regions: 1. Model description and validation. J Geophys Res Ocean 104(C4):7649–7666. https://doi.org/10.1029/98JC02622Article Google Scholar 
  4. Bouffanais R (2010) Advances and challenges of applied large-eddy simulation. Comput Fluids 39:735–738. https://doi.org/10.1016/j.compfluid.2009.12.003Article Google Scholar 
  5. Celliers L, Schleyer MH (2002) Coral bleaching on high-latitude marginal reefs at Sodwana Bay, South Africa. Mar Pollut Bull 44:1380–1387Article Google Scholar 
  6. Celliers L, Schleyer MH (2008) Coral community structure and risk assessment of high-latitude reefs at Sodwana Bay, South Africa. Biodivers Conserv 17(13):3097–3117. https://doi.org/10.1007/s10531-007-9271-6Article Google Scholar 
  7. Chen SC (2018) Performance assessment of FLOW-3D and XFlow in the numerical modelling of fish-bone type fishway hydraulics https://doi.org/10.15142/T3HH1J
  8. Corbella S, Pringle J, Stretch DD (2015) Assimilation of ocean wave spectra and atmospheric circulation patterns to improve wave modelling. Coast Eng 100:1–10. https://doi.org/10.1016/j.coastaleng.2015.03.003Article Google Scholar 
  9. Davis KA, Pawlak G, Monismith SG (2021) Turbulence and coral reefs. Ann Rev Mar Sci. https://doi.org/10.1146/annurev-marine-042120-071823Article Google Scholar 
  10. Flow Science Inc (2018) FLOW-3D, Version 12.0 Users Manual. Santa Fe, NM, https://www.flow3d.com/
  11. Flow Science Inc (2019) FLOW-3D, Version 12.0 [Computer Software]. Santa Fe, NM, https://www.flow3d.com/
  12. Franco A, Moernaut J, Schneider-Muntau B, Strasser M, Gems B (2020) The 1958 Lituya Bay tsunami – pre-event bathymetry reconstruction and 3D numerical modelling utilising the computational fluid dynamics software Flow-3D. Nat Hazards Earth Syst Sci 20(8):2255–2279Article Google Scholar 
  13. Fringer OB, Gerritsen M, Street RL (2006) An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator. Ocean Model 14(3):139–173Article Google Scholar 
  14. Fringer OB, Dawson CN, He R, Ralston DK, Zhang YJ (2019) The future of coastal and estuarine modeling: findings from a workshop. Ocean Model 143(September):101458. https://doi.org/10.1016/j.ocemod.2019.101458Article Google Scholar 
  15. Glassom D, Celliers L, Schleyer MH (2006) Coral recruitment patterns at Sodwana Bay, South Africa. Coral Reefs 25(3):485–492. https://doi.org/10.1007/s00338-006-0117-6Article Google Scholar 
  16. Gomes A, Pinho JLS, Valente T, do Carmo JS, Hegde VA (2020) Performance assessment of a semi-circular breakwater through CFD modelling. J Mar Sci Eng. https://doi.org/10.3390/jmse8030226Article Google Scholar 
  17. Green RH, Lowe RJ, Buckley ML (2018) Hydrodynamics of a tidally forced coral reef atoll. J Geophys Res Oceans 123(10):7084–7101. https://doi.org/10.1029/2018JC013946Article Google Scholar 
  18. Hansen AB, Carstensen S, Christensen DF, Aagaard T (2017) Performance of a tilt current meter in the surf zone. Coastal dynamics
  19. Hench JL, Rosman JH (2013) Observations of spatial flow patterns at the coral colony scale on a shallow reef flat. J Geophys Res Ocean 118(3):1142–1156. https://doi.org/10.1002/jgrc.20105Article Google Scholar 
  20. Hirt CW (1993) Volume-fraction techniques: powerful tools for wind engineering. J Wind Eng Ind Aerodyn 46–47:327–338. https://doi.org/10.1016/0167-6105(93)90298-3Article Google Scholar 
  21. Hirt CW, Sicilian JM (1985) A porosity technique for the definition of obstacles in rectangular cell meshes. In: Proceedings of 4th International Conference on Ship Hydrodynamics https://ci.nii.ac.jp/naid/10009570543/en/
  22. Hocker LO, Hruska MA (2004) Interleaving synchronous data and asynchronous data in a single data storage file
  23. Hossain MM, Staples AE (2020) Effects of coral colony morphology on turbulent flow dynamics. PLoS ONE 15(10):e0225676. https://doi.org/10.1371/journal.pone.0225676Article Google Scholar 
  24. Jacob B, Stanev EV (2021) Understanding the impact of bathymetric changes in the german bight on coastal hydrodynamics: one step toward realistic morphodynamic modeling. Front Mar Sci. https://doi.org/10.3389/fmars.2021.640214Article Google Scholar 
  25. Koehl MAR, Hadfield MG (2010) Hydrodynamics of larval settlement from a larva’s point of view. Integr Comp Biol 50(4):539–551. https://doi.org/10.1093/icb/icq101Article Google Scholar 
  26. Lim A, Wheeler AJ, Price DM, O’Reilly L, Harris K, Conti L (2020) Influence of benthic currents on cold-water coral habitats: a combined benthic monitoring and 3D photogrammetric investigation. Sci Rep 10(1):19433. https://doi.org/10.1038/s41598-020-76446-yArticle Google Scholar 
  27. Limer BD, Bloomberg J, Holstein DM (2020) The influence of eddies on coral larval retention in the flower garden banks. Front Mar Sci 7:372. https://doi.org/10.3389/fmars.2020.00372Article Google Scholar 
  28. Monismith SG (2007) Hydrodynamics of coral reefs. Annu Rev Fluid Mech 39(1):37–55. https://doi.org/10.1146/annurev.fluid.38.050304.092125Article Google Scholar 
  29. Morris T (2009) Physical oceanography of Sodwana Bay and its effect on larval transport and coral bleaching. PhD thesis, Cape Peninsula University of Technology
  30. Morris T, Lamont T, Roberts MJ (2013) Effects of deep-sea eddies on the northern KwaZulu-Natal shelf, South Africa. Afr J Mar Sci 35(3):343–350. https://doi.org/10.2989/1814232X.2013.827991Article Google Scholar 
  31. Perry C, Larcombe P (2003) Marginal and non-reef-building coral environments. Coral Reefs 22:427–432. https://doi.org/10.1007/s00338-003-0330-5Article Google Scholar 
  32. Pope SB (2001) Turbulent flows. Cambridge University Press, CambridgeGoogle Scholar 
  33. Porter SN (2009) Biogeography and potential factors regulating shallow subtidal reef communities in the Western Indian Ocean. PhD thesis, University of Cape Town
  34. Porter SN, Schleyer MH (2017) Long-term dynamics of a high-latitude coral reef community at Sodwana Bay, South Africa. Coral Reefs 36(2):369–382. https://doi.org/10.1007/s00338-016-1531-zArticle Google Scholar 
  35. Porter SN, Schleyer MH (2019) Environmental variation and how its spatial structure influences the cross-shelf distribution of high-latitude coral communities in South Africa. Diversity. https://doi.org/10.3390/d11040057Article Google Scholar 
  36. Ramsay PJ (1994) Marine geology of the Sodwana Bay shelf, southeast Africa. Mar Geol 120(3–4):225–247. https://doi.org/10.1016/0025-3227(94)90060-4Article Google Scholar 
  37. Ramsay PJ, Mason TR (1990) Development of a type zoning model for Zululand coral reefs, Sodwana Bay, South Africa. J Coastal Res 6(4):829–852Google Scholar 
  38. Reguero BG, Beck MW, Agostini VN, Kramer P, Hancock B (2018) Coral reefs for coastal protection: a new methodological approach and engineering case study in Grenada. J Environ Manag 210:146–161. https://doi.org/10.1016/j.jenvman.2018.01.024Article Google Scholar 
  39. Reidenbach M, Stocking J, Szczyrba L, Wendelken C (2021) Hydrodynamic interactions with coral topography and its impact on larval settlement. Coral Reefs 40:1–15. https://doi.org/10.1007/s00338-021-02069-yArticle Google Scholar 
  40. Reidenbach MA, Koseff JR, Koehl MAR (2009) Hydrodynamic forces on larvae affect their settlement on coral reefs in turbulent, wave-driven flow. Limnol Oceanogr 54(1):318–330. https://doi.org/10.4319/lo.2009.54.1.0318Article Google Scholar 
  41. Roberts H, Richardson J, Lagumbay R, Meselhe E, Ma Y (2013) Hydrodynamic and sediment transport modeling using FLOW-3D for siting and optimization of the LCA medium diversion at white ditch hydrodynamic and sediment transport modeling using FLOW-3D for siting and optimization of the LCA medium diversion at white D (December)
  42. Roberts MJ, Ribbink AJ, Morris T, Berg MAVD, Engelbrecht DC, Harding RT (2006) Oceanographic environment of the Sodwana Bay coelacanths (Latimeria chalumnae), South Africa: coelacanth research. South Afr J Sci 102(9):435–443Google Scholar 
  43. Rogers JS, Monismith SG, Feddersen F, Storlazzi CD (2013) Hydrodynamics of spur and groove formations on a coral reef. J Geophys Res Ocean 118(6):3059–3073. https://doi.org/10.1002/jgrc.20225Article Google Scholar 
  44. Rogers JS, Monismith SG, Koweek DA, Torres WI, Dunbar RB (2016) Thermodynamics and hydrodynamics in an atoll reef system and their influence on coral cover. Limnol Oceanogr 61(6):2191–2206. https://doi.org/10.1002/lno.10365Article Google Scholar 
  45. Schleyer MH, Celliers L (2003) Coral dominance at the reef-sediment interface in marginal coral communities at Sodwana Bay, South Africa. Mar Freshw Res 54(8):967–972. https://doi.org/10.1071/MF02049Article Google Scholar 
  46. Schleyer MH, Porter SN (2018) Chapter One – drivers of soft and stony coral community distribution on the high-latitude coral reefs of South Africa. advances in marine biology, vol 80, Academic Press, pp 1–55, https://doi.org/10.1016/bs.amb.2018.09.001
  47. Scott F, Antolinez JAA, McCall R, Storlazzi C, Reniers A, Pearson S (2020) Hydro-morphological characterization of coral reefs for wave runup prediction. Front Mar Sci 7:361. https://doi.org/10.3389/fmars.2020.00361Article Google Scholar 
  48. Sebens KP, Grace SP, Helmuth B, Maney EJ Jr, Miles JS (1998) Water flow and prey capture by three scleractinian corals, Madracis mirabilis, Montastrea cavernosa and Porites porites, in a field enclosure. Mar Biol 131(2):347–360Article Google Scholar 
  49. Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91(3):99–164Article Google Scholar 
  50. Stocking J, Laforsch C, Sigl R, Reidenbach M (2018) The role of turbulent hydrodynamics and surface morphology on heat and mass transfer in corals. J R Soc Interface 15:20180448. https://doi.org/10.1098/rsif.2018.0448Article Google Scholar 
  51. Van Leer B (1977) Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow. J Comput Phys 23(3):263–275. https://doi.org/10.1016/0021-9991(77)90094-8Article Google Scholar 
  52. Wells C, Pringle J, Stretch D (2021) Cold water temperature anomalies on the Sodwana reefs and their driving mechanisms. South Afr J Sci. https://doi.org/10.17159/sajs.2021/9304Article Google Scholar 
  53. Wyatt ASJ, Lowe RJ, Humphries S, Waite AM (2010) Particulate nutrient fluxes over a fringing coral reef: relevant scales of phytoplankton production and mechanisms of supply. Mar Ecol Prog Ser 405:113–130Article Google Scholar 
  54. Yao Y, He T, Deng Z, Chen L, Guo H (2019) Large eddy simulation modeling of tsunami-like solitary wave processes over fringing reefs. Nat Hazards Earth Syst Sci 19(6):1281–1295. https://doi.org/10.5194/nhess-19-1281-2019Article Google Scholar 
  55. Zhao Q, Tanimoto K (1998) Numerical simulation of breaking waves by large eddy simulation and vof method. Coastal Engineering Proceedings 1(26), 10.9753/icce.v26.%p, https://journals.tdl.org/icce/index.php/icce/article/view/5656

Text and image taken from Deoraj, et al. (2022), On the reef scale hydrodynamics at Sodwana Bay, South Africa. Preprint courtesy the authors.

Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade and Abaunza Tabares, 2021)

Three-dimensional Numerical Evaluation of Hydraulic Efficiency and Discharge Coefficient in Grate Inlets

쇠창살 격자 유입구의 수리효율 및 배출계수에 대한 3차원 수치적 평가

Melquisedec Cortés Zambrano*, Helmer Edgardo Monroy González,
Wilson Enrique Amaya Tequia
Faculty of Civil Engineering, Santo Tomas Tunja University. Address Av. Universitaria No. 45-202.
Tunja – Boyacá – Colombia

Abstract

홍수는 지반이동 및 이동의 원인 중 하나이며, 급속한 도시화 및 도시화로 인해 이전보다 빈번하게 발생할 수 있다. 도시 배수 시스템의 특성은 집수 요소가 결정적인 역할을 하는 범람의 발생 및 범위를 정의할 수 있습니다. 이 문서는 7가지 유형의 화격자 유입구의 수력 유입 효율 및 배출 계수에 대한 수치 조사를 제시합니다. FLOW-3D® 시뮬레이터는 Q = 24, 34.1, 44, 100, 200 및 300 L/s의 유속에서 풀 스케일로 격자를 테스트하는 데 사용되며 종방향 기울기가 1.0인 실험 프로토타입의 구성을 유지합니다. %, 1.5% 및 2.0% 및 고정 횡단 경사, 총 126개 모델. 그 결과를 바탕으로 종류별 및 종단경사 조건에 따른 수력유입구 효율곡선과 토출계수를 구성하였다. 결과는 다른 조사에서 제안된 경험적 공식으로 조정되어 프로토타입의 물리적 테스트 결과를 검증하는 역할을 합니다.

Floods are one of the causes of ground movement and displacement, and due to rapid urbanization and urban growth may occur more frequently than before. The characteristics of an urban drainage system can define the occurrence and extent of flooding, where catchment elements have a determining role. This document presents the numerical investigation of the hydraulic inlet efficiency and the discharge coefficient of seven types of grate inlets. The FLOW-3D® simulator is used to test the gratings at a full scale, under flow rates of Q = 24, 34.1, 44, 100, 200 and 300 L/s, preserving the configuration of the experimental prototype with longitudinal slopes of 1.0%, 1.5% and 2.0% and a fixed cross slope, for a total of 126 models. Based on the results, hydraulic inlet efficiency curves and discharge coefficients are constructed for each type and a longitudinal slope condition. The results are adjusted with empirical formulations proposed in other investigations, serving to verify the results of physical testing of prototypes.

Keywords

grate inlet, inlet efficiency, discharge coefficient, computational fluid dynamic, 3D modelling.

Fig. 1. Physical model of the experimental campaign (source: Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 1. Physical model of the experimental campaign (source: Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade
and Abaunza Tabares, 2021)
Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 4. Comparison between the results obtained during physical experimentation in prototype 7 and simulation results with FLOW-3D® (source:
made with FlowSight® and photographic record by Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 4. Comparison between the results obtained during physical experimentation in prototype 7 and simulation results with FLOW-3D® (source: made with FlowSight® and photographic record by Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 6. Example of the results of flow depth and velocity vectors in the xy plane, for a stable flow condition in a grate inlet type and free surface
configuration and flow regime, of some grating types (source: produced with FlowSight®)
Fig. 6. Example of the results of flow depth and velocity vectors in the xy plane, for a stable flow condition in a grate inlet type and free surface configuration and flow regime, of some grating types (source: produced with FlowSight®)

References

Alia Md., S., and Sabtu, N. (2020). Comparison of Different Methodologies for Determining the Efficiency of Gully Inlets. In F. M.
Nazri (Ed.), Proceedings of AICCE‘19: Transforming the Nation
for a Sustainable Tomorrow (Vol. 53, pp. 1275-1284). Springer
Nature Switzerland AG. https://doi.org/10.1007/978-3-030-
32816-0_99
Antunes do Carmo, J. S. (2020). Physical Modelling vs. Numerical Modelling: Complementarity and Learning. July. https://doi.
org/10.20944/preprints202007.0753.v1
Aragón-Hernández, J. L. (2013). Modelación numérica integrada de los procesos hidráulicos en el drenaje urbano [Universidad Politécnica de Cataluña]. In Doctoral Tesis. https://
upcommons.upc.edu/handle/2117/95059?locale-attribute=es
Argue, J. R., and Pezzaniti, D. (1996). How reliable are inlet
(hydraulic) models at representing stormwater flow? Science
of the Total Environment, 189-190, 355-359. https://doi.org/10.1016/0048-9697(96)05231-X
Banco Mundial, O. (2019). Agua: Panorama general. https://
www.bancomundial.org/es/topic/water/overview
Cárdenas-Quintero, M., Carvajal-Serna, L. F., and Marbello-Pérez, R. (2018). Evaluación numérica tridimensional de un
sumidero de reja de fondo (Three-Dimensional Numerical Assessment of Grate Inlet). SSRN Electronic Journal, November.
https://doi.org/10.2139/ssrn.3112980
Carvalho, R. F., Lopes, P., Leandro, J., and David, L. M. (2019).
Numerical Research of Flows into Gullies with Different Outlet Locations. Water, 11(2), 794. https://doi.org/10.3390/
w11040794
Chaparro Andrade, F. G., and Abaunza Tabares, K. V. (2021). Importancia de los sumideros, su funcionamiento y diseño en redes de alcantarillado caso de estudio sector nororiental Tunja.
Universidad Santo Tomás.
Cortés Zambrano, M., Amaya Tequia, W. E., and Gamba Fernández, D. S. (2020). Implementation of the hydraulic modelling of
urban drainage in the northeast sector, Tunja, Boyacá. Revista
Facultad de Ingeniería Universidad de Antioquia. https://doi.
org/10.17533/udea.redin.20200578
Cosco, C., Gómez, M., Russo, B., Tellez-Alvarez, J., Macchione, F., Costabile, P., and Costanzo, C. (2020). Discharge coefficients for specific grated inlets. Influence of the Froude
number. Urban Water Journal, 17(7), 656-668. https://doi.org/10.1080/1573062X.2020.1811881
Despotovic, J., Plavsic, J., Stefanovic, N., and Pavlovic, D. (2005).
Inefficiency of storm water inlets as a source of urban floods.
Water Science and Technology, 51(2), 139-145. https://doi.
org/10.2166/wst.2005.0041
Ellis, J. B., and Marsalek, J. (1996). Overview of urban drainage:
Environmental impacts and concerns, means of mitigation and
implementation policies. Journal of Hydraulic Research, 34(6),
723-732. https://doi.org/10.1080/00221689609498446
Fang, X., Jiang, S., and Alam, S. R. (2010). Numerical simulations of efficiency of curb-opening inlets. Journal of Hydraulic
Engineering, 136(1), 62-66. https://doi.org/10.1061/(ASCE)
HY.1943-7900.0000131
Faram, M. G., and Harwood, R. (2000). CFD for the Water Industry; The Role of CFD as a Tool for the Development of Wastewater Treatment Systems. Hydro International, 21-22.
Faram, M. G., and Harwood, R. (2002). Assessment of the
effectiveness of stormwater treatment chambers using
computational fluid dynamics. Global Solutions for Urban Drainage, 40644(September 2002), 1-14. https://doi.
org/10.1061/40644(2002)7
Flow Science, I. (2018). FLOW-3D® Version 12.0 Users Manual.
In FLOW-3D [Computer software]. https://www.flow3d.com
Flow Science, I. (2019). FLOW-3D® Version 12.0 [Computer software] (No. 12). https://www.flow3d.com
Ghanbari, R., and Heidarnejad, M. (2020). Experimental and numerical analysis of flow hydraulics in triangular and rectangular
piano key weirs. Water Science, 00(00), 1-7. https://doi.org/10.
1080/11104929.2020.1724649

Gómez, M., and Russo, B. (2005a). Comparative study of methodologies to determine inlet efficiency from test data. HEC-12
methodology vs UPC method. Water Resources Management,
Algarve, Portugal., 80(October 2014), 623-632. https://doi.
org/10.2495/WRM050621
Gómez, M., and Russo, B. (2005b). Comparative study among
different methodologies to determine storm sewer inlet efficiency from test data. 10th International Conference on Urban
Drainage, August, 21-26. https://www.researchgate.net/publication/255602448_Comparative_study_among_different_methodologies_to_determine_storm_sewer_inlet_efficiency_
from_test_data
Gómez, M., Recasens, J., Russo, B., and Martínez-Gomariz, E.
(2016). Assessment of inlet efficiency through a 3D simulation: Numerical and experimental comparison. Water Science
and Technology, 74(8), 1926-1935. https://doi.org/10.2166/
wst.2016.326
Gómez, M., and Russo, B. (2011). Methodology to estimate hydraulic efficiency of drain inlets. Proceedings of the Institution of
Civil Engineers: Water Management, 164(2), 81-90. https://doi.
org/10.1680/wama.900070
Gómez Valentin, M. (2007). Hidrología urbana. In Hidrología Urbana (pp. 135-147). Instituto Flumen.
Jakeman, A. J., Letcher, R. A., and Norton, J. P. (2006). Ten iterative steps in development and evaluation of environmental
models. Environmental Modelling and Software, 21, 602-614.
https://doi.org/10.1016/j.envsoft.2006.01.004
Jang, J. H., Hsieh, C. T., and Chang, T. H. (2019). The importance of gully flow modelling to urban flood simulation. Urban Water Journal, 16(5), 377-388. https://doi.org/10.1080/1573062X.2019.1669198
Kaushal, D. R., Thinglas, T., Tomita, Y., Kuchii, S., and Tsukamoto, H. (2012). Experimental investigation on optimization of
invert trap configuration for sewer solid management. Powder Technology, 215-216, 1-14. https://doi.org/10.1016/j.powtec.2011.08.029
Khazaee, I., and Mohammadiun, M. (2010). Effects of flow field
on open channel flow properties using numerical investigation
and experimental comparison. International Journal of Energy
and Environment, 1(6), 1083-1096. https://doi.org/10.1016/
S0031-9384(10)00122-8
Kleidorfer, M., Tscheikner-Gratl, F., Vonach, T., and Rauch, W.
(2018). What can we learn from a 500-year event? Experiences
from urban drainage in Austria. Water Science and Technology,
77(8), 2146-2154. https://doi.org/10.2166/wst.2018.138
Leitão, J. P., Simões, N. E., Pina, R. D., Ochoa-Rodriguez, S.,
Onof, C., and Sá Marques, A. (2017). Stochastic evaluation of
the impact of sewer inlets‘ hydraulic capacity on urban pluvial
flooding. Stochastic Environmental Research and Risk Assessment, 31(8), 1907-1922. https://doi.org/10.1007/s00477-016-
1283-x
Lopes, P., Leandro, J., Carvalho, R. F., Russo, B., and Gómez, M.
(2016). Assessment of the ability of a volume of fluid model to
reproduce the efficiency of a continuous transverse gully with
grate. Journal of Irrigation and Drainage Engineering, 142(10),
1-9. https://doi.org/10.1061/(ASCE)IR.1943-4774.0001058
Mohsin, M., and Kaushal, D. R. (2016). 3D CFD validation of invert trap efficiency for sewer solid management using VOF model. Water Science and Engineering, 9(2), 106-114. https://doi.
org/10.1016/j.wse.2016.06.006
Palla, A., Colli, M., Candela, A., Aronica, G. T., and Lanza, L.
G. (2018). Pluvial flooding in urban areas: the role of surface
drainage efficiency. Journal of Flood Risk Management, 11,
S663-S676. https://doi.org/10.1111/jfr3.12246
Russo, B. (2010). Design of surface drainage systems according
to hazard criteria related to flooding of urban areas [Universitat
Politècnica de Catalunya]. https://dialnet.unirioja.es/servlet/
tesis?codigo=258828
Sedano-Cruz, K., Carvajal-Escoar, Y., and Ávila Díaz, A. J. (2013).
ANÁLISIS DE ASPECTOS QUE INCREMENTAN EL RIESGO
DE INUNDACIONES EN COLOMBIA. Luna Azul, 37, 219-218.
https://www.redalyc.org/articulo.oa?id=321729206014
Spaliviero, F., May, R. W. P., Escarameia, M. (2000). Spacing of road gullies. Hydraulic performance of BS EN 124 gully gratings. HR Walingford, 44(0). https://doi.org/10.13140/
RG.2.1.1344.0889
Téllez-Álvarez, J., Gómez, M., and Russo, B. (2020). Quantification of energy loss in two grated inlets under pressure. Water
(Switzerland), 12(6). https://doi.org/10.3390/w12061601
Téllez Álvarez, J., Gómez, V., Russo, B., and Redondo, J. M.
(2003). Performance assessment of numerical modelling
for hydraulic efficiency of a grated inlet. 1, 6-8. https://doi.org/10.16309/j.cnki.issn.1007-1776.2003.03.004
Téllez Álvarez, J., Gómez Valentin, M., Paindelli, A., and Russo,
B. (2017). ACTIVIDAD EXPERIMENTAL DE I+D+i EN INGENIERÍA
HIDRÁULICA EN ESPAÑA. In L. J. Balairón Pérez and D. López
Gómez (Eds.), Seminario 2017, Comunicaciones de las líneas prioritarias (pp. 41-43). Universitat Politècnica de València.
https://doi.org/10.1017/CBO9781107415324.004
Téllez Álvarez, J., Gómez Valentin, M., and Russo, B. (2019).
Modelling of Surcharge Flow Through Grated Inlet. In P. Gourbesville and G. Caignaert (Eds.), Advances in Hydroinformati-

cs. Springer, Singapore. https://doi.org/10.1007/978-981-
4451-42-0
UNDRR, I., and CRED, I. (2018). Pérdidas económicas, pobreza y
Desastres 1998 – 2017 (Vol. 6, Issue 1). https://doi.org/10.12962/
j23373520.v6i1.22451
Vyzikas, T., and Greaves, D. (2018). Numerial Modelling.
In D. Greaves and G. Iglesias (Eds.), Wave and Tidal Energy (pp. 289-363). John Wiley and Sons Ltd. https://doi.
org/10.1002/9781119014492
Yakhot, V., and Orszag, S. A. (1986). Renormalization Group Analysis of Turbulence. I . Basic Theory. Journal of Scientific Computing, 1(1), 3-51. https://doi.org/10.1007/BF01061452
Yakhot, V., and Smith, L. M. (1992). The renormalization group,
the ɛ-expansion and derivation of turbulence models. Journal
of Scientific Computing, 7(l), 35-61. https://doi.org/10.1007/
BF01060210
Yazdanfar, Z., and Sharma, A. (2015). Urban drainage system
planning and design – Challenges with climate change and urbanization: A review. Water Science and Technology, 72(2), 165-https://doi.org/10.2166/wst.2015.207

Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system

데이터 기반 방법을 활용한 재생 가능 에너지 변환기의 전력 및 수소 생성 예측 지속 가능한 스마트 그리드 사례 연구

Fatemehsadat Mirshafiee1, Emad Shahbazi 2, Mohadeseh Safi 3, Rituraj Rituraj 4,*
1Department of Electrical and Computer Engineering, K.N. Toosi University of Technology, Tehran 1999143344 , Iran
2Department of Mechatronic, Amirkabir University of Technology, Tehran 158754413, Iran
3Department of Mechatronic, Electrical and Computer Engineering, University of Tehran, Tehran 1416634793, Iran
4 Faculty of Informatics, Obuda University, 1023, Budapest, Hungary

  • Correspondence: rituraj88@stud.uni-obuda.hu

ABSTRACT

본 연구는 지속가능한 에너지 변환기의 전력 및 수소 발생 모델링을 위한 데이터 기반 방법론을 제안합니다. 파고와 풍속을 달리하여 파고와 수소생산을 예측합니다.

또한 이 연구는 파도에서 수소를 추출할 수 있는 가능성을 강조하고 장려합니다. FLOW-3D 소프트웨어 시뮬레이션에서 추출한 데이터와 해양 특수 테스트의 실험 데이터를 사용하여 두 가지 데이터 기반 학습 방법의 비교 분석을 수행합니다.

결과는 수소 생산의 양은 생성된 전력의 양에 비례한다는 것을 보여줍니다. 제안된 재생 에너지 변환기의 신뢰성은 지속 가능한 스마트 그리드 애플리케이션으로 추가로 논의됩니다.

This study proposes a data-driven methodology for modeling power and hydrogen generation of a sustainable energy converter. The wave and hydrogen production at different wave heights and wind speeds are predicted. Furthermore, this research emphasizes and encourages the possibility of extracting hydrogen from ocean waves. By using the extracted data from FLOW-3D software simulation and the experimental data from the special test in the ocean, the comparison analysis of two data-driven learning methods is conducted. The results show that the amount of hydrogen production is proportional to the amount of generated electrical power. The reliability of the proposed renewable energy converter is further discussed as a sustainable smart grid application.

Key words

Cavity, Combustion efficiency, hydrogen fuel, Computational Fluent and Gambit.

Figure 1. The process of power and hydrogen production with Searaser.
Figure 1. The process of power and hydrogen production with Searaser.
Figure 2. The cross-section A-A of the two essential parts of a Searaser
Figure 2. The cross-section A-A of the two essential parts of a Searaser
Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system
Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system
Figure 4. The boundary conditions of the control volume
Figure 4. The boundary conditions of the control volume
Figure 5. The wind velocity during the period of the experimental test
Figure 5. The wind velocity during the period of the experimental test

REFERENCES

  1. Kalbasi, R., Jahangiri, M., Dehshiri, S.J.H., Dehshiri, S.S.H., Ebrahimi, S., Etezadi, Z.A.S. and Karimipour, A., 2021. Finding the
    best station in Belgium to use residential-scale solar heating, one-year dynamic simulation with considering all system losses:
    economic analysis of using ETSW. Sustainable Energy Technologies and Assessments, 45, p.101097.
  2. Megura M, Gunderson R. Better poison is the cure? Critically examining fossil fuel companies, climate change framing, and
    corporate sustainability reports. Energy Research & Social Science. 2022 Mar 1;85:102388.
  3. Holechek JL, Geli HM, Sawalhah MN, Valdez R. A global assessment: can renewable energy replace fossil fuels by 2050?.
    Sustainability. 2022 Jan;14(8):4792.
  4. Ahmad M, Kumar A, Ranjan R. Recent Developments of Tidal Energy as Renewable Energy: An Overview. River and Coastal
    Engineering. 2022:329-43.
  5. Amini E, Mehdipour H, Faraggiana E, Golbaz D, Mozaffari S, Bracco G, Neshat M. Optimization of hydraulic power take-off
    system settings for point absorber wave energy converter. Renewable Energy. 2022 Jun 4.
  6. Claywell, R., Nadai, L., Felde, I., Ardabili, S. 2020. Adaptive neuro-fuzzy inference system and a multilayer perceptron model
    trained with grey wolf optimizer for predicting solar diffuse fraction. Entropy, 22(11), p.1192.
  7. McLeod I, Ringwood JV. Powering data buoys using wave energy: a review of possibilities. Journal of Ocean Engineering and
    Marine Energy. 2022 Jun 20:1-6.
  8. Olsson G. Water interactions: A systemic view: Why we need to comprehend the water-climate-energy-food-economics-lifestyle connections.
  9. Malkowska A, Malkowski A. Green Energy in the Political Debate. InGreen Energy 2023 (pp. 17-39). Springer, Cham.
  10. Mayon R, Ning D, Ding B, Sergiienko NY. Wave energy converter systems–status and perspectives. InModelling and Optimisation of Wave Energy Converters (pp. 3-58). CRC Press.
  11. Available online at: https://www.offshore-energy.biz/uk-ecotricity-introduces-wave-power-device-searaser/ (9/27/2022)
  12. Mousavi SM, et al.,. Deep learning for wave energy converter modeling using long short-term memory. Mathematics. 2021 Apr
    15;9(8):871.
  13. Mega V. The Energy Race to Decarbonisation. InHuman Sustainable Cities 2022 (pp. 105-141). Springer, Cham.
  14. Li R, Tang BJ, Yu B, Liao H, Zhang C, Wei YM. Cost-optimal operation strategy for integrating large scale of renewable energy
    in China’s power system: From a multi-regional perspective. Applied Energy. 2022 Nov 1;325:119780.
  15. Ardabili S., Abdolalizadeh L., Mako C., Torok B., Systematic Review of Deep Learning and Machine Learning for Building
    Energy, Frontiers in Energy Research, 10, 2022.
  16. Penalba M, Aizpurua JI, Martinez-Perurena A, Iglesias G. A data-driven long-term metocean data forecasting approach for the
    design of marine renewable energy systems. Renewable and Sustainable Energy Reviews. 2022 Oct 1;167:112751.
  17. Torabi, M., Hashemi, S., Saybani, M.R., 2019. A Hybrid clustering and classification technique for forecasting short‐term energy
    consumption. Environmental progress & sustainable energy, 38(1), pp.66-76.
  18. Rivera FP, Zalamea J, Espinoza JL, Gonzalez LG. Sustainable use of spilled turbinable energy in Ecuador: Three different energy
    storage systems. Renewable and Sustainable Energy Reviews. 2022 Mar 1;156:112005.
  19. Raza SA, Jiang J. Mathematical foundations for balancing single-phase residential microgrids connected to a three-phase distribution system. IEEE Access. 2022 Jan 6;10:5292-303.
  20. Takach M, Sarajlić M, Peters D, Kroener M, Schuldt F, von Maydell K. Review of Hydrogen Production Techniques from Water
    Using Renewable Energy Sources and Its Storage in Salt Caverns. Energies. 2022 Feb 15;15(4):1415.
  21. Lv Z, Li W, Wei J, Ho F, Cao J, Chen X. Autonomous Chemistry Enabling Environment-Adaptive Electrochemical Energy
    Storage Devices. CCS Chemistry. 2022 Jul 7:1-9.
  22. Dehghan Manshadi, Mahsa, Milad Mousavi, M. Soltani, Amir Mosavi, and Levente Kovacs. 2022. “Deep Learning for Modeling
    an Offshore Hybrid Wind–Wave Energy System” Energies 15, no. 24: 9484. https://doi.org/10.3390/en15249484
  23. Ishaq H, Dincer I, Crawford C. A review on hydrogen production and utilization: Challenges and opportunities. International
    Journal of Hydrogen Energy. 2022 Jul 22;47(62):26238-64.
  24. Maguire JF, Woodcock LV. On the Thermodynamics of Aluminum Cladding Oxidation: Water as the Catalyst for Spontaneous
    Combustion. Journal of Failure Analysis and Prevention. 2022 Sep 10:1-5.
  25. Mohammadi, M. R., Hadavimoghaddam, F., Pourmahdi, M., Atashrouz, S., Munir, M. T., Hemmati-Sarapardeh, A., … & Mohaddespour, A. (2021). Modeling hydrogen solubility in hydrocarbons using extreme gradient boosting and equations of state.
    Scientific reports, 11(1).
  26. Ma S, Qin J, Xiu X, Wang S. Design and performance evaluation of an underwater hybrid system of fuel cell and battery. Energy
    Conversion and Management. 2022 Jun 15;262:115672.
  27. Ahamed R, McKee K, Howard I. A Review of the Linear Generator Type of Wave Energy Converters’ Power Take-Off Systems.
    Sustainability. 2022 Jan;14(16):9936.
  28. Nejad, H.D., Nazari, M., Nazari, M., Mardan, M.M.S., 2022. Fuzzy State-Dependent Riccati Equation (FSDRE) Control of the
    Reverse Osmosis Desalination System With Photovoltaic Power Supply. IEEE Access, 10, pp.95585-95603.
  29. Zou S, Zhou X, Khan I, Weaver WW, Rahman S. Optimization of the electricity generation of a wave energy converter using
    deep reinforcement learning. Ocean Engineering. 2022 Jan 15;244:110363.
  30. Wu J, Qin L, Chen N, Qian C, Zheng S. Investigation on a spring-integrated mechanical power take-off system for wave energy
    conversion purpose. Energy. 2022 Apr 15;245:123318.
  31. Papini G, Dores Piuma FJ, Faedo N, Ringwood JV, Mattiazzo G. Nonlinear Model Reduction by Moment-Matching for a Point
    Absorber Wave Energy Conversion System. Journal of Marine Science and Engineering. 2022 May;10(5):656.
  32. Forbush DD, Bacelli G, Spencer SJ, Coe RG, Bosma B, Lomonaco P. Design and testing of a free floating dual flap wave energy
    converter. Energy. 2022 Feb 1;240:122485.
  33. Rezaei, M.A., 2022. A New Hybrid Cascaded Switched-Capacitor Reduced Switch Multilevel Inverter for Renewable Sources
    and Domestic Loads. IEEE Access, 10, pp.14157-14183.
  34. Lin Z, Cheng L, Huang G. Electricity consumption prediction based on LSTM with attention mechanism. IEEJ Transactions on
    Electrical and Electronic Engineering. 2020;15(4):556-562.
  35. Tavoosi, J., Mohammadzadeh, A., Pahlevanzadeh, B., Kasmani, M.B., 2022. A machine learning approach for active/reactive
    power control of grid-connected doubly-fed induction generators. Ain Shams Engineering Journal, 13(2), p.101564.
  36. Ghalandari, M., 2019. Flutter speed estimation using presented differential quadrature method formulation. Engineering Applications of Computational Fluid Mechanics, 13(1), pp.804-810.
  37. Li Z, Bouscasse B, Ducrozet G, Gentaz L, Le Touzé D, Ferrant P. Spectral wave explicit navier-stokes equations for wavestructure interactions using two-phase computational fluid dynamics solvers. Ocean Engineering. 2021 Feb 1;221:108513.
  38. Zhou Y. Ocean energy applications for coastal communities with artificial intelligencea state-of-the-art review. Energy and AI.
    2022 Jul 29:100189.
  39. Miskati S, Farin FM. Performance evaluation of wave-carpet in wave energy extraction at different coastal regions: an analytical
    approach (Doctoral dissertation, Department of Mechanical and Production Engineering).
  40. Gu C, Li H. Review on Deep Learning Research and Applications in Wind and Wave Energy. Energies. 2022 Feb 17;15(4):1510.
  41. Aazami, R., 2022. Optimal Control of an Energy-Storage System in a Microgrid for Reducing Wind-Power Fluctuations. Sustainability, 14(10), p.6183.
  42. Kabir M, Chowdhury MS, Sultana N, Jamal MS, Techato K. Ocean renewable energy and its prospect for developing economies.
    InRenewable Energy and Sustainability 2022 Jan 1 (pp. 263-298). Elsevier.
  43. Babajani A, Jafari M, Hafezisefat P, Mirhosseini M, Rezania A, Rosendahl L. Parametric study of a wave energy converter
    (Searaser) for Caspian Sea. Energy Procedia. 2018 Aug 1;147:334-42.
  44. He J. Coherence and cross-spectral density matrix analysis of random wind and wave in deep water. Ocean Engineering.
    2020;197:106930
  45. Ijadi Maghsoodi, A., 2018. Renewable energy technology selection problem using integrated h-swara-multimoora approach.
    Sustainability, 10(12), p.4481.
  46. Band, S.S., Ardabili, S., Sookhak, M., Theodore, A., Elnaffar, S., Moslehpour, M., Csaba, M., Torok, B., Pai, H.T., 2022. When
    Smart Cities Get Smarter via Machine Learning: An In-depth Literature Review. IEEE Access.
  47. Shamshirband, S., Rabczuk, T., Nabipour, N. and Chau, K.W., 2020. Prediction of significant wave height; comparison between
    nested grid numerical model, and machine learning models of artificial neural networks, extreme learning and support vector
    machines. Engineering Applications of Computational Fluid Mechanics, 14(1), pp.805-817.
  48. Liu, Z., Mohammadzadeh, A., Turabieh, H., Mafarja, M., 2021. A new online learned interval type-3 fuzzy control system for
    solar energy management systems. IEEE Access, 9, pp.10498-10508.
  49. Bavili, R.E., Mohammadzadeh, A., Tavoosi, J., Mobayen, S., Assawinchaichote, W., Asad, J.H. 2021. A New Active Fault Tolerant Control System: Predictive Online Fault Estimation. IEEE Access, 9, pp.118461-118471.
  50. Akbari, E., Teimouri, A.R., Saki, M., Rezaei, M.A., Hu, J., Band, S.S., Pai, H.T., 2022. A Fault-Tolerant Cascaded SwitchedCapacitor Multilevel Inverter for Domestic Applications in Smart Grids. IEEE Access.
  51. Band, S.S., Ardabili, S., 2022. Feasibility of soft computing techniques for estimating the long-term mean monthly wind speed.
    Energy Reports, 8, pp.638-648.
  52. Tavoosi, J., Mohammadzadeh, A., Pahlevanzadeh, B., Kasmani, M.B., 2022. A machine learning approach for active/reactive
    power control of grid-connected doubly-fed induction generators. Ain Shams Engineering Journal, 13(2), p.101564.
  53. Ponnusamy, V. K., Kasinathan, P., Madurai Elavarasan, R., Ramanathan, V., Anandan, R. K., Subramaniam, U., … & Hossain,
    E. A Comprehensive Review on Sustainable Aspects of Big Data Analytics for the Smart Grid. Sustainability, 2021; 13(23),
    13322.
  54. Ahmad, T., Zhang, D., Huang, C., Zhang, H., Dai, N., Song, Y., & Chen, H. Artificial intelligence in sustainable energy industry:
    Status Quo, challenges and opportunities. Journal of Cleaner Production, 2021; 289, 125834.
  55. Wang, G., Chao, Y., Cao, Y., Jiang, T., Han, W., & Chen, Z. A comprehensive review of research works based on evolutionary
    game theory for sustainable energy development. Energy Reports, 2022; 8, 114-136.
  56. Iranmehr H., Modeling the Price of Emergency Power Transmission Lines in the Reserve Market Due to the Influence of Renewable Energies, Frontiers in Energy Research, 9, 2022
  57. Farmanbar, M., Parham, K., Arild, Ø., & Rong, C. A widespread review of smart grids towards smart cities. Energies, 2019;
    12(23), 4484.
  58. Quartier, N., Crespo, A. J., Domínguez, J. M., Stratigaki, V., & Troch, P. Efficient response of an onshore Oscillating Water
    Column Wave Energy Converter using a one-phase SPH model coupled with a multiphysics library. Applied Ocean Research,
    2021; 115, 102856.
  59. Mahmoodi, K., Nepomuceno, E., & Razminia, A. Wave excitation force forecasting using neural networks. Energy, 2022; 247,
    123322.
  60. Wang, H., Alattas, K.A., 2022. Comprehensive review of load forecasting with emphasis on intelligent computing approaches.
    Energy Reports, 8, pp.13189-13198.
  61. Clemente, D., Rosa-Santos, P., & Taveira-Pinto, F. On the potential synergies and applications of wave energy converters: A
    review. Renewable and Sustainable Energy Reviews, 2021; 135, 110162.
  62. Felix, A., V. Hernández-Fontes, J., Lithgow, D., Mendoza, E., Posada, G., Ring, M., & Silva, R. Wave energy in tropical regions:
    deployment challenges, environmental and social perspectives. Journal of Marine Science and Engineering, 2019; 7(7), 219.
  63. Farrok, O., Ahmed, K., Tahlil, A. D., Farah, M. M., Kiran, M. R., & Islam, M. R. Electrical power generation from the oceanic
    wave for sustainable advancement in renewable energy technologies. Sustainability, 2020; 12(6), 2178.
  64. Guo, B., & Ringwood, J. V. A review of wave energy technology from a research and commercial perspective. IET Renewable
    Power Generation, 2021; 15(14), 3065-3090.
  65. López-Ruiz, A., Bergillos, R. J., Lira-Loarca, A., & Ortega-Sánchez, M. A methodology for the long-term simulation and uncertainty analysis of the operational lifetime performance of wave energy converter arrays. Energy, 2018; 153, 126-135.
  66. Safarian, S., Saryazdi, S. M. E., Unnthorsson, R., & Richter, C. Artificial neural network integrated with thermodynamic equilibrium modeling of downdraft biomass gasification-power production plant. Energy, 2020; 213, 118800.
  67. Kushwah, S. An oscillating water column (OWC): the wave energy converter. Journal of The Institution of Engineers (India):
    Series C, 2021; 102(5), 1311-1317.
  68. Pap, J., Mako, C., Illessy, M., Kis, N., 2022. Modeling Organizational Performance with Machine Learning. Journal of Open
    Innovation: Technology, Market, and Complexity, 8(4), p.177.
  69. Pap, J., Mako, C., Illessy, M., Dedaj, Z., Ardabili, S., Torok, B., 2022. Correlation Analysis of Factors Affecting Firm Performance
    and Employees Wellbeing: Application of Advanced Machine Learning Analysis. Algorithms, 15(9), p.300.
  70. Alanazi, A., 2022. Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method. Applied Sciences, 12(16), p.7959.
  71. Shakibjoo, A.D., Moradzadeh, M., Din, S.U., 2021. Optimized Type-2 Fuzzy Frequency Control for Multi-Area Power Systems.
    IEEE access, 10, pp.6989-7002.
  72. Zhang, G., 2021. Solar radiation estimation in different climates with meteorological variables using Bayesian model averaging
    and new soft computing models. Energy Reports, 7, pp.8973-8996.
  73. Cao, Y., Raise, A., Mohammadzadeh, A., Rathinasamy, S., 2021. Deep learned recurrent type-3 fuzzy system: Application for
    renewable energy modeling/prediction. Energy Reports, 7, pp.8115-8127.
  74. Tavoosi, J., Suratgar, A.A., Menhaj, M.B., 2021. Modeling renewable energy systems by a self-evolving nonlinear consequent
    part recurrent type-2 fuzzy system for power prediction. Sustainability, 13(6), p.3301.
  75. Bourouis, S., Band, S.S., 2022. Meta-Heuristic Algorithm-Tuned Neural Network for Breast Cancer Diagnosis Using Ultrasound
    Images. Frontiers in Oncology, 12, p.834028.
  76. Mosavi, A.H., Mohammadzadeh, A., Rathinasamy, S., Zhang, C., Reuter, U., Levente, K. and Adeli, H., 2022. Deep learning
    fuzzy immersion and invariance control for type-I diabetes. Computers in Biology and Medicine, 149, p.105975.
  77. Almutairi, K., Algarni, S., Alqahtani, T., Moayedi, H., 2022. A TLBO-Tuned Neural Processor for Predicting Heating Load in
    Residential Buildings. Sustainability, 14(10), p.5924.
  78. Ahmad, Z., Zhong, H., 2020. Machine learning modeling of aerobic biodegradation for azo dyes and hexavalent chromium.
    Mathematics, 8(6), p.913.
  79. Mosavi, A., Shokri, M., Mansor, Z., Qasem, S.N., Band, S.S. and Mohammadzadeh, A., 2020. Machine learning for modeling
    the singular multi-pantograph equations. Entropy, 22(9), p.1041.
  80. Ardabili, S., 2019, September. Deep learning and machine learning in hydrological processes climate change and earth systems
    a systematic review. In International conference on global research and education (pp. 52-62). Springer, Cham.
  81. Moayedi, H., (2021). Suggesting a stochastic fractal search paradigm in combination with artificial neural network for early
    prediction of cooling load in residential buildings. Energies, 14(6), 1649.
  82. Rezakazemi, M., et al., 2019. ANFIS pattern for molecular membranes separation optimization. Journal of Molecular Liquids,
    274, pp.470-476.
  83. Mosavi, A., Faghan, Y., Ghamisi, P., Duan, P., Ardabili, S.F., Salwana, E. and Band, S.S., 2020. Comprehensive review of deep
    reinforcement learning methods and applications in economics. Mathematics, 8(10), p.1640.
  84. Samadianfard, S., Jarhan, S., Salwana, E., 2019. Support vector regression integrated with fruit fly optimization algorithm for
    river flow forecasting in Lake Urmia Basin. Water, 11(9), p.1934.
  85. Moayedi, H., (2021). Double-target based neural networks in predicting energy consumption in residential buildings. Energies,
    14(5), 1331.
  86. Choubin, B., 2019. Earth fissure hazard prediction using machine learning models. Environmental research, 179, p.108770.
  87. Mohammadzadeh S, D., Kazemi, S.F., 2019. Prediction of compression index of fine-grained soils using a gene expression programming model. Infrastructures, 4(2), p.26.
  88. Karballaeezadeh, N., Mohammadzadeh S, D., Shamshirband, S., Hajikhodaverdikhan, P., 2019. Prediction of remaining service
    life of pavement using an optimized support vector machine (case study of Semnan–Firuzkuh road). Engineering Applications
    of Computational Fluid Mechanics, 13(1), pp.188-198.
  89. Rezaei, M. Et al., (2022). Adaptation of A Real-Time Deep Learning Approach with An Analog Fault Detection Technique for
    Reliability Forecasting of Capacitor Banks Used in Mobile Vehicles. IEEE Access v. 21 pp. 89-99.
  90. Khakian, R., et al., (2020). Modeling nearly zero energy buildings for sustainable development in rural areas. Energies, 13(10),
    2593.
Figure 1 | Laboratory channel dimensions.

강화된 조도 계수 및 인버트 레벨 변화가 있는 90도 측면 턴아웃에서의 유동에 대한 실험적 및 수치적 연구

Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

Maryam Bagheria, Seyed M. Ali Zomorodianb, Masih Zolghadrc, H. Md. Azamathulla d,*
and C. Venkata Siva Rama Prasade
a Hydraulic Structures, Department of Water Engineering, Shiraz University, Shiraz, Iran
b Department of Water Engineering, College of Agriculture, Shiraz University, Shiraz, Iran
c Department of Water Sciences Engineering, College of Agriculture, Jahrom University, Jahrom, Iran
d Civil & Environmental Engineering, The University of the West Indies, St. Augustine Campus, Port of Spain, Trinidad
e Department of Civil Engineering, St. Peters Engineering College, Hyderabad, India
*Corresponding author. E-mail: azmatheditor@gmail.com

ABSTRACT

측면 분기기(흡입구)의 상류측에서 유동 분리는 분기기 입구에서 맴돌이 전류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 분기 용량 및 효율성을 감소시킵니다. 따라서 분리구역의 크기를 파악하고 그 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다.

본 연구에서는 분리 구역의 크기를 줄이기 위한 방법으로 분출구 입구에 7가지 유형의 조면화 요소와 4가지 다른 방류가 있는 3가지 다른 베드 인버트 레벨의 설치(총 84회 실험)를 조사했습니다. 또한 3D 전산 유체 역학(CFD) 모델을 사용하여 분리 구역의 흐름 패턴과 치수를 평가했습니다.

결과는 조도 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면 드롭 구현 효과는 사용된 조도 계수에 따라 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 방법을 결합하면 분리 구역 치수를 최대 63%까지 줄일 수 있습니다.

Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions.

Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone.

Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.

Key words

discharge ratio, flow separation zone, intake, three dimensional simulation

Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced
roughness coefficient and invert level changes
Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes
Figure 1 | Laboratory channel dimensions.
Figure 1 | Laboratory channel dimensions.
Figure 2 | Roughness plates.
Figure 2 | Roughness plates.
Figure 4 | Effect of roughness on separation zone dimensions.
Figure 4 | Effect of roughness on separation zone dimensions.
Figure 10 | Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).
Figure 10 | Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).
Figure 11 | Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.
Figure 11 | Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.
Figure 12 | Velocity vector for flow condition Q¼22 l/s, near surface.
Figure 12 | Velocity vector for flow condition Q¼22 l/s, near surface.

REFERENCES

Abbasi, A., Ghodsian, M., Habibi, M. & Salehi Neishabouri, S. A. 2004 Experimental investigation on dimensions of flow separation zone at
lateral intakeentrance. Research & Construction; Pajouhesh va Sazandegi 62, 38–44. (In Persian).
Al-Zubaidy, R. & Hilo, A. 2021 Numerical investigation of flow behavior at the lateral intake using Computational Fluid Dynamics (CFD).
Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2021.11.172.
Chow, V. T. 1959 Open Channel Hydraulics. McGraw-Hill, New York.
Jalili, H., Hosseinzadeh Dalir, A. & Farsadizadeh, D. 2011 Effect of intake geometry on the sediment transport and lateral flow pattern.
Iranian Water Research Journal 5 (9), 1–10. (In Persian).
Jamshidi, A., Farsadizadeh, D. & Hosseinzadeh Dalir, A. 2016 Variations of flow separation zone at lateral intake entrance using submerged
vanes. Journal of Civil Engineering Urban 6 (3), 54–63. Journal homepage. Available from: www.ojceu.ir/main.
Karami Moghaddam, K. & Keshavarzi, A. 2007 Investigation of flow structure in lateral intakes of 55° and 90° with rounded entrance edge.
In: 03 National Congress on Civil Engineering University of Tabriz. Available from: https://civilica.com/doc/16317. (In Persian).
Karami, H., Farzin, S., Sadrabadi, M. T. & Moazeni, H. 2017 Simulation of flow pattern at rectangular lateral intake with different dike and
submerged vane scenarios. Journal of Water Science and Engineering 10 (3), 246–255. https://doi.org/10.1016/j.wse.2017.10.001.
Kasthuri, B. & Pundarikanthan, N. V. 1987 Discussion on separation zone at open- channel junction. Journal of Hydraulic Engineering
113 (4), 543–548.
Keshavarzi, A. & Habibi, L. 2005 Optimizing water intake angle by flow separation analysis. Journal of Irrigation and Drain 54, 543–552.
https://doi.org/10.1002/ird.207.
Kirkgöz, M. S. & Ardiçlioğ
lu, M. 1997 Velocity profiles of developing and developed open channel flow. Journal of Hydraulic Engineering
1099–1105. 10.1061/(ASCE)0733-9429(1997)123:12(1099).
Nakato, T., Kennedy, J. F. & Bauerly, D. 1990 Pumpstation intake-shoaling control with submerge vanes. Journal of Hydraulic Engineering.
https://doi.org/10.1061/(ASCE)0733-9429(1990)116:1(119).
Neary, V. S. & Odgaard, J. A. 1993 Three-dimensional flow structure at open channel diversions. Journal of Hydraulic Engineering. ASCE 119
(11), 1224–1230. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:11(1223).
Nikbin, S. & Borghei, S. M. 2011 Experimental investigation of submerged vanes effect on dimensions of flow separation zone at a 90°
openchannel junction. In: 06rd National Congress on Civil Engineering University of Semnan. (In Persian). Available from: https://
civilica.com/doc/120494.
Odgaard, J. A. & Wang, Y. 1991 Sediment management with submerged vanes, I: theory. Journal of Hydraulic Engineering 117 (3), 267–283.

Ramamurthy, A. S., Junying, Q. & Diep, V. 2007 Numerical and experimental study of dividing open-channel flows. Journal of Hydraulic
Engineering. See: https://doi.org/10.1061/(ASCE)0733-9429(2007)133:10(1135).
Seyedian, S., Karami Moghaddam, K. & Shafai Begestan, M. 2008 Determining the optimal radius in lateral intakes of 55° and 90° using
variation of flow velocity. In: 07th Iranian Hydraulic Conference. Power & Water University of Technology (PWUT). (In Persian).
Available from: https://civilica.com/doc/56251.
Zolghadr, M. & Shafai Bejestan, M. 2020 Six legged concrete (SLC) elements as scour countermeasures at wing wall bridge abutments.
International Journal of River Basin Management. doi: 10.1080/15715124.2020.1726357.
Zolghadr, M., Zomorodian, S. M. A., Shabani, R. & Azamatulla Md., H. 2021 Migration of sand mining pit in rivers: an experimental,
numerical and case study. Measurement. https://doi.org/10.1016/j.measurement.2020.108944

Figure 3: Wave pattern at sea surface at 20 knots (10.29 m/s) for mesh 1

Flow-3D에서 CFD 시뮬레이션을 사용한 선박 저항 분석

Ship resistance analysis using CFD simulations in Flow-3D

Author

Deshpande, SujaySundsbø, Per-ArneDas, Subhashis

Abstract

선박의 동력 요구 사항을 설계할 때 고려해야 할 가장 중요한 요소는 선박 저항 또는 선박에 작용하는 항력입니다. 항력을 극복하는 데 필요한 동력이 추진 시스템의 ‘손실’에 기여하기 때문에 추진 시스템을 설계하는 동안 선박 저항을 추정하는 것이 중요합니다. 선박 저항을 계산하는 세 가지 주요 방법이 있습니다:

Holtrop-Mennen(HM) 방법과 같은 통계적 방법, 수치 분석 또는 CFD(전산 유체 역학) 시뮬레이션 및 모델 테스트, 즉 예인 탱크에서 축소된 모델 테스트. 설계 단계 초기에는 기본 선박 매개변수만 사용할 수 있을 때 HM 방법과 같은 통계 모델만 사용할 수 있습니다.

수치 해석/CFD 시뮬레이션 및 모델 테스트는 선박의 완전한 3D 설계가 완료된 경우에만 수행할 수 있습니다. 본 논문은 Flow-3D 소프트웨어 패키지를 사용하여 CFD 시뮬레이션을 사용하여 잔잔한 수상 선박 저항을 예측하는 것을 목표로 합니다.

롤온/롤오프 승객(RoPax) 페리에 대한 사례 연구를 조사했습니다. 선박 저항은 다양한 선박 속도에서 계산되었습니다. 메쉬는 모든 CFD 시뮬레이션의 결과에 영향을 미치기 때문에 메쉬 민감도를 확인하기 위해 여러 개의 메쉬가 사용되었습니다. 시뮬레이션의 결과를 HM 방법의 추정치와 비교했습니다.

시뮬레이션 결과는 낮은 선박 속도에 대한 HM 방법과 잘 일치했습니다. 더 높은 선속을 위한 HM 방법에 비해 결과의 차이가 상당히 컸다. 선박 저항 분석을 수행하는 Flow-3D의 기능이 시연되었습니다.

While designing the power requirements of a ship, the most important factor to be considered is the ship resistance, or the sea drag forces acting on the ship. It is important to have an estimate of the ship resistance while designing the propulsion system since the power required to overcome the sea drag forces contribute to ‘losses’ in the propulsion system. There are three main methods to calculate ship resistance: Statistical methods like the Holtrop-Mennen (HM) method, numerical analysis or CFD (Computational Fluid Dynamics) simulations, and model testing, i.e. scaled model tests in towing tanks. At the start of the design stage, when only basic ship parameters are available, only statistical models like the HM method can be used. Numerical analysis/ CFD simulations and model tests can be performed only when the complete 3D design of the ship is completed. The present paper aims at predicting the calm water ship resistance using CFD simulations, using the Flow-3D software package. A case study of a roll-on/roll-off passenger (RoPax) ferry was investigated. Ship resistance was calculated at various ship speeds. Since the mesh affects the results in any CFD simulation, multiple meshes were used to check the mesh sensitivity. The results from the simulations were compared with the estimate from the HM method. The results from simulations agreed well with the HM method for low ship speeds. The difference in the results was considerably high compared to the HM method for higher ship speeds. The capability of Flow-3D to perform ship resistance analysis was demonstrated.

Figure 1: Simplified ship geometry
Figure 1: Simplified ship geometry
Figure 3: Wave pattern at sea surface at 20 knots (10.29 m/s) for mesh 1
Figure 3: Wave pattern at sea surface at 20 knots (10.29 m/s) for mesh 1
Figure 4: Ship Resistance (kN) vs Ship Speed (knots)
Figure 4: Ship Resistance (kN) vs Ship Speed (knots)

Publisher

International Society of Multiphysics

Citation

Deshpande SR, Sundsbø P, Das S. Ship resistance analysis using CFD simulations in Flow-3D. The International Journal of Multiphysics. 2020;14(3):227-236

REFERENCES

[1] K. Min and S. Kang, “Study on the form factor and full-scale ship resistance prediction
method,” Journal of Marine Science and Technology, vol. 15, pp. 108-118, June 2010.
[2] A. Molland, S. Turnock and D. Hudson, “Ship Resistance and Propulsion” Second
Edition. In Ship Resistance and Propulsion: Practical Estimation of Ship Propulsive
Power (pp. 12-69), August 2017, Cambridge University Press.
[3] K. Niklas and H. Pruszko, “Full-scale CFD simulations for the determination of ship
resistance as a rational, alternative method to towing tank experiments,” Ocean
Engineering, vol. 190, October 2019.
[4] A. Elkafas, M. Elgohary and A. Zeid, “Numerical study on the hydrodynamic drag force
of a container ship model,” Alexandria Engineering Journal, vol. 58, no. 3, pp. 849-859,
September 2019.
[5] J. Holtrop and G. Mennen, “An approximate power prediction method,” International
Shipbuilding Progress, vol. 29, no. 335, pp. 166-170, July 1982.
[6] E. Bøckmann and S. Steen, “Model test and simulation of a ship with wavefoils,” Applied
Ocean research, vol. 57, pp. 8-18, April 2016.
[7] K. Atreyapurapu, B. Tallapragada and K. Voonna, “Simulation of a Free Surface Flow
over a Container Vessel Using CFD,” International Journal of Engineering Trends and
Technology (IJETT), vol. 18, no. 7, pp. 334-339, December 2014.
[8] J. Petersen, D. Jacobsen and O. Winther, “Statistical modelling for ship propulsion
efficiency,” Journal of Marine Science and Technology, vol. 17, pp. 30-39, December
2011.
[9] H. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics: the
finite volume method (second edition), Harlow, England: Pearson Education Ltd, 2007.
[10]C. Hirth and B. Nichols, “Volume of fluid (VOF) method for the dynamics of free
boundaries,” Journal of Computational Physics, vol. 39, no. 1, pp. 201-225, January 1981.
[11] A. Nordli and H. Khawaja, “Comparison of Explicit Method of Solution for CFD Euler
Problems using MATLAB® and FORTRAN 77,” International Journal of Multiphysics,
vol. 13, no. 2, 2019.
[12] FLOW-3D® Version 12.0 User’s Manual (2018). FLOW-3D [Computer software]. Santa
Fe, NM: Flow Science, Inc. https://www.flow3d.com.
[13] D. McCluskey and A. Holdø, “Optimizing the hydrocyclone for ballast water treatment
using computational fluid dynamics,” International Journal of Multiphysics, vol. 3, no. 3,
2009.
[14]M. Breuer, D. Lakehal and W. Rodi, “Flow around a Surface Mounted Cubical Obstacle:
Comparison of Les and Rans-Results,” Computation of Three-Dimensional Complex
Flows. Notes on Numerical Fluid Mechanics, vol. 49, p. 1996.
[15] G. Wei, “A Fixed-Mesh Method for General Moving Objects in Fluid Flow”, Modern
Physics Letters B, vol. 19, no. 28, pp. 1719-1722, 2005.
[16]J. Michell, “The wave-resistance of a ship,” The London, Edinburgh, and Dublin
Philosophical Magazine and Journal of Science, Vols. 45, 1898, no. 272, pp. 106-123,
May 2009.

Figure 7. Comparison of Archimedean screw power performances P(W) for Q = 0.15 m3 /s and 0.30m3 /s and angles of orientation 22ο & 32ο .

CFD Simulations of Tubular Archimedean Screw Turbines Harnessing the Small Hydropotential of Greek Watercourses

Alkistis Stergiopoulou 1, Vassilios Stergiopoulos 2
1 Institut für Wasserwirtschaft, Hydrologie und Konstruktiven Wasserbau, B.O.K.U. University, Muthgasse 18, 1190 Vienna, (actually Senior Process Engineer at the VTU Engineering in Vienna, Zieglergasse 53/1/24, 1070 Vienna, Austria).2 School of Pedagogical and Technological Education, Department of Civil Engineering Educators, ASPETE Campus, Eirini Station, 15122 Amarousio, Athens, Greece.

Abstract

이 논문은 최초의 아르키메데스 나사 터빈 CFD 모델링 결과에 대한 간략한 견해를 제시하며, 이는 “그리스에서 아르키메데스의 부활: 수리 역학 및 아르키메데스 달팽이관 물레방아의 유체역학적 거동 연구에 대한 기여”라는 제목의 최근 연구에서 수행되었습니다.
그리스 자연 및 기술 수로의 수력 잠재력”. Flow-3D 코드를 기반으로 하는 이 CFD 분석은 일반적인 TAST(Tubular Archimedean Screw Turbines)와 관련이 있으며 몇 TWh 정도의 그리스 자연 및 기술 수로의 중요한 미개발 수력 잠재력을 활용하는 연간 및 수천 MW 범위의 총 설치 용량인 소규모 수력 발전 시스템에 대한 몇 가지 유망한 성능을 보여줍니다.

This paper presents a short view of the first Archimedean Screw Turbines CFD modelling results, which were carried out within the recent research entitled “Rebirth of Archimedes in Greece: contribution to the study of hydraulic mechanics and hydrodynamic behavior of Archimedean cochlear waterwheels, for recovering the hydraulic potential of Greek natural and technical watercourses”. This CFD analysis, based to the Flow-3D code, concerns typical Tubular Archimedean Screw Turbines (TASTs) and shows some promising performances for such small hydropower systems harnessing the important unexploited hydraulic potential of natural and technical watercourses of Greece, of the order of several TWh / year and of a total installed capacity in the range of thousands MWs.

Keywords

CFD; Flow-3D; TAST; Small Hydro; Renewable Energy; Greek Watercourses.

Figure 1. Photorealistic view of an inclined axis TAST (photo A. Stergiopoulou).
Figure 1. Photorealistic view of an inclined axis TAST (photo A. Stergiopoulou).
Figure 3. The spectrum of all the screw axis orientation cases.
Figure 3. The spectrum of all the screw axis orientation cases.
Figure 4. Creation of the 3bladed Archimedean Screw with Solidworks
Figure 4. Creation of the 3bladed Archimedean Screw with Solidworks
Figure 6. “Meshing & Geometry” tab Operations (Flow 3-D).
Figure 6. “Meshing & Geometry” tab Operations (Flow 3-D).
Figure 7. Comparison of Archimedean screw power performances P(W) for Q = 0.15 m3
/s and 0.30m3
/s
and angles of orientation 22ο & 32ο
.
Figure 7. Comparison of Archimedean screw power performances P(W) for Q = 0.15 m3 /s and 0.30m3 /s and angles of orientation 22ο & 32ο .
Figure 12. Various performances of the Archimedean Screw (MKE/Mean Kinetic Energy, Torque,
Turbulent Kinetic Energy, Turbulent Dissipation) for flow discharge Q = 0.45 m3
/s and an angle of
orientation θ = 32ο
Figure 12. Various performances of the Archimedean Screw (MKE/Mean Kinetic Energy, Torque, Turbulent Kinetic Energy, Turbulent Dissipation) for flow discharge Q = 0.45 m3 /s and an angle of orientation θ = 32ο

References

[1] A. Stergiopoulou, Computational and experimental investigation of the hydrodynamic behaviour of
screw hydro turbine, Ph.D. Thesis, NTUA, 2017.
[2] B. Pelikan, A. Lashofer, Verbesserung der Strömungseigenschaften sowie Planungs-und
Betriebsoptimierung von Wasserkraftschnecken, Research Project, BOKU University, Vienna,
2012.
[3] G. Müller, J. Senior, Simplified theory of Archimedean screws, Journal of Hydraulic Research 47
(5) (2009) 666-669.
[4] C. Rorres, The turn of the screw: Optimal design of an Archimedes screw, Journal of Hydraulic
Engineering, 80 (2000) 72-80.
[5] A. Stergiopoulou, V. Stergiopoulos, Return of Archimedes: Harnessing with new Archimedean
spirals the hydraulic potential of the Greek watercourses, in: Proceedings of the Conference for
Climate Change, Thessaloniki, 2009.
[6] A. Stergiopoulou, V. Stergiopoulos, from the old Archimedean screw pumps to the new
Archimedean screw turbines for hydropower production in Greece, in: Proceedings of CEMEPE
Conference, Mykonos, June 21-26, 2009.

[7] V. Stergiopoulos, A. Stergiopoulou, E. Kalkani, Quo Vadis Archimedes Nowadays in Greece?
Towards Modern Archimedean Turbines for Recovering Greek Small Hydropower Potential, in:
Proceedings of 3rd International Scientific “Energy and Climate Change” Conference, Athens, 2010.
[8] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Greece beyond the horizon of the era of transition:
Archimedean screw hydropower development terra incognita, International Journal of Energy and
Development, v.6, Issue 6, pp. 627-536, 2015.
[9] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Experimental and theoretical research of zero head
innovative horizontal axis Archimedean screw turbines, Journal of Energy and Development, v.6,
Issue 5, pp. 471-478, 2015.
[10] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Back to the Future: Rediscovering the Archimedean
screws as modern turbines for harnessing Greek small hydropower potential, in: Proceedings of the
Third International Conference CEMEPE 2011 & SECOTOX, Skiathos, 2011.
[11] A. Stergiopoulou, V. Stergiopoulos, Educational Renewable Energy Screw Wheel Technologies for
Pico Hydropower Generation, Modern Environmental Science and Engineering, v.4, No.5, pp. 439-
445, May 2018.
[12] A. Stergiopoulou, V. Stergiopoulos, Educational Renewable Energy Screw Wheel Technologies for
Pico Hydropower Generation, Modern Environmental Science and Engineering, v.4, No.5, pp. 439-
445, May 2018.
[13] A. Stergiopoulou, V. Stergiopoulos, Towards an inventory of the archimedean small hydropower
potential of Greece, INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT
Volume 11, Issue 2, 2020 pp.137-144.
[14] Flow Science, FLOW-3D Manual, 2013.
[15] K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics, Pearson,
2007.
[16] C. Hirsch, Numerical Computation of internal and external flows: The fundamentals of
Computational Fluid dynamics, John Wiley & Sons, 2007.
[17] A. Stergiopoulou, V. Stergiopoulos and E. Kalkani, An eagle’s CFD view of Studying Innovative
Archimedean Screw Renewable Hydraulic Energy Systems, Proceedings of the 4th International
Conference on Environmental Management, Engineering, Planning and Economics (CEMEPE) and
SECOTOX Conference, Mykonos island, Greece, pp.454-460 June 24-28, 2013.
[18] A. Stergiopoulou, V. Stergiopoulos, A., E. Kalkani, Computational Fluid Dynamics Study on a 3D
Graphic Solid Model of Archimedean Screw Turbines, Fresenius Environmental Bulletin, vol.23-
No1, 2014.
[19] Α. Stergiopoulou, Kalkani E., “Towards a First C.F.D. Study of Innovative Archimedean Inclined
Axis Hydropower Turbines”, International Journal of Engineering Research & Technology (IJERT),
Vol. 2 Issue 9, September – 2013, pp. 193-199.
[20] A. Stergiopoulou, V. Stergiopoulos, A first CFD study of small hydro energy recovery from the
Attica water supply network, INTERNATIONAL JOURNAL OF ENERGY AND
ENVIRONMENT, Volume 11, Issue 3, 2020 pp.157-166.

Figure 5. Schematic view of flap and support structure [32]

Design Optimization of Ocean Renewable Energy Converter Using a Combined Bi-level Metaheuristic Approach

결합된 Bi-level 메타휴리스틱 접근법을 사용한 해양 재생 에너지 변환기의 설계 최적화

Erfan Amini a1, Mahdieh Nasiri b1, Navid Salami Pargoo a, Zahra Mozhgani c, Danial Golbaz d, Mehrdad Baniesmaeil e, Meysam Majidi Nezhad f, Mehdi Neshat gj, Davide Astiaso Garcia h, Georgios Sylaios i

Abstract

In recent years, there has been an increasing interest in renewable energies in view of the fact that fossil fuels are the leading cause of catastrophic environmental consequences. Ocean wave energy is a renewable energy source that is particularly prevalent in coastal areas. Since many countries have tremendous potential to extract this type of energy, a number of researchers have sought to determine certain effective factors on wave converters’ performance, with a primary emphasis on ambient factors. In this study, we used metaheuristic optimization methods to investigate the effects of geometric factors on the performance of an Oscillating Surge Wave Energy Converter (OSWEC), in addition to the effects of hydrodynamic parameters. To do so, we used CATIA software to model different geometries which were then inserted into a numerical model developed in Flow3D software. A Ribed-surface design of the converter’s flap is also introduced in this study to maximize wave-converter interaction. Besides, a Bi-level Hill Climbing Multi-Verse Optimization (HCMVO) method was also developed for this application. The results showed that the converter performs better with greater wave heights, flap freeboard heights, and shorter wave periods. Additionally, the added ribs led to more wave-converter interaction and better performance, while the distance between the flap and flume bed negatively impacted the performance. Finally, tracking the changes in the five-dimensional objective function revealed the optimum value for each parameter in all scenarios. This is achieved by the newly developed optimization algorithm, which is much faster than other existing cutting-edge metaheuristic approaches.

Keywords

Wave Energy Converter

OSWEC

Hydrodynamic Effects

Geometric Design

Metaheuristic Optimization

Multi-Verse Optimizer

1Introduction

The increase in energy demand, the limitations of fossil fuels, as well as environmental crises, such as air pollution and global warming, are the leading causes of calling more attention to harvesting renewable energy recently [1][2][3]. While still in its infancy, ocean wave energy has neither reached commercial maturity nor technological convergence. In recent decades, remarkable progress has been made in the marine energy domain, which is still in the early stage of development, to improve the technology performance level (TPL) [4][5]and technology readiness level (TRL) of wave energy converters (WECs). This has been achieved using novel modeling techniques [6][7][8][9][10][11][12][13][14] to gain the following advantages [15]: (i) As a source of sustainable energy, it contributes to the mix of energy resources that leads to greater diversity and attractiveness for coastal cities and suppliers. [16] (ii) Since wave energy can be exploited offshore and does not require any land, in-land site selection would be less expensive and undesirable visual effects would be reduced. [17] (iii) When the best layout and location of offshore site are taken into account, permanent generation of energy will be feasible (as opposed to using solar energy, for example, which is time-dependent) [18].

In general, the energy conversion process can be divided into three stages in a WEC device, including primary, secondary, and tertiary stages [19][20]. In the first stage of energy conversion, which is the subject of this study, the wave power is converted to mechanical power by wave-structure interaction (WSI) between ocean waves and structures. Moreover, the mechanical power is transferred into electricity in the second stage, in which mechanical structures are coupled with power take-off systems (PTO). At this stage, optimal control strategies are useful to tune the system dynamics to maximize power output [10][13][12]. Furthermore, the tertiary energy conversion stage revolves around transferring the non-standard AC power into direct current (DC) power for energy storage or standard AC power for grid integration [21][22]. We discuss only the first stage regardless of the secondary and tertiary stages. While Page 1 of 16 WECs include several categories and technologies such as terminators, point absorbers, and attenuators [15][23], we focus on oscillating surge wave energy converters (OSWECs) in this paper due to its high capacity for industrialization [24].

Over the past two decades, a number of studies have been conducted to understand how OSWECs’ structures and interactions between ocean waves and flaps affect converters performance. Henry et al.’s experiment on oscillating surge wave energy converters is considered as one of the most influential pieces of research [25], which demonstrated how the performance of oscillating surge wave energy converters (OSWECs) is affected by seven different factors, including wave period, wave power, flap’s relative density, water depth, free-board of the flap, the gap between the tubes, gap underneath the flap, and flap width. These parameters were assessed in their two models in order to estimate the absorbed energy from incoming waves [26][27]. In addition, Folly et al. investigated the impact of water depth on the OSWECs performance analytically, numerically, and experimentally. According to this and further similar studies, the average annual incident wave power is significantly reduced by water depth. Based on the experimental results, both the surge wave force and the power capture of OSWECs increase in shallow water [28][29]. Following this, Sarkar et al. found that under such circumstances, the device that is located near the coast performs much better than those in the open ocean [30]. On the other hand, other studies are showing that the size of the converter, including height and width, is relatively independent of the location (within similar depth) [31]. Subsequently, Schmitt et al. studied OSWECs numerically and experimentally. In fact, for the simulation of OSWEC, OpenFOAM was used to test the applicability of Reynolds-averaged Navier-Stokes (RANS) solvers. Then, the experimental model reproduced the numerical results with satisfying accuracy [32]. In another influential study, Wang et al. numerically assessed the effect of OSWEC’s width on their performance. According to their findings, as converter width increases, its efficiency decreases in short wave periods while increases in long wave periods [33]. One of the main challenges in the analysis of the OSWEC is the coupled effect of hydrodynamic and geometric variables. As a result, numerous cutting-edge geometry studies have been performed in recent years in order to find the optimal structure that maximizes power output and minimizes costs. Garcia et al. reviewed hull geometry optimization studies in the literature in [19]. In addition, Guo and Ringwood surveyed geometric optimization methods to improve the hydrodynamic performance of OSWECs at the primary stage [14]. Besides, they classified the hull geometry of OSWECs based on Figure 1. Subsequently, Whittaker et al. proposed a different design of OSWEC called Oyster2. There have been three examples of different geometries of oysters with different water depths. Based on its water depth, they determined the width and height of the converter. They also found that in the constant wave period the less the converter’s width, the less power captures the converter has [34]. Afterward, O’Boyle et al. investigated a type of OSWEC called Oyster 800. They compared the experimental and numerical models with the prototype model. In order to precisely reproduce the shape, mass distribution, and buoyancy properties of the prototype, a 40th-scale experimental model has been designed. Overall, all the models were fairly accurate according to the results [35].

Inclusive analysis of recent research avenues in the area of flap geometry has revealed that the interaction-based designs of such converters are emerging as a novel approach. An initiative workflow is designed in the current study to maximizing the wave energy extrication by such systems. To begin with, a sensitivity analysis plays its role of determining the best hydrodynamic values for installing the converter’s flap. Then, all flap dimensions and characteristics come into play to finalize the primary model. Following, interactive designs is proposed to increase the influence of incident waves on the body by adding ribs on both sides of the flap as a novel design. Finally, a new bi-level metaheuristic method is proposed to consider the effects of simultaneous changes in ribs properties and other design parameters. We hope this novel approach will be utilized to make big-scale projects less costly and justifiable. The efficiency of the method is also compared with four well known metaheuristic algorithms and out weight them for this application.

This paper is organized as follows. First, the research methodology is introduced by providing details about the numerical model implementation. To that end, we first introduced the primary model’s geometry and software details. That primary model is later verified with a benchmark study with regard to the flap angle of rotation and water surface elevation. Then, governing equations and performance criteria are presented. In the third part of the paper, we discuss the model’s sensitivity to lower and upper parts width (we proposed a two cross-sectional design for the flap), bottom elevation, and freeboard. Finally, the novel optimization approach is introduced in the final part and compared with four recent metaheuristic algorithms.

2. Numerical Methods

In this section, after a brief introduction of the numerical software, Flow3D, boundary conditions are defined. Afterwards, the numerical model implementation, along with primary model properties are described. Finally, governing equations, as part of numerical process, are discussed.

2.1Model Setup

FLOW-3D is a powerful and comprehensive CFD simulation platform for studying fluid dynamics. This software has several modules to solve many complex engineering problems. In addition, modeling complex flows is simple and effective using FLOW-3D’s robust meshing capabilities [36]. Interaction between fluid and moving objects might alter the computational range. Dynamic meshes are used in our modeling to take these changes into account. At each time step, the computational node positions change in order to adapt the meshing area to the moving object. In addition, to choose mesh dimensions, some factors are taken into account such as computational accuracy, computational time, and stability. The final grid size is selected based on the detailed procedure provided in [37]. To that end, we performed grid-independence testing on a CFD model using three different mesh grid sizes of 0.01, 0.015, and 0.02 meters. The problem geometry and boundary conditions were defined the same, and simulations were run on all three grids under the same conditions. The predicted values of the relevant variable, such as velocity, was compared between the grids. The convergence behavior of the numerical solution was analyzed by calculating the relative L2 norm error between two consecutive grids. Based on the results obtained, it was found that the grid size of 0.02 meters showed the least error, indicating that it provided the most accurate and reliable solution among the three grids. Therefore, the grid size of 0.02 meters was selected as the optimal spatial resolution for the mesh grid.

In this work, the flume dimensions are 10 meters long, 0.1 meters wide, and 2.2 meters high, which are shown in figure2. In addition, input waves with linear characteristics have a height of 0.1 meters and a period of 1.4 seconds. Among the linear wave methods included in this software, RNGk-ε and k- ε are appropriate for turbulence model. The research of Lopez et al. shows that RNGk- ε provides the most accurate simulation of turbulence in OSWECs [21]. We use CATIA software to create the flap primary model and other innovative designs for this project. The flap measures 0.1 m x 0.65 m x 0.360 m in x, y and z directions, respectively. In Figure 3, the primary model of flap and its dimensions are shown. In this simulation, five boundaries have been defined, including 1. Inlet, 2. Outlet, 3. Converter flap, 4. Bed flume, and 5. Water surface, which are shown in figure 2. Besides, to avoid wave reflection in inlet and outlet zones, Flow3D is capable of defining some areas as damping zones, the length of which has to be one to one and a half times the wavelength. Therefore, in the model, this length is considered equal to 2 meters. Furthermore, there is no slip in all the boundaries. In other words, at every single time step, the fluid velocity is zero on the bed flume, while it is equal to the flap velocity on the converter flap. According to the wave theory defined in the software, at the inlet boundary, the water velocity is called from the wave speed to be fed into the model.

2.2Verification

In the current study, we utilize the Schmitt experimental model as a benchmark for verification, which was developed at the Queen’s University of Belfast. The experiments were conducted on the flap of the converter, its rotation, and its interaction with the water surface. Thus, the details of the experiments are presented below based up on the experimental setup’s description [38]. In the experiment, the laboratory flume has a length of 20m and a width of 4.58m. Besides, in order to avoid incident wave reflection, a wave absorption source is devised at the end of the left flume. The flume bed, also, includes two parts with different slops. The flap position and dimensions of the flume can be seen in Figure4. In addition, a wave-maker with 6 paddles is installed at one end. At the opposite end, there is a beach with wire meshes. Additionally, there are 6 indicators to extract the water level elevation. In the flap model, there are three components: the fixed support structure, the hinge, and the flap. The flap measures 0.1m x 0.65m x 0.341m in x, y and z directions, respectively. In Figure5, the details are given [32]. The support structure consists of a 15 mm thick stainless steel base plate measuring 1m by 1.4m, which is screwed onto the bottom of the tank. The hinge is supported by three bearing blocks. There is a foam centerpiece on the front and back of the flap which is sandwiched between two PVC plates. Enabling changes of the flap, three metal fittings link the flap to the hinge. Moreover, in this experiment, the selected wave is generated based on sea wave data at scale 1:40. The wave height and the wave period are equal to 0.038 (m) and 2.0625 (s), respectively, which are tantamount to a wave with a period of 13 (s) and a height of 1.5 (m).

Two distinct graphs illustrate the numerical and experi-mental study results. Figure6 and Figure7 are denoting the angle of rotation of flap and surface elevation in computational and experimental models, respectively. The two figures roughly represent that the numerical and experimental models are a good match. However, for the purpose of verifying the match, we calculated the correlation coefficient (C) and root mean square error (RMSE). According to Figure6, correlation coefficient and RMSE are 0.998 and 0.003, respectively, and in Figure7 correlation coefficient and RMSE are respectively 0.999 and 0.001. Accordingly, there is a good match between the numerical and empirical models. It is worth mentioning that the small differences between the numerical and experimental outputs may be due to the error of the measuring devices and the calibration of the data collection devices.

Including continuity equation and momentum conserva- tion for incompressible fluid are given as [32][39]:(1)

where P represents the pressure, g denotes gravitational acceleration, u represents fluid velocity, and Di is damping coefficient. Likewise, the model uses the same equation. to calculate the fluid velocity in other directions as well. Considering the turbulence, we use the two-equation model of RNGK- ε. These equations are:

(3)��t(��)+����(����)=����[�eff�������]+��-��and(4)���(��)+����(����)=����[�eff�������]+�1�∗����-��2��2�Where �2� and �1� are constants. In addition, �� and �� represent the turbulent Prandtl number of � and k, respectively.

�� also denote the production of turbulent kinetic energy of k under the effect of velocity gradient, which is calculated as follows:(5)��=�eff[�����+�����]�����(6)�eff=�+��(7)�eff=�+��where � is molecular viscosity,�� represents turbulence viscosity, k denotes kinetic energy, and ∊∊ is energy dissipation rate. The values of constant coefficients in the two-equation RNGK ∊-∊ model is as shown in the Table 1 [40].Table 2.

Table 1. Constant coefficients in RNGK- model

Factors�0�1�2������
Quantity0.0124.381.421.681.391.390.084

Table 2. Flap properties

Joint height (m)0.476
Height of the center of mass (m)0.53
Weight (Kg)10.77

It is worth mentioning that the volume of fluid method is used to separate water and air phases in this software [41]. Below is the equation of this method [40].(8)����+����(���)=0where α and 1 − α are portion of water phase and air phase, respectively. As a weighting factor, each fluid phase portion is used to determine the mixture properties. Finally, using the following equations, we calculate the efficiency of converters [42][34][43]:(9)�=14|�|2�+�2+(�+�a)2(�n2-�2)2where �� represents natural frequency, I denotes the inertia of OSWEC, Ia is the added inertia, F is the complex wave force, and B denotes the hydrodynamic damping coefficient. Afterward, the capture factor of the converter is calculated by [44]:(10)��=�1/2��2����gw where �� represents the capture factor, which is the total efficiency of device per unit length of the wave crest at each time step [15], �� represent the dimensional amplitude of the incident wave, w is the flap’s width, and Cg is the group velocity of the incident wave, as below:(11)��=��0·121+2�0ℎsinh2�0ℎwhere �0 denotes the wave number, h is water depth, and H is the height of incident waves.

According to previous sections ∊,����-∊ modeling is used for all models simulated in this section. For this purpose, the empty boundary condition is used for flume walls. In order to preventing wave reflection at the inlet and outlet of the flume, the length of wave absorption is set to be at least one incident wavelength. In addition, the structured mesh is chosen, and the mesh dimensions are selected in two distinct directions. In each model, all grids have a length of 2 (cm) and a height of 1 (cm). Afterwards, as an input of the software for all of the models, we define the time step as 0.001 (s). Moreover, the run time of every simulation is 30 (s). As mentioned before, our primary model is Schmitt model, and the flap properties is given in table2. For all simulations, the flume measures 15 meters in length and 0.65 meters in width, and water depth is equal to 0.335 (m). The flap is also located 7 meters from the flume’s inlet.

Finally, in order to compare the results, the capture factor is calculated for each simulation and compared to the primary model. It is worth mentioning that capture factor refers to the ratio of absorbed wave energy to the input wave energy.

According to primary model simulation and due to the decreasing horizontal velocity with depth, the wave crest has the highest velocity. Considering the fact that the wave’s orbital velocity causes the flap to move, the contact between the upper edge of the flap and the incident wave can enhance its performance. Additionally, the numerical model shows that the dynamic pressure decreases as depth increases, and the hydrostatic pressure increases as depth increases.

To determine the OSWEC design, it is imperative to understand the correlation between the capture factor, wave period, and wave height. Therefore, as it is shown in Figure8, we plot the change in capture factor over the variations in wave period and wave height in 3D and 2D. In this diagram, the first axis features changes in wave period, the second axis displays changes in wave height, and the third axis depicts changes in capture factor. According to our wave properties in the numerical model, the wave period and wave height range from 2 to 14 seconds and 2 to 8 meters, respectively. This is due to the fact that the flap does not oscillate if the wave height is less than 2 (m), and it does not reverse if the wave height is more than 8 (m). In addition, with wave periods more than 14 (s), the wavelength would be so long that it would violate the deep-water conditions, and with wave periods less than 2 (s), the flap would not oscillate properly due to the shortness of wavelength. The results of simulation are shown in Figure 8. As it can be perceived from Figure 8, in a constant wave period, the capture factor is in direct proportion to the wave height. It is because of the fact that waves with more height have more energy to rotate the flap. Besides, in a constant wave height, the capture factor increases when the wave period increases, until a given wave period value. However, the capture factor falls after this point. These results are expected since the flap’s angular displacement is not high in lower wave periods, while the oscillating motion of that is not fast enough to activate the power take-off system in very high wave periods.

As is shown in Figure 9, we plot the change in capture factor over the variations in wave period (s) and water depth (m) in 3D. As it can be seen in this diagram, the first axis features changes in water depth (m), the second axis depicts the wave period (s), and the third axis displays OSWEC’s capture factor. The wave period ranges from 0 to 10 seconds based on our wave properties, which have been adopted from Schmitt’s model, while water depth ranges from 0 to 0.5 meters according to the flume and flap dimensions and laboratory limitations. According to Figure9, for any specific water depth, the capture factor increases in a varying rate when the wave period increases, until a given wave period value. However, the capture factor falls steadily after this point. In fact, the maximum capture factor occurs when the wave period is around 6 seconds. This trend is expected since, in a specific water depth, the flap cannot oscillate properly when the wavelength is too short. As the wave period increases, the flap can oscillate more easily, and consequently its capture factor increases. However, the capture factor drops in higher wave periods because the wavelength is too large to move the flap. Furthermore, in a constant wave period, by changing the water depth, the capture factor does not alter. In other words, the capture factor does not depend on the water depth when it is around its maximum value.

3Sensitivity Analysis

Based on previous studies, in addition to the flap design, the location of the flap relative to the water surface (freeboard) and its elevation relative to the flume bed (flap bottom elevation) play a significant role in extracting energy from the wave energy converter. This study measures the sensitivity of the model to various parameters related to the flap design including upper part width of the flap, lower part width of the flap, the freeboard, and the flap bottom elevation. Moreover, as a novel idea, we propose that the flap widths differ in the lower and upper parts. In Figure10, as an example, a flap with an upper thickness of 100 (mm) and a lower thickness of 50 (mm) and a flap with an upper thickness of 50 (mm) and a lower thickness of 100 (mm) are shown. The influence of such discrepancy between the widths of the upper and lower parts on the interaction between the wave and the flap, or in other words on the capture factor, is evaluated. To do so, other parameters are remained constant, such as the freeboard, the distance between the flap and the flume bed, and the wave properties.

In Figure11, models are simulated with distinct upper and lower widths. As it is clear in this figure, the first axis depicts the lower part width of the flap, the second axis indicates the upper part width of the flap, and the colors represent the capture factor values. Additionally, in order to consider a sufficient range of change, the flap thickness varies from half to double the value of the primary model for each part.

According to this study, the greater the discrepancy in these two parts, the lower the capture factor. It is on account of the fact that when the lower part of the flap is thicker than the upper part, and this thickness difference in these two parts is extremely conspicuous, the inertia against the motion is significant at zero degrees of rotation. Consequently, it is difficult to move the flap, which results in a low capture factor. Similarly, when the upper part of the flap is thicker than the lower part, and this thickness difference in these two parts is exceedingly noticeable, the inertia is so great that the flap can not reverse at the maximum degree of rotation. As the results indicate, the discrepancy can enhance the performance of the converter if the difference between these two parts is around 20%. As it is depicted in the Figure11, the capture factor reaches its own maximum amount, when the lower part thickness is from 5 to 6 (cm), and the upper part thickness is between 6 and 7 (cm). Consequently, as a result of this discrepancy, less material will be used, and therefore there will be less cost.

As illustrated in Figure12, this study examines the effects of freeboard (level difference between the flap top and water surface) and the flap bottom elevation (the distance between the flume bed and flap bottom) on the converter performance. In this diagram, the first axis demonstrates the freeboard and the second axis on the left side displays the flap bottom elevation, while the colors indicate the capture factor. In addition, the feasible range of freeboard is between -15 to 15 (cm) due to the limitation of the numerical model, so that we can take the wave slamming and the overtopping into consideration. Additionally, based on the Schmitt model and its scaled model of 1:40 of the base height, the flap bottom should be at least 9 (cm) high. Since the effect of surface waves is distributed over the depth of the flume, it is imperative to maintain a reasonable flap height exposed to incoming waves. Thus, the maximum flap bottom elevation is limited to 19 (cm). As the Figure12 pictures, at constant negative values of the freeboard, the capture factor is in inverse proportion with the flap bottom elevation, although slightly.

Furthermore, at constant positive values of the freeboard, the capture factor fluctuates as the flap bottom elevation decreases while it maintains an overall increasing trend. This is on account of the fact that increasing the flap bottom elevation creates turbulence flow behind the flap, which encumbers its rotation, as well as the fact that the flap surface has less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, the capture factor increases by raising the freeboard. This is due to the fact that there is overtopping with adverse impacts on the converter performance when the freeboard is negative and the flap is under the water surface. Besides, increasing the freeboard makes the wave slam more vigorously, which improves the converter performance.

Adding ribs to the flap surface, as shown in Figure13, is a novel idea that is investigated in the next section. To achieve an optimized design for the proposed geometry of the flap, we determine the optimal number and dimensions of ribs based on the flap properties as our decision variables in the optimization process. As an example, Figure13 illustrates a flap with 3 ribs on each side with specific dimensions.

Figure14 shows the flow velocity field around the flap jointed to the flume bed. During the oscillation of the flap, the pressure on the upper and lower surfaces of the flap changes dynamically due to the changing angle of attack and the resulting change in the direction of fluid flow. As the flap moves upwards, the pressure on the upper surface decreases, and the pressure on the lower surface increases. Conversely, as the flap moves downwards, the pressure on the upper surface increases, and the pressure on the lower surface decreases. This results in a cyclic pressure variation around the flap. Under certain conditions, the pressure field around the flap can exhibit significant variations in magnitude and direction, forming vortices and other flow structures. These flow structures can affect the performance of the OSWEC by altering the lift and drag forces acting on the flap.

4Design Optimization

We consider optimizing the design parameters of the flap of converter using a nature-based swarm optimization method, that fall in the category of metaheuristic algorithms [45]. Accordingly, we choose four state-of-the-art algorithms to perform an optimization study. Then, based on their performances to achieve the highest capture factor, one of them will be chosen to be combined with the Hill Climb algorithm to carry out a local search. Therefore, in the remainder of this section, we discuss the search process of each algorithm and visualize their performance and convergence curve as they try to find the best values for decision variables.

4.1. Metaheuristic Approaches

As the first considered algorithm, the Gray Wolf Optimizer (GWO) algorithm simulates the natural leadership and hunting performance of gray wolves which tend to live in colonies. Hunters must obey the alpha wolf, the leader, who is responsible for hunting. Then, the beta wolf is at the second level of the gray wolf hierarchy. A subordinate of alpha wolf, beta stands under the command of the alpha. At the next level in this hierarchy, there are the delta wolves. They are subordinate to the alpha and beta wolves. This category of wolves includes scouts, sentinels, elders, hunters, and caretakers. In this ranking, omega wolves are at the bottom, having the lowest level and obeying all other wolves. They are also allowed to eat the prey just after others have eaten. Despite the fact that they seem less important than others, they are really central to the pack survival. Since, it has been shown that without omega wolves, the entire pack would experience some problems like fighting, violence, and frustration. In this simulation, there are three primary steps of hunting including searching, surrounding, and finally attacking the prey. Mathematically model of gray wolves’ hunting technique and their social hierarchy are applied in determined by optimization. this study. As mentioned before, gray wolves can locate their prey and surround them. The alpha wolf also leads the hunt. Assuming that the alpha, beta, and delta have more knowledge about prey locations, we can mathematically simulate gray wolf hunting behavior. Hence, in addition to saving the top three best solutions obtained so far, we compel the rest of the search agents (also the omegas) to adjust their positions based on the best search agent. Encircling behavior can be mathematically modeled by the following equations: [46].(12)�→=|�→·��→(�)-�→(�)|(13)�→(�+1)=��→(�)-�→·�→(14)�→=2.�2→(15)�→=2�→·�1→-�→Where �→indicates the position vector of gray wolf, ��→ defines the vector of prey, t indicates the current iteration, and �→and �→are coefficient vectors. To force the search agent to diverge from the prey, we use �→ with random values greater than 1 or less than -1. In addition, C→ contains random values in the range [0,2], and �→ 1 and �2→ are random vectors in [0,1]. The second considered technique is the Moth Flame Optimizer (MFO) algorithm. This method revolves around the moths’ navigation mechanism, which is realized by positioning themselves and maintaining a fixed angle relative to the moon while flying. This effective mechanism helps moths to fly in a straight path. However, when the source of light is artificial, maintaining an angle with the light leads to a spiral flying path towards the source that causes the moth’s death [47]. In MFO algorithm, moths and flames are both solutions. The moths are actual search agents that fly in hyper-dimensional space by changing their position vectors, and the flames are considered pins that moths drop when searching the search space [48]. The problem’s variables are the position of moths in the space. Each moth searches around a flame and updates it in case of finding a better solution. The fitness value is the return value of each moth’s fitness (objective) function. The position vector of each moth is passed to the fitness function, and the output of the fitness function is assigned to the corresponding moth. With this mechanism, a moth never loses its best solution [49]. Some attributes of this algorithm are as follows:

  • •It takes different values to converge moth in any point around the flame.
  • •Distance to the flame is lowered to be eventually minimized.
  • •When the position gets closer to the flame, the updated positions around the flame become more frequent.

As another method, the Multi-Verse Optimizer is based on a multiverse theory which proposes there are other universes besides the one in which we all live. According to this theory, there are more than one big bang in the universe, and each big bang leads to the birth of a new universe [50]. Multi-Verse Optimizer (MVO) is mainly inspired by three phenomena in cosmology: white holes, black holes, and wormholes. A white hole has never been observed in our universe, but physicists believe the big bang could be considered a white hole [51]. Black holes, which behave completely in contrast to white holes, attract everything including light beams with their extremely high gravitational force [52]. In the multiverse theory, wormholes are time and space tunnels that allow objects to move instantly between any two corners of a universe (or even simultaneously from one universe to another) [53]. Based on these three concepts, mathematical models are designed to perform exploration, exploitation, and local search, respectively. The concept of white and black holes is implied as an exploration phase, while the concept of wormholes is considered as an exploitation phase by MVO. Additionally, each solution is analogous to a universe, and each variable in the solution represents an object in that universe. Furthermore, each solution is assigned an inflation rate, and the time is used instead of iterations. Following are the universe rules in MVO:

  • •The possibility of having white hole increases with the inflation rate.
  • •The possibility of having black hole decreases with the inflation rate.
  • •Objects tend to pass through black holes more frequently in universes with lower inflation rates.
  • •Regardless of inflation rate, wormholes may cause objects in universes to move randomly towards the best universe. [54]

Modeling the white/black hole tunnels and exchanging objects of universes mathematically was accomplished by using the roulette wheel mechanism. With every iteration, the universes are sorted according to their inflation rates, then, based on the roulette wheel, the one with the white hole is selected as the local extremum solution. This is accomplished through the following steps:

Assume that

(16)���=����1<��(��)����1≥��(��)

Where ��� represents the jth parameter of the ith universe, Ui indicates the ith universe, NI(Ui) is normalized inflation rate of the ith universe, r1 is a random number in [0,1], and j xk shows the jth parameter of the kth universe selected by a roulette wheel selection mechanism [54]. It is assumed that wormhole tunnels always exist between a universe and the best universe formed so far. This mechanism is as follows:(17)���=if�2<���:��+���×((���-���)×�4+���)�3<0.5��-���×((���-���)×�4+���)�3≥0.5����:���where Xj indicates the jth parameter of the best universe formed so far, TDR and WEP are coefficients, where Xj indicates the jth parameter of the best universelbjshows the lower bound of the jth variable, ubj is the upper bound of the jth variable, and r2, r3, and r4 are random numbers in [1][54].

Finally, one of the newest optimization algorithms is WOA. The WOA algorithm simulates the movement of prey and the whale’s discipline when looking for their prey. Among several species, Humpback whales have a specific method of hunting [55]. Humpback whales can recognize the location of prey and encircle it before hunting. The optimal design position in the search space is not known a priori, and the WOA algorithm assumes that the best candidate solution is either the target prey or close to the optimum. This foraging behavior is called the bubble-net feeding method. Two maneuvers are associated with bubbles: upward spirals and double loops. A unique behavior exhibited only by humpback whales is bubble-net feeding. In fact, The WOA algorithm starts with a set of random solutions. At each iteration, search agents update their positions for either a randomly chosen search agent or the best solution obtained so far [56][55]. When the best search agent is determined, the other search agents will attempt to update their positions toward that agent. It is important to note that humpback whales swim around their prey simultaneously in a circular, shrinking circle and along a spiral-shaped path. By using a mathematical model, the spiral bubble-net feeding maneuver is optimized. The following equation represents this behavior:(18)�→(�+1)=�′→·�bl·cos(2��)+�∗→(�)

Where:(19)�′→=|�∗→(�)-�→(�)|

X→(t+ 1) indicates the distance of the it h whale to the prey (best solution obtained so far),� is a constant for defining the shape of the logarithmic spiral, l is a random number in [−1, 1], and dot (.) is an element-by-element multiplication [55].

Comparing the four above-mentioned methods, simulations are run with 10 search agents for 400 iterations. In Figure 15, there are 20 plots the optimal values of different parameters in optimization algorithms. The five parameters of this study are freeboard, bottom elevations, number of ribs on the converter, rib thickness, and rib Height. The optimal value for each was found by optimization algorithms, naming WOA, MVO, MFO, and GWO. By looking through the first row, the freeboard parameter converges to its maximum possible value in the optimization process of GWO after 300 iterations. Similarly, MFO finds the same result as GWO. In contrast, the freeboard converges to its minimum possible value in MVO optimizing process, which indicates positioning the converter under the water. Furthermore, WOA found the optimal value of freeboard as around 0.02 after almost 200 iterations. In the second row, the bottom elevation is found at almost 0.11 (m) in all algorithms; however, the curves follow different trends in each algorithm. The third row shows the number of ribs, where results immediately reveal that it should be over 4. All algorithms coincide at 5 ribs as the optimal number in this process. The fourth row displays the trends of algorithms to find optimal rib thickness. MFO finds the optimal value early and sets it to around 0.022, while others find the same value in higher iterations. Finally, regarding the rib height, MVO, MFO, and GWO state that the optimal value is 0.06 meters, but WOA did not find a higher value than 0.039.

4.2. HCMVO Bi-level Approach

Despite several strong search characteristics of MVO and its high performance in various optimization problems, it suffers from a few deficiencies in local and global search mechanisms. For instance, it is trapped in the local optimum when wormholes stochastically generate many solutions near the best universe achieved throughout iterations, especially in solving complex multimodal problems with high dimensions [57]. Furthermore, MVO needs to be modified by an escaping strategy from the local optima to enhance the global search abilities. To address these shortages, we propose a fast and effective meta-algorithm (HCMVO) to combine MVO with a Random-restart hill-climbing local search. This meta-algorithm uses MVO on the upper level to develop global tracking and provide a range of feasible and proper solutions. The hill-climbing algorithm is designed to develop a comprehensive neighborhood search around the best-found solution proposed by the upper-level (MVO) when MVO is faced with a stagnation issue or falling into a local optimum. The performance threshold is formulated as follows.(20)Δ����THD=∑�=1�����TH��-����TH��-1�where BestTHDis the best-found solution per generation, andM is related to the domain of iterations to compute the average performance of MVO. If the proposed best solution by the local search is better than the initial one, the global best of MVO will be updated. HCMVO iteratively runs hill climbing when the performance of MVO goes down, each time with an initial condition to prepare for escaping such undesirable situations. In order to get a better balance between exploration and exploitation, the search step size linearly decreases as follows:(21)��=��-����Ma�iter��+1where iter and Maxiter are the current iteration and maximum number of evaluation, respectively. �� stands for the step size of the neighborhood search. Meanwhile, this strategy can improve the convergence rate of MVO compared with other algorithms.

Algorithm 1 shows the technical details of the proposed optimization method (HCMVO). The initial solution includes freeboard (�), bottom elevation (�), number of ribs (Nr), rib thickness (�), and rib height(�).

5. Conclusion

The high trend of diminishing worldwide energy resources has entailed a great crisis upon vulnerable societies. To withstand this effect, developing renewable energy technologies can open doors to a more reliable means, among which the wave energy converters will help the coastal residents and infrastructure. This paper set out to determine the optimized design for such devices that leads to the highest possible power output. The main goal of this research was to demonstrate the best design for an oscillating surge wave energy converter using a novel metaheuristic optimization algorithm. In this regard, the methodology was devised such that it argued the effects of influential parameters, including wave characteristics, WEC design, and interaction criteria.

To begin with, a numerical model was developed in Flow 3D software to simulate the response of the flap of a wave energy converter to incoming waves, followed by a validation study based upon a well-reputed experimental study to verify the accuracy of the model. Secondly, the hydrodynamics of the flap was investigated by incorporating the turbulence. The effect of depth, wave height, and wave period are also investigated in this part. The influence of two novel ideas on increasing the wave-converter interaction was then assessed: i) designing a flap with different widths in the upper and lower part, and ii) adding ribs on the surface of the flap. Finally, four trending single-objective metaheuristic optimization methods

Empty CellAlgorithm 1: Hill Climb Multiverse Optimization
01:procedure HCMVO
02:�=30,�=5▹���������������������������������
03:�=〈F1,B1,N,R,H1〉,…〈FN,B2,N,R,HN〉⇒lb1N⩽�⩽ubN
04:Initialize parameters�ER,�DR,�EP,Best�,���ite��▹Wormhole existence probability (WEP)
05:��=����(��)
06:��=Normalize the inflation rate��
07:for iter in[1,⋯,���iter]do
08:for�in[1,⋯,�]do
09:Update�EP,�DR,Black����Index=�
10:for���[1,⋯,�]��
11:�1=����()
12:if�1≤��(��)then
13:White HoleIndex=Roulette�heelSelection(-��)
14:�(Black HoleIndex,�)=��(White HoleIndex,�)
15:end if
16:�2=����([0,�])
17:if�2≤�EPthen
18:�3=����(),�4=����()
19:if�3<0.5then
20:�1=((��(�)-��(�))�4+��(�))
21:�(�,�)=Best�(�)+�DR�
22:else
23:�(�,�)=Best�(�)-�DR�
24:end if
25:end if
26:end for
27:end for
28:�HD=����([�1,�2,⋯,�Np])
29:Bes�TH�itr=����HD
30:ΔBestTHD=∑�=1�BestTII��-BestTII��-1�
31:ifΔBestTHD<��then▹Perform hill climbing local search
32:BestTHD=����-�lim��������THD
33:end if
34:end for
35:return�,BestTHD▹Final configuration
36:end procedure

The implementation details of the hill-climbing algorithm applied in HCMPA can be seen in Algorithm 2. One of the critical parameters isg, which denotes the resolution of the neighborhood search around the proposed global best by MVO. If we set a small step size for hill-climbing, the convergence speed will be decreased. On the other hand, a large step size reinforces the exploration ability. Still, it may reduce the exploitation ability and in return increase the act of jumping from a global optimum or surfaces with high-potential solutions. Per each decision variable, the neighborhood search evaluates two different direct searches, incremental or decremental. After assessing the generated solutions, the best candidate will be selected to iterate the search algorithm. It is noted that the hill-climbing algorithm should not be applied in the initial iteration of the optimization process due to the immense tendency for converging to local optima. Meanwhile, for optimizing largescale problems, hill-climbing is not an appropriate selection. In order to improve understanding of the proposed hybrid optimization algorithm’s steps, the flowchart of HCMVO is designed and can be seen in Figure 16.

Figure 17 shows the observed capture factor (which is the absorbed energy with respect to the available energy) by each optimization algorithm from iterations 1 to 400. The algorithms use ten search agents in their modified codes to find the optimal solutions. While GWO and MFO remain roughly constant after iterations 54 and 40, the other three algorithms keep improving the capture factor. In this case, HCMVO and MVO worked very well in the optimizing process with a capture factor obtained by the former as 0.594 and by the latter as 0.593. MFO almost found its highest value before the iteration 50, which means the exploration part of the algorithm works out well. Similarly, HCMVO does the same. However, it keeps finding the better solution during the optimization process until the last iteration, indicating the strong exploitation part of the algorithm. GWO reveals a weakness in exploration and exploitation because not only does it evoke the least capture factor value, but also the curve remains almost unchanged throughout 350 iterations.

Figure 18 illustrates complex interactions between the five optimization parameters and the capture factor for HCMVO (a), MPA (b), and MFO (c) algorithms. The first interesting observation is that there is a high level of nonlinear relationships among the setting parameters that can make a multi-modal search space. The dark blue lines represent the best-found configuration throughout the optimisation process. Based on both HCMVO (a) and MVO (b), we can infer that the dark blue lines concentrate in a specific range, showing the high convergence ability of both HCMVO and MVO. However, MFO (c) could not find the exact optimal range of the decision variables, and the best-found solutions per generation distribute mostly all around the search space.

Empty CellAlgorithm 1: Hill Climb Multiverse Optimization
01:procedure HCMVO
02:Initialization
03:Initialize the constraints��1�,��1�
04:�1�=Mi�1�+���1�/�▹Compute the step size,�is search resolution
05:So�1=〈�,�,�,�,�〉▹���������������
06:�������1=����So�1▹���������ℎ���������
07:Main loop
08:for iter≤���ita=do
09:���=���±��
10:while�≤���(Sol1)do
11:���=���+�,▹����ℎ���ℎ��������ℎ
12:fitness��iter=�������
13:t = t+1
14:end while
15:〈�����,������max〉=����������
16:���itev=���Inde�max▹�������ℎ�������������������������������ℎ�������
17:��=��-����Max��+1▹�����������������
18:end for
19:return���iter,����
20:end procedure

were utilized to illuminate the optimum values of the design parameters, and the best method was chosen to develop a new algorithm that performs both local and global search methods.

The correlation between hydrodynamic parameters and the capture factor of the converter was supported by the results. For any given water depth, the capture factor increases as the wave period increases, until a certain wave period value (6 seconds) is reached, after which the capture factor gradually decreases. It is expected since the flap cannot oscillate effectively when the wavelength is too short for a certain water depth. Conversely, when the wavelength is too long, the capture factor decreases. Furthermore, under a constant wave period, increasing the water depth does not affect the capture factor. Regarding the sensitivity analysis, the study found that increasing the flap bottom elevation causes turbulence flow behind the flap and limitation of rotation, which leads to less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, increasing the freeboard improves the capture factor. Overtopping happens when the freeboard is negative and the flap is below the water surface, which has a detrimental influence on converter performance. Furthermore, raising the freeboard causes the wave impact to become more violent, which increases converter performance.

In the last part, we discussed the search process of each algorithm and visualized their performance and convergence curves as they try to find the best values for decision variables. Among the four selected metaheuristic algorithms, the Multi-verse Optimizer proved to be the most effective in achieving the best answer in terms of the WEC capture factor. However, the MVO needed modifications regarding its escape approach from the local optima in order to improve its global search capabilities. To overcome these constraints, we presented a fast and efficient meta-algorithm (HCMVO) that combines MVO with a Random-restart hill-climbing local search. On a higher level, this meta-algorithm employed MVO to generate global tracking and present a range of possible and appropriate solutions. Taken together, the results demonstrated that there is a significant degree of nonlinearity among the setup parameters that might result in a multimodal search space. Since MVO was faced with a stagnation issue or fell into a local optimum, we constructed a complete neighborhood search around the best-found solution offered by the upper level. In sum, the newly-developed algorithm proved to be highly effective for the problem compared to other similar optimization methods. The strength of the current findings may encourage future investigation on design optimization of wave energy converters using developed geometry as well as the novel approach.

CRediT authorship contribution statement

Erfan Amini: Conceptualization, Methodology, Validation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Mahdieh Nasiri: Conceptualization, Methodology, Validation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Navid Salami Pargoo: Writing – original draft, Writing – review & editing. Zahra Mozhgani: Conceptualization, Methodology. Danial Golbaz: Writing – original draft. Mehrdad Baniesmaeil: Writing – original draft. Meysam Majidi Nezhad: . Mehdi Neshat: Supervision, Conceptualization, Writing – original draft, Writing – review & editing, Visualization. Davide Astiaso Garcia: Supervision. Georgios Sylaios: Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research has been carried out within ILIAD (Inte-grated Digital Framework for Comprehensive Maritime Data and Information Services) project that received funding from the European Union’s H2020 programme.

Data availability

Data will be made available on request.

References

Nerva-derived reactor coolant channel model for Mars mission applications

화성 임무 적용을 위한 Nerva 파생 원자로 냉각수 채널 모델

Edward W PortaUniversity of Nevada, Las Vegas

Abstract

화성 미션 애플리케이션을 위한 NERVA 파생 원자로 냉각수 채널 모델은 1.3m NERVA 파생 원자로(NDR) 냉각수 채널의 전산유체역학(CFD) 연구 결과를 제시합니다. CFD 코드 FLOW-3D는 NDR 코어를 통과하는 기체 수소의 흐름을 모델링하는 데 사용되었습니다. 수소는 냉각제 채널을 통해 노심을 통과하여 원자로의 냉각제 및 로켓의 추진제 역할을 합니다. 수소는 고밀도/저온 상태로 채널에 들어가고 저밀도/고온 상태로 빠져나오므로 압축성 모델을 사용해야 합니다. 기술 문서의 설계 사양이 모델에 사용되었습니다. 채널 길이에 걸친 압력 강하가 이전에 추정한 것(0.9MPa)보다 높은 것으로 확인되었으며, 이는 더 강력한 냉각수 펌프가 필요하고 설계 사양을 재평가해야 함을 나타냅니다.

NERVA-Derived Reactor Coolant Channel Model for Mars Mission Applications presents the results of a computational fluid dynamics (CFD) study of a 1.3m NERVA-Derived Reactor (NDR) coolant channel; The CFD code FLOW-3D was used to model the flow of gaseous hydrogen through the core of a NDR. Hydrogen passes through the core by way of coolant channels, acting as the coolant for the reactor as well as the propellant for the rocket. Hydrogen enters the channel in a high density/low temperature state and exits in a low density/high temperature state necessitating the use of a compressible model. Design specifications from a technical paper were used for the model; It was determined that the pressure drop across the length of the channel was higher than previously estimated (0.9 MPa), indicating the possible need for more powerful coolant pumps and a re-evaluation of the design specifications.

Keywords

Application; Channel; Coolant; Derived; Mars; Mission; Model; Nerva; Reactor

Figure 1 Nuclear Rocket Schematic Diagram
Figure 1 Nuclear Rocket Schematic Diagram
Figure 2 Fuel Element - Tip View
Figure 2 Fuel Element – Tip View
Figure 3 Fuel Element - Tie-Tube Structure (Tie-tubes are black)
Figure 3 Fuel Element – Tie-Tube Structure (Tie-tubes are black)
Figure 5 Three-Dimensional Coolant Channel Model
Figure 5 Three-Dimensional Coolant Channel Model
Figure 6 Two-Dimensional Coolant Channel Model
Figure 6 Two-Dimensional Coolant Channel Model

REFERENCES

Anderson, J. D., Jr., (1990) Modern Compressible Flow, 2d ed., McGraw-Hill, New
York.
Avallone E. A. and T. Baumeister III, eds., (1987) Mark’s Standard Handbookfor
Mechanical Engineers, 9th ed., McGraw-Hill, New York.
Bennett, G. L. and T. J. Miller (1992) “Nuclear Propulsion: A Key Transportation
Technology for the Exploration of Mars,” Proceedings o f the 9th Symposium on
Space Nuclear Power Systems, CONF-920104, M. S. El-Genk and M. D. Hoover,
eds., American Institute of Physics, New York, AIP Conference Proceedings No.
246, 2: 383-388.
Black, D. L., and S. V. Gunn (1991) “A Technical Summary of Engine and Reactor
Subsystem Design Performance during the NERVA Program,” AIAA-91-3450,
American Institute of Aeronautics and Astronautics, Washington, D. C.
Borowski, S. K., et al. (1992) “Nuclear Thermal Rockets: Key to Moon-Mars
Exploration,” Aerospace America, July 1992, pp. 34(5).
Borowski, S. K., et al. (1993) “ Nuclear Thermal Rocket/Vehicle Design Options for
Future NASA Missions to the Moon and Mars,” AIAA-93-4170, American Institute
of Aeronautics and Astronautics, Washington, D. C.
Borowski, S. K., et al. (1994) “Nuclear Thermal Rocket/Stage Technology Options for
NASA’s Future Human Exploration Missions to the Moon and Mars,” Proceedings
o f the 11th Symposium on Space Nuclear Power and Propulsion, CONF-940101, M.
S. El-Genk and M. D. Hoover, eds., American Institute of Physics, New York, NY,
AIP Conference Proceedings No. 301, 2: 745 – 758.
Burmeister, L. C. (1993) Convective Heat Transfer, 2d ed., John Wiley & Sons, New
York.
Chi, J., R. Holman, and B. Pierce (1989) “Nerva Derivative Reactors for Thermal and
Electrical Propulsion,” AIAA-89-2770, American Institute of Aeronautics and
Astronautics, Washington, D. C.
FIDAP (1993) FIDAP 7.0 User’s Manual, Fluid Dynamics International, Inc.
FL0W-3D (1994) FL0W-3D Version 6.0 Quick Reference Guide, Flow Science, Inc.,
Los Alamos, NM.
Hill, P. G. and C. R. Peterson (1970) Mechanics and Thermodynamics o f Propulsion,
Addison-Wesley, Reading, MA.
Lamarsh, J. R. (1983) Introduction to Nuclear Engineering, 2d ed., Addison-Wesley,
Reading, MA.
Nassersharif, B. (1991) Notes from a Nuclear Propulsion Short Course, 3-5 January
1991, American Institute of Physics.
Nassersharif, B., E. Porta, and D. Hailes (1994) “A Proposal Entitled: Scenario Based
Design of Nuclear Propulsion for Manned Mars Mission,” NSCEE, Las Vegas, NV.
Shepard, K., et al. (1992) “A Split Sprint Mission to Mars,” Proceedings o f the 9th
Symposium on Space Nuclear Power Systems, CONF-920104, M. S. El-Genk and M.
D. Hoover, eds., American Institute of Physics, New York, AIP Conference
Proceedings No. 246, 1: 58 – 63.
Sutton, G. P. (1986) Rocket Propulsion Elements: An Introduction to the Engineering
o f Rockets, 5th ed., John Wiley & Sons, New York.
U.S. President (1989) “Remarks on the 20th Anniversary of the Apollo 11 Moon
Landing July 20, 1989,” Administration o f George Bush, Office of the Federal
Register. National Archives and Records Service, 1989, Washington D. C., George
Bush, 1989, p. 992.
VSAERO (1994) VSAERO User’s Manual E.5, Analytical Methods, Inc., Redmond,
WA.
White, F. M. (1991) Viscous Fluid Flow, 2d ed., McGraw-Hill, Inc., New York.
Zweig, H. R. and M. H. Cooper (1993) “NERVA-Derived Rocket Module for Solar
System Exploration,” AIAA-93-2110, American Institute of Aeronautics and
Astronautics, Washington, D. C.

Flow Hydrodynamics Influences Due to Flood Plain Sand Mining in a Meandering Channel

Flow Hydrodynamics Influences Due to Flood Plain Sand Mining in a Meandering Channel

Abstract

Flow hydrodynamics in the main channel due to floodplain sand mining is important for a better understanding of maintaining the natural habitat or the reliance between the flood plain and the main channel for the river’s long-term survival and also facilitates more effective river restoration engineering. Day by day anthropogenic stresses are increasing in the river corridor system, indiscriminate sand mining is one of them. In this study, a computational fluid dynamics (CFD)-based software Flow-3D hydro (renormalized group K-ε turbulence model used) is used to study the flow hydrodynamics of sinuous (sinuosity index = 1.25) channel 18 m long, 1 m width, and 0.3 m height with floodplain sand mining pit. Sand mining additionally increases the secondary current near the outer bank of the channel, therefore leading to scouring or erosion at the outer bank, as a result, rivers migrate laterally. The turbulence kinetic energy (TKE) is concentrated in the mining pit and near the inner bank. This study result can be used to understand the flow hydrodynamic of the river system due to the series of sand mining.

Keywords

  • Flow hydrodynamics
  • Turbulence modeling
  • Flow-3D
  • Sinuosity
  • Sand mining

References

  1. Best, J.: Anthropogenic stresses on the world’s big rivers. Nat. Geosci. 12(1), 7–21 (2019)CrossRef CAS Google Scholar 
  2. Bagnold, R.A.: Some Aspects of the Shape of River Meanders. US Government Printing Office (1960)Google Scholar 
  3. Kondolf, G.M.: Freshwater Gravel Mining and Dredging Issues: White Paper. Washington Department of Fish and Wildlife (2002)Google Scholar 
  4. Molnár, P., Ramírez, J.A.: Energy dissipation theories and optimal channel characteristics of river networks. Water Resour. Res. 34(7), 1809–1818 (1998)CrossRef Google Scholar 
  5. Padmalal, D., Maya, K.: Sand Mining: Environmental Impacts and Selected Case Studies. Springer (2014)Google Scholar 
  6. Hübler, M., Pothen, F.: Can smart policies solve the sand mining problem? PLoS ONE 16(4), e0248882 (2021)CrossRef Google Scholar 
  7. Khan, S., Sugie, A.: Sand mining and its social impacts on local society in rural Bangladesh: a case study of a village in Tangail district. J. Urban Reg. Stud. Contemp. India 2(1), 1–11 (2015)Google Scholar 
  8. Daneshfaraz, R. et al.: The experimental study of the effects of river mining holes on the bridge piers. Iranian J. Soil Water Res. 50(7), 1619–1633 (2019)Google Scholar 
  9. Hackney, C. R., Darby, S. E., Parsons, D. R., Leyland, J., Best, J. L., Aalto, R., … & Houseago, R. C.: River bank instability from unsustainable sand mining in the lower Mekong River. Nat. Sustain. 3(3), 217–225 (2020)Google Scholar 
  10. Callander, R.A.: River meandering. Annu. Rev. Fluid Mech. 10(1), 129–158 (1978)CrossRef Google Scholar 
  11. Koehnken, L., Rintoul, M.: Impacts of sand mining on ecosystem structure, process and biodiversity in rivers. World Wildlife Fund International (2018)Google Scholar 
  12. Gavriletea, M.D.: Environmental impacts of sand exploitation. Analysis of sand market. Sustainability 9(7), 1118 (2017)Google Scholar 
  13. Koehnken, L., et al.: Impacts of riverine sand mining on freshwater ecosystems: a review of the scientific evidence and guidance for future research. River Res. Appl. 36(3), 362–370 (2020)Google Scholar 
  14. Myers, W.R.C.: Momentum transfer in a compound channel. J. Hydraul. Res. 16(2), 139–150 (1978)CrossRef Google Scholar 
  15. Rajaratnam, N., Ahmadi, R.M.: Interaction between main channel and flood-plain flows. J. Hydraul. Div. 105(5), 573–588 (1979)CrossRef Google Scholar 
  16. Sellin, R.H.J.: A laboratory investigation into the interaction between the flow in the channel of a river and that over its flood plain. La Houille Blanche 7, 793–802 (1964)CrossRef Google Scholar 
  17. Karami, H., et al.: Verification of numerical study of scour around spur dikes using experimental data. Water Environ. J. 28(1), 124–134 (2014)Google Scholar 
  18. Bathurst, J.C., et al.: Overbank sediment deposition patterns for straight and meandering flume channels. Earth Surf. Proc. Land. 27(6), 659–665 (2002)CrossRef Google Scholar 
  19. Xu, D., Bai, Y.: Experimental study on the bed topography evolution in alluvial meandering rivers with various sinuousnesses. J. Hydro-Environ. Res. 7(2), 92–102 (2013)CrossRef Google Scholar 
  20. Priego-Hernández, G.A., Rivera-Trejo, F.: Secondary currents: measurement and analysis. Atmósfera 29(1), 23–34 (2016)Google Scholar 
  21. Alshamani, K.M.M.: Correlations among turbulent shear stress, turbulent kinetic energy, and axial turbulence intensity. AIAA J. 16(8), 859–861 (1978)CrossRef Google Scholar 
  22. Biron, P.M., et al.: Comparing different methods of bed shear stress estimates in simple and complex flow fields. Earth Surface Process. Landforms: J. British Geomorphol. Res. Group 29(11), 1403–1415 (2004)Google Scholar 
  23. Clark, L.A., Theresa, M.W.: Boundary Shear Stress Along Vegetated Streambanks (2007)Google Scholar 
  24. Kim, S.-C., et al.: Estimating bottom stress in tidal boundary layer from acoustic Doppler velocimeter data. J. Hydraul. Eng. 126(6), 399–406 (2000)CrossRef Google Scholar 

  1. Home  
  2. Sustainable Environment  
  3. Conference paper

Flow Hydrodynamics Influences Due to Flood Plain Sand Mining in a Meandering Channel

  • 14 Accesses

Abstract

Flow hydrodynamics in the main channel due to floodplain sand mining is important for a better understanding of maintaining the natural habitat or the reliance between the flood plain and the main channel for the river’s long-term survival and also facilitates more effective river restoration engineering. Day by day anthropogenic stresses are increasing in the river corridor system, indiscriminate sand mining is one of them. In this study, a computational fluid dynamics (CFD)-based software Flow-3D hydro (renormalized group K-ε turbulence model used) is used to study the flow hydrodynamics of sinuous (sinuosity index = 1.25) channel 18 m long, 1 m width, and 0.3 m height with floodplain sand mining pit. Sand mining additionally increases the secondary current near the outer bank of the channel, therefore leading to scouring or erosion at the outer bank, as a result, rivers migrate laterally. The turbulence kinetic energy (TKE) is concentrated in the mining pit and near the inner bank. This study result can be used to understand the flow hydrodynamic of the river system due to the series of sand mining.

Keywords

  • Flow hydrodynamics
  • Turbulence modeling
  • Flow-3D
  • Sinuosity
  • Sand mining

This is a preview of subscription content, access via your institution.

References

  1. Best, J.: Anthropogenic stresses on the world’s big rivers. Nat. Geosci. 12(1), 7–21 (2019)CrossRef CAS Google Scholar 
  2. Bagnold, R.A.: Some Aspects of the Shape of River Meanders. US Government Printing Office (1960)Google Scholar 
  3. Kondolf, G.M.: Freshwater Gravel Mining and Dredging Issues: White Paper. Washington Department of Fish and Wildlife (2002)Google Scholar 
  4. Molnár, P., Ramírez, J.A.: Energy dissipation theories and optimal channel characteristics of river networks. Water Resour. Res. 34(7), 1809–1818 (1998)CrossRef Google Scholar 
  5. Padmalal, D., Maya, K.: Sand Mining: Environmental Impacts and Selected Case Studies. Springer (2014)Google Scholar 
  6. Hübler, M., Pothen, F.: Can smart policies solve the sand mining problem? PLoS ONE 16(4), e0248882 (2021)CrossRef Google Scholar 
  7. Khan, S., Sugie, A.: Sand mining and its social impacts on local society in rural Bangladesh: a case study of a village in Tangail district. J. Urban Reg. Stud. Contemp. India 2(1), 1–11 (2015)Google Scholar 
  8. Daneshfaraz, R. et al.: The experimental study of the effects of river mining holes on the bridge piers. Iranian J. Soil Water Res. 50(7), 1619–1633 (2019)Google Scholar 
  9. Hackney, C. R., Darby, S. E., Parsons, D. R., Leyland, J., Best, J. L., Aalto, R., … & Houseago, R. C.: River bank instability from unsustainable sand mining in the lower Mekong River. Nat. Sustain. 3(3), 217–225 (2020)Google Scholar 
  10. Callander, R.A.: River meandering. Annu. Rev. Fluid Mech. 10(1), 129–158 (1978)CrossRef Google Scholar 
  11. Koehnken, L., Rintoul, M.: Impacts of sand mining on ecosystem structure, process and biodiversity in rivers. World Wildlife Fund International (2018)Google Scholar 
  12. Gavriletea, M.D.: Environmental impacts of sand exploitation. Analysis of sand market. Sustainability 9(7), 1118 (2017)Google Scholar 
  13. Koehnken, L., et al.: Impacts of riverine sand mining on freshwater ecosystems: a review of the scientific evidence and guidance for future research. River Res. Appl. 36(3), 362–370 (2020)Google Scholar 
  14. Myers, W.R.C.: Momentum transfer in a compound channel. J. Hydraul. Res. 16(2), 139–150 (1978)CrossRef Google Scholar 
  15. Rajaratnam, N., Ahmadi, R.M.: Interaction between main channel and flood-plain flows. J. Hydraul. Div. 105(5), 573–588 (1979)CrossRef Google Scholar 
  16. Sellin, R.H.J.: A laboratory investigation into the interaction between the flow in the channel of a river and that over its flood plain. La Houille Blanche 7, 793–802 (1964)CrossRef Google Scholar 
  17. Karami, H., et al.: Verification of numerical study of scour around spur dikes using experimental data. Water Environ. J. 28(1), 124–134 (2014)Google Scholar 
  18. Bathurst, J.C., et al.: Overbank sediment deposition patterns for straight and meandering flume channels. Earth Surf. Proc. Land. 27(6), 659–665 (2002)CrossRef Google Scholar 
  19. Xu, D., Bai, Y.: Experimental study on the bed topography evolution in alluvial meandering rivers with various sinuousnesses. J. Hydro-Environ. Res. 7(2), 92–102 (2013)CrossRef Google Scholar 
  20. Priego-Hernández, G.A., Rivera-Trejo, F.: Secondary currents: measurement and analysis. Atmósfera 29(1), 23–34 (2016)Google Scholar 
  21. Alshamani, K.M.M.: Correlations among turbulent shear stress, turbulent kinetic energy, and axial turbulence intensity. AIAA J. 16(8), 859–861 (1978)CrossRef Google Scholar 
  22. Biron, P.M., et al.: Comparing different methods of bed shear stress estimates in simple and complex flow fields. Earth Surface Process. Landforms: J. British Geomorphol. Res. Group 29(11), 1403–1415 (2004)Google Scholar 
  23. Clark, L.A., Theresa, M.W.: Boundary Shear Stress Along Vegetated Streambanks (2007)Google Scholar 
  24. Kim, S.-C., et al.: Estimating bottom stress in tidal boundary layer from acoustic Doppler velocimeter data. J. Hydraul. Eng. 126(6), 399–406 (2000)CrossRef Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, IndiaO. P. Maurya, K. K. Nandi, S. Modalavalasa & S. Dutta

Corresponding author

Correspondence to O. P. Maurya .

Editor information

Editors and Affiliations

  1. Centre for the Environment, Indian Institute of Technology Guwahati, Guwahati, IndiaDeepmoni Deka
  2. Department of Chemical engineering, Indian Institute of Technology Guwahati, Guwahati, IndiaSubrata Kumar Majumder
  3. Department of Chemical engineering, Indian Institute of Technology Guwahati, Guwahati, IndiaMihir Kumar Purkait
Figure 4.24 - Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling

Optimization of filling systems for low pressure by Flow-3D

Dissertação de Mestrado
Ciclo de Estudos Integrados Conducentes ao
Grau de Mestre em Engenharia Mecânica
Trabalho efectuado sob a orientação do
Doutor Hélder de Jesus Fernades Puga
Professor Doutor José Joaquim Carneiro Barbosa

ABSTRACT

논문의 일부로 튜터 선택 가능성과 해결해야 할 주제가 설정되는 매개변수를 염두에 두고 개발 주제 ‘Flow- 3D ®에 의한 저압 충전 시스템 최적화’가 선택되었습니다. 이를 위해서는 달성해야 할 목표와 이를 달성하기 위한 방법을 정의하는 것이 필요했습니다.

충전 시스템을 시뮬레이션하고 검증할 수 있는 광범위한 소프트웨어에도 불구하고 Flow-3D®는 시장에서 최고의 도구 중 하나로 표시되어 전체 충전 프로세스 및 행동 표현과 관련하여 탁월한 정확도로 시뮬레이션하는 능력을 입증했습니다.

이를 위해 관련 프로세스를 더 잘 이해하고 충진 시스템 시뮬레이션을 위한 탐색적 기반 역할을 하기 위해 이 도구를 탐색하는 것이 중요합니다. 지연 및 재료 낭비에 반영되는 실제적인 측면에서 충전 장치의 치수를 완벽하게 만드는 비용 및 시간 낭비. 이러한 방식으로 저압 주조 공정에서 충진 시스템을 설계하고 물리적 모델을 탐색하여 특성화하는 방법론을 검증하기 위한 것입니다.

이를 위해 다음 주요 단계를 고려하십시오.

시뮬레이션 소프트웨어 Flow 3D® 탐색;
충전 시스템 모델링;
모델의 매개변수를 탐색하여 모델링된 시스템의 시뮬레이션, 검증 및 최적화.

따라서 연구 중인 압력 곡선과 주조 분석에서 가장 관련성이 높은 정보의 최종 마이닝을 검증하기 위한 것입니다.

사용된 압력 곡선은 수집된 문헌과 이전에 수행된 실제 작업을 통해 얻었습니다. 결과를 통해 3단계 압력 곡선이 층류 충진 체계의 의도된 목적과 관련 속도가 0.5 𝑚/𝑠를 초과하지 않는다는 결론을 내릴 수 있었습니다.

충전 수준이 2인 압력 곡선은 0.5 𝑚/𝑠 이상의 속도로 영역을 채우는 더 난류 시스템을 갖습니다. 열전달 매개변수는 이전에 얻은 값이 주물에 대한 소산 거동을 확증하지 않았기 때문에 연구되었습니다.

이러한 방식으로 주조 공정에 더 부합하는 새로운 가치를 얻었습니다. 달성된 결과는 유사한 것으로 나타난 NovaFlow & Solid®에 의해 생성된 결과와 비교되어 시뮬레이션에서 설정된 매개변수를 검증했습니다. Flow 3D®는 주조 부품 시뮬레이션을 위한 강력한 도구로 입증되었습니다.

As part of the dissertation and bearing in mind the parameters in which the possibility of a choice of tutor and the subject to be addressed is established, the subject for development ’Optimization of filling systems for low pressure by Flow 3D ®’ was chosen. For this it was necessary to define the objectives to achieve and the methods to attain them. Despite the wide range of software able to simulate and validate filling systems, Flow 3D® has been shown as one of the best tools in the market, demonstrating its ability to simulate with distinctive accuracy with respect to the entire process of filling and the behavioral representation of the fluid obtained. To this end, it is important to explore this tool for a better understanding of the processes involved and to serve as an exploratory basis for the simulation of filling systems, simulation being one of the great strengths of the current industry due to the need to reduce costs and time waste, in practical terms, that lead to the perfecting of the dimensioning of filling devices, which are reflected in delays and wasted material. In this way it is intended to validate the methodology to design a filling system in lowpressure casting process, exploring their physical models and thus allowing for its characterization. For this, consider the following main phases: The exploration of the simulation software Flow 3D®; modeling of filling systems; simulation, validation and optimization of systems modeled by exploring the parameters of the models. Therefore, it is intended to validate the pressure curves under study and the eventual mining of the most relevant information in a casting analysis. The pressure curves that were used were obtained through the gathered literature and the practical work previously performed. Through the results it was possible to conclude that the pressure curve with 3 levels meets the intended purpose of a laminar filling regime and associated speeds never exceeding 0.5 𝑚/𝑠. The pressure curve with 2 filling levels has a more turbulent system, having filling areas with velocities above 0.5 𝑚/𝑠. The heat transfer parameter was studied due to the values previously obtained didn’t corroborate the behavior of dissipation regarding to the casting. In this way, new values, more in tune with the casting process, were obtained. The achieved results were compared with those generated by NovaFlow & Solid®, which were shown to be similar, validating the parameters established in the simulations. Flow 3D® was proven a powerful tool for the simulation of casting parts.

키워드

저압, Flow 3D®, 시뮬레이션, 파운드리, 압력-시간 관계,Low Pressure, Flow 3D®, Simulation, Foundry, Pressure-time relation

Figure 4.24 - Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling
Figure 4.24 – Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling
Figure 4.39 - Values of temperature contours using full energy heat transfer parameter for simula
Figure 4.39 – Values of temperature contours using full energy heat transfer parameter for simula
Figure 4.40 – Comparison between software simulations (a) Flow 3D® simulation,
(b) NovaFlow & Solid® simulation
Figure 4.40 – Comparison between software simulations (a) Flow 3D® simulation, (b) NovaFlow & Solid® simulation

BIBLIOGRAPHY

[1] E. Stanley and D. B. Sc, “Fluid Flow Aspects of Solidification Modelling : Simulation
of Low Pressure Die Casting .”
[2] Y. Sahin, “Computer aided foundry die-design,” Metallography, vol. 24, no. 8, pp.
671–679, 2003.
[3] F. Bonollo, J. Urban, B. Bonatto, and M. Botter, “Gravity and low pressure die casting
of aluminium alloys : a technical and economical benchmark,” La Metall. Ital., vol. 97,
no. 6, pp. 23–32, 2005.
[4] P. a and R. R, “Study of the effect of process parameters on the production of a nonsimmetric low pressure die casting part,” La Metall. Ital., pp. 57–63, 2009.
[5] “Fundição em baixa pressão | Aluinfo.” [Online]. Available:
http://www.aluinfo.com.br/novo/materiais/fundicao-em-baixa-pressao. [Accessed: 18-
Sep-2015].
[6] “Low Pressure Sand Casting by Wolverine Bronze.” [Online]. Available:
http://www.wolverinebronze.com/low-pressure-sand-casting.php. [Accessed: 18-Sep2015].
[7] A. Reikher, “Numerical Analysis of Die-Casting Process in Thin Cavities Using
Lubrication Approximation,” no. December, 2012.
[8] P. Fu, A. a. Luo, H. Jiang, L. Peng, Y. Yu, C. Zhai, and A. K. Sachdev, “Low-pressure
die casting of magnesium alloy AM50: Response to process parameters,” J. Mater.
Process. Technol., vol. 205, no. 1–3, pp. 224–234, 2008.
[9] X. Li, Q. Hao, W. Jie, and Y. Zhou, “Development of pressure control system in
counter gravity casting for large thin-walled A357 aluminum alloy components,”
Trans. Nonferrous Met. Soc. China, vol. 18, no. 4, pp. 847–851, 2008.
[10] J. a. Hines, “Determination of interfacial heat-transfer boundary conditions in an
aluminum low-pressure permanent mold test casting,” Metall. Mater. Trans. B, vol. 35,
no. 2, pp. 299–311, 2004.
[11] A. Lima, A. Freitas, and P. Magalhães, “Processos de vazamento em moldações
permanentes,” pp. 40–49, 2003.
[12] Y. B. Choi, K. Matsugi, G. Sasaki, K. Arita, and O. Yanagisawa, “Analysis of
Manufacturing Processes for Metal Fiber Reinforced Aluminum Alloy Composite
Fabricated by Low-Pressure Casting,” Mater. Trans., vol. 47, no. 4, pp. 1227–1231,
68
2006.
[13] G. Mi, X. Liu, K. Wang, and H. Fu, “Numerical simulation of low pressure die-casting
aluminum wheel,” China Foundry, vol. 6, no. 1, pp. 48–52, 2009.
[14] J. Kuo, F. Hsu, and W. Hwang, “ADVANCED Development of an interactive
simulation system for the determination of the pressure ± time relationship during the
® lling in a low pressure casting process,” vol. 2, pp. 131–145, 2001.
[15] S.-G. Liu, F.-Y. Cao, X.-Y. Zhao, Y.-D. Jia, Z.-L. Ning, and J.-F. Sun, “Characteristics
of mold filling and entrainment of oxide film in low pressure casting of A356 alloy,”
Mater. Sci. Eng. A, vol. 626, pp. 159–164, 2015.
[16] “Casting Training Class – Lecture 10 – Solidification and Shrinkage-Casting.” FLOW3D®.
[17] “UAB Casting Engineering Laboratory.” [Online]. Available:
file:///C:/Users/Jos%C3%A9 Belo/Desktop/Artigo_Software/UAB Casting
Engineering Laboratory.htm. [Accessed: 09-Nov-2015].
[18] A. Louvo, “Casting Simulation as a Tool in Concurrent Engineering,” pp. 1–12, 1997.
[19] T. R. Vijayaram and P. Piccardo, “Computers in Foundries,” vol. 30, 2012.
[20] M. Sadaiah, D. R. Yadav, P. V. Mohanram, and P. Radhakrishnan, “A generative
computer-aided process planning system for prismatic components,” Int. J. Adv.
Manuf. Technol., vol. 20, no. 10, pp. 709–719, 2002.
[21] Ministry_of_Planning, “Digital Data,” vol. 67, pp. 1–6, 2004.
[22] S. Shamasundar, D. Ramachandran, and N. S. Shrinivasan, “COMPUTER
SIMULATION AND ANALYSIS OF INVESTMENTCASTING PROCESS.”
[23] J. M. Siqueira and G. Motors, “Simulation applied to Aluminum High Pressure Die
Casting,” pp. 1–5, 1998.
[24] C. Fluid, COMPUTATIONAL FLUID DYNAMICS. Abdulnaser Sayma & Ventus
Publishing ApS, 2009.
[25] C. a. Felippa, “1 – Overview,” Adv. Finite Elem. Methods, pp. 1–9.
[26] a. Meena and M. El Mansori, “Correlative thermal methodology for castability
simulation of ductile iron in ADI production,” J. Mater. Process. Technol., vol. 212,
no. 11, pp. 2484–2495, 2012.
[27] T. R. Vijayaram, S. Sulaiman, a. M. S. Hamouda, and M. H. M. Ahmad, “Numerical
simulation of casting solidification in permanent metallic molds,” J. Mater. Process.
69
Technol., vol. 178, pp. 29–33, 2006.
[28] “General CFD FAQ — CFD-Wiki, the free CFD reference.” [Online]. Available:
http://www.cfd-online.com/Wiki/General_CFD_FAQ. [Accessed: 10-Nov-2015].
[29] “FEM | FEA | CFD.” [Online]. Available: http://fem4analyze.blogspot.pt/. [Accessed:
09-Nov-2015].
[30] “Fundição; revista da Associação portuguesa de fundição,” Fundição, vol. N
o
227.
[31] “Casting Training Class – Lecture 1 – Introduction_to_FLOW-3D – Casting.” FLOW3D®.
[32] F. Science, “FLOW-3D Cast Documentation,” no. 3.5, p. 80, 2012.
[33] “Casting Training Class – Lecture 4 – Geometry Building – General.” FLOW-3D®.
[34] F. Science, “FLOW-3D v11.0.3 User Manual,” pp. 1–132, 2015.
[35] “Casting Training Class – Lecture 5 Meshing Concept – General.” FLOW-3D®.
[36] “Casting Training Class – Lecture 6 – Boundary_Conditions – Casting.” FLOW-3D®.
[37] “Casting Training Class – Lecture 9 – Physical Models-castings.” FLOW-3D®.
[38] P. A. D. Jácome, M. C. Landim, A. Garcia, A. F. Furtado, and I. L. Ferreira, “The
application of computational thermodynamics and a numerical model for the
determination of surface tension and Gibbs–Thomson coefficient of aluminum based
alloys,” Thermochim. Acta, vol. 523, no. 1–2, pp. 142–149, 2011.
[39] J. P. Anson, R. A. L. Drew, and J. E. Gruzleski, “The surface tension of molten
aluminum and Al-Si-Mg alloy under vacuum and hydrogen atmospheres,” Metall.
Mater. Trans. B Process Metall. Mater. Process. Sci., vol. 30, no. 6, pp. XVI–1032,
1999.

Figure 1: Mold drawings

3D Flow and Temperature Analysis of Filling a Plutonium Mold

플루토늄 주형 충전의 3D 유동 및 온도 분석

Authors: Orenstein, Nicholas P. [1]

Publication Date:2013-07-24
Research Org.: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.: DOE/LANL
OSTI Identifier: 1088904
Report Number(s): LA-UR-13-25537
DOE Contract Number: AC52-06NA25396
Resource Type: Technical Report
Country of Publication: United States
Language: English
Subject: Engineering(42); Materials Science(36); Radiation Chemistry, Radiochemistry, & Nuclear Chemistry(38)

Introduction

The plutonium foundry at Los Alamos National Laboratory casts products for various special nuclear applications. However, plutonium’s radioactivity, material properties, and security constraints complicate the ability to perform experimental analysis of mold behavior. The Manufacturing Engineering and Technologies (MET-2) group previously developed a graphite mold to vacuum cast small plutonium disks to be used by the Department of Homeland Security as point sources for radiation sensor testing.

A two-stage pouring basin consisting of a funnel and an angled cavity directs the liquid into a vertical runner. A stack of ten disk castings connect to the runner by horizontal gates. Volumetric flow rates were implemented to limit overflow into the funnel and minimize foundry returns. Models using Flow-3D computational fluid dynamics software are employed here to determine liquid Pu flow paths, optimal pour regimes, temperature changes, and pressure variations.

Setup

Hardcopy drawings provided necessary information to create 3D .stl models for import into Flow-3D (Figs. 1 and 2). The mesh was refined over several iterations to isolate the disk cavities, runner, angled cavity, funnel, and input pour. The final flow and mold-filling simulation utilizes a fine mesh with ~5.5 million total cells. For the temperature study, the mesh contained 1/8 as many cells to reduce computational time and set temperatures to 850 °C for the molten plutonium and 500 °C for the solid graphite mold components (Fig. 3).

Flow-3D solves mass continuity and Navier-Stokes momentum equations over the structured rectangular grid model using finite difference and finite volume numerical algorithms. The solver includes terms in the momentum equation for body and viscous accelerations and uses convective heat transfer.

Simulation settings enabled Flow-3D physics calculations for gravity at 980.665 cm/s 2 in the negative Z direction (top of mold to bottom); viscous, turbulent, incompressible flow using dynamically-computed Renormalized Group Model turbulence calculations and no-slip/partial slip wall shear, and; first order, full energy equation heat transfer.

Mesh boundaries were all set to symmetric boundary conditions except for the Zmin boundary set to outflow and the Zmax boundary set to a volume flow. Vacuum casting conditions and the high reactivity of remaining air molecules with Pu validate the assumption of an initially fluidless void.

Results

The flow follows a unique three-dimensional path. The mold fills upwards with two to three disks receiving fluid in a staggered sequence. Figures 5-9 show how the fluid fills the cavity, and Figure 7 includes the color scale for pressure levels in these four figures. The narrow gate causes a high pressure region which forces the fluid to flow down the cavity centerline.

It proceeds to splash against the far wall and then wrap around the circumference back to the gate (Figs. 5 and 6). Flow in the angled region of the pouring basin cascades over the bottom ledge and attaches to the far wall of the runner, as seen in Figure 7.

This channeling becomes less pronounced as fluid volume levels increase. Finally, two similar but non-uniform depressed regions form about the centerline. These regions fill from their perimeter and bottom until completion (Fig. 8). Such a pattern is counter, for example, to a steady scenario in which a circle of molten Pu encompassing the entire bottom surface rises as a growing cylinder.

Cavity pressure becomes uniform when the cavity is full. Pressure levels build in the rising well section of the runner, where impurities were found to settle in actual casting. Early test simulations optimized the flow as three pours so that the fluid would never overflow to the funnel, the cavities would all fill completely, and small amounts of fluid would remain as foundry returns in the angled cavity.

These rates and durations were translated to the single 2.7s pour at 100 cm 3 per second used here. Figure 9 shows anomalous pressure fluctuations which occurred as the cavities became completely filled. Multiple simulations exhibited a rapid change in pressure from positive to negative and back within the newly-full disk and surrounding, already-full disks.

The time required to completely fill each cavity is plotted in Figure 10. Results show negligible temperature change within the molten Pu during mold filling and, as seen in Figure 11, at fill completion.

Figure 1: Mold drawings
Figure 1: Mold drawings
Figure 2: Mold Assembly
Figure 2: Mold Assembly
Figure 4: Actual mold and cast Pu
Figure 4: Actual mold and cast Pu
Figure 5: Bottom cavity filling
from runner
Figure 5: Bottom cavity filling from runner
Figure 6: Pouring and filling
Figure 6: Pouring and filling
Figure 8: Edge detection of cavity fill geometry. Two similar depressed areas form
about the centerline. Top cavity shown; same pressure scale as other figures
Figure 8: Edge detection of cavity fill geometry. Two similar depressed areas form about the centerline. Top cavity shown; same pressure scale as other figures
Figure 10: Cavity fill times,from first fluid contact with pouring basin, Figure 11:Fluid temperature remains essentially constant
Figure 10: Cavity fill times,from first fluid contact with pouring basin, Figure 11:Fluid temperature remains essentially constant

Conclusions

Non-uniform cavity filling could cause crystal microstructure irregularities during solidification. However, the small temperature changes seen – due to large differences in specific heat between Pu and graphite – over a relatively short time make such problems unlikely in this case.

In the actual casting, cooling required approximately ten minutes. This large difference in time scales further reduces the chance for temperature effects in such a superheated scenario. Pouring basin emptying decreases pressure at the gate which extends fill time of the top two cavities.

The bottom cavity takes longer to fill because fluid must first enter the runner and fill the well. Fill times continue linearly until the top two cavities. The anomalous pressure fluctuations may be due to physical attempts by the system to reach equilibrium, but they are more likely due to numerical errors in the Flow3D solver.

Unsuccessful tests were performed to remove them by halving fluid viscosity. The fine mesh reduced, but did not eliminate, the extent of the fluctuations. Future work is planned to study induction and heat transfer in the full Pu furnace system, including quantifying temporal lag of the cavity void temperature to the mold wall temperature during pre-heat and comparing heat flux levels between furnace components during cool-down.

Thanks to Doug Kautz for the opportunity to work with MET-2 and for assigning an interesting unclassified project. Additional thanks to Mike Bange for CFD guidance, insight of the project’s history, and draft review.

Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.

Numerical modelling of air-water flows in sewer drops

하수구 방울의 공기-물 흐름 수치 모델링

Paula Beceiro (corresponding author)
Maria do Céu Almeida
Hydraulic and Environment Department (DHA), National Laboratory for Civil Engineering, Avenida do Brasil 101, 1700-066 Lisbon, Portugal
E-mail: pbeceiro@lnec.pt
Jorge Matos
Department of Civil Engineering, Arquitecture and Geosources,
Technical University of Lisbon (IST), Avenida Rovisco Pais 1, 1049-001 Lisbon, Portugal

ABSTRACT

물 흐름에 용존 산소(DO)의 존재는 해로운 영향의 발생을 방지하는 데 유익한 것으로 인식되는 호기성 조건을 보장하는 중요한 요소입니다.

하수도 시스템에서 흐르는 폐수에 DO를 통합하는 것은 공기-액체 경계면 또는 방울이나 접합부와 같은 특이점의 존재로 인해 혼입된 공기를 통한 연속 재방출의 영향을 정량화하기 위해 광범위하게 조사된 프로세스입니다. 공기 혼입 및 후속 환기를 향상시키기 위한 하수구 드롭의 위치는 하수구의 호기성 조건을 촉진하는 효과적인 방법입니다.

본 논문에서는 수직 낙하, 배경 및 계단식 낙하를 CFD(전산유체역학) 코드 FLOW-3D®를 사용하여 모델링하여 이러한 유형의 구조물의 존재로 인해 발생하는 난류로 인한 공기-물 흐름을 평가했습니다. 이용 가능한 실험적 연구에 기초한 수력학적 변수의 평가와 공기 혼입의 분석이 수행되었습니다.

이러한 구조물에 대한 CFD 모델의 결과는 Soares(2003), Afonso(2004) 및 Azevedo(2006)가 개발한 해당 물리적 모델에서 얻은 방류, 압력 헤드 및 수심의 측정을 사용하여 검증되었습니다.

유압 거동에 대해 매우 잘 맞았습니다. 수치 모델을 검증한 후 공기 연행 분석을 수행했습니다.

The presence of dissolved oxygen (DO) in water flows is an important factor to ensure the aerobic conditions recognised as beneficial to prevent the occurrence of detrimental effects. The incorporation of DO in wastewater flowing in sewer systems is a process widely investigated in order to quantify the effect of continuous reaeration through the air-liquid interface or air entrained due the presence of singularities such as drops or junctions. The location of sewer drops to enhance air entrainment and subsequently reaeration is an effective practice to promote aerobic conditions in sewers. In the present paper, vertical drops, backdrops and stepped drop was modelled using the computational fluid dynamics (CFD) code FLOW-3D® to evaluate the air-water flows due to the turbulence induced by the presence of this type of structures. The assessment of the hydraulic variables and an analysis of the air entrainment based in the available experimental studies were carried out. The results of the CFD models for these structures were validated using measurements of discharge, pressure head and water depth obtained in the corresponding physical models developed by Soares (2003), Afonso (2004) and Azevedo (2006). A very good fit was obtained for the hydraulic behaviour. After validation of numerical models, analysis of the air entrainment was carried out.

Key words | air entrainment, computational fluid dynamics (CFD), sewer drops

Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.
Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.
Figure 3. Comparison between the experimental and numerical pressure head along of the invert of the outlet pipe.
Figure 3. Comparison between the experimental and numerical pressure head along of the invert of the outlet pipe.
Figure 4. Average void fraction along the longitudinal axis of the outlet pipe for the lower discharges in the vertical drop and backdrop.
Figure 4. Average void fraction along the longitudinal axis of the outlet pipe for the lower discharges in the vertical drop and backdrop.

REFERENCES

Afonso, J. Dissipação de energia e rearejamento em quedas em colectores. M.Sc. Thesis, UTL/IST, Lisboa, Portugal.
Almeida, M. C., Butler, D. & Matos, J. S. Reaeration by sewer drops. In: 8th Int. Conf. on Urban Storm Drainage, Sydney, Australia.
Azevedo, R. I. Transferência de oxigénio em quedas guiadas em colectores. M.Sc. Thesis, IST, Lisboa, Portugal.
Beceiro, P., Almeida, M. C. & Matos, J. Numerical Modelling of air-water flows in a vertical drop and a backdrop. In: 3rd IAHR Europe Congress, Porto, Portugal.
Bombardelli, F. A., Meireles, I. & Matos, J. S. Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of step stepped spillways. Environ. Fluid Mech. 11 (3), 263–288.
Brethour, J. M. & Hirt, C. W. Drift Model for TwoComponent Flows. Flow Science, Inc., Los Alamos, NM, USA.
Chamani, M. R. Jet Flow on Stepped Spillways and Drops. M.Sc. Thesis, University of Alberta, Alberta, Canada.
Chanson, H. Air Bubble Entrainment in Free-Surface Turbulent Shear Flow. Academic Press Inc., California, USA.
Chanson, H. Air bubble entrainment in open channels: flow structure and bubble size distribution. Int. J. Multiphase 23 (1), 193–203.
Chanson, H. Hydraulics of aerated flows: qui pro quo? Journal of Hydraulic Research 51 (3), 223–243.
Dufresne, M., Vazques, J., Terfous, A., Ghenaim, A. & Poulet, J. Experimental investigation and CFD modelling of flow, sedimentation, and solids separation in a combined sewer detention tank. Computer and Fluids 38, 1042–1049.
Durve, A. P. & Patwardhan, A. W. Numerical and experimental investigation of onset of gas entrainment phenomenon. Chemical Engineering Science 73, 140–150.
Felder, S. & Chanson, H. Air–water flows and free-surface profiles on a non-uniform stepped chute. Journal of Hydraulic Research 52 (2), 253–263.
Flow Science FLOW-3D User’s Manuals Version 10.0. Vol.1/2. Flow Science Inc., Los Alamos, NM, USA.
Granata, F., Marinis, G., Gargano, R. & Hager, W. H. Energy loss in circular drop manholes. In: 33rd IAHR Congress: Water Engineering for Sustainable Environment, British
Columbia, Vancouver, Canada. Hirt, C. W. Modeling Turbulent Entrainment of air at A Free Surface. Flow Science Inc., Los Alamos, NM, USA.
Hirt, C. W. & Nichols, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39, 201–225.
Hirt, C. W. & Sicilian, J. M. A porosity technique for the definition of obstacles in rectangular cell meshes. In: Proc. 4th Int, Conf. Ship Hydro., National Academy of Science, Washington, DC, USA.
Isfahani, A. H. G. & Brethour, J. On the Implementation of Two-Equation Turbulence Models in FLOW-3D. Flow Science Inc., Los Alamos, NM, USA.
Kouyi, G. L., Bret, P., Didier, J. M., Chocat, B. & Billat, C. The use of CFD modelling to optimise measurement of overflow rates in a downstream-controlled dual-overflow structure. Water Science and Technology 64 (2), 521–527.
Lopes, P., Leandro, J., Carvalho, R. F., Páscoa, P. & Martins, R. Numerical and experimental investigation of a gully under surcharge conditions. Urban Water Journal 12 (6), 468–476.
Martins, R., Leandro, J. & Carvalho, R. F. Characterization of the hydraulic performance of a gully under drainage conditions. Water Science and Technology 69 (12), 2423–2430.
Matias, N., Nielsel, A. H., Vollertsen, J., Ferreira, F. & Matos, J. S. Reaeration and hydrogen sulfide release at drop structures. In: 8th International Conference on Sewer Processes and Networks (SPN8), Rotterdam, Netherlands.
Matos, J. S. & Sousa, E. R. Prediction of dissolved oxygen concentration along sanitary sewers. Water Science and Technology 34 (5–6), 525–532.
Mignot, E., Bonakdari, H., Knothe, P., Lipeme Kouyi, G., Bessette, A., Rivière, N. & Bertrand-Krajewski, J. L. Experiments and 3D simulations of flow structures in junctions and of their influence on location of flowmeters. In: 12th International Conference on Urban Drainage, Porto Alegre, Brazil.
Ozmen-Cagatay, H. & Kocaman, S. Dam-break flow in the presence of obstacle: experiment and CFD Simulation. Engineering Applications of Computational Fluid Mechanics 5 (4), 541–552.
Shojaee Fard, M. H. & Boyaghchi, F. A. Studies of the influence of various blade outlet angles in a centrifugal pump when handling viscous fluids. American Journal of Applied Sciences 4 (9), 718–724.
Soares, A. Rearejamento em Quedas em Colectores de Águas Residuais. M.Sc. Thesis, FCTUC, Coimbra, Portugal.
Sousa, C. M. & Lopes, R. R. Hidráulica e rearejamento em quedas verticais em colectores. Estudo Experimental. Research Report, UTL/IST, Lisboa, Portugal.
Sousa, V., Meireles, I., Matos, J. & Almeida, M. C. Numerical modelling of air-water flow in a vertical drop manhole. In: 7th International Conference on Sewer Processes and Networks (SPN7), Shefield, UK.
Stovin, V., Guymer, I. & Lau, S. D. Approaches to validating a 3D CFD manhole model. In: 11th International Conference on Urban Drainage, Edinburgh, Scotland, UK.
Tota, P. V. Turbulent Flow Over A Backward-Facing Step Using the RNG Model. Flow Science Inc., Los Alamos, NM, USA.
Valero, D. & García-Bartual, R. Calibration of an air entrainment model for CFD spillway applications. In: Advances in Hydroinformatics. Springer, Singapore, pp. 571–582.
Versteeg, H. K. & Malalasekera, W. An Introduction to Computational Fluid Dynamics. The Finite Volume Method. Longman Group limited, England.
Yang, Y., Yang, J., Zuo, J., Li, Y., He, S., Yang, X. & Zhang, K. Study on two operating conditions of a full-scale oxidation ditch for optimization of energy consumption and effluent quality by using CFD model. Water Research 45 (11), 3439–3452.
Zhai, A. J., Zhang, Z., Zhang, W. & Chen, Q. Y. Evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by CFD: part 1— summary of prevalent Turbulence models. HVAC&R Research 13 (6), 853–870.
Zhao, C., Zhu, D. Z. & Rajaratnam, N. Computational and experimental study of surcharged flow at a 90W combining sewer junction. Journal of Hydraulic Engineering 134 (6), 688–700.

Fig. 6 LH2 isotherms at 1020 s.

액체-수소 탱크를 위한 결합된 열역학-유체-역학 솔루션

Coupled thermodynamic-fluid-dynamic solution for a liquid-hydrogen tank

G. D. Grayson

Published Online:23 May 2012 https://doi.org/10.2514/3.26706

Tools Share

Free first page

Introduction

ROPELLANT 열 성층화 및 외부 교란에 대한 유체 역학적 반응은 발사체와 우주선 모두에서 중요합니다. 과거에는 결합된 솔루션을 제공할 수 있는 충분한 계산 기술이 부족하여 이러한 문제를 개별적으로 해결했습니다.1

이로 인해 모델링 기술의 불확실성을 허용하기 위해 큰 안전 계수를 가진 시스템이 과도하게 설계되었습니다. 고중력 환경과 저중력 환경 모두에서 작동하도록 설계된 미래 시스템은 기술적으로나 재정적으로 실현 가능하도록 과잉 설계 및 안전 요소가 덜 필요합니다.

이러한 유체 시스템은 열역학 및 유체 역학이 모두 중요한 환경에서 모델의 기능을 광범위하게 검증한 후에만 고충실도 수치 모델을 기반으로 할 수 있습니다. 상용 컴퓨터 코드 FLOW-3D2는 유체 역학 및 열 모델링 모두에서 가능성을 보여주었으며,1 따라서 열역학-유체-역학 엔지니어링 문제에서 결합된 질량, 운동량 및 에너지 방정식을 푸는 데 적합함을 시사합니다.

발사체의 복잡한 액체 가스 시스템에 대한 포괄적인 솔루션을 달성하기 위한 첫 번째 단계로 액체 유체 역학과 열역학을 통합하는 제안된 상단 단계 액체-수소(Lit) 탱크의 간단한 모델이 여기에 제시됩니다. FLOW-3D FLOW-3D 프로그램은 Los Alamos Scientific Laboratory에서 시작되었으며 마커 및 셀 방법에서 파생된 것입니다.3 현재 상태로 가져오기 위해 수년에 걸쳐 광범위한 코드 수정이 이루어졌습니다.2

프로그램은 다음과 같습니다. 일반 Navier-Stokes 방정식을 풀기 위해 수치 근사의 중앙 유한 차분 방법을 사용하는 3차원 유체 역학 솔버입니다. 모멘텀 및 에너지 방정식의 섹션은 특정 응용 프로그램에 따라 활성화 또는 비활성화할 수 있습니다.

코드는 1994년 9월 13일 접수를 인용하기 위해 무액체 표면, 복잡한 용기 기하학, 여러 점성 모델, 표면 장력, 다공성 매체를 통한 흐름 및 응고와 함께 압축성 또는 비압축성 유동 가정을 제공합니다. 1995년 1월 15일에 받은 개정; 1995년 2월 17일 출판 승인.

ROPELLANT thermal stratification and fluid-dynamic response to external disturbances are of concern in both launch vehicles and spacecraft. In the past these problems have been addressed separately for want of sufficient computational technology to provide for coupled solutions.1 This has resulted in overdesigned systems with large safety factors to allow for the uncertainty in modeling techniques. Future systems designed to perform in both highand low-gravity environments will require less overdesign and safety factors to be technically and financially feasible. Such fluid systems can be based on high-fidelity numerical models only after extensive validation of the models’ capabilities in environments where both the thermodynamics and the fluid dynamics are important. The commercial computer code FLOW-3D2 has shown promise in both fluid-dynamic and thermal modeling,1 thus suggesting suitability for solving the coupled mass, momentum, and energy equations in thermodynamic-fluid-dynamic engineering problems. As a first step to achieving a comprehensive solution for complex liquidgas systems in a launch vehicle, a simple model of a proposed upper-stage liquid-hydrogen (Lit) tank incorporating the liquid fluid dynamics and thermodynamics is presented here. FLOW-3D The FLOW-3D program originated at the Los Alamos Scientific Laboratory and is a derivative of the marker-and-cell method.3 Extensive code modifications have been made over the years to bring it to its present state.2 The program is a three-dimensional fluiddynamic solver that uses a central finite-difference method of numerical approximation to solve the general Navier-Stokes equations. Sections of the momentum and energy equations can be enabled or disabled depending on the particular application. The code provides compressible or incompressible flow assumptions with liquid free surfaces, complex container geometries, several viscosity models, surface tension, flow though porous media, and solidification, to cite Received Sept. 13, 1994; revision received Jan. 15, 1995; accepted for publication Feb. 17, 1995. Copyright © 1995 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. *Engineer/Scientist, Propulsion Analysis and Hydraulics, Space Transportation Division, MS 13-3, 5301 Bolsa Avenue. Member AIAA. a few of the possibilities. Further information on FLOW-3D’s capabilities and details of the numerical algorithms can be found in Ref. 2

Fig. 1 Axial-acceleration history.
Fig. 1 Axial-acceleration history.
Fig. 2 Heat flux histories.
Fig. 2 Heat flux histories.
Fig. 3 LHi isotherms at 50 s.
Fig. 3 LHi isotherms at 50 s.
Fig. 4 LH2 isotherms at 300 s
Fig. 4 LH2 isotherms at 300 s
Fig. 5 LH2 isotherms at 880 s.
Fig. 5 LH2 isotherms at 880 s.
Fig. 6 LH2 isotherms at 1020 s.
Fig. 6 LH2 isotherms at 1020 s.
Fig. 7 Tank-outlet temperature history.
Fig. 7 Tank-outlet temperature history.
Fig. 1 Geometrical 3D model of Caisson

환기실에서 의도된 삼중수소 방출 후 삼중수소 거동 시뮬레이션

Simulation of Tritium Behavior after Intended Tritium Release in Ventilated Room


Yasunori IWAI
, Takumi HAYASHI, Toshihiko YAMANISHI, Kazuhiro KOBAYASHI & Masataka NISHI

Abstract

일본원자력연구소(JAERI) 산하 삼중수소공정연구소(TPL)에서는 핵융합로의 안전성 확인 및 강화를 위해 12m3의 대형 밀폐용기(Caisson)로 삼중수소 안전 연구(CATS)용 케이슨 조립체를 제작하여 추정 삼중수소 누출 이벤트가 발생해야 하는 경우 삼중수소 거동. 본 연구의 주요 목적 중 하나는 환기실에서 삼중수소 누출 사건이 발생한 후 삼중수소 거동을 예측하기 위한 시뮬레이션 방법을 확립하는 것입니다.

RNG 모델은 허용 가능한 엔지니어링 정밀도로 50m3/h 환기 케이슨에서 맴돌이 흐름 계산에 유효한 것으로 밝혀졌습니다. 의도된 삼중수소 방출 후 계산된 초기 및 제거 삼중수소 농도 이력은 50m3/h 환기 케이슨에서 실험 관찰과 일치했습니다.

환기실의 삼중수소 수송에는 벽 근처의 흐름이 중요한 역할을 하는 것으로 밝혀졌다. 한편, 3,000m3의 삼중수소 취급실에서 의도적으로 방출된 삼중수소 거동은 미일 협력하에 실험적으로 조사되었습니다. 동일한 방법으로 계산된 삼중수소 농도 이력은 실험적 관찰과 일치하였으며, 이는 현재 개발된 방법이 삼중수소 취급실의 실제 규모에 적용될 수 있음을 입증한다.

At the Tritium Process Laboratory (TPL) at the Japan Atomic Energy Research Institute (JAERI), Caisson Assembly for Tritium Safety study (CATS) with 12 m3 of large airtight vessel (Caisson) was fabricated for confirmation and enhancement of fusion reactor safety to estimate tritium behavior in the case where a tritium leak event should happen. One of the principal objectives of the present studies is the establishment of simulation method to predict the tritium behavior after the tritium leak event should happen in a ventilated room. The RNG model was found to be valid for eddy flow calculation in the 50m3/h ventilated Caisson with acceptable engineering precision. The calculated initial and removal tritium concentration histories after intended tritium release were consistent with the experimental observations in the 50 m3/h ventilated Caisson. It is found that the flow near a wall plays an important role for the tritium transport in the ventilated room. On the other hand, tritium behavior intentionally released in the 3,000 m3 of tritium handling room was investigated experimentally under a US-Japan collaboration. The tritium concentration history calculated with the same method was consistent with the experimental observations, which proves that the present developed method can be applied to the actual scale of tritium handling room.

KEYWORDS: 

Fig. 1 Geometrical 3D model of Caisson
Fig. 1 Geometrical 3D model of Caisson
Fig. 2 Geometrical 3D model of "main cell" of TSTA
Fig. 2 Geometrical 3D model of “main cell” of TSTA

REFERENCES

(1) Los Alamos National Laboratory: Final Safety Analysis Report of Tritium Systems Test Assembly at the Los Alamos National Laboratory, TSTA-SAR, (1996).
(2) Naruse, Y., Matsuda, Y., Tanaka, K.: Fusion Eng. Des., 12, 293 (1990).
(3) Schira, P., Hutter, E., Jourdan, G., Penzhone, R.: Fu-VOL. 38, NO. 1, JANUARY 2001 sion Eng. Des., 18, 19 (1991).
(4) Bartlit, J. R., Anderson, J. L., Jalbert, R. A., Carl-son, R. V., Okuno, K., Ide, T., Fukui, H., Enoeda, M., Naruse, Y.: Proc. 13th SOFE, Knoxville, TN., U.S.A., 798 (1989).
(5) Hayashi, T., Kobayashi, K., Iwai, Y., Yamanishi, T., Nishi, M., Okuno, K., Carlson, R. V., Willms, R. S., Hyatt, D., Roybal, B.: Fusion Thecnol., 34, 521 (1998).
(6) Hayashi, T., Kobayashi, K., Iwai, Y., Yamada, M., Suzuki, T., O’hira, S., Nakamura, H., Shu, W., Yama-nishi, T., Kawamura, Y., Isobe, K., Konishi, S., Nishi, M.: Submitted to Fusion Eng. Des. (1999).
(7) Yakhot, V., Orgazag, S. A.: J. Sci. Comput., 1, 3 (1986).
(8) Hirt, C. W., Cook, J. L.: J. Comp. Phys., 10, 324 (1972).
(9) Daiguji, H., Miyake, Y., Yoshizawa, A.: “Computa-tional Fluid Dynamics of Turbulent Flow-Models and Numerical Methods”, Univ. of Tokyo Press, Tokyo, 183 (1998), [in Japanese].
(10) Hinze, J. 0.: “Turbulence”, McGraw-Hill, New York, 227 (1959).
(11) Launder, B. E., Spalding, D. B.: “Mathematical Models of Turbulence”, Academics, London, (1972).
(12) Jones, W. P., Launder, B. E.: Int. J. Heat Mass Trans-fer, 15, 301 (1972).
(13) Jones, W. P., Launder, B. E.: Int. J. Heat Mass Trans-fer, 16, 1119 (1973).
(14) Hanjalic, K., Launder, B. E.: J. Fluid Mech., 52, 609 (1972).
(15) Harlow, F. W., Nakayama, P. I.: Phys. Fluids, 10, 2303 (1967).
(16) Nakayama, P. I.: 8th Aerospace Science Meeting, AIAA paper No. 70-3, (1970).
(17) Boussinesq, J.: “Theorie Analytique de la chaleur”, Ganthier-Villars, Paris, 157 (1903).
(18) Hashimoto, K.: “Chemical Reaction Engineering”, (1st ed.), Baifuukan, Tokyo, 173 (1979), [in Japanese].
(19) Iwai, Y., Hayashi, T., Kobayashi, K., O’hira, S., Nishi, M.: Submitted to Fusion Eng. Des. (2000).

Figura 7. Influencia del modelo de turbulencia. Qmodelo=27.95l/s.

Flow-3D를 사용하여 전산유체역학(CFD)을 적용한 빠른 단계의 플러시 유동 수치 모델링

Numerical Modeling of Flush Flow in a Rapid Step Applying Computational Fluid Dynamics (CFD) Using Flow-3D.

레브 폴리텍. (Quito) [온라인]. 2018, vol.41, n.2, pp.53-64. ISSN 2477-8990.

이 프로젝트의 주요 목표는 FLOW-3D를 사용하여 계단식 여수로에서 스키밍 흐름의 수치 모델링을 개발하는 것입니다. 이러한 구조의 설계는 물리적 모델링에서 얻은 경험적 표현과 CFD 코드를 지원하는 계단식 여수로를 통한 흐름의 수치 모델링에서 보완 연구를 기반으로 합니다. 수치 모델은 균일한 영역의 유속과 계단 여수로의 마찰 계수를 추정하는 데 사용됩니다(ϴ = 45º, Hd=4.61m). 흐름에 대한 자동 통기의 표현은 복잡하므로 프로그램은 공기 연행 모델을 사용하여 특정 제한이 있는 솔루션에 근접합니다.

The main objective of this project is to develop the numerical modeling of the skimming flow in a stepped spillway using FLOW-3D. The design of these structures is based on the use of empirical expressions obtained from physical modeling and complementary studies in the numerical modeling of flow over the stepped spillway with support of CFD code. The numerical model is used to estimate the flow velocity in the uniform region and the friction coefficient of the stepped spillway (ϴ = 45º, Hd=4.61m). The representation of auto aeration a flow is complex, so the program approximates the solution with certain limitations, using an air entrainment model; drift flux model and turbulence model k-ԑ RNG. The results obtained with numerical modeling and physical modeling at the beginning of natural auto aeration of flow and depth of the biphasic flow in the uniform region presents deviations above to 10% perhaps the flow is highly turbulent.

Keywords : Stepped spillway; skimming flow; air entrainment; drift flux; numerical modeling; FLOW-3D.

Keywords : 계단식 여수로; 스키밍 흐름; 공기 연행; 드리프트 플럭스; 수치 모델링; 흐름-3D.· 

스페인어로 된 초록 · 스페인어 로 된 텍스트 · 스페인어로 된 텍스트( pdf 

Figure 1. Grazing flow over a rapid step.
Figure 1. Grazing flow over a rapid step.
Figura 2. Principales regiones existentes en un flujo rasante.
Figura 2. Principales regiones existentes en un flujo rasante.
Figure 3. Dimensions of the El Batán stepped rapid.
Figure 3. Dimensions of the El Batán stepped rapid.
Figure 4. 3D physical model of the El Batán stepped rapid
Figure 4. 3D physical model of the El Batán stepped rapid
Figura 7. Influencia del modelo de turbulencia. Qmodelo=27.95l/s.
Figura 7. Influencia del modelo de turbulencia. Qmodelo=27.95l/s.

REFERENCIAS

ARAGUA. (2013). “Modelación numérica y experimental de flujos aire-agua
en caídas en colectores.”, Laboratório Nacional de Engenharia Civil, I.
P. Av do Brasil 101 • 1700-066 Lisboa.
Bombardelli, F.A., Meireles, I. and Matos, J., (2010), “Laboratory
measurement and multi-block numerical simulations of the mean flow
and turbulence in the non-aerated skimming flow region of steep stepped
spillways”, Environ Fluid Mechanics.
Castro M. (2015) “Análisis Dimensional y Modelación física en Hidráulica”.
Escuela Politécnica Nacional. Quito Ecuador. 50 p.
Chanson H., D. B. Bung., J. Matos (2015). “Stepped spillways and cascades”.
IAHR Monograph. School of Civil Engineering, University of
Queensland, Brisbane, Australia.
Chanson H. (1993). “Stepped Spillway Flows and Air Entrainment.” Can. Jl
of Civil Eng., Vol. 20, No. 3, June, pp. 422-435 (ISSN 0315-1468).
CIERHI, EPN TECH, (2016). “Estudio experimental en modelo físico de las
rápidas con perfil escalonado y liso de la quebrada el Batán Fase I y Fase
II”, Escuela Politécnica Nacional, Quito Ecuador.
Fernández Oro J. M. (2012)., “Técnicas Numéricas en Ingeniería de Fluidos:
Introducción a la Dinámica de Fluidos Computacional (CFD) por el
Método de Volúmenes Finitos”. Barcelona: Reverté.
Flow Science, Inc. (2012). “FLOW 3D 10.1.0 Documentation Release.
Manual de Usuario”, Los Alamos National Laboratory. Santa Fe, New
México
Khatsuria, R.M., (2005)., “Hydraulics of Spillways and Energy Dissipators”.
Department of Civil and Environmental Engineering Georgia Institute
of Technology Atlanta.
Lucio I., Matos J., Meireles I. (2015). “Stepped spillway flow over small
embankment dams: some computational experiments”. 15th FLOW-3D
European users conference.
Mohammad S., Jalal A. and Michael P., (2012). “Numerical Computation of
Inception Point Location for Steeply Sloping Stepped Spillways” 9th
International Congress on Civil Engineering. Isfahan University of
Technology (IUT), Isfahan, Iran
Pfister M., Chanson H., (2013), “Scale Effects in Modelling Two-phase Airwater Flows”, Proceedings of 2013 IAHR World Congress.
Sarfaraz, M. and Attari, J. (2011), “Numerical Simulation of Uniform Flow
Region over a Steeply Sloping Stepped Spillway”, 6th National
Congress on Civil Engineering, Semnan University, Semnan, Iran.
Valero, D., Bung, D., (2015), “Hybrid investigation of air transport processes
in moderately sloped stepped spillway flows”, E-proceedings of the 36th
IAHR World Congress 28 June – 3 July, 2015, The Hague, the Netherlands.

Serife Yurdagul Kumcu−2−KSCE Journal of Civil Engineeringthe use of CFD for the assessment of a design, as well as screeningand optimizing of hydraulic structures and cofferdam layouts. Theyconclude that CFD has been successful in optimizing the finalconceptual configuration for the hydraulics design of the project,but recommend that physical modeling still be used as a finalconfirmation.This paper provides experimental studies performed on Kav akDam and analyses the stability of spillway design by usingFLOW-3D model. It compares the hydraulic model tests withFLOW-3D simulation results and gives information on howaccurately a commercially available Computational Fluid Dynamic(CFD) model can predict the spillway discharge capacity andpressure distribution along the spillway bottom surface. 2. Physical ModelA 1/50-scaled undistorted physical model of the Kavsak Damspillway and stilling basin was built and tested at the HydraulicModel Laboratory of State Hydraulic Works of Turkey (DSI).The model was constructed of plexiglas and was fabricated toconform to the distinctive shape of an ogee crest. The spillwayhas 45.8 m in width and 57 m long with a bottom slope of 125%.The length of the stilling basin is about 90 m. During model tests,flow velocities were measured with an ultrasonic flow meter.Pressures on the spillway were measured using a piezometerssçTable 1. Upstream and Downstream Operating Conditions of theKavsak DamRun Upstream reservoir elevation (m)Downstream tailwater elevation (m)1 306.55 168.002 311.35 174.503 314.00 178.904 316.50 182.55Fig. 1. (a) Original Project Design and Final Project Design after Experimental Investigations and Flow Measurement Sections at theApproach, (b) Top View Experimentally Modified Approach in the Laboratory, (c) Side View of the Experimentally Modified Approachin the Laboratory

Investigation of flow over spillway modeling and comparison between experimental data and CFD analysis

여수로 모델링 및 실험 데이터와 CFD 해석의 비교에 대한 조사

DOI:10.1007/s12205-016-1257-z

Authors:

Serife Yurdagul Kumcu at Necmettin Erbakan Üniversitesi

Serife Yurdagul Kumcu

Abstract and Figures

As a part of design process for hydro-electric generating stations, hydraulic engineers typically conduct some form of model testing. The desired outcome from the testing can vary considerably depending on the specific situation, but often characteristics such as velocity patterns, discharge rating curves, water surface profiles, and pressures at various locations are measured. Due to recent advances in computational power and numerical techniques, it is now also possible to obtain much of this information through numerical modeling. In this paper, hydraulic characteristics of Kavsak Dam and Hydroelectric Power Plant (HEPP), which are under construction and built for producing energy in Turkey, were investigated experimentally by physical model studies. The 1/50-scaled physical model was used in conducting experiments. Flow depth, discharge and pressure data were recorded for different flow conditions. Serious modification was made on the original project with the experimental study. In order to evaluate the capability of the computational fluid dynamics on modeling spillway flow a comparative study was made by using results obtained from physical modeling and Computational Fluid Dynamics (CFD) simulation. A commercially available CFD program, which solves the Reynolds-averaged Navier-Stokes (RANS) equations, was used to model the numerical model setup by defining cells where the flow is partially or completely restricted in the computational space. Discharge rating curves, velocity patterns and pressures were used to compare the results of the physical model and the numerical model. It was shown that there is reasonably good agreement between the physical and numerical models in flow characteristics.

수력 발전소 설계 프로세스의 일부로 수력 엔지니어는 일반적으로 어떤 형태의 모델 테스트를 수행합니다. 테스트에서 원하는 결과는 특정 상황에 따라 상당히 다를 수 있지만 속도 패턴, 방전 등급 곡선, 수면 프로파일 및 다양한 위치에서의 압력과 같은 특성이 측정되는 경우가 많습니다. 최근 계산 능력과 수치 기법의 발전으로 인해 이제는 수치 모델링을 통해 이러한 정보의 대부분을 얻을 수도 있습니다.

본 논문에서는 터키에서 에너지 생산을 위해 건설 중인 Kavsak 댐과 수력발전소(HEPP)의 수력학적 특성을 물리적 모델 연구를 통해 실험적으로 조사하였다. 1/50 스케일의 물리적 모델이 실험 수행에 사용되었습니다. 다양한 흐름 조건에 대해 흐름 깊이, 배출 및 압력 데이터가 기록되었습니다. 실험 연구를 통해 원래 프로젝트에 대대적인 수정이 이루어졌습니다.

배수로 흐름 모델링에 대한 전산유체역학의 능력을 평가하기 위해 물리적 모델링과 전산유체역학(CFD) 시뮬레이션 결과를 이용하여 비교 연구를 수행하였습니다. RANS(Reynolds-averaged Navier-Stokes) 방정식을 푸는 상업적으로 이용 가능한 CFD 프로그램은 흐름이 계산 공간에서 부분적으로 또는 완전히 제한되는 셀을 정의하여 수치 모델 설정을 모델링하는 데 사용되었습니다.

물리적 모델과 수치 모델의 결과를 비교하기 위해 배출 등급 곡선, 속도 패턴 및 압력을 사용했습니다. 유동 특성에서 물리적 모델과 수치 모델 간에 상당히 좋은 일치가 있는 것으로 나타났습니다.

Serife Yurdagul Kumcu−2−KSCE Journal of Civil Engineeringthe use of CFD for the assessment of a design, as well as screeningand optimizing of hydraulic structures and cofferdam layouts. Theyconclude that CFD has been successful in optimizing the finalconceptual configuration for the hydraulics design of the project,but recommend that physical modeling still be used as a finalconfirmation.This paper provides experimental studies performed on Kav akDam and analyses the stability of spillway design by usingFLOW-3D model. It compares the hydraulic model tests withFLOW-3D simulation results and gives information on howaccurately a commercially available Computational Fluid Dynamic(CFD) model can predict the spillway discharge capacity andpressure distribution along the spillway bottom surface. 2. Physical ModelA 1/50-scaled undistorted physical model of the Kavsak Damspillway and stilling basin was built and tested at the HydraulicModel Laboratory of State Hydraulic Works of Turkey (DSI).The model was constructed of plexiglas and was fabricated toconform to the distinctive shape of an ogee crest. The spillwayhas 45.8 m in width and 57 m long with a bottom slope of 125%.The length of the stilling basin is about 90 m. During model tests,flow velocities were measured with an ultrasonic flow meter.Pressures on the spillway were measured using a piezometerssçTable 1. Upstream and Downstream Operating Conditions of theKavsak DamRun Upstream reservoir elevation (m)Downstream tailwater elevation (m)1 306.55 168.002 311.35 174.503 314.00 178.904 316.50 182.55Fig. 1. (a) Original Project Design and Final Project Design after Experimental Investigations and Flow Measurement Sections at theApproach, (b) Top View Experimentally Modified Approach in the Laboratory, (c) Side View of the Experimentally Modified Approachin the Laboratory
Serife Yurdagul Kumcu−2−KSCE Journal of Civil Engineeringthe use of CFD for the assessment of a design, as well as screeningand optimizing of hydraulic structures and cofferdam layouts. Theyconclude that CFD has been successful in optimizing the finalconceptual configuration for the hydraulics design of the project,but recommend that physical modeling still be used as a finalconfirmation.This paper provides experimental studies performed on Kav akDam and analyses the stability of spillway design by usingFLOW-3D model. It compares the hydraulic model tests withFLOW-3D simulation results and gives information on howaccurately a commercially available Computational Fluid Dynamic(CFD) model can predict the spillway discharge capacity andpressure distribution along the spillway bottom surface. 2. Physical ModelA 1/50-scaled undistorted physical model of the Kavsak Damspillway and stilling basin was built and tested at the HydraulicModel Laboratory of State Hydraulic Works of Turkey (DSI).The model was constructed of plexiglas and was fabricated toconform to the distinctive shape of an ogee crest. The spillwayhas 45.8 m in width and 57 m long with a bottom slope of 125%.The length of the stilling basin is about 90 m. During model tests,flow velocities were measured with an ultrasonic flow meter.Pressures on the spillway were measured using a piezometerssçTable 1. Upstream and Downstream Operating Conditions of theKavsak DamRun Upstream reservoir elevation (m)Downstream tailwater elevation (m)1 306.55 168.002 311.35 174.503 314.00 178.904 316.50 182.55Fig. 1. (a) Original Project Design and Final Project Design after Experimental Investigations and Flow Measurement Sections at theApproach, (b) Top View Experimentally Modified Approach in the Laboratory, (c) Side View of the Experimentally Modified Approachin the Laboratory

References

Bureau of Reclamation (1977). Design of small dams, U.S. Government Printing Office, Washington, D.C., U.S.

Bureau of Reclamation (1990). Cavitation in chute and spillways, Engineering Monograph, No.42, U.S. Chanel, P. G. (2008). An evaluation of computational fluid dynamics for

spillway modeling, MSc Thesis, University of Manitoba Winnipeg, Manitoba, Canada.

Chanson, H. (2002). The hydraulics of stepped chutes and spillways,Balkema, Lisse, The Netherlands.

Chanson, H. and Gonzalez, C. A. (2005). “Physical modeling and scale effects of air-water flows on stepped spillways.” Journal of Zhejiang University Science, Vol. 6A, No. 3, pp. 243-250.

Demiroz, E. (1986). “Specifications of aeration structures which are added to the spillways.” DSI Report, HI-754, DSI-TAKK Publications, Ankara, Turkey.

Erfanain-Azmoudeh, M. H. and Kamanbedast, A. A. (2013). “Determine the appropriate location of aerator system on gotvandoliadam’s spillway using Flow 3D.” American-Eurasian J. Agric. & Environ. Sci., Vol. 13, No. 3, pp. 378-383, DOI: 10.5829/idosi.aejaes.2013. 13.03. 458.

Falvey, H. T. (1990). Cavitation in chutes and spillways, Engineering Monograph 42 Water Resources Technical Publication US Printing Office, Bureau of Reclamation, Denver.

Flow-3D User ’s Manual (2012). Flow science, Inc., Santa Fe, N.M.

Hirt, C. W. (1992). “Volume-fraction techniques: Powerful tools for flow

modeling.” Flow Science Report, No. FSI-92-00-02, Flow Science, Inc., Santa Fe, N.M.

Hirt C. W. and Nichols B. D. (1981). “Volume of Fluid (VOF) method for the dynamics of free boundaries.”Jornal of Computational Physics, Vol. 39, pp. 201-225, DOI: 10.1016/0021-9991(81)90145-5.

Hirt, C. W. and Sicilian, J. M. (1985). “A Porosity technique for the definition of obstacles in rectangular cell meshes.” Proceedings of the 4th International Conference on Ship Hydro-dynamics, 24-27 September 1985, National Academic of Sciences, Washington DC.

Ho, D., Boyes, K., Donohoo, S., and Cooper, B. (2003). “Numerical flow analysis for spillways.” 43rd ANCOLD Conference, Hobart, Tas m a nia .

Johnson, M. C. and Savage, B. M. (2006). “Physical and numerical comparison of flow over ogee spillway in the presence of tailwater.”

Journal of Hydraulic Engineering, Vol. 132, No. 12, pp. 1353-135, DOI: 10.1061/(ASCE)0733-9429.

Kim, S. D., Lee, H. J., and An, S. D. (2010). “Improvement of hydraulic stability for spillway using CFD model.” Int. Journal of the Physical Sciences, Vol. 5, No. 6, pp. 774-780.

Kokpinar, M. A. and Gogus, M. (2002). “High speed jet flows over spillway aerators.” Canadian Journal of Civil Engineering, Vol. 29, No. 6, pp. 885-898, DOI: 10.1139/l02-088.

Kumcu, S. Y. (2010). Hydraulic model studies of Kavsak Dam and HEPP, DSI Report, HI-1005, DSI-TAKK Publications, Ankara, Turkey.

Margeirsson, B. (2007). Computational modeling of flow over a spillway, MSc Thesis, Chalmers University of Technology, Gothenburg, Sweden.

Nichols, B. D. and Hirt, C. W. (1975). “Methods for calculating multi-dimensional, transient free surface flows past bodies.” Proc. First Intern. Conf. Num., Ship Hydrodynamics, Gaithersburg, ML.

Savage, B. M. and Johnson, M. C. (2001). “Flow over ogee spillway: Physical and numerical model case study.” Journal of Hydraulic Engineering, ASCE, Vol. 127, No. 8, pp. 640-649, DOI: 10.1061/(ASCE)0733-9429.

Souders, D. T. and Hirt, C. W. (2004). “Modeling entrainment of air at turbulent free surfaces.” Critical Transitions in Water and Environmental resources Management, pp. 1-10.

entürk, F. (1994). Hydraulics of dams and reservoirs, Water Resources Publication Colorado, USA.

Teklemariam, E., Korbaylo, B, Groeneveld, J., Sydor, K., and Fuchs, D. (2001). Optimization of hydraulic design using computational fluid dynamics, Waterpower XII, Salt Lake City, Utah.

Teklemariam, E., Shumilak, B., Sydor, K., Murray, D., Fuchs, D., and Holder, G. (2008). “An integral approach using both physical and computational modeling can be beneficial in addressing the full range of hydraulic design issues.” CDA Annual Conference, Winnipeg, Canada.

Usta, E. (2014). Numerical investigation of hydraulic characteristics of Laleli Dam spillway and comparison with physical model study, Master Thesis, Middle East Technical University, Ankara, Turkey.

Versteeg, H. K. and Malalasekera, W. (1996). An introduction to computational fluid dynamics, Longman Scientific and Technical, Longman Group Limited, Harlow, England.

Vischer, D. L. and Hager, W. H. (1997). Dam hydraulics, J. Wiley & Sons Ltd., England.

Wagner, W. E. (1967). “Glen Canyon diversion tunnel outlets.” J. Hydraulic Division, ASCE, Vol. 93, No. HY6, pp. 113-134.

Willey, J., Ewing, T., Wark, B., and Lesleighter, E. (2012). Comple-mentary use of physical and numerical modeling techniques in spillway design refinement, Commission Internationale Des Grands Barrages, Kyoto, June 2012.

Fig. 1. Averaged error trend.

Assessment of spillway modeling using computational fluid dynamics

전산유체역학을 이용한 여수로 모델링 평가

Authors: Paul G. Chanel and John C. Doering AUTHORS INFO & AFFILIATIONS

Publication: Canadian Journal of Civil Engineering

3 December 2008

Abstract

Throughout the design and planning period for future hydroelectric generating stations, hydraulic engineers are increasingly integrating computational fluid dynamics (CFD) into the process. As a result, hydraulic engineers are interested in the reliability of CFD software to provide accurate flow data for a wide range of structures, including a variety of different spillways. In the literature, CFD results have generally been in agreement with physical model experimental data. Despite past success, there has not been a comprehensive assessment that looks at the ability of CFD to model a range of different spillway configurations, including flows with various gate openings. In this article, Flow-3D is used to model the discharge over ogee-crested spillways. The numerical model results are compared with physical model studies for three case study evaluations. The comparison indicates that the accuracy of Flow-3D is related to the parameter P/Hd.

미래의 수력 발전소를 위한 설계 및 계획 기간 동안 유압 엔지니어는 전산유체역학(CFD)을 프로세스에 점점 더 많이 통합하고 있습니다. 결과적으로 유압 엔지니어는 다양한 여수로를 포함하여 광범위한 구조에 대한 정확한 흐름 데이터를 제공하는 CFD 소프트웨어의 신뢰성에 관심을 갖고 있습니다. 문헌에서 CFD 결과는 일반적으로 물리적 모델 실험 데이터와 일치했습니다. 과거의 성공에도 불구하고 다양한 게이트 개구부가 있는 흐름을 포함하여 다양한 여수로 구성을 모델링하는 CFD의 기능을 살펴보는 포괄적인 평가는 없었습니다. 이 기사에서는 Flow-3D를 사용하여 ogee-crested 방수로의 배출을 모델링합니다. 세 가지 사례 연구 평가를 위해 수치 모델 결과를 물리적 모델 연구와 비교합니다. 비교는 Flow-3D의 정확도가 매개변수 P/Hd와 관련되어 있음을 나타냅니다.

Résumé

Les ingénieurs en hydraulique intègrent de plus en plus la dynamique des fluides numérique (« CFD ») dans le processus de conception et de planification des futures centrales. Ainsi, les ingénieurs en hydraulique s’intéressent à la fiabilité du logiciel de « CFD » afin de fournir des données précises sur le débit pour une large gamme de structures, incluant différents types d’évacuateurs. Les résultats de « CFD » dans la littérature ont été globalement sont généralement en accord avec les données expérimentales des essais physiques. Malgré les succès antérieurs, il n’y avait aucune évaluation complète de la capacité des « CFD » à modéliser une plage de configuration des évacuateurs, incluant les débits à diverses ouvertures de vannes. Dans le présent article, le logiciel Flow-3D est utilisé pour modéliser le débit par des évacuateurs en doucine. Les résultats du modèle de calcul sont comparés à ceux des essais physiques pour trois études de cas. La comparaison montre que la précision du logiciel Flow-3D est associée au paramètre P/Hd.

Fig. 1. Averaged error trend.
Fig. 1. Averaged error trend.

Get full access to this article

View all available purchase options and get full access to this article.

GET ACCESSALREADY A SUBSCRIBER? SIGN IN AS AN INDIVIDUAL OR VIA YOUR INSTITUTION

References

Chanel, P.G., and Doering, J.C. 2007. An evaluation of computational fluid dynamics for spillway modelling. In Proceedings of the 16th Australasian Fluid Mechanics Conference (AFMC), Gold Coast, Queensland, Australia, 3–7 December 2007. pp. 1201–1206.

Google Scholar

Flow Science, Inc. 2007. Flow-3D user’s manuals. Version 9.2. Flow Science, Inc., Santa Fe, N.M.

Google Scholar

Gessler, D. 2005. CFD modeling of spillway performance, EWRI 2005: Impacts of global climate change. In Proceedings of the World Water and Environmental Resources Congress, Anchorage, Alaska, 15–19 May 2005. Edited by R. Walton. American Society of Civil Engineers, Reston, Va.

Google Scholar

Hirt, C.W., and Nichols, B.D. 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1): 201–225.

Crossref

ISI

Google Scholar

Hirt, C.W., and Sicilian, J.M. 1985. A porosity technique for the definition of obstacles in rectangular cell meshes. In Proceedings of the 4th International Conference on Ship Hydro-dynamics, Washington, D.C., 24–27 September 1985. National Academy of Sciences, Washington, D.C.

Google Scholar

Ho, D., Cooper, B., Riddette, K., and Donohoo, S. 2006. Application of numerical modelling to spillways in Australia. In Dams and Reservoirs, Societies and Environment in the 21st Century. Edited by Berga et al. Taylor and Francis Group, London.

Google Scholar

LaSalle Consulting Group Inc. 1992. Conawapa generating station. Sectional model study of the spillway. LaSalle Consulting Group Inc., Montréal, Que.

Google Scholar

Lemke, D.E. 1989. A comparison of the hydraulic performance of an orifice and an overflow spillway in a northern application using physical modeling. M.Sc. thesis, University of Manitoba, Winnipeg, Man.

Google Scholar

Savage, B.M., and Johnson, M.C. 2001. Flow over ogee spillway: Physical and numerical model case study. Journal of Hydraulic Engineering, 127(8): 640–649.

Crossref

ISI

Google Scholar

Teklemariam, E., Korbaylo, B., Groeneveld, J., Sydor, K., and Fuchs, D. 2001. Optimization of hydraulic design using computational fluid dynamics. In Proceedings of Waterpower XII, Salt Lake City, Utah, 9–11 July 2001.

Google Scholar

Teklemariam, E., Korbaylo, B., Groeneveld, J., and Fuchs, D. 2002. Computational fluid dynamics: Diverse applications in hydropower project’s design and analysis. In Proceedings of the CWRA 55th Annual Conference, Winnipeg, Man., 11–14 June 2002. Canadian Water Resources Association, Cambridge, Ontario.

Google Scholar

Western Canadian Hydraulic Laboratories Inc. 1980. Hydraulics model studies limestone generating station spillway/diversion structure flume study. Final report. Western Canadian Hydraulic Laboratories Inc., Port Coquitlam, B.C.

Google Scholar

Sketch of approach channel and spillway of the Kamal-Saleh dam

CFD modeling of flow pattern in spillway’s approach channel

Sustainable Water Resources Management volume 1, pages245–251 (2015)Cite this article

Abstract

Analysis of behavior and hydraulic characteristics of flow over the dam spillway is a complicated task that takes lots of money and time in water engineering projects planning. To model those hydraulic characteristics, several methods such as physical and numerical methods can be used. Nowadays, by utilizing new methods in computational fluid dynamics (CFD) and by the development of fast computers, the numerical methods have become accessible for use in the analysis of such sophisticated flows. The CFD softwares have the capability to analyze two- and three-dimensional flow fields. In this paper, the flow pattern at the guide wall of the Kamal-Saleh dam was modeled by Flow 3D. The results show that the current geometry of the left wall causes instability in the flow pattern and making secondary and vortex flow at beginning approach channel. This shape of guide wall reduced the performance of weir to remove the peak flood discharge.

댐 여수로 흐름의 거동 및 수리학적 특성 분석은 물 공학 프로젝트 계획에 많은 비용과 시간이 소요되는 복잡한 작업입니다. 이러한 수력학적 특성을 모델링하기 위해 물리적, 수치적 방법과 같은 여러 가지 방법을 사용할 수 있습니다. 요즘에는 전산유체역학(CFD)의 새로운 방법을 활용하고 빠른 컴퓨터의 개발로 이러한 정교한 흐름의 해석에 수치 방법을 사용할 수 있게 되었습니다. CFD 소프트웨어에는 2차원 및 3차원 유동장을 분석하는 기능이 있습니다. 본 논문에서는 Kamal-Saleh 댐 유도벽의 흐름 패턴을 Flow 3D로 모델링하였다. 결과는 왼쪽 벽의 현재 형상이 흐름 패턴의 불안정성을 유발하고 시작 접근 채널에서 2차 및 와류 흐름을 만드는 것을 보여줍니다. 이러한 형태의 안내벽은 첨두방류량을 제거하기 위해 둑의 성능을 저하시켰다.

Introduction

Spillways are one of the main structures used in the dam projects. Design of the spillway in all types of dams, specifically earthen dams is important because the inability of the spillway to remove probable maximum flood (PMF) discharge may cause overflow of water which ultimately leads to destruction of the dam (Das and Saikia et al. 2009; E 2013 and Novak et al. 2007). So study on the hydraulic characteristics of this structure is important. Hydraulic properties of spillway including flow pattern at the entrance of the guide walls and along the chute. Moreover, estimating the values of velocity and pressure parameters of flow along the chute is very important (Chanson 2004; Chatila and Tabbara 2004). The purpose of the study on the flow pattern is the effect of wall geometry on the creation transverse waves, flow instability, rotating and reciprocating flow through the inlet of spillway and its chute (Parsaie and Haghiabi 2015ab; Parsaie et al. 2015; Wang and Jiang 2010). The purpose of study on the values of velocity and pressure is to calculate the potential of the structure to occurrence of phenomena such as cavitation (Fattor and Bacchiega 2009; Ma et al. 2010). Sometimes, it can be seen that the spillway design parameters of pressure and velocity are very suitable, but geometry is considered not suitable for conducting walls causing unstable flow pattern over the spillway, rotating flows at the beginning of the spillway and its design reduced the flood discharge capacity (Fattor and Bacchiega 2009). Study on spillway is usually conducted using physical models (Su et al. 2009; Suprapto 2013; Wang and Chen 2009; Wang and Jiang 2010). But recently, with advances in the field of computational fluid dynamics (CFD), study on hydraulic characteristics of this structure has been done with these techniques (Chatila and Tabbara 2004; Zhenwei et al. 2012). Using the CFD as a powerful technique for modeling the hydraulic structures can reduce the time and cost of experiments (Tabbara et al. 2005). In CFD field, the Navier–Stokes equation is solved by powerful numerical methods such as finite element method and finite volumes (Kim and Park 2005; Zhenwei et al. 2012). In order to obtain closed-form Navier–Stokes equations turbulence models, such k − ε and Re-Normalisation Group (RNG) models have been presented. To use the technique of computational fluid dynamics, software packages such as Fluent and Flow 3D, etc., are provided. Recently, these two software packages have been widely used in hydraulic engineering because the performance and their accuracy are very suitable (Gessler 2005; Kim 2007; Kim et al. 2012; Milési and Causse 2014; Montagna et al. 2011). In this paper, to assess the flow pattern at Kamal-Saleh guide wall, numerical method has been used. All the stages of numerical modeling were conducted in the Flow 3D software.

Materials and methods

Firstly, a three-dimensional model was constructed according to two-dimensional map that was prepared for designing the spillway. Then a small model was prepared with scale of 1:80 and entered into the Flow 3D software; all stages of the model construction was conducted in AutoCAD 3D. Flow 3D software numerically solved the Navier–Stokes equation by finite volume method. Below is a brief reference on the equations that used in the software. Figure 1 shows the 3D sketch of Kamal-Saleh spillway and Fig. 2 shows the uploading file of the Kamal-Saleh spillway in Flow 3D software.

figure 1
Fig. 1
figure 2
Fig. 2

Review of the governing equations in software Flow 3D

Continuity equation at three-dimensional Cartesian coordinates is given as Eq (1).

vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,

(1)

where uvz are velocity component in the x, y, z direction; A xA yA z cross-sectional area of the flow; ρ fluid density; PSOR the source term; v f is the volume fraction of the fluid and three-dimensional momentum equations given in Eq (2).

∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,

(2)

where P is the fluid pressure; G xG yG z the acceleration created by body fluids; f xf yf z viscosity acceleration in three dimensions and v f is related to the volume of fluid, defined by Eq. (3). For modeling of free surface profile the VOF technique based on the volume fraction of the computational cells has been used. Since the volume fraction F represents the amount of fluid in each cell, it takes value between 0 and 1.

∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0

(3)

Turbulence models

Flow 3D offers five types of turbulence models: Prantl mixing length, k − ε equation, RNG models, Large eddy simulation model. Turbulence models that have been proposed recently are based on Reynolds-averaged Navier–Stokes equations. This approach involves statistical methods to extract an averaged equation related to the turbulence quantities.

Steps of solving a problem in Flow 3D software

(1) Preparing the 3D model of spillway by AutoCAD software. (2) Uploading the file of 3D model in Flow 3D software and defining the problem in the software and checking the final mesh. (3) Choosing the basic equations that should be solved. (4) Defining the characteristics of fluid. (5) Defining the boundary conditions; it is notable that this software has a wide range of boundary conditions. (6) Initializing the flow field. (7) Adjusting the output. (8) Adjusting the control parameters, choice of the calculation method and solution formula. (9) Start of calculation. Figure 1 shows the 3D model of the Kamal-Saleh spillway; in this figure, geometry of the left and right guide wall is shown.

Figure 2 shows the uploading of the 3D spillway dam in Flow 3D software. Moreover, in this figure the considered boundary condition in software is shown. At the entrance and end of spillway, the flow rate or fluid elevation and outflow was considered as BC. The bottom of spillway was considered as wall and left and right as symmetry.

Model calibration

Calibration of the Flow 3D for modeling the effect of geometry of guide wall on the flow pattern is included for comparing the results of Flow 3D with measured water surface profile. Calibration the Flow 3D software could be conducted in two ways: first, changing the value of upstream boundary conditions is continued until the results of water surface profile of the Flow 3D along the spillway successfully covered the measurement water surface profile; second is the assessment the mesh sensitivity. Analyzing the size of mesh is a trial-and-error process where the size of mesh is evaluated form the largest to the smallest. With fining the size of mesh the accuracy of model is increased; whereas, the cost of computation is increased. In this research, the value of upstream boundary condition was adjusted with measured data during the experimental studies on the scaled model and the mesh size was equal to 1 × 1 × 1 cm3.

Results and discussion

The behavior of water in spillway is strongly affected by the flow pattern at the entrance of the spillway, the flow pattern formation at the entrance is affected by the guide wall, and choice of an optimized form for the guide wall has a great effect on rising the ability of spillway for easy passing the PMF, so any nonuniformity in flow in the approach channel can cause reduction of spillway capacity, reduction in discharge coefficient of spillway, and even probability of cavitation. Optimizing the flow guiding walls (in terms of length, angle and radius) can cause the loss of turbulence and flow disturbances on spillway. For this purpose, initially geometry proposed for model for the discharge of spillway dam, Kamal-Saleh, 80, 100, and 120 (L/s) were surveyed. These discharges of flow were considered with regard to the flood return period, 5, 100 and 1000 years. Geometric properties of the conducting guidance wall are given in Table 1.Table 1 Characteristics and dimensions of the guidance walls tested

Full size table

Results of the CFD simulation for passing the flow rate 80 (L/s) are shown in Fig. 3. Figure 3 shows the secondary flow and vortex at the left guide wall.

figure 3
Fig. 3

For giving more information about flow pattern at the left and right guide wall, Fig. 4 shows the flow pattern at the right side guide wall and Fig. 5 shows the flow pattern at the left side guide wall.

figure 4
Fig. 4
figure 5
Fig. 5

With regard to Figs. 4 and 5 and observing the streamlines, at discharge equal to 80 (L/s), the right wall has suitable performance but the left wall has no suitable performance and the left wall of the geometric design creates a secondary and circular flow, and vortex motion in the beginning of the entrance of spillway that creates cross waves at the beginning of spillway. By increasing the flow rate (Q = 100 L/s), at the inlet spillway secondary flows and vortex were removed, but the streamline is severely distorted. Results of the guide wall performances at the Q = 100 (L/s) are shown in Fig. 6.

figure 6
Fig. 6

Also more information about the performance of each guide wall can be derived from Figs. 7 and 8. These figures uphold that the secondary and vortex flows were removed, but the streamlines were fully diverted specifically near the left side guide wall.

figure 7
Fig. 7
figure 8
Fig. 8

As mentioned in the past, these secondary and vortex flows and diversion in streamline cause nonuniformity and create cross wave through the spillway. Figure 9 shows the cross waves at the crest of the spillway.

figure 9
Fig. 9

The performance of guide walls at the Q = 120 (L/s) also was assessed. The result of simulation is shown in Fig. 10. Figures 11 and 12 show a more clear view of the streamlines near to right and left side guide wall, respectively. As seen in Fig. 12, the left side wall still causes vortex flow and creation of and diversion in streamline.

figure 10
Fig. 10
figure 11
Fig. 11
figure 12
Fig. 12

The results of the affected left side guide wall shape on the cross wave creation are shown in Fig. 13. As seen from Fig. 3, the left side guide wall also causes cross wave at the spillway crest.

figure 13
Fig. 13

As can be seen clearly in Figs. 9 and 13, by moving from the left side to the right side of the spillway, the cross waves and the nonuniformity in flow is removed. By reviewing Figs. 9 and 13, it is found that the right side guide wall removes the cross waves and nonuniformity. With this point as aim, a geometry similar to the right side guide wall was considered instead of the left side guide wall. The result of simulation for Q = 120 (L/s) is shown in Fig. 14. As seen from this figure, the proposed geometry for the left side wall has suitable performance smoothly passing the flow through the approach channel and spillway.

figure 14
Fig. 14

More information about the proposed shape for the left guide wall is shown in Fig. 15. As seen from this figure, this shape has suitable performance for removing the cross waves and vortex flows.

figure 15
Fig. 15

Figure 16 shows the cross section of flow at the crest of spillway. As seen in this figure, the proposed shape for the left side guide wall is suitable for removing the cross waves and secondary flows.

figure 16
Fig. 16

Conclusion

Analysis of behavior and hydraulic properties of flow over the spillway dam is a complicated task which is cost and time intensive. Several techniques suitable to the purposes of study have been undertaken in this research. Physical modeling, usage of expert experience, usage of mathematical models on simulation flow in one-dimensional, two-dimensional and three-dimensional techniques, are some of the techniques utilized to study this phenomenon. The results of the modeling show that the CFD technique is a suitable tool for simulating the flow pattern in the guide wall. Using this tools helps the designer for developing the optimal shape for hydraulic structure which the flow pattern through them are important.

References

  • Chanson H (2004) 19—Design of weirs and spillways. In: Chanson H (ed) Hydraulics of open channel flow, 2nd edn. Butterworth-Heinemann, Oxford, pp 391–430Chapter Google Scholar 
  • Chatila J, Tabbara M (2004) Computational modeling of flow over an ogee spillway. Comput Struct 82:1805–1812Article Google Scholar 
  • Das MM, Saikia MD (2009) Irrigation and water power engineering. PHI Learning, New DelhiGoogle Scholar 
  • E, Department Of Army: U.S. Army Corps (2013) Hydraulic Design of Spillways. BiblioBazaar, CharlestonGoogle Scholar 
  • Fattor C, Bacchiega J (2009) Design conditions for morning-glory spillways: application to potrerillos dam spillway. Adv Water Res Hydraul Eng Springer, Berlin, pp 2123–2128Google Scholar 
  • Gessler D (2005) CFD modeling of spillway performance. Impacts Glob Clim Change. doi:10.1061/40792(173)398
  • Kim D-G (2007) Numerical analysis of free flow past a sluice gate. KSCE J Civ Eng 11:127–132Article Google Scholar 
  • Kim D, Park J (2005) Analysis of flow structure over ogee-spillway in consideration of scale and roughness effects by using CFD model. KSCE J Civ Eng 9:161–169Article Google Scholar 
  • Kim S, Yu K, Yoon B, Lim Y (2012) A numerical study on hydraulic characteristics in the ice Harbor-type fishway. KSCE J Civ Eng 16:265–272Article Google Scholar 
  • Ma X-D, Dai G-Q, Yang Q, Li G-J, Zhao L (2010) Analysis of influence factors of cavity length in the spillway tunnel downstream of middle gate chamber outlet with sudden lateral enlargement and vertical drop aerator. J Hydrodyn Ser B 22:680–686Article Google Scholar 
  • Milési G, Causse S (2014) 3D numerical modeling of a side-channel spillway. In: Gourbesville P, Cunge J, Caignaert G (eds) Advances in hydroinformatics. Springer, Singapore, pp 487–498Chapter Google Scholar 
  • Montagna F, Bellotti G, Di Risio M (2011) 3D numerical modeling of landslide-generated tsunamis around a conical island. Nat Hazards 58:591–608Article Google Scholar 
  • Novak P, Moffat AIB, Nalluri C, Narayanan R (2007) Hydraulic structures. Taylor & Francis, LondonGoogle Scholar 
  • Parsaie A, Haghiabi A (2015a) Computational modeling of pollution transmission in rivers. Appl Water Sci. doi:10.1007/s13201-015-0319-6
  • Parsaie A, Haghiabi A (2015b) The effect of predicting discharge coefficient by neural network on increasing the numerical modeling accuracy of flow over side weir. Water Res Manag 29:973–985Article Google Scholar 
  • Parsaie A, Yonesi H, Najafian S (2015) Predictive modeling of discharge in compound open channel by support vector machine technique. Model Earth Syst Environ 1:1–6Article Google Scholar 
  • Su P-L, Liao H-S, Qiu Y, Li CJ (2009) Experimental study on a new type of aerator in spillway with low Froude number and mild slope flow. J Hydrodyn Ser B 21:415–422Article Google Scholar 
  • Suprapto M (2013) Increase spillway capacity using Labyrinth Weir. Procedia Eng 54:440–446Article Google Scholar 
  • Tabbara M, Chatila J, Awwad R (2005) Computational simulation of flow over stepped spillways. Comput Struct 83:2215–2224Article Google Scholar 
  • Wang J, Chen H (2009) Experimental study of elimination of vortices along guide wall of bank spillway. Adv Water Res Hydraul Eng Springer, Berlin, pp 2059–2063Google Scholar 
  • Wang Y, Jiang C (2010) Investigation of the surface vortex in a spillway tunnel intake. Tsinghua Sci Technol 15:561–565Article Google Scholar 
  • Zhenwei MU, Zhiyan Z, Tao Z (2012) Numerical simulation of 3-D flow field of spillway based on VOF method. Procedia Eng 28:808–812Article Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Water Engineering, Lorestan University, Khorram Abad, IranAbbas Parsaie, Amir Hamzeh Haghiabi & Amir Moradinejad

Corresponding author

Correspondence to Abbas Parsaie.

Reprints and Permissions

About this article

Cite this article

Parsaie, A., Haghiabi, A.H. & Moradinejad, A. CFD modeling of flow pattern in spillway’s approach channel. Sustain. Water Resour. Manag. 1, 245–251 (2015). https://doi.org/10.1007/s40899-015-0020-9

Download citation

  • Received28 April 2015
  • Accepted28 August 2015
  • Published15 September 2015
  • Issue DateSeptember 2015
  • DOIhttps://doi.org/10.1007/s40899-015-0020-9

Share this article

Anyone you share the following link with will be able to read this content:Get shareable link

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Approach channel
  • Kamal-Saleh dam
  • Guide wall
  • Flow pattern
  • Numerical modeling
  • Flow 3D software
    Figure 10. Flow distribution at the approach channel in PMF based on revised plan design. A. Hydarulic model test; B. Numerical simulation; C. Section view.

    Improvement of hydraulic stability for spillway using CFD model

    Hydraulic model test was used to analyze the rapidly varied flow on the spillway. But, it has some shortcomings such as error of scale effect and expensive costs. Recently, through the development of three dimensional computational fluid dynamics (CFD), rapidly varied flow and turbulence can be simulated. In this study, the applicability of CFD model to simulate flow on the spillway was reviewed. The Karian dam in Indonesia was selected as the study area. The FLOW-3d model, which is well known to simulate a flow having a free surface, was used to analyze flow. The flow stability in approach channel was investigated with the initial plan design, and the results showed that the flow in approach channel is unstable in the initial plan design. To improve flow stability in the spillway, therefore, the revised plan design was formulated. The appropriateness of the revised design was examined by a numerical modeling. The results showed that the flow in spillway is stable in the revised design.

    여수로의 급격하게 변화하는 흐름을 분석하기 위해 수리학적 모델 테스트를 사용했습니다. 그러나 스케일 효과의 오차와 고가의 비용 등의 단점이 있다. 최근에는 3차원 전산유체역학(CFD)의 발달로 급변하는 유동과 난류를 모사할 수 있다. 본 연구에서는 여수로의 흐름을 시뮬레이션하기 위한 CFD 모델의 적용 가능성을 검토했습니다. 인도네시아의 Karian 댐이 연구 지역으로 선정되었습니다. 자유표면을 갖는 유동을 모의하는 것으로 잘 알려진 FLOW-3d 모델을 유동해석에 사용하였다. 접근수로의 흐름 안정성은 초기 계획설계와 함께 조사한 결과 초기 계획설계에서 접근수로의 흐름이 불안정한 것으로 나타났다. 따라서 방수로의 흐름 안정성을 향상시키기 위해 수정된 계획 설계가 공식화되었습니다. 수정된 설계의 적합성을 수치모델링을 통해 검토하였다. 결과는 수정된 설계에서 여수로의 흐름이 안정적이라는 것을 보여주었습니다.

    Key words

    Spillway, FLOW-3D, approach channel, flow stability, numerical modeling, hydraulic model test.

    Figure 6. Two dimensional flow velocity distribution at the
approach channel (Flow velocity distribution at depth EL. 68.12 m).
    Figure 6. Two dimensional flow velocity distribution at the approach channel (Flow velocity distribution at depth EL. 68.12 m).
    Figure 7. Flow distribution at the approach channel in PMF.
A. Hydraulic model test; B. Numerial simulatio
C. Cross section view.
    Figure 7. Flow distribution at the approach channel in PMF. A. Hydraulic model test; B. Numerial simulatio C. Cross section view.
    Figure 8. Revised approach channel section.
A. Initial plan design; B. Revised plan design.
    Figure 8. Revised approach channel section. A. Initial plan design; B. Revised plan design.
    Figure 9. Two dimensional flow velocity distribution at the approach channel
based on revised plan design (Flow velocity distribution at depth EL. 68.12 m).
    Figure 9. Two dimensional flow velocity distribution at the approach channel based on revised plan design (Flow velocity distribution at depth EL. 68.12 m).
    Figure 10. Flow distribution at the approach channel in PMF based on revised plan design.
A. Hydarulic model test; B. Numerical simulation; C. Section view.
    Figure 10. Flow distribution at the approach channel in PMF based on revised plan design. A. Hydarulic model test; B. Numerical simulation; C. Section view.

    REFERENCES

    Betts PL (1979). A variation principle in terms of stream function for free
    surface flows and its application to finite element method. Comp.
    Fluids, 7(2): 145-153.
    Cassidy JJ (1965). Irrotational flow over spillways of finite height. J.
    Eng. Mech. Div. ASCE., 91(6): 155-173.
    Flow Science (2002). FLOW-3D -Theory manual. Los Alamos, NM.
    Guo Y, Wen X, Wu C, Fang D (1998). Numerical modeling of spillway
    flow with free drop and initially unknown discharge. J. Hydraulic Res.
    IAHR, 36(5): 785-801.
    Ho DKH, Donohoo SM (2001). Investigation of spillway behavior under
    increased maximum flood by computational fluid dynamics technique.
    Proceeding 14
    th Australasian Fluid Mech. Conference, Adelaide
    University, Adelaide, Australia, pp. 10-14.
    Ikegawa M, Washizu K (1973). Finite element method applied to
    analysis of flow over a spillway crest. Int. J. Numerical Methods Eng.,
    6: 179-189.
    Kim DG, Park JH (2005). Analysis of flow structure over ogee-spillway
    in consideration of scale and roughness effects by using CFD model.
    J. Civil Eng. KSCE., pp. 161-169.
    KRA, KWATER (2006). Feasibility study and detail design of the Karian
    dam project. Indonesia.
    Li W, Xie Q, Chen CJ (1989). Finite analytic solution of flow over
    spillways, J. Eng. Mech. ASCE, 115(2): 2645-2648.
    Olsen NR, Kjellesvig HM (1998).Three-dimensional numerical flow
    modeling for estimation of spillway capacity. J. Hydraulic Res. IAHR.,
    36(5): 775-784.
    Savage BM, Johnson MC (2001). Flow over ogee spillway: Physical and
    numerical model case study. J. Hydraulic Eng. ASCE., 127(8): 640-
    649.
    Tabbara M, Chatial J, Awwad R (2005). Computational simulation of
    flow over stepped spillways. Comput. Structure, 83: 2215-2224.

    Fig. 8. Comparison of the wave pattern for : (a) Ship wave only; (b) Ship wave in the presence of a following current.

    균일한 해류가 존재하는 선박 파도의 수치 시뮬레이션

    Numerical simulation of ship waves in the presence of a uniform current

    CongfangAiYuxiangMaLeiSunGuohaiDongState Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Highlights

    • Ship waves in the presence of a uniform current are studied by a non-hydrostatic model.

    • Effects of a following current on characteristic wave parameters are investigated.

    • Effects of an opposing current on characteristic wave parameters are investigated.

    • The response of the maximum water level elevation to the ship draft is discussed.

    Abstract

    이 논문은 균일한 해류가 존재할 때 선박파의 생성 및 전파를 시뮬레이션하기 위한 비정역학적 모델을 제시합니다. 선박 선체의 움직임을 표현하기 위해 움직이는 압력장 방법이 모델에 통합되었습니다.

    뒤따르거나 반대 방향의 균일한 흐름이 있는 경우의 선박 파도의 수치 결과를 흐름이 없는 선박 파도의 수치 결과와 비교합니다. 추종 또는 반대 균일 전류가 존재할 때 계산된 첨단선 각도는 분석 솔루션과 잘 일치합니다. 추종 균일 전류와 반대 균일 전류가 특성파 매개변수에 미치는 영향을 제시하고 논의합니다.

    선박 흘수에 대한 최대 수위 상승의 응답은 추종 또는 반대의 균일한 흐름이 있는 경우에도 표시되며 흐름이 없는 선박 파도의 응답과 비교됩니다. 선박 선체 측면의 최대 수위 상승은 Froude 수 Fr’=Us/gh의 특정 범위에 대해 다음과 같은 균일한 흐름의 존재에 의해 증가될 수 있음이 밝혀졌습니다.

    여기서 Us는 선박 속도이고 h는 물입니다. 깊이. 균일한 해류를 무시하면 추종류나 반대류가 존재할 때 선박 흘수에 대한 최대 수위 상승의 응답이 과소평가될 수 있습니다.

    본 연구는 선박파의 해석에 있어 균일한 해류의 영향을 고려해야 함을 시사합니다.

    This paper presents a non-hydrostatic model to simulate the generation and propagation of ship waves in the presence of a uniform current. A moving pressure field method is incorporated into the model to represent the movement of a ship hull. Numerical results of ship waves in the presence of a following or an opposing uniform current are compared with those of ship waves without current. The calculated cusp-line angles in the presence of a following or opposing uniform current agree well with analytical solutions. The effects of a following uniform current and an opposing uniform current on the characteristic wave parameters are presented and discussed. The response of the maximum water level elevation to the ship draft is also presented in the presence of a following or an opposing uniform current and is compared with that for ship waves without current. It is found that the maximum water level elevation lateral to the ship hull can be increased by the presence of a following uniform current for a certain range of Froude numbers Fr′=Us/gh, where Us is the ship speed and h is the water depth. If the uniform current is neglected, the response of the maximum water level elevation to the ship draft in the presence of a following or an opposing current can be underestimated. The present study indicates that the effect of a uniform current should be considered in the analysis of ship waves.

    Keywords

    Ship waves, Non-hydrostatic model, Following current, Opposing current, Wave parameters

    1. Introduction

    Similar to wind waves, ships sailing across the sea can also create free-surface undulations ranging from ripples to waves of large size (Grue, 20172020). Ship waves can cause sediment suspension and engineering structures damage and even pose a threat to flora and fauna living near the embankments of waterways (Dempwolff et al., 2022). It is quite important to understand ship waves in various environments. The study of ship waves has been conducted over a century. A large amount of research (Almström et al., 2021Bayraktar and Beji, 2013David et al., 2017Ertekin et al., 1986Gourlay, 2001Havelock, 1908Lee and Lee, 2019Samaras and Karambas, 2021Shi et al., 2018) focused on the generation and propagation of ship waves without current. When a ship navigates in the sea or in a river where tidal flows or river flows always exist, the effect of currents should be taken into account. However, the effect of currents on the characteristic parameters of ship waves is still unclear, because very few publications have been presented on this topic.

    Over the past two decades, many two-dimensional (2D) Boussinesq-type models (Bayraktar and Beji, 2013Dam et al., 2008David et al., 2017Samaras and Karambas, 2021Shi et al., 2018) were developed to examine ship waves. For example, Bayraktar and Beji (2013) solved Boussinesq equations with improved dispersion characteristics to simulate ship waves due to a moving pressure field. David et al. (2017) employed a Boussinesq-type model to investigate the effects of the pressure field and its propagation speed on characteristic wave parameters. All of these Boussinesq-type models aimed to simulate ship waves without current except for that of Dam et al. (2008), who investigated the effect of currents on the maximum wave height of ship waves in a narrow channel.

    In addition to Boussinesq-type models, numerical models based on the Navier-Stokes equations (NSE) or Euler equations are also capable of resolving ship waves. Lee and Lee (20192021) employed the FLOW-3D model to simulate ship waves without current and ship waves in the presence of a uniform current to confirm their equations for ship wave crests. FLOW-3D is a computational fluid dynamics (CFD) software based on the NSE, and the volume of fluid (VOF) method is used to capture the moving free surface. However, VOF-based NSE models are computationally expensive due to the treatment of the free surface. To efficiently track the free surface, non-hydrostatic models employ the so-called free surface equation and can be solved efficiently. One pioneering application for the simulation of ship waves by the non-hydrostatic model was initiated by Ma (2012) and named XBeach. Recently, Almström et al. (2021) validated XBeach with improved dispersive behavior by comparison with field measurements. XBeach employed in Almström et al. (2021) is a 2-layer non-hydrostatic model and is accurate up to Kh=4 for the linear dispersion relation (de Ridder et al., 2020), where K=2π/L is the wavenumber. L is the wavelength, and h is the still water depth. However, no applications of non-hydrostatic models on the simulation of ship waves in the presence of a uniform current have been published. For more advances in the numerical modelling of ship waves, the reader is referred to Dempwolff et al. (2022).

    This paper investigates ship waves in the presence of a uniform current by using a non-hydrostatic model (Ai et al., 2019), in which a moving pressure field method is incorporated to represent the movement of a ship hull. The model solves the incompressible Euler equations by using a semi-implicit algorithm and is associated with iterating to solve the Poisson equation. The model with two, three and five layers is accurate up to Kh= 7, 15 and 40, respectively (Ai et al., 2019) in resolving the linear dispersion relation. To the best of our knowledge, ship waves in the presence of currents have been studied theoretically (Benjamin et al., 2017Ellingsen, 2014Li and Ellingsen, 2016Li et al., 2019.) and numerically (Dam et al., 2008Lee and Lee, 20192021). However, no publications have presented the effects of a uniform current on characteristic wave parameters except for Dam et al. (2008), who investigated only the effect of currents on the maximum wave height in a narrow channel for the narrow relative Froude number Fr=(Us−Uc)/gh ranging from 0.47 to 0.76, where Us is the ship speed and Uc is the current velocity. To reveal the effect of currents on the characteristic parameters of ship waves, the main objectives of this paper are (1) to validate the capability of the proposed model to resolve ship waves in the presence of a uniform current, (2) to investigate the effects of a following or an opposing current on characteristic wave parameters including the maximum water level elevation and the leading wave period in the ship wave train, (3) to show the differences in characteristic wave parameters between ship waves in the presence of a uniform current and those without current when the same relative Froude number Fr is specified, and (4) to examine the response of the maximum water level elevation to the ship draft in the presence of a uniform current.

    The remainder of this paper is organized as follows. The non-hydrostatic model for ship waves is described in Section 2. Section 3 presents numerical validations for ship waves. Numerical results and discussions about the effects of a uniform current on characteristic wave parameters are provided in Section 4, and a conclusion is presented in Section 5.

    2. Non-hydrostatic model for ship waves

    2.1. Governing equations

    The 3D incompressible Euler equations are expressed in the following form:(1)∂u∂x+∂v∂y+∂w∂z=0(2)∂u∂t+∂u2∂x+∂uv∂y+∂uw∂z=−∂p∂x(3)∂v∂t+∂uv∂x+∂v2∂y+∂vw∂z=−∂p∂y(4)∂w∂t+∂uw∂x+∂vw∂y+∂w2∂z=−∂p∂z−gwhere t is the time; u(x,y,z,t), v(x,y,z,t) and w(x,y,z,t) are the velocity components in the horizontal x, y and vertical z directions, respectively; p(x,y,z,t) is the pressure divided by a constant reference density; and g is the gravitational acceleration.

    The pressure p(x,y,z,t) can be expressed as(5)p=ps+g(η−z)+qwhere ps(x,y,t) is the pressure at the free surface, η(x,y,t) is the free surface elevation, and q(x,y,z,t) is the non-hydrostatic pressure.

    η(x,y,t) is calculated by the following free-surface equation:(6)∂η∂t+∂∂x∫−hηudz+∂∂y∫−hηvdz=0where z=−h(x,y) is the bottom surface.

    To generate ship waves, ps(x,y,t) is determined by the following slender-body type pressure field (Bayraktar and Beji, 2013David et al., 2017Samaras and Karambas, 2021):

    For −L/2≤x’≤L/2,−B/2≤y’≤B/2(7)ps(x,y,t)|t=0=pm[1−cL(x′/L)4][1−cB(y′/B)2]exp⁡[−a(y′/B)2]where x′=x−x0 and y′=y−y0. (x0,y0) is the center of the pressure field, pm is the peak pressure defined at (x0,y0), and L and B are the lengthwise and breadthwise parameters, respectively. cL, cB and a are set to 16, 2 and 16, respectively.

    2.2. Numerical algorithms

    In this study, the generation of ship waves is incorporated into the semi-implicit non-hydrostatic model developed by Ai et al. (2019). The 3D grid system used in the model is built from horizontal rectangular grids by adding horizontal layers. The horizontal layers are distributed uniformly along the water depth, which means the layer thickness is defined by Δz=(η+h)/Nz, where Nz is the number of horizontal layers.

    In the solution procedure, the first step is to generate ship waves by implementing Eq. (7) together with the prescribed ship track. In the second step, Eqs. (1)(2)(3)(4) are solved by the pressure correction method, which can be subdivided into three stages. The first stage is to compute intermediate velocities un+1/2, vn+1/2, and wn+1/2 by solving Eqs. (2)(3)(4), which contain the non-hydrostatic pressure at the preceding time level. In the second stage, the Poisson equation for the non-hydrostatic pressure correction term is solved on the graphics processing unit (GPU) in conjunction with the conjugate gradient method. The third stage is to compute the new velocities un+1, vn+1, and wn+1 by correcting the intermediate values after including the non-hydrostatic pressure correction term. In the discretization of Eqs. (2)(3), the gradient terms of the water surface ∂η/∂x and ∂η/∂y are discretized by means of the semi-implicit method (Vitousek and Fringer, 2013), in which the implicitness factor θ=0.5 is used. The model is second-order accurate in time for free-surface flows. More details about the model can be found in Ai et al. (2019).

    3. Model validation

    In this section, we validate the proposed model in resolving ship waves. The numerical experimental conditions are provided in Table 1 and Table 2. In Table 2, Case A with the current velocity of Uc = 0.0 m/s represents ship waves without current. Both Case B and Case C correspond to the cases in the presence of a following current, while Case D and Case E represent the cases in the presence of an opposing current. The current velocities are chosen based on the observed currents at 40.886° N, 121.812° E, which is in the Liaohe Estuary. The measured data were collected from 14:00 on September 18 (GMT + 08:00) to 19:00 on September 19 in 2021. The maximum flood velocity is 1.457 m/s, and the maximum ebb velocity is −1.478 m/s. The chosen current velocities are between the maximum flood velocity and the maximum ebb velocity.

    Table 1. Summary of ship speeds.

    CaseWater depth h (m)Ship speed Us (m/s)Froude number Fr′=Us/gh
    16.04.570.6
    26.05.350.7
    36.06.150.8
    46.06.900.9
    56.07.0930.925
    66.07.280.95
    76.07.4760.975
    86.07.861.025
    96.08.061.05
    106.08.2431.075
    116.08.451.1
    126.09.201.2
    136.09.971.3
    146.010.751.4
    156.011.501.5
    166.012.301.6
    176.013.051.7
    186.013.801.8
    196.014.601.9
    206.015.352.0

    Table 2. Summary of current velocities.

    CaseABCDE
    Current velocity
    Uc (m/s)
    0.00.51.0−0.5−1.0

    Notably, the Froude number Fr′=Us/gh presented in Table 1 is defined by the ship speed Us only and is different from the relative Froude number Fr when a uniform current is presented. According to the theory of Lee and Lee (2021), with the same relative Froude number, the cusp-line angles in the presence of a following or an opposing uniform current are identical to those without current. As a result, for the test cases presented in Table 1Table 2, all calculated cusp-line angles follow the analytical solution of Havelock (1908), when the relative Froude number Fr is introduced.

    As shown in Fig. 1, the dimensions of the computational domain are −420≤x≤420 m and −200≤y≤200 m, which are similar to those of David et al. (2017). The ship track follows the x axis and ranges from −384 m to 384 m. The ship hull is represented by Eq. (7), in which the length L and the beam B are set to 14.0 m and 7.0 m, respectively, and the peak pressure value is pm= 5000 Pa. In the numerical simulations, grid convergence tests reveal that the horizontal grid spacing of Δx=Δy= 1.0 m and two horizontal layers are adequate. The numerical results with different numbers of horizontal layers are shown in the Appendix.

    Fig. 1

    Fig. 2Fig. 3 compare the calculated cusp-line angles θc with the analytical solutions of Havelock (1908) for ship waves in the presence of a following uniform current and an opposing uniform current, respectively. The calculated cusp-line angles without current are also depicted in Fig. 2Fig. 3. All calculated cusp-line angles are in good agreement with the analytical solutions, except that the model tends to underpredict the cusp-line angle for 0.9<Fr<1.0. Notably, a similar underprediction of the cusp-line angle can also be found in David et al. (2017).

    Fig. 2
    Fig. 3

    4. Results and discussions

    This section presents the effects of a following current and opposing current on the maximum water level elevation and the leading wave period in the wave train based on the test cases presented in Table 1Table 2. Moreover, the response of the maximum water level elevation to the ship draft in the presence of a uniform current is examined.

    4.1. Effects of a following current on characteristic wave parameters

    To present the effect of a following current on the maximum wave height, the variations of the maximum water level elevation ηmax with the Froude number Fr′ at gauge points G1 and G2 are depicted in Fig. 4. The positions of gauge points G1 and G2 are shown in Fig. 1. The maximum water level elevation is an analogue to the maximum wave height and is presented in this study, because maximum wave heights at different positions away from the ship track vary throughout the wave train (David et al., 2017). In general, the variations of ηmax with the Froude number Fr′ in the three cases show a similar behavior, in which with the increase in Fr′, ηmax increases and then decreases. The presence of the following currents decreases ηmax for Fr′≤0.8 and Fr′≥1.2. Specifically, the following currents have a significant effect on ηmax for Fr′≤0.8. Notably, ηmax can be increased by the presence of the following currents for 0.9≤Fr′≤1.1. Compared with Case A, at location G1 ηmax is amplified 1.25 times at Fr′=0.925 in Case B and 1.31 times at Fr′=1.025 in Case C. Similarly, at location G2 ηmax is amplified 1.15 times at Fr′=1.025 in Case B and 1.11 times at Fr′=1.075 in Case C. The fact that ηmax can be increased by the presence of a following current for 0.9≤Fr′≤1.1 implies that if a following uniform current is neglected, then ηmax may be underestimated.

    Fig. 4

    To show the effect of a following current on the wave period, Fig. 5 depicts the variation of the leading wave period Tp in the wave train at gauge point G2 with the Froude number Fr′. Similar to David et al. (2017), Tp is defined by the wave period of the first wave with a leading trough in the wave train. The leading wave periods for Fr′= 0.6 and 0.7 were not given in Case B and Case C, because the leading wave heights for Fr′= 0.6 and 0.7 are too small to discern the leading wave periods. Compared with Case A, the presence of a following current leads to a larger Tp for 0.925≤Fr′≤1.1 and a smaller Tp for Fr′≥1.3. For Fr′= 0.8 and 0.9, Tp in Case B is larger than that in Case A and Tp in Case C is smaller than that in Case A. In all three cases, Tp decreases with increasing Fr′ for Fr′>1.0. However, this decreasing trend becomes very gentle after Fr′≥1.4. Notably, as shown in Fig. 5, Fr′=1.2 tends to be a transition point at which the following currents have a very limited effect on Tp. Moreover, before the transition point, Tp in Case B and Case C are larger than that in Case A (only for 0.925≤Fr′≤1.2), but after the transition point the reverse is true.

    Fig. 5

    As mentioned previously, the cusp-line angles for ship waves in the presence of a following or an opposing current are identical to those for ship waves only with the same relative Froude number Fr. However, with the same Fr, the characteristic parameters of ship waves in the presence of a following or an opposing current are quite different from those of ship waves without current. Fig. 6 shows the variations of the maximum water level elevation ηmax with Fr at gauge points G1 and G2 for ship waves in the presence of a following uniform current. Overall, the relationship curves between ηmax and Fr in Case B and Case C are lower than those in Case A. It is inferred that with the same Fr, ηmax in the presence of a following current is smaller than that without current. Fig. 7 shows the variation of the leading wave period Tp in the wave train at gauge point G2 with Fr for ship waves in the presence of a following uniform current. The overall relationship curves between Tp and Fr in Case B and Case C are also lower than those in Case A for 0.9≤Fr≤2.0. It can be inferred that with the same Fr, Tp in the presence of a following current is smaller than that without current for Fr≥0.9.

    Fig. 6
    Fig. 7

    To compare the numerical results between the case of ship waves only and the case of ship waves in the presence of a following current with the same Fr, Fig. 8 shows the wave patterns for Fr=1.2. To obtain the case of ship waves in the presence of a following current with Fr=1.2, the ship speed Us=9.7 m/s and the current velocity Uc=0.5 m/s are adopted. Fig. 8 indicates that both the calculated cusp-line angles for the case of Us=9.2 m/s and Uc=0.0 m/s and the case of Us=9.7 m/s and Uc=0.5 m/s are equal to 56.5°, which follows the theory of Lee and Lee (2021)Fig. 9 depicts the comparison of the time histories of the free surface elevation at gauge point G2 for Fr=1.2 between the case of ship waves only and the case of ship waves in the presence of a following current. The time when the ship wave just arrived at gauge point G2 is defined as t′=0. Both the maximum water level elevation and the leading wave period in the case of Us=9.2 m/s and Uc=0.0 m/s are larger than those in the case of Us=9.7 m/s and Uc=0.5 m/s, which is consistent with the inferences based on Fig. 6Fig. 7.

    Fig. 8
    Fig. 8. Comparison of the wave pattern for Fr=1.2: (a) Ship wave only; (b) Ship wave in the presence of a following current.
    Fig. 9
    Fig. 9. Comparison of the time histories of the free surface elevation at gauge point G2 for between case of ship waves only and case of ship waves in the presence of a following current.

    Fig. 10 shows the response of the maximum water level elevation ηmax to the ship draft at gauge point G2 for Fr′= 1.2 in the presence of a following uniform current. pm ranges from 2500 Pa to 40,000 Pa with an interval of Δp= 2500 Pa pm0= 2500 Pa represents a reference case. ηmax0 denotes the maximum water level elevation corresponding to the case of pm0= 2500 Pa. The best-fit linear trend lines obtained by linear regression analysis for the three responses are also depicted in Fig. 10. In general, all responses of ηmax to the ship draft show a linear relationship. The coefficients of determination for the three linear trend lines are R2= 0.9901, 0.9941 and 0.9991 for Case A, Case B and Case C, respectively. R2 is used to measure how close the numerical results are to the linear trend lines. The closer R2 is to 1.0, the more linear the numerical results tend to be. As a result, the relationship curve between ηmax and the ship draft in the presence of a following uniform current tends to be more linear than that without current. Notably, with the increase in pmpm0, ηmax increases faster in Case B and Case C than Case A. This implies that neglecting the following currents can lead to the underestimation of the response of ηmax to the ship draft.

    Fig. 10

    4.2. Effects of an opposing current on characteristic wave parameters

    Fig. 11 shows the variations of the maximum water level elevation ηmax with the Froude number Fr′ at gauge points G1 and G2 for ship waves in the presence of an opposing uniform current. The presence of opposing uniform currents leads to a significant reduction in ηmax at the two gauge points for 0.6≤Fr′≤2.0. Especially for Fr′=0.6, the decrease in ηmax is up to 73.8% in Case D and 78.4% in Case E at location G1 and up to 93.8% in Case D and 95.3% in Case E at location G2 when compared with Case A. Fig. 12 shows the variations of the leading wave period Tp at gauge point G2 with the Froude number Fr′ for ship waves in the presence of an opposing uniform current. The leading wave periods for Fr′= 0.6 and 0.7 were also not provided in Case D and Case E due to the small leading wave heights. In general, Tp decreases with increasing Fr′ in Case D and Case E for 0.8≤Fr′≤2.0. Tp in Case D and Case E are larger than that in Case A for Fr′≥1.0.

    Fig. 11
    Fig. 12

    Fig. 13 depicts the variations of the maximum water level elevation ηmax with the relative Froude number Fr at gauge points G1 and G2 for ship waves in the presence of an opposing uniform current. Similar to Case B and Case C shown in Fig. 6, the overall relationship curves between ηmax and Fr in Case D and Case E are lower than those in Case A. This implies that with the same Fr, ηmax in the presence of an opposing current is also smaller than that without current. Fig. 14 depicts the variations of the leading wave period Tp in the wave train at gauge point G2 with Fr for ship waves in the presence of an opposing uniform current. Similar to Case B and Case C shown in Fig. 7, the overall relationship curves between Tp and Fr in Case D and Case E are lower than those in Case A for 0.9≤Fr≤2.0. This also implies that with the same Fr, Tp in the presence of an opposing current is smaller than that without current.

    Fig. 13
    Fig. 14

    Fig. 15 shows a comparison of the wave pattern for Fr=1.2 between the case of ship waves only and the case of ship waves in the presence of an opposing current. The case of the ship wave in the presence of an opposing current with Fr=1.2 is obtained by setting the ship speed Us=8.7 m/s and the current velocity Uc=−0.5 m/s. As expected (Lee and Lee, 2021), both calculated cusp-line angles are identical. Fig. 16 depicts the comparison of the time histories of the free surface elevation at gauge point G2 for Fr=1.2 between the case of ship waves only and the case of ship waves in the presence of an opposing current. The maximum water level elevation in the case of Us=9.2 m/s and Uc=0.0 m/s is larger than that in the case of Us=8.7 m/s and Uc=−0.5 m/s, while the reverse is true for the leading wave period. Fig. 16 is consistent with the inferences based on Fig. 13Fig. 14.

    Fig. 15
    Fig. 16

    Fig. 17 depicts the response of the maximum water level elevation ηmax to the ship draft at gauge point G2 for Fr′= 1.2 in the presence of an opposing uniform current. Similarly, the response of ηmax to the ship draft in the presence of an opposing uniform current shows a linear relationship. The coefficients of determination for the three linear trend lines are R2= 0.9901, 0.9955 and 0.9987 for Case A, Case D and Case E, respectively. This indicates that the relationship curve between ηmax and the ship draft in the presence of an opposing uniform current also tends to be more linear than that without current. In addition, ηmax increases faster with increasing pmpm0 in Case D and Case E than Case A, implying that the response of ηmax to the ship draft can also be underestimated by neglecting opposing currents.

    Fig. 17

    5. Conclusions

    A non-hydrostatic model incorporating a moving pressure field method was used to investigate characteristic wave parameters for ship waves in the presence of a uniform current. The calculated cusp-line angles for ship waves in the presence of a following or an opposing uniform current were in good agreement with analytical solutions, demonstrating that the proposed model can accurately resolve ship waves in the presence of a uniform current.

    The model results showed that the presence of a following current can result in an increase in the maximum water level elevation ηmax for 0.9≤Fr′≤1.1, while the presence of an opposing current leads to a significant reduction in ηmax for 0.6≤Fr′≤2.0. The leading wave period Tp can be increased for 0.925≤Fr′≤1.2 and reduced for Fr′≥1.3 due to the presence of a following current. However, the presence of an opposing current leads to an increase in Tp for Fr′≥1.0.

    Although with the same relative Froude number Fr, the cusp-line angles for ship waves in the presence of a following or an opposing current are identical to those for ship waves without current, the maximum water level elevation ηmax and leading wave period Tp in the presence of a following or an opposing current are quite different from those without current. The present model results imply that with the same Fr, ηmax in the presence of a following or an opposing current is smaller than that without current for Fr≥0.6, and Tp in the presence of a following or an opposing current is smaller than that without current for Fr≥0.9.

    The response of ηmax to the ship draft in the presence of a following current or an opposing current is similar to that without current and shows a linear relationship. However, the presence of a following or an opposing uniform current results in more linear responses of ηmax to the ship draft. Moreover, more rapid responses of ηmax to the ship draft are obtained when a following current or an opposing current is presented. This implies that the response of ηmax to the ship draft in the presence of a following current or an opposing current can be underestimated if the uniform current is neglected.

    The present results have implications for ships sailing across estuarine and coastal environments, where river flows or tidal flows are significant. In these environments, ship waves can be larger than expected and the response of the maximum water level elevation to the ship draft may be more remarkable. The effect of a uniform current should be considered in the analysis of ship waves.

    The present study considered only slender-body type ships. For different hull shapes, the effects of a uniform current on characteristic wave parameters need to be further investigated. Moreover, the effects of an oblique uniform current on ship waves need to be examined in future work.

    CRediT authorship contribution statement

    Congfang Ai: Conceptualization, Methodology, Software, Validation, Writing – original draft, Funding acquisition. Yuxiang Ma: Conceptualization, Methodology, Funding acquisition, Writing – review & editing. Lei Sun: Conceptualization, Methodology. Guohai Dong: Supervision, Funding acquisition.

    Declaration of competing interest

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

    Acknowledgments

    This research is financially supported by the National Natural Science Foundation of China (Grant No. 521712485172010501051979029), LiaoNing Revitalization Talents Program (Grant No. XLYC1807010) and the Fundamental Research Funds for the Central Universities (Grant No. DUT21LK01).

    Appendix. Numerical results with different numbers of horizontal layers

    Fig. 18 shows comparisons of the time histories of the free surface elevation at gauge point G1 for Case B and Fr′= 1.2 between the three sets of numerical results with different numbers of horizontal layers. The maximum water level elevations ηmax obtained by Nz= 3 and 4 are 0.24% and 0.35% larger than ηmax with Nz= 2, respectively. Correspondingly, the leading wave periods Tp obtained by Nz= 3 and 4 are 0.45% and 0.55% larger than Tp with Nz= 2, respectively. In general, the three sets of numerical results are very close. To reduce the computational cost, two horizontal layers Nz= 2 were chosen for this study.

    Fig. 18

    Data availability

    Data will be made available on request.

    References

    Ai et al., 2019

    C. Ai, Y. Ma, C. Yuan, G. Dong

    Development and assessment of semi-implicit nonhydrostatic models for surface water waves

    Ocean Model., 144 (2019), Article 101489

    ArticleDownload PDFView Record in ScopusGoogle ScholarAlmström et al., 2021

    B. Almström, D. Roelvink, M. Larson

    Predicting ship waves in sheltered waterways – an application of XBeach to the Stockholm Archipelago, Sweden

    Coast. Eng., 170 (2021), Article 104026

    ArticleDownload PDFView Record in ScopusGoogle ScholarBayraktar and Beji, 2013

    D. Bayraktar, S. Beji

    Numerical simulation of waves generated by a moving pressure field

    Ocean Eng., 59 (2013), pp. 231-239

    Google ScholarBenjamin et al., 2017

    K. Benjamin, B.K. Smelzer, S.A. Ellingsen

    Surface waves on currents with arbitrary vertical shear

    Phys. Fluids, 29 (2017), Article 047102

    Google ScholarDam et al., 2008

    K.T. Dam, K. Tanimoto, E. Fatimah

    Investigation of ship waves in a narrow channel

    J. Mar. Sci. Technol., 13 (2008), pp. 223-230 View PDF

    CrossRefView Record in ScopusGoogle ScholarDavid et al., 2017

    C.G. David, V. Roeber, N. Goseberg, T. Schlurmann

    Generation and propagation of ship-borne waves – solutions from a Boussinesq-type model

    Coast. Eng., 127 (2017), pp. 170-187

    ArticleDownload PDFView Record in ScopusGoogle Scholarde Ridder et al., 2020

    M.P. de Ridder, P.B. Smit, A. van Dongeren, R. McCall, K. Nederhoff, A.J.H.M. Reniers

    Efficient two-layer non-hydrostatic wave model with accurate dispersive behaviour

    Coast. Eng., 164 (2020), Article 103808

    Google ScholarDempwolff et al., 2022

    L.-C. Dempwolff, G. Melling, C. Windt, O. Lojek, T. Martin, I. Holzwarth, H. Bihs, N. Goseberg

    Loads and effects of ship-generated, drawdown waves in confined waterways – a review of current knowledge and methods

    J. Coast. Hydraul. Struct., 2 (2022), pp. 2-46

    Google ScholarEllingsen, 2014

    S.A. Ellingsen

    Ship waves in the presence of uniform vorticity

    J. Fluid Mech., 742 (2014), p. R2

    View Record in ScopusGoogle ScholarErtekin et al., 1986

    R.C. Ertekin, W.C. Webster, J.V. Wehausen

    Waves caused by a moving disturbance in a shallow channel of finite width

    J. Fluid Mech., 169 (1986), pp. 275-292

    View Record in ScopusGoogle ScholarGrue, 2017

    J. Grue

    Ship generated mini-tsunamis

    J. Fluid Mech., 816 (2017), pp. 142-166 View PDF

    CrossRefView Record in ScopusGoogle ScholarGrue, 2020

    J. Grue

    Mini-tsunamis made by ship moving across a depth change

    J. Waterw. Port, Coast. Ocean Eng., 146 (2020), Article 04020023

    View Record in ScopusGoogle ScholarGourlay, 2001

    T.P. Gourlay

    The supercritical bore produced by a high-speed ship in a channel

    J. Fluid Mech., 434 (2001), pp. 399-409 View PDF

    CrossRefView Record in ScopusGoogle ScholarHavelock, 1908

    T.H. Havelock

    The propagation of groups of waves in dispersive media with application to waves on water produced by a travelling disturbance

    Proc. Royal Soc. London Series A (1908), pp. 398-430

    Google ScholarLee and Lee, 2019

    B.W. Lee, C. Lee

    Equation for ship wave crests in the entire range of water depths

    Coast. Eng., 153 (2019), Article 103542

    ArticleDownload PDFView Record in ScopusGoogle ScholarLee and Lee, 2021

    B.W. Lee, C. Lee

    Equation for ship wave crests in a uniform current in the entire range of water depths

    Coast. Eng., 167 (2021), Article 103900

    ArticleDownload PDFView Record in ScopusGoogle ScholarLi and Ellingsen, 2016

    Y. Li, S.A. Ellingsen

    Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

    J. Fluid Mech., 791 (2016), pp. 539-567 View PDF

    CrossRefView Record in ScopusGoogle ScholarLi et al., 2019

    Y. Li, B.K. Smeltzer, S.A. Ellingsen

    Transient wave resistance upon a real shear current

    Eur. J. Mech. B Fluid, 73 (2019), pp. 180-192

    ArticleDownload PDFCrossRefView Record in ScopusGoogle ScholarMa, 2012

    H. Ma

    Passing Ship Effects in a 2DH Non- Hydrostatic Flow Model

    UNESCO-IHE, Delft, The Netherlands (2012)

    Google ScholarSamaras and Karambas, 2021

    A.G. Samaras, T.V. Karambas

    Numerical simulation of ship-borne waves using a 2DH post-Boussinesq model

    Appl. Math. Model., 89 (2021), pp. 1547-1556

    ArticleDownload PDFView Record in ScopusGoogle ScholarShi et al., 2018

    F. Shi, M. Malej, J.M. Smith, J.T. Kirby

    Breaking of ship bores in a Boussinesq-type ship-wake model

    Coast. Eng., 132 (2018), pp. 1-12

    ArticleDownload PDFCrossRefView Record in ScopusGoogle ScholarVitousek and Fringer, 2013

    S. Vitousek, O.B. Fringer

    Stability and consistency of nonhydrostatic free-surface models using the semi-implicit θ-method

    Int. J. Numer. Methods Fluid., 72 (2013), pp. 550-582 View PDF

    CrossRefView Record in ScopusGoogle Scholar

    Numerical analysis of energy dissipator options using computational fluid dynamics modeling — a case study of Mirani Dam

    전산 유체 역학 모델링을 사용한 에너지 소산자 옵션의 수치적 해석 — Mirani 댐의 사례 연구

    Arabian Journal of Geosciences volume 15, Article number: 1614 (2022) Cite this article

    Abstract

    이 연구에서 FLOW 3D 전산 유체 역학(CFD) 소프트웨어를 사용하여 파키스탄 Mirani 댐 방수로에 대한 에너지 소산 옵션으로 미국 매립지(USBR) 유형 II 및 USBR 유형 III 유역의 성능을 추정했습니다. 3D Reynolds 평균 Navier-Stokes 방정식이 해결되었으며, 여기에는 여수로 위의 자유 표면 흐름을 캡처하기 위해 공기 유입, 밀도 평가 및 드리프트-플럭스에 대한 하위 그리드 모델이 포함되었습니다. 본 연구에서는 5가지 모델을 고려하였다. 첫 번째 모델에는 길이가 39.5m인 USBR 유형 II 정수기가 있습니다. 두 번째 모델에는 길이가 44.2m인 USBR 유형 II 정수기가 있습니다. 3번째와 4 번째모델에는 길이가 각각 48.8m인 USBR 유형 II 정수조와 39.5m의 USBR 유형 III 정수조가 있습니다. 다섯 번째 모델은 네 번째 모델과 동일하지만 마찰 및 슈트 블록 높이가 0.3m 증가했습니다. 최상의 FLOW 3D 모델 조건을 설정하기 위해 메쉬 민감도 분석을 수행했으며 메쉬 크기 0.9m에서 최소 오차를 산출했습니다. 세 가지 경계 조건 세트가 테스트되었으며 최소 오류를 제공하는 세트가 사용되었습니다. 수치적 검증은 USBR 유형 II( L = 48.8m), USBR 유형 III( L = 35.5m) 및 USBR 유형 III 의 물리적 모델 에너지 소산을 0.3m 블록 단위로 비교하여 수행되었습니다( L= 35.5m). 통계 분석 결과 평균 오차는 2.5%, RMSE(제곱 평균 제곱근 오차) 지수는 3% 미만이었습니다. 수리학적 및 경제성 분석을 바탕으로 4 번째 모델이 최적화된 에너지 소산기로 밝혀졌습니다. 흡수된 에너지 백분율 측면에서 물리적 모델과 수치적 모델 간의 최대 차이는 5% 미만인 것으로 나타났습니다.

    In this study, the FLOW 3D computational fluid dynamics (CFD) software was used to estimate the performance of the United States Bureau of Reclamation (USBR) type II and USBR type III stilling basins as energy dissipation options for the Mirani Dam spillway, Pakistan. The 3D Reynolds-averaged Navier–Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift–flux, to capture free-surface flow over the spillway. Five models were considered in this research. The first model has a USBR type II stilling basin with a length of 39.5 m. The second model has a USBR type II stilling basin with a length of 44.2 m. The 3rd and 4th models have a USBR type II stilling basin with a length of 48.8 m and a 39.5 m USBR type III stilling basin, respectively. The fifth model is identical to the fourth, but the friction and chute block heights have been increased by 0.3 m. To set up the best FLOW 3D model conditions, mesh sensitivity analysis was performed, which yielded a minimum error at a mesh size of 0.9 m. Three sets of boundary conditions were tested and the set that gave the minimum error was employed. Numerical validation was done by comparing the physical model energy dissipation of USBR type II (L = 48.8 m), USBR type III (L =35.5 m), and USBR type III with 0.3-m increments in blocks (L = 35.5 m). The statistical analysis gave an average error of 2.5% and a RMSE (root mean square error) index of less than 3%. Based on hydraulics and economic analysis, the 4th model was found to be an optimized energy dissipator. The maximum difference between the physical and numerical models in terms of percentage energy absorbed was found to be less than 5%.

    Keywords

    • Numerical modeling
    • Spillway
    • Hydraulic jump
    • Energy dissipation
    • FLOW 3D

    References

    • Abbasi S, Fatemi S, Ghaderi A, Di Francesco S (2021) The effect of geometric parameters of the antivortex on a triangular labyrinth side weir. Water (Switzerland) 13(1). https://doi.org/10.3390/w13010014
    • Amorim JCC, Amante RCR, Barbosa VD (2015) Experimental and numerical modeling of flow in a stilling basin. Proceedings of the 36th IAHR World Congress 28 June–3 July, the Hague, the Netherlands, 1, 1–6
    • Asaram D, Deepamkar G, Singh G, Vishal K, Akshay K (2016) Energy dissipation by using different slopes of ogee spillway. Int J Eng Res Gen Sci 4(3):18–22Google Scholar 
    • Boes RM, Hager WH (2003) Hydraulic design of stepped spillways. J Hydraul Eng 129(9):671–679. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:9(671)Article Google Scholar 
    • Celik IB, Ghia U, Roache PJ, Freitas CJ, Coleman H, Raad PE (2008) Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J Fluids Eng Trans ASME 130(7):0780011–0780014. https://doi.org/10.1115/1.2960953Article Google Scholar 
    • Chen Q, Dai G, Liu H (2002) Volume of fluid model for turbulence numerical simulation of stepped spillway overflow. J Hydraul Eng 128(7):683–688. 10.1061/共ASCE兲0733-9429共2002兲128:7共683兲 CE
    • Damiron R (2015) CFD modelling of dam spillway aerator. Lund University Sweden
    • Dunlop SL, Willig IA, Paul GE (2016) Cabinet Gorge Dam spillway modifications for TDG abatement – design evolution and field performance. 6th International Symposium on Hydraulic Structures: Hydraulic Structures and Water System Management, ISHS 2016, 3650628160, 460–470. 10.15142/T3650628160853
    • Fleit G, Baranya S, Bihs H (2018) CFD modeling of varied flow conditions over an ogee-weir. Period Polytech Civ Eng 62(1):26–32. https://doi.org/10.3311/PPci.10821Article Google Scholar 
    • Frizell KW, Frizell KH (2015) Guidelines for hydraulic design of stepped spillways. Hydraulic Laboratory Report HL-2015-06, May
    • Ghaderi A, Abbasi S (2021) Experimental and numerical study of the effects of geometric appendance elements on energy dissipation over stepped spillway. Water (Switzerland) 13(7). https://doi.org/10.3390/w13070957
    • Ghaderi A, Dasineh M, Aristodemo F, Ghahramanzadeh A (2020) Characteristics of free and submerged hydraulic jumps over different macroroughnesses. J Hydroinform 22(6):1554–1572. https://doi.org/10.2166/HYDRO.2020.298Article Google Scholar 
    • Güven A, Mahmood AH (2021) Numerical investigation of flow characteristics over stepped spillways. Water Sci Technol Water Supply 21(3):1344–1355. https://doi.org/10.2166/ws.2020.283Article Google Scholar 
    • Herrera-Granados O, Kostecki SW (2016) Numerical and physical modeling of water flow over the ogee weir of the new Niedów barrage. J Hydrol Hydromech 64(1):67–74. https://doi.org/10.1515/johh-2016-0013Article Google Scholar 
    • Ho DKH, Riddette KM (2010) Application of computational fluid dynamics to evaluate hydraulic performance of spillways in australia. Aust J Civ Eng 6(1):81–104. https://doi.org/10.1080/14488353.2010.11463946Article Google Scholar 
    • Kocaer Ö, Yarar A (2020) Experimental and numerical investigation of flow over ogee spillway. Water Resour Manag 34(13):3949–3965. https://doi.org/10.1007/s11269-020-02558-9Article Google Scholar 
    • Kumcu SY (2017) Investigation of flow over spillway modeling and comparison between experimental data and CFD analysis. KSCE J Civ Eng 21(3):994–1003. https://doi.org/10.1007/s12205-016-1257-zArticle Google Scholar 
    • Li S, Li Q, Yang J (2019) CFD modelling of a stepped spillway with various step layouts. Math Prob Eng 2019:1–12. https://doi.org/10.1155/2019/6215739Article Google Scholar 
    • Muthukumaran N, Prince Arulraj G (2020) Experimental investigation on augmenting the discharge over ogee spillways with nanocement. Civ Eng Archit 8(5):838–845. https://doi.org/10.13189/cea.2020.080511Article Google Scholar 
    • Naderi V, Farsadizadeh D, Lin C, Gaskin S (2019) A 3D study of an air-core vortex using HSPIV and flow visualization. Arab J Sci Eng 44(10):8573–8584. https://doi.org/10.1007/s13369-019-03764-3Article Google Scholar 
    • Nangare PB, Kote AS (2017) Experimental investigation of an ogee stepped spillway with plain and slotted roller bucket for energy dissipation. Int J Civ Eng Technol 8(8):1549–1555Google Scholar 
    • Parsaie A, Moradinejad A, Haghiabi AH (2018) Numerical modeling of flow pattern in spillway approach channel. Jordan J Civ Eng 12(1):1–9Google Scholar 
    • Pasbani Khiavi M, Ali Ghorbani M, Yusefi M (2021) Numerical investigation of the energy dissipation process in stepped spillways using finite volume method. J Irrig Water Eng 11(4):22–37Google Scholar 
    • Peng Y, Zhang X, Yuan H, Li X, Xie C, Yang S, Bai Z (2019) Energy dissipation in stepped spillways with different horizontal face angles. Energies 12(23). https://doi.org/10.3390/en12234469
    • Raza A, Wan W, Mehmood K (2021) Stepped spillway slope effect on air entrainment and inception point location. Water (Switzerland) 13(10). https://doi.org/10.3390/w13101428
    • Reeve DE, Zuhaira AA, Karunarathna H (2019) Computational investigation of hydraulic performance variation with geometry in gabion stepped spillways. Water Sci Eng 12(1):62–72. https://doi.org/10.1016/j.wse.2019.04.002Article Google Scholar 
    • Rice CE, Kadavy KC (1996) Model study of a roller compacted concrete stepped spillway. J Hydraul Eng 122(6):292–297. https://doi.org/10.1061/(ASCE)0733-9429(1996)122:6(292)Article Google Scholar 
    • Rong Y, Zhang T, Peng L, Feng P (2019) Three-dimensional numerical simulation of dam discharge and flood routing in Wudu reservoir. Water (Switzerland) 11(10). https://doi.org/10.3390/w11102157
    • Saqib N, Akbar M, Pan H, Ou G, Mohsin M, Ali A, Amin A (2022) Numerical analysis of pressure profiles and energy dissipation across stepped spillways having curved risers. Appl Sci 12(448):1–18Google Scholar 
    • Saqib N, Ansari K, Babar M (2021) Analysis of pressure profiles and energy dissipation across stepped spillways having curved treads using computational fluid dynamics. Intl Conf Adv Mech Eng :1–10
    • Saqib Nu, Akbar M, Huali P, Guoqiang O (2022) Numerical investigation of pressure profiles and energy dissipation across the stepped spillway having curved treads using FLOW 3D. Arab J Geosci 15(1):1363–1400. https://doi.org/10.1007/s12517-022-10505-8Article Google Scholar 
    • Sarkardeh H, Marosi M, Roshan R (2015) Stepped spillway optimization through numerical and physical modeling. Int J Energy Environ 6(6):597–606Google Scholar 
    • Serafeim A, Avgeris V, Hrissanthou V (2015) Experimental and numerical modeling of flow over a spillway. Eur Water Publ 14(2015):55–59. https://doi.org/10.15224/978-1-63248-042-2-11Article Google Scholar 
    • Sorensen RM (1986) Stepped spillway model investigation. J Hydraul Eng I(12):1461–1472. https://ascelibrary.org/doi/full/10.1061/%28ASCE%290733-
    • Tabbara M, Chatila J, Awwad R (2005) Computational simulation of flow over stepped spillways. Comput Struct 83(27):2215–2224. https://doi.org/10.1016/j.compstruc.2005.04.005Article Google Scholar 
    • Valero D, Bung DB, Crookston BM, Matos J (2016) Numerical investigation of USBR type III stilling basin performance downstream of smooth and stepped spillways. 6th International Symposium on Hydraulic Structures: Hydraulic Structures and Water System Management, ISHS 2016, 3406281608, 635–646. https://doi.org/10.15142/T340628160853
    • Versteeg H, Malalasekera W (1979) An introduction to computational fluid mechanics. (Vol. 2). https://doi.org/10.1016/0010-4655(80)90010-7
    • WAPDA model studies cell, IRI Lahore (2003) Mirani Dam Project hydraulic model studies for the spillway. November 2003
    • Yakhot V, Orszag S (1986) Renormalization group analysis of turbulence. I. Basic theory. J Sci Comput 1(1):3–51Article Google Scholar 
    Fig. 8 Distribution of solidification properties on the yz cross section at the maximum width of the melt pool.(a) thermal gradient G, (b) solidification velocity vT, (c) cooling rate G×vT, and (d) morphology factor G/vT. These profiles are calculated with a laser power 300 W and velocity 400 mm/s using (a1 through d1) analytical Rosenthal simulation and (a2 through d2) high-fidelity CFD simulation. The laser is moving out of the page from the upper left corner of each color map (Color figure online)

    Quantifying Equiaxed vs Epitaxial Solidification in Laser Melting of CMSX-4 Single Crystal Superalloy

    CMSX -4 단결정 초합금의 레이저 용융에서 등축 응고와 에피택셜 응고 정량화

    본 논문은 독자의 편의를 위해 기계번역된 내용이어서 자세한 내용은 원문을 참고하시기 바랍니다.

    Abstract

    에피택셜 과 등축 응고 사이의 경쟁은 적층 제조에서 실행되는 레이저 용융 동안 CMSX-4 단결정 초합금에서 조사되었습니다. 단일 트랙 레이저 스캔은 레이저 출력과 스캐닝 속도의 여러 조합으로 방향성 응고된 CMSX-4 합금의 분말 없는 표면에서 수행되었습니다. EBSD(Electron Backscattered Diffraction) 매핑은 새로운 방향의 식별을 용이하게 합니다. 영역 분율 및 공간 분포와 함께 융합 영역 내에서 핵을 형성한 “스트레이 그레인”은 충실도가 높은 전산 유체 역학 시뮬레이션을 사용하여 용융 풀 내의 온도 및 유체 속도 필드를 모두 추정했습니다. 이 정보를 핵 생성 모델과 결합하여 용융 풀에서 핵 생성이 발생할 확률이 가장 높은 위치를 결정했습니다. 금속 적층 가공의 일반적인 경험에 따라 레이저 용융 트랙의 응고된 미세 구조는 에피택셜 입자 성장에 의해 지배됩니다. 더 높은 레이저 스캐닝 속도와 더 낮은 출력이 일반적으로 흩어진 입자 감소에 도움이 되지만,그럼에도 불구하고 길쭉한 용융 풀에서 흩어진 입자가 분명했습니다.

    The competition between epitaxial vs. equiaxed solidification has been investigated in CMSX-4 single crystal superalloy during laser melting as practiced in additive manufacturing. Single-track laser scans were performed on a powder-free surface of directionally solidified CMSX-4 alloy with several combinations of laser power and scanning velocity. Electron backscattered diffraction (EBSD) mapping facilitated identification of new orientations, i.e., “stray grains” that nucleated within the fusion zone along with their area fraction and spatial distribution. Using high-fidelity computational fluid dynamics simulations, both the temperature and fluid velocity fields within the melt pool were estimated. This information was combined with a nucleation model to determine locations where nucleation has the highest probability to occur in melt pools. In conformance with general experience in metals additive manufacturing, the as-solidified microstructure of the laser-melted tracks is dominated by epitaxial grain growth; nevertheless, stray grains were evident in elongated melt pools. It was found that, though a higher laser scanning velocity and lower power are generally helpful in the reduction of stray grains, the combination of a stable keyhole and minimal fluid velocity further mitigates stray grains in laser single tracks.

    Introduction

    니켈 기반 초합금은 고온에서 긴 노출 시간 동안 높은 인장 강도, 낮은 산화 및 우수한 크리프 저항성을 포함하는 우수한 특성의 고유한 조합으로 인해 가스 터빈 엔진 응용 분야에서 광범위하게 사용됩니다. CMSX-4는 특히 장기 크리프 거동과 관련하여 초고강도의 2세대 레늄 함유 니켈 기반 단결정 초합금입니다. 1 , 2 ]입계의 존재가 크리프를 가속화한다는 인식은 가스 터빈 엔진의 고온 단계를 위한 단결정 블레이드를 개발하게 하여 작동 온도를 높이고 효율을 높이는 데 기여했습니다. 이러한 구성 요소는 사용 중 마모될 수 있습니다. 즉, 구성 요소의 무결성을 복원하고 단결정 미세 구조를 유지하는 수리 방법을 개발하기 위한 지속적인 작업이 있었습니다. 3 , 4 , 5 ]

    적층 제조(AM)가 등장하기 전에는 다양한 용접 공정을 통해 단결정 초합금에 대한 수리 시도가 수행되었습니다. 균열 [ 6 , 7 ] 및 흩어진 입자 8 , 9 ] 와 같은 심각한 결함 이 이 수리 중에 자주 발생합니다. 일반적으로 “스트레이 그레인”이라고 하는 응고 중 모재의 방향과 다른 결정학적 방향을 가진 새로운 그레인의 형성은 니켈 기반 단결정 초합금의 수리 중 유해한 영향으로 인해 중요한 관심 대상입니다. 3 , 10 ]결과적으로 재료의 단결정 구조가 손실되고 원래 구성 요소에 비해 기계적 특성이 손상됩니다. 이러한 흩어진 입자는 특정 조건에서 에피택셜 성장을 대체하는 등축 응고의 시작에 해당합니다.

    떠돌이 결정립 형성을 완화하기 위해 이전 작업은 용융 영역(FZ) 내에서 응고하는 동안 떠돌이 결정립 형성에 영향을 미치는 수지상 응고 거동 및 처리 조건을 이해하는 데 중점을 두었습니다. 11 , 12 , 13 , 14 ] 연구원들은 단결정 합금의 용접 중에 표류 결정립 형성에 대한 몇 가지 가능한 메커니즘을 제안했습니다. 12 , 13 , 14 , 15 ]응고 전단에 앞서 국부적인 구성 과냉각은 이질적인 핵 생성 및 등축 결정립의 성장을 유발할 수 있습니다. 또한 용융 풀에서 활발한 유체 흐름으로 인해 발생하는 덴드라이트 조각화는 용융 풀 경계 근처에서 새로운 결정립을 형성할 수도 있습니다. 두 메커니즘 모두에서, 표류 결정립 형성은 핵 생성 위치에 의존하며, 차이점은 수상 돌기 조각화는 수상 돌기 조각이 핵 생성 위치로 작용한다는 것을 의미하는 반면 다른 메커니즘은 재료,  를 들어 산화물 입자에서 발견되는 다른 유형의 핵 생성 위치를 사용한다는 것을 의미합니다. 잘 알려진 바와 같이, 많은 주물에 대한 반대 접근법은 TiB와 같은 핵제의 도입을 통해 등축 응고를 촉진하는 것입니다.22알루미늄 합금에서.

    헌법적 과냉 메커니즘에서 Hunt 11 ] 는 정상 상태 조건에서 기둥에서 등축으로의 전이(CET)를 설명하는 모델을 개발했습니다. Gaumann과 Kurz는 Hunt의 모델을 수정하여 단결정이 응고되는 동안 떠돌이 결정립이 핵을 생성하고 성장할 수 있는 정도를 설명했습니다. 12 , 14 ] 이후 연구에서 Vitek은 Gaumann의 모델을 개선하고 출력 및 스캐닝 속도와 같은 용접 조건의 영향에 대한 보다 자세한 분석을 포함했습니다. Vitek은 또한 실험 및 모델링 기술을 통해 표류 입자 형성에 대한 기판 방향의 영향을 포함했습니다. 3 , 10 ]일반적으로 높은 용접 속도와 낮은 출력은 표류 입자의 양을 최소화하고 레이저 용접 공정 중 에피택셜 단결정 성장을 최대화하는 것으로 나타났습니다. 3,10 ] 그러나 Vitek은 덴드라이트 조각화를 고려하지 않았으며 그의 연구는 불균질 핵형성이 레이저 용접된 CMSX -4 단결정 합금에서 표류 결정립 형성을 이끄는 주요 메커니즘임을 나타냅니다. 현재 작업에서 Vitek의 수치적 방법이 채택되고 금속 AM의 급속한 특성의 더 높은 속도와 더 낮은 전력 특성으로 확장됩니다.

    AM을 통한 금속 부품 제조 는 지난 10년 동안 급격한 인기 증가를 목격했습니다. 16 ] EBM(Electron Beam Melting)에 의한 CMSX-4의 제작 가능성은 자주 조사되었으나 17 , 18 , 19 , 20 , 21 ] CMSX의 제조 및 수리에 대한 조사는 매우 제한적이었다. – 4개의 단결정 구성요소는 레이저 분말 베드 융합(LPBF)을 사용하며, AM의 인기 있는 하위 집합으로, 특히 표류 입자 형성을 완화하는 메커니즘과 관련이 있습니다. 22 ]이러한 조사 부족은 주로 이러한 합금 시스템과 관련된 처리 문제로 인해 발생합니다. 2 , 19 , 22 , 23 , 24 ] 공정 매개변수( 예: 열원 전력, 스캐닝 속도, 스폿 크기, 예열 온도 및 스캔 전략)의 엄격한 제어는 완전히 조밀한 부품을 만들고 유지 관리할 수 있도록 하는 데 필수적입니다. 단결정 미세구조. 25 ] EBM을 사용하여 단결정 합금의 균열 없는 수리가 현재 가능하지만 19 , 24 ] 표류 입자를 생성하지 않는 수리는 쉽게 달성할 수 없습니다.23 , 26 ]

    이 작업에서 LPBF를 대표하는 조건으로 레이저 용융을 사용하여 단결정 CMSX-4에서 표류 입자 완화를 조사했습니다. LPBF는 스캐닝 레이저 빔을 사용하여 금속 분말의 얇은 층을 기판에 녹이고 융합합니다. 층별 증착에서 레이저 빔의 사용은 급격한 온도 구배, 빠른 가열/냉각 주기 및 격렬한 유체 흐름을 경험하는 용융 풀을 생성 합니다 이것은 일반적으로 부품에 결함을 일으킬 수 있는 매우 동적인 물리적 현상으로 이어집니다. 28 , 29 , 30 ] 레이저 유도 키홀의 동역학( 예:, 기화 유발 반동 압력으로 인한 위상 함몰) 및 열유체 흐름은 AM 공정에서 응고 결함과 강하게 결합되고 관련됩니다. 31 , 32 , 33 , 34 ] 기하 구조의 급격한 변화가 발생하기 쉬운 불안정한 키홀은 다공성, 볼링, 스패터 형성 및 흔하지 않은 미세 구조 상을 포함하는 유해한 물리적 결함을 유발할 수 있습니다. 그러나 키홀 진화와 유체 흐름은 자연적으로 다음을 통해 포착 하기 어렵 습니다 .전통적인 사후 특성화 기술. 고충실도 수치 모델링을 활용하기 위해 이 연구에서는 전산유체역학(CFD)을 적용하여 표면 아래의 레이저-물질 상호 작용을 명확히 했습니다. 36 ] 이것은 응고된 용융물 풀의 단면에 대한 오랫동안 확립된 사후 특성화와 비교하여 키홀 및 용융물 풀 유체 흐름 정량화를 실행합니다.

    CMSX-4 구성 요소의 레이저 기반 AM 수리 및 제조를 위한 적절한 절차를 개발하기 위해 적절한 공정 창을 설정하고 응고 중 표류 입자 형성 경향에 대한 예측 기능을 개발하는 것부터 시작합니다. 다중 합금에 대한 단일 트랙 증착은 분말 층이 있거나 없는 AM 공정에서 용융 풀 형상 및 미세 구조의 정확한 분석을 제공하는 것으로 나타났습니다. 37 , 38 , 39 ]따라서 본 연구에서는 CMSX-4의 응고 거동을 알아보기 위해 분말을 사용하지 않는 단일 트랙 레이저 스캔 실험을 사용하였다. 이는 CMSX-4 단결정의 LPBF 제조를 위한 예비 실험 지침을 제공합니다. 또한 응고 모델링은 기존 용접에서 LPBF와 관련된 급속 용접으로 확장되어 표류 입자 감소를 위한 최적의 레이저 용융 조건을 식별했습니다. 가공 매개변수 최적화를 위한 추가 지침을 제공하기 위해 용융물 풀의 매우 동적인 유체 흐름을 모델링했습니다.

    재료 및 방법

    단일 트랙 실험

    방전 가공(EDM)을 사용하여 CMSX-4 방향성 응고 단결정 잉곳으로부터 샘플을 제작했습니다. 샘플의 최종 기하학은 치수 20의 직육면체 형태였습니다.××20××6mm. 6개 중 하나⟨ 001 ⟩⟨001⟩잉곳의 결정학적 방향은 레이저 트랙이 이 바람직한 성장 방향을 따라 스캔되도록 절단 표면에 수직으로 위치했습니다. 단일 레이저 용융 트랙은 EOS M290 기계를 사용하여 분말이 없는 샘플 표면에 만들어졌습니다. 이 기계는 최대 출력 400W, 가우시안 빔 직경 100의 이터븀 파이버 레이저가 장착된 LPBF 시스템입니다. μμ초점에서 m. 실험 중에 직사각형 샘플을 LPBF 기계용 맞춤형 샘플 홀더의 포켓에 끼워 표면을 동일한 높이로 유지했습니다. 이 맞춤형 샘플 홀더에 대한 자세한 내용은 다른 곳에서 설명합니다. 실험 은 아르곤 퍼지 분위기에서 수행되었으며 예열은 적용되지 않았습니다 단일 트랙 레이저 용융 실험은 다양한 레이저 출력(200~370W)과 스캔 속도(0.4~1.4m/s)에서 수행되었습니다.

    성격 묘사

    레이저 스캐닝 후, 레이저 빔 스캐닝 방향에 수직인 평면에서 FZ를 통해 다이아몬드 톱을 사용하여 샘플을 절단했습니다. 그 후, 샘플을 장착하고 220 그릿 SiC 페이퍼로 시작하여 콜로이드 실리카 현탁액 광택제로 마무리하여 자동 연마했습니다. 결정학적 특성화는 20kV의 가속 전압에서 TESCAN MIRA 3XMH 전계 방출 주사 전자 현미경(SEM)에서 수행되었습니다. EBSD 지도는0.4μm _0.4μ미디엄단계 크기. Bruker 시스템을 사용하여 EBSD 데이터를 정리하고 분석했습니다. EBSD 클린업은 그레인을 접촉시키기 위한 그레인 확장 루틴으로 시작한 다음 인덱스되지 않은 회절 패턴과 관련된 검은색 픽셀을 해결하기 위해 이웃 방향 클린업 루틴으로 이어졌습니다. 용융 풀 형태를 분석하기 위해 단면을 광학 현미경으로 분석했습니다. 광학 특성화의 대비를 향상시키기 위해 10g CuSO로 구성된 Marbles 시약의 변형으로 샘플을 에칭했습니다.44, 50mL HCl 및 70mL H22영형.

    응고 모델링

    구조적 과냉 기준에 기반한 응고 모델링을 수행하여 표유 입자의 성향 및 분포에 대한 가공 매개변수의 영향을 평가했습니다. 이 분석 모델링 접근 방식에 대한 자세한 내용은 이전 작업에서 제공됩니다. 3 , 10 ] 참고문헌 3 에 기술된 바와 같이 , 기본 재료의 결정학적 배향을 가진 용융 풀에서 총 표유 입자 면적 분율의 변화는 최소이므로 기본 재료 배향의 영향은 이 작업에서 고려되지 않았습니다. 우리의 LPBF 결과를 이전 작업과 비교하기 위해 Vitek의 작업에서 사용된 수학적으로 간단한 Rosenthal 방정식 3 ]또한 레이저 매개변수의 함수로 용융 풀의 모양과 FZ의 열 조건을 계산하기 위한 기준으로 여기에서 채택되었습니다. Rosenthal 솔루션은 열이 일정한 재료 특성을 가진 반무한 판의 정상 상태 점원을 통해서만 전도를 통해 전달된다고 가정하며 일반적으로 다음과 같이 표현 됩니다 40 , 41 ] .

    티=티0+η피2 파이케이엑스2+와이2+지2———-√경험치[- 브이(엑스2+와이2+지2———-√− 엑스 )2α _] ,티=티0+η피2파이케이엑스2+와이2+지2경험치⁡[-V(엑스2+와이2+지2-엑스)2α],(1)

    여기서 T 는 온도,티0티0본 연구에서 313K(  , EOS 기계 챔버 온도)로 설정된 주변 온도, P 는 레이저 빔 파워, V 는 레이저 빔 스캐닝 속도,ηη는 레이저 흡수율, k 는 열전도율,αα베이스 합금의 열확산율입니다. x , y , z 는 각각 레이저 스캐닝 방향, 가로 방향 및 세로 방향의 반대 방향과 정렬된 방향입니다 . 이 직교 좌표는 참조 3 의 그림 1에 있는 시스템을 따랐습니다 . CMSX-4에 대한 고상선 온도(1603K)와 액상선 온도(1669K)의 등온선 평균으로 응고 프런트( 즉 , 고체-액체 계면)를 정의했습니다. 42 , 43 , 44 ] 시뮬레이션에 사용된 열물리적 특성은 표 I 에 나열되어 있습니다.표 I CMSX-4의 응고 모델링에 사용된 열물리적 특성

    풀 사이즈 테이블

    열 구배는 외부 열 흐름에 의해 결정되었습니다.∇ 티∇티45 ] 에 의해 주어진 바와 같이 :

    지 = | ∇ 티| =∣∣∣∂티∂엑스나^^+∂티∂와이제이^^+∂티∂지케이^^∣∣∣=(∂티∂엑스)2+(∂티∂와이)2+(∂티∂지)2————————√,G=|∇티|=|∂티∂엑스나^^+∂티∂와이제이^^+∂티∂지케이^^|=(∂티∂엑스)2+(∂티∂와이)2+(∂티∂지)2,(2)

    어디나^^나^^,제이^^제이^^, 그리고케이^^케이^^는 각각 x , y 및 z 방향 을 따른 단위 벡터 입니다. 응고 등온선 속도,V티V티는 다음 관계에 의해 레이저 빔 스캐닝 속도 V 와 기하학적으로 관련됩니다.

    V티= V코사인θ =V∂티∂엑스(∂티∂엑스)2+(∂티∂와이)2+(∂티∂지)2——————-√,V티=V코사인⁡θ=V∂티∂엑스(∂티∂엑스)2+(∂티∂와이)2+(∂티∂지)2,(삼)

    어디θθ는 스캔 방향과 응고 전면의 법선 방향(  , 최대 열 흐름 방향) 사이의 각도입니다. 이 연구의 용접 조건과 같은 제한된 성장에서 수지상 응고 전면은 고체-액체 등온선의 속도로 성장하도록 강제됩니다.V티V티. 46 ]

    응고 전선이 진행되기 전에 새로 핵 생성된 입자의 국지적 비율ΦΦ, 액체 온도 구배 G 에 의해 결정 , 응고 선단 속도V티V티및 핵 밀도N0N0. 고정된 임계 과냉각에서 모든 입자가 핵형성된다고 가정함으로써△티N△티N, 등축 결정립의 반경은 결정립이 핵 생성을 시작하는 시점부터 주상 전선이 결정립에 도달하는 시간까지의 성장 속도를 통합하여 얻습니다. 과냉각으로 대체 시간d (ΔT_) / dt = – _V티G디(△티)/디티=-V티G, 열 구배 G 사이의 다음 관계 , 등축 입자의 국부적 부피 분율ΦΦ, 수상 돌기 팁 과냉각ΔT _△티, 핵 밀도N0N0, 재료 매개변수 n 및 핵생성 과냉각△티N△티N, Gäumann 외 여러분 에 의해 파생되었습니다 . 12 , 14 ] Hunt의 모델 11 ] 의 수정에 기반함 :

    지 =1엔 + 1- 4π _N03 인치( 1 − Φ )———√삼ΔT _( 1 -△티엔 + 1N△티엔 + 1) .G=1N+1-4파이N0삼인⁡(1-Φ)삼△티(1-△티NN+1△티N+1).(4)

    계산을 단순화하기 위해 덴드라이트 팁 과냉각을 전적으로 구성 과냉각의 것으로 추정합니다.△티씨△티씨, 멱법칙 형식으로 근사화할 수 있습니다.△티씨= ( _V티)1 / 엔△티씨=(ㅏV티)1/N, 여기서 a 와 n 은 재료 종속 상수입니다. CMSX-4의 경우 이 값은a = 1.25 ×106ㅏ=1.25×106 s K 3.4m− 1-1,엔 = 3.4N=3.4, 그리고N0= 2 ×1015N0=2×1015미디엄− 3,-삼,참고문헌 3 에 의해 보고된 바와 같이 .△티N△티N2.5K이며 보다 큰 냉각 속도에서 응고에 대해 무시할 수 있습니다.106106 K/s. 에 대한 표현ΦΦ위의 방정식을 재배열하여 해결됩니다.

    Φ= 1 -이자형에스\ 여기서\  S=- 4π _N0삼(1( 엔 + 1 ) (GN/ 아V티)1 / 엔)삼=−2.356×1019(vTG3.4)33.4.Φ=1−eS\ where\ S=−4πN03(1(n+1)(Gn/avT)1/n)3=−2.356×1019(vTG3.4)33.4.

    (5)

    As proposed by Hunt,[11] a value of Φ≤0.66Φ≤0.66 pct represents fully columnar epitaxial growth condition, and, conversely, a value of Φ≥49Φ≥49 pct indicates that the initial single crystal microstructure is fully replaced by an equiaxed microstructure. To calculate the overall stray grain area fraction, we followed Vitek’s method by dividing the FZ into roughly 19 to 28 discrete parts (depending on the length of the melt pool) of equal length from the point of maximum width to the end of melt pool along the x direction. The values of G and vTvT were determined at the center on the melt pool boundary of each section and these values were used to represent the entire section. The area-weighted average of ΦΦ over these discrete sections along the length of melt pool is designated as Φ¯¯¯¯Φ¯, and is given by:

    Φ¯¯¯¯=∑kAkΦk∑kAk,Φ¯=∑kAkΦk∑kAk,

    (6)

    where k is the index for each subsection, and AkAk and ΦkΦk are the areas and ΦΦ values for each subsection. The summation is taken over all the sections along the melt pool. Vitek’s improved model allows the calculation of stray grain area fraction by considering the melt pool geometry and variations of G and vTvT around the tail end of the pool.

    수년에 걸쳐 용융 풀 현상 모델링의 정확도를 개선하기 위해 많은 고급 수치 방법이 개발되었습니다. 우리는 FLOW-3D와 함께 고충실도 CFD를 사용했습니다. FLOW-3D는 여러 물리 모델을 통합하는 상용 FVM(Finite Volume Method)입니다. 47 , 48 ] CFD는 유체 운동과 열 전달을 수치적으로 시뮬레이션하며 여기서 사용된 기본 물리 모델은 레이저 및 표면력 모델이었습니다. 레이저 모델에서는 레이 트레이싱 기법을 통해 다중 반사와 프레넬 흡수를 구현합니다. 36 ]먼저, 레이저 빔은 레이저 빔에 의해 조명되는 각 그리드 셀을 기준으로 여러 개의 광선으로 이산화됩니다. 그런 다음 각 입사 광선에 대해 입사 벡터가 입사 위치에서 금속 표면의 법선 벡터와 정렬될 때 에너지의 일부가 금속에 의해 흡수됩니다. 흡수율은 Fresnel 방정식을 사용하여 추정됩니다. 나머지 에너지는 반사광선 에 의해 유지되며 , 반사광선은 재료 표면에 부딪히면 새로운 입사광선으로 처리됩니다. 두 가지 주요 힘이 액체 금속 표면에 작용하여 자유 표면을 변형시킵니다. 금속의 증발에 의해 생성된 반동 압력은 증기 억제를 일으키는 주요 힘입니다. 본 연구에서 사용된 반동 압력 모델은피아르 자형= 특급 _{ B ( 1- _티V/ 티) }피아르 자형=ㅏ경험치⁡{비(1-티V/티)}, 어디피아르 자형피아르 자형는 반동압력, A 와 B 는 재료의 물성에 관련된 계수로 각각 75와 15이다.티V티V는 포화 온도이고 T 는 키홀 벽의 온도입니다. 표면 흐름 및 키홀 형성의 다른 원동력은 표면 장력입니다. 표면 장력 계수는 Marangoni 흐름을 포함하기 위해 온도의 선형 함수로 추정되며,σ =1.79-9.90⋅10− 4( 티− 1654케이 )σ=1.79-9.90⋅10-4(티-1654년케이)엔엠− 1-1. 49 ] 계산 영역은 베어 플레이트의 절반입니다(2300 μμ미디엄××250 μμ미디엄××500 μμm) xz 평면 에 적용된 대칭 경계 조건 . 메쉬 크기는 8입니다. μμm이고 시간 단계는 0.15입니다. μμs는 계산 효율성과 정확성 간의 균형을 제공합니다.

    결과 및 논의

    용융 풀 형태

    이 작업에 사용된 5개의 레이저 파워( P )와 6개의 스캐닝 속도( V )는 서로 다른 29개의 용융 풀을 생성했습니다.피- 브이피-V조합. P 와 V 값이 가장 높은 것은 그림 1 을 기준으로 과도한 볼링과 관련이 있기 때문에 본 연구에서는 분석하지 않았다  .

    단일 트랙 용융 풀은 그림  1 과 같이 형상에 따라 네 가지 유형으로 분류할 수 있습니다 39 ] : (1) 전도 모드(파란색 상자), (2) 키홀 모드(빨간색), (3) 전환 모드(마젠타), (4) 볼링 모드(녹색). 높은 레이저 출력과 낮은 스캐닝 속도의 일반적인 조합인 키홀 모드에서 용융물 풀은 일반적으로 너비/깊이( W / D ) 비율이 0.5보다 훨씬 큰 깊고 가느다란 모양을 나타냅니다 . 스캐닝 속도가 증가함에 따라 용융 풀이 얕아져 W / D 가 약 0.5인 반원형 전도 모드 용융 풀을 나타냅니다. W / D _전환 모드 용융 풀의 경우 1에서 0.5 사이입니다. 스캐닝 속도를 1200 및 1400mm/s로 더 높이면 충분히 큰 캡 높이와 볼링 모드 용융 풀의 특징인 과도한 언더컷이 발생할 수 있습니다.

    힘과 속도의 함수로서의 용융 풀 깊이와 너비는 각각 그림  2 (a)와 (b)에 표시되어 있습니다. 용융 풀 폭은 기판 표면에서 측정되었습니다. 그림  2 (a)는 깊이가 레이저 출력과 매우 선형적인 관계를 따른다는 것을 보여줍니다. 속도가 증가함에 따라 깊이  파워 곡선의 기울기는 꾸준히 감소하지만 더 높은 속도 곡선에는 약간의 겹침이 있습니다. 이러한 예상치 못한 중첩은 종종 용융 풀 형태의 동적 변화를 유발하는 유체 흐름의 영향과 레이저 스캔당 하나의 이미지만 추출되었다는 사실 때문일 수 있습니다. 이러한 선형 동작은 그림 2 (b) 의 너비에 대해 명확하지 않습니다  . 그림  2(c)는 선형 에너지 밀도 P / V 의 함수로서 용융 깊이와 폭을 보여줍니다 . 선형 에너지 밀도는 퇴적물의 단위 길이당 에너지 투입량을 측정한 것입니다. 50 ] 용융 풀 깊이는 에너지 밀도에 따라 달라지며 너비는 더 많은 분산을 나타냅니다. 동일한 에너지 밀도가 준공 부품의 용융 풀, 미세 구조 또는 속성에서 반드시 동일한 유체 역학을 초래하지는 않는다는 점에 유의하는 것이 중요합니다. 50 ]

    그림 1
    그림 1
    그림 2
    그림 2

    레이저 흡수율 평가

    레이저 흡수율은 LPBF 조건에서 재료 및 가공 매개변수에 따라 크게 달라진다는 것은 잘 알려져 있습니다. 31 , 51 , 52 ] 적분구를 이용한 전통적인 흡수율의 직접 측정은 일반적으로 높은 비용과 구현의 어려움으로 인해 쉽게 접근할 수 없습니다. 51 ] 그  . 39 ] 전도 모드 용융 풀에 대한 Rosenthal 방정식을 기반으로 경험적 레이저 흡수율 모델을 개발했지만 기본 가정으로 인해 키홀 용융 풀에 대한 정확한 예측을 제공하지 못했습니다. 40 ] 최근 간 . 53 ] Ti–6Al–4V에 대한 30개의 고충실도 다중 물리 시뮬레이션 사례를 사용하여 레이저 흡수에 대한 스케일링 법칙을 확인했습니다. 그러나 연구 중인 특정 재료에 대한 최소 흡수(평평한 용융 표면의 흡수율)에 대한 지식이 필요하며 이는 CMSX-4에 대해 알려지지 않았습니다. 다양한 키홀 모양의 용융 풀에 대한 레이저 흡수의 정확한 추정치를 얻기가 어렵기 때문에 상한 및 하한 흡수율로 분석 시뮬레이션을 실행하기로 결정했습니다. 깊은 키홀 모양의 용융 풀의 경우 대부분의 빛을 가두는 키홀 내 다중 반사로 인해 레이저 흡수율이 0.8만큼 높을 수 있습니다. 이것은 기하학적 현상이며 기본 재료에 민감하지 않습니다. 5152 , 54 ] 따라서 본 연구에서는 흡수율의 상한을 0.8로 설정하였다. 참고 문헌 51 에 나타낸 바와 같이 , 전도 용융 풀에 해당하는 최저 흡수율은 약 0.3이었으며, 이는 이 연구에서 합리적인 하한 값입니다. 따라서 레이저 흡수율이 스트레이 그레인 형성에 미치는 영향을 보여주기 위해 흡수율 값을 0.55 ± 0.25로 설정했습니다. Vitek의 작업에서는 1.0의 고정 흡수율 값이 사용되었습니다. 3 ]

    퓨전 존 미세구조

    그림  3 은 200~300W 및 600~300W 및 600~300W 범위의 레이저 출력 및 속도로 9가지 다른 처리 매개변수에 의해 생성된 CMSX-4 레이저 트랙의 yz 단면 에서 취한 EBSD 역극점도와 해당 역극점도를 보여 줍니다. 각각 1400mm/s. EBSD 맵에서 여러 기능을 쉽게 관찰할 수 있습니다. 스트레이 그레인은 EBSD 맵에서 그 방향에 해당하는 다른 RGB 색상으로 나타나고 그레인 경계를 묘사하기 위해 5도의 잘못된 방향이 사용되었습니다. 여기, 그림  3 에서 스트레이 그레인은 대부분 용융 풀의 상단 중심선에 집중되어 있으며, 이는 용접된 단결정 CMSX-4의 이전 보고서와 일치합니다. 10 ]역 극점도에서, 점 근처에 집중된 클러스터⟨ 001 ⟩⟨001⟩융합 경계에서 유사한 방향을 유지하는 단결정 기반 및 에피택셜로 응고된 덴드라이트를 나타냅니다. 그러나 흩어진 곡물은 식별할 수 있는 질감이 없는 흩어져 있는 점으로 나타납니다. 단결정 기본 재료의 결정학적 방향은 주로⟨ 001 ⟩⟨001⟩비록 샘플을 절단하는 동안 식별할 수 없는 기울기 각도로 인해 또는 단결정 성장 과정에서 약간의 잘못된 방향이 있었기 때문에 약간의 편차가 있지만. 용융 풀 내부의 응고된 수상 돌기의 기본 방향은 다시 한 번⟨ 001 ⟩⟨001⟩주상 결정립 구조와 유사한 에피택셜 성장의 결과. 그림 3 과 같이 용융 풀에서 수상돌기의 성장 방향은 하단의 수직 방향에서 상단의 수평 방향으로 변경되었습니다  . 이 전이는 주로 온도 구배 방향의 변화로 인한 것입니다. 두 번째 전환은 CET입니다. FZ의 상단 중심선 주변에서 다양한 방향의 흩어진 입자가 관찰되며, 여기서 안쪽으로 성장하는 수상돌기가 서로 충돌하여 용융 풀에서 응고되는 마지막 위치가 됩니다.

    더 깊은 키홀 모양을 특징으로 하는 샘플에서 용융 풀의 경계 근처에 침전된 흩어진 입자가 분명합니다. 이러한 새로운 입자는 나중에 모델링 섹션에서 논의되는 수상돌기 조각화 메커니즘에 의해 잠재적으로 발생합니다. 결정립이 강한 열 구배에서 핵을 생성하고 성장한 결과, 대부분의 흩어진 결정립은 모든 방향에서 동일한 크기를 갖기보다는 장축이 열 구배 방향과 정렬된 길쭉한 모양을 갖습니다. 그림 3 의 전도 모드 용융 풀 흩어진 입자가 없는 것으로 입증되는 더 나은 단결정 품질을 나타냅니다. 상대적으로 낮은 출력과 높은 속도의 스캐닝 레이저에 의해 생성된 이러한 더 얕은 용융 풀에서 최소한의 결정립 핵형성이 발생한다는 것은 명백합니다. 더 큰 면적 분율을 가진 스트레이 그레인은 고출력 및 저속으로 생성된 깊은 용융 풀에서 더 자주 관찰됩니다. 국부 응고 조건에 대한 동력 및 속도의 영향은 후속 모델링 섹션에서 조사할 것입니다.

    그림 3
    그림 3

    응고 모델링

    서론에서 언급한 바와 같이 연구자들은 단결정 용접 중에 표류 결정립 형성의 가능한 메커니즘을 평가했습니다. 12 , 13 , 14 , 15 , 55 ]논의된 가장 인기 있는 두 가지 메커니즘은 (1) 응고 전단에 앞서 구성적 과냉각에 의해 도움을 받는 이종 핵형성 및 (2) 용융물 풀의 유체 흐름으로 인한 덴드라이트 조각화입니다. 첫 번째 메커니즘은 광범위하게 연구되었습니다. 이원 합금을 예로 들면, 고체는 액체만큼 많은 용질을 수용할 수 없으므로 응고 중에 용질을 액체로 거부합니다. 결과적으로, 성장하는 수상돌기 앞에서 용질 분할은 실제 온도가 국부 평형 액상선보다 낮은 과냉각 액체를 생성합니다. 충분히 광범위한 체질적으로 과냉각된 구역의 존재는 새로운 결정립의 핵형성 및 성장을 촉진합니다. 56 ]전체 과냉각은 응고 전면에서의 구성, 동역학 및 곡률 과냉각을 포함한 여러 기여의 합입니다. 일반적인 가정은 동역학 및 곡률 과냉각이 합금에 대한 용질 과냉각의 더 큰 기여와 관련하여 무시될 수 있다는 것입니다. 57 ]

    서로 다른 기본 메커니즘을 더 잘 이해하려면피- 브이피-V조건에서 응고 모델링이 수행됩니다. 첫 번째 목적은 스트레이 그레인의 전체 범위를 평가하는 것입니다(Φ¯¯¯¯Φ¯) 처리 매개 변수의 함수로 국부적 표류 입자 비율의 변화를 조사하기 위해 (ΦΦ) 용융 풀의 위치 함수로. 두 번째 목적은 금속 AM의 빠른 응고 동안 응고 미세 구조와 표류 입자 형성 메커니즘 사이의 관계를 이해하는 것입니다.

    그림 4
    그림 4

    그림  4 는 해석적으로 시뮬레이션된 표류 입자 비율을 보여줍니다.Φ¯¯¯¯Φ¯세 가지 레이저 흡수율 값에서 다양한 레이저 스캐닝 속도 및 레이저 출력에 대해. 결과는 스트레이 그레인 면적 비율이 흡수된 에너지에 민감하다는 것을 보여줍니다. 흡수율을 0.30에서 0.80으로 증가시키면Φ¯¯¯¯Φ¯약 3배이며, 이 효과는 저속 및 고출력 영역에서 더욱 두드러집니다. 다른 모든 조건이 같다면, 흡수된 전력의 큰 영향은 평균 열 구배 크기의 일반적인 감소와 용융 풀 내 평균 응고율의 증가에 기인합니다. 스캐닝 속도가 증가하고 전력이 감소함에 따라 평균 스트레이 그레인 비율이 감소합니다. 이러한 일반적인 경향은 Vitek의 작업에서 채택된 그림 5 의 파란색 영역에서 시뮬레이션된 용접 결과와 일치합니다  . 3 ] 더 큰 과냉각 구역( 즉, 지 /V티G/V티영역)은 용접 풀의 표유 입자의 면적 비율이 분홍색 영역에 해당하는 LPBF 조건의 면적 비율보다 훨씬 더 크다는 것을 의미합니다. 그럼에도 불구하고 두 데이터 세트의 일반적인 경향은 유사합니다.  , 레이저 출력이 감소하고 레이저 속도가 증가함에 따라 표류 입자의 비율이 감소합니다. 또한 그림  5 에서 스캐닝 속도가 LPBF 영역으로 증가함에 따라 표유 입자 면적 분율에 대한 레이저 매개변수의 변화 효과가 감소한다는 것을 추론할 수 있습니다. 그림  6 (a)는 그림 3 의 EBSD 분석에서 나온 실험적 표류 결정립 면적 분율  과 그림 4 의 해석 시뮬레이션 결과를  비교합니다.. 열쇠 구멍 모양의 FZ에서 정확한 값이 다르지만 추세는 시뮬레이션과 실험 데이터 모두에서 일관되었습니다. 키홀 모양의 용융 풀, 특히 전력이 300W인 2개는 분석 시뮬레이션 예측보다 훨씬 더 많은 양의 흩어진 입자를 가지고 있습니다. Rosenthal 방정식은 일반적으로 열 전달이 순전히 전도에 의해 좌우된다는 가정으로 인해 열쇠 구멍 체제의 열 흐름을 적절하게 반영하지 못하기 때문에 이러한 불일치가 실제로 예상됩니다. 39 , 40 ] 그것은 또한 그림  4 의 발견 , 즉 키홀 모드 동안 흡수된 전력의 증가가 표류 입자 형성에 더 이상적인 조건을 초래한다는 것을 검증합니다. 그림  6 (b)는 실험을 비교Φ¯¯¯¯Φ¯수치 CFD 시뮬레이션Φ¯¯¯¯Φ¯. CFD 모델이 약간 초과 예측하지만Φ¯¯¯¯Φ¯전체적으로피- 브이피-V조건에서 열쇠 구멍 조건에서의 예측은 분석 모델보다 정확합니다. 전도 모드 용융 풀의 경우 실험 값이 분석 시뮬레이션 값과 더 가깝게 정렬됩니다.

    그림 5
    그림 5

    모의 온도 구배 G 분포 및 응고율 검사V티V티분석 모델링의 쌍은 그림  7 (a)의 CMSX-4 미세 구조 선택 맵에 표시됩니다. 제공지 /V티G/V티(  , 형태 인자)는 형태를 제어하고지 ×V티G×V티(  , 냉각 속도)는 응고된 미세 구조의 규모를 제어하고 , 58 , 59 ]지 -V티G-V티플롯은 전통적인 제조 공정과 AM 공정 모두에서 미세 구조 제어를 지원합니다. 이 플롯의 몇 가지 분명한 특징은 등축, 주상, 평면 전면 및 이러한 경계 근처의 전이 영역을 구분하는 경계입니다. 그림  7 (a)는 몇 가지 선택된 분석 열 시뮬레이션에 대한 미세 구조 선택 맵을 나타내는 반면 그림  7 (b)는 수치 열 모델의 결과와 동일한 맵을 보여줍니다. 등축 미세구조의 형성은 낮은 G 이상 에서 명확하게 선호됩니다.V티V티정황. 이 플롯에서 각 곡선의 평면 전면에 가장 가까운 지점은 용융 풀의 최대 너비 위치에 해당하는 반면 등축 영역에 가까운 지점의 끝은 용융 풀의 후면 꼬리에 해당합니다. 그림  7 (a)에서 대부분의지 -V티G-V티응고 전면의 쌍은 원주형 영역에 속하고 점차 CET 영역으로 위쪽으로 이동하지만 용융 풀의 꼬리는 다음에 따라 완전히 등축 영역에 도달하거나 도달하지 않을 수 있습니다.피- 브이피-V조합. 그림 7 (a) 의 곡선 중 어느 것도  평면 전면 영역을 통과하지 않지만 더 높은 전력의 경우에 가까워집니다. 저속 레이저 용융 공정을 사용하는 이전 작업에서는 곡선이 평면 영역을 통과할 수 있습니다. 레이저 속도가 증가함에 따라 용융 풀 꼬리는 여전히 CET 영역에 있지만 완전히 등축 영역에서 멀어집니다. CET 영역으로 떨어지는 섹션의 수도 감소합니다.Φ¯¯¯¯Φ¯응고된 물질에서.

    그림 6
    그림 6

    그만큼지 -V티G-V티CFD 모델을 사용하여 시뮬레이션된 응고 전면의 쌍이 그림  7 (b)에 나와 있습니다. 세 방향 모두에서 각 점 사이의 일정한 간격으로 미리 정의된 좌표에서 수행된 해석 시뮬레이션과 달리, 고충실도 CFD 모델의 출력은 불규칙한 사면체 좌표계에 있었고 G 를 추출하기 전에 일반 3D 그리드에 선형 보간되었습니다. 그리고V티V티그런 다음 미세 구조 선택 맵에 플롯됩니다. 일반적인 경향은 그림  7 (a)의 것과 일치하지만 이 방법으로 모델링된 매우 동적인 유체 흐름으로 인해 결과에 더 많은 분산이 있었습니다. 그만큼지 -V티G-V티분석 열 모델의 쌍 경로는 더 연속적인 반면 수치 시뮬레이션의 경로는 용융 풀 꼬리 모양의 차이를 나타내는 날카로운 굴곡이 있습니다(이는 G 및V티V티) 두 모델에 의해 시뮬레이션됩니다.

    그림 7
    그림 7
    그림 8
    그림 8

    유체 흐름을 통합한 응고 모델링

    수치 CFD 모델을 사용하여 유동 입자 형성 정도에 대한 유체 흐름의 영향을 이해하고 시뮬레이션 결과를 분석 Rosenthal 솔루션과 비교했습니다. 그림  8 은 응고 매개변수 G 의 분포를 보여줍니다.V티V티,지 /V티G/V티, 그리고지 ×V티G×V티yz 단면에서 x  FLOW-3D에서 (a1–d1) 분석 열 모델링 및 (a2–d2) FVM 방법을 사용하여 시뮬레이션된 용융 풀의 최대 폭입니다. 그림  8 의 값은 응고 전선이 특정 위치에 도달할 때 정확한 값일 수도 있고 아닐 수도 있지만 일반적인 추세를 반영한다는 의미의 임시 가상 값입니다. 이 프로파일은 출력 300W 및 속도 400mm/s의 레이저 빔에서 시뮬레이션됩니다. 용융 풀 경계는 흰색 곡선으로 표시됩니다. (a2–d2)의 CFD 시뮬레이션 용융 풀 깊이는 342입니다. μμm, 측정 깊이 352와 잘 일치 μμ일치하는 길쭉한 열쇠 구멍 모양과 함께 그림 1 에 표시된 실험 FZ의 m  . 그러나 분석 모델은 반원 모양의 용융 풀을 출력하고 용융 풀 깊이는 264에 불과합니다. μμ열쇠 구멍의 경우 현실과는 거리가 멀다. CFD 시뮬레이션 결과에서 열 구배는 레이저 반사 증가와 불안정한 액체-증기 상호 작용이 발생하는 증기 함몰의 동적 부분 근처에 있기 때문에 FZ 하단에서 더 높습니다. 대조적으로 해석 결과의 열 구배 크기는 경계를 따라 균일합니다. 두 시뮬레이션 결과 모두 그림 8 (a1) 및 (a2) 에서 응고가 용융 풀의 상단 중심선을 향해 진행됨에 따라 열 구배가 점차 감소합니다  . 응고율은 그림 8 과 같이 경계 근처에서 거의 0입니다. (b1) 및 (b2). 이는 경계 영역이 응고되기 시작할 때 국부 응고 전면의 법선 방향이 레이저 스캐닝 방향에 수직이기 때문입니다. 이것은 드라이브θ → π/ 2θ→파이/2그리고V티→ 0V티→0식에서 [ 3 ]. 대조적으로 용융 풀의 상단 중심선 근처 영역에서 응고 전면의 법선 방향은 레이저 스캐닝 방향과 잘 정렬되어 있습니다.θ → 0θ→0그리고V티→ 브이V티→V, 빔 스캐닝 속도. G 와 _V티V티값이 얻어지면 냉각 속도지 ×V티G×V티및 형태 인자지 /V티G/V티계산할 수 있습니다. 그림 8 (c2)는 용융 풀 바닥 근처의 온도 구배가 매우 높고 상단에서 더 빠른 성장 속도로  인해 냉각 속도가 용융 풀의 바닥 및 상단 중심선 근처에서 더 높다는 것을 보여줍니다. 지역. 그러나 이러한 추세는 그림  8 (c1)에 캡처되지 않았습니다. 그림 8 의 형태 요인 (d1) 및 (d2)는 중심선에 접근함에 따라 눈에 띄게 감소합니다. 경계에서 큰 값은 열 구배를 거의 0인 성장 속도로 나누기 때문에 발생합니다. 이 높은 형태 인자는 주상 미세구조 형성 가능성이 높음을 시사하는 반면, 중앙 영역의 값이 낮을수록 등축 미세구조의 가능성이 더 크다는 것을 나타냅니다. Tanet al. 또한 키홀 모양의 용접 풀 59 ] 에서 이러한 응고 매개변수의 분포 를 비슷한 일반적인 경향으로 보여주었습니다. 그림  3 에서 볼 수 있듯이 용융 풀의 상단 중심선에 있는 흩어진 입자는 낮은 특징을 나타내는 영역과 일치합니다.지 /V티G/V티그림  8 (d1) 및 (d2)의 값. 시뮬레이션과 실험 간의 이러한 일치는 용융 풀의 상단 중심선에 축적된 흩어진 입자의 핵 생성 및 성장이 등온선 속도의 증가와 온도 구배의 감소에 의해 촉진됨을 보여줍니다.

    그림 9
    그림 9

    그림  9 는 유체 속도 및 국부적 핵형성 성향을 보여줍니다.ΦΦ300W의 일정한 레이저 출력과 400, 800 및 1200mm/s의 세 가지 다른 레이저 속도에 의해 생성된 3D 용융 풀 전체에 걸쳐. 그림  9 (d)~(f)는 로컬ΦΦ해당 3D 보기에서 밝은 회색 평면으로 표시된 특정 yz 단면의 분포. 이 yz 섹션은 가장 높기 때문에 선택되었습니다.Φ¯¯¯¯Φ¯용융 풀 내의 값은 각각 23.40, 11.85 및 2.45pct입니다. 이들은 그림  3 의 실험 데이터와 비교하기에 적절하지 않을 수 있는 액체 용융 풀의 과도 값이며Φ¯¯¯¯Φ¯그림  6 의 값은 이 값이 고체-액체 계면에 가깝지 않고 용융 풀의 중간에서 취해졌기 때문입니다. 온도가 훨씬 낮아서 핵이 생존하고 성장할 수 있기 때문에 핵 형성은 용융 풀의 중간이 아닌 고체-액체 계면에 더 가깝게 발생할 가능성이 있습니다.

    그림  3 (a), (d), (g), (h)에서 위쪽 중심선에서 멀리 떨어져 있는 흩어진 결정립이 있었습니다. 그들은 훨씬 더 높은 열 구배와 더 낮은 응고 속도 필드에 위치하기 때문에 과냉각 이론은 이러한 영역에서 표류 입자의 형성에 대한 만족스러운 설명이 아닙니다. 이것은 떠돌이 결정립의 형성을 야기할 수 있는 두 번째 메커니즘,  수상돌기의 팁을 가로지르는 유체 흐름에 의해 유발되는 수상돌기 조각화를 고려하도록 동기를 부여합니다. 유체 흐름이 열 구배를 따라 속도 성분을 갖고 고체-액체 계면 속도보다 클 때, 주상 수상돌기의 국지적 재용융은 용질이 풍부한 액체가 흐물흐물한 구역의 깊은 곳에서 액상선 등온선까지 이동함으로써 발생할 수 있습니다. . 55] 분리된 수상돌기는 대류에 의해 열린 액체로 운반될 수 있습니다. 풀이 과냉각 상태이기 때문에 이러한 파편은 고온 조건에서 충분히 오래 생존하여 길 잃은 입자의 핵 생성 사이트로 작용할 수 있습니다. 결과적으로 수상 돌기 조각화 과정은 활성 핵의 수를 효과적으로 증가시킬 수 있습니다.N0N0) 용융 풀 15 , 60 , 61 ] 에서 생성된 미세 구조에서 표류 입자의 면적을 증가시킵니다.

    그림  9 (a) 및 (b)에서 반동 압력은 용융 유체를 아래쪽으로 흐르게 하여 결과 흐름을 지배합니다. 유체 속도의 역방향 요소는 V = 400 및 800mm/s에 대해 각각 최대값 1.0 및 1.6m/s로 더 느려집니다 . 그림  9 (c)에서 레이저 속도가 더 증가함에 따라 증기 침하가 더 얕고 넓어지고 반동 압력이 더 고르게 분포되어 증기 침강에서 주변 영역으로 유체를 밀어냅니다. 역류는 최대값 3.5m/s로 더 빨라집니다. 용융 풀의 최대 너비에서 yz 단면  의 키홀 아래 평균 유체 속도는 그림에 표시된 경우에 대해 0.46, 0.45 및 1.44m/s입니다.9 (a), (b) 및 (c). 키홀 깊이의 변동은 각 경우의 최대 깊이와 최소 깊이의 차이로 정의되는 크기로 정량화됩니다. 240 범위의 강한 증기 내림 변동 μμm은 그림 9 (a)의 V = 400mm/s 경우에서  발견 되지만 이 변동은 그림  9 (c)에서 16의 범위로  크게 감소합니다.μμ미디엄. V = 400mm/s인 경우 의 유체장과 높은 변동 범위는 이전 키홀 동역학 시뮬레이션과 일치합니다. 34 ]

    따라서 V = 400mm/s 키홀 케이스의 무질서한 변동 흐름이 용융 풀 경계를 따라 응고된 주상 수상돌기에서 분리된 조각을 구동할 가능성이 있습니다. V = 1200mm/s의 경우 강한 역류 는 그림 3 에서 관찰되지 않았지만 동일한 효과를 가질 수 있습니다. . 덴드라이트 조각화에 대한 유체 유동장의 영향에 대한 이 경험적 설명은 용융 풀 경계 근처에 떠돌이 입자의 존재에 대한 그럴듯한 설명을 제공합니다. 분명히 하기 위해, 우리는 이 가설을 검증하기 위해 이 현상에 대한 직접적인 실험적 관찰을 하지 않았습니다. 이 작업에서 표유 입자 면적 분율을 계산할 때 단순화를 위해 핵 생성 모델링에 일정한 핵 생성 수 밀도가 적용되었습니다. 이는 그림  9 의 표류 입자 영역 비율 이 수지상정 조각화가 발생하는 경우 이러한 높은 유체 흐름 용융 풀에서 발생할 수 있는 것,  강화된 핵 생성 밀도를 반영하지 않는다는 것을 의미합니다.

    위의 이유로 핵 형성에 대한 수상 돌기 조각화의 영향을 아직 배제할 수 없습니다. 그러나 단편화 이론은 용접 문헌 [ 62 ] 에서 검증될 만큼 충분히 개발되지 않았 으므로 부차적인 중요성만 고려된다는 점에 유의해야 합니다. 1200mm/s를 초과하는 레이저 스캐닝 속도는 최소한의 표류 결정립 면적 분율을 가지고 있음에도 불구하고 분명한 볼링을 나타내기 때문에 단결정 수리 및 AM 처리에 적합하지 않습니다. 따라서 낮은 P 및 높은 V 에 의해 생성된 응고 전면 근처에서 키홀 변동이 최소화되고 유체 속도가 완만해진 용융 풀이 생성된다는 결론을 내릴 수 있습니다., 처리 창의 극한은 아니지만 흩어진 입자를 나타낼 가능성이 가장 적습니다.

    마지막으로 단일 레이저 트랙의 응고 거동을 조사하면 에피택셜 성장 동안 표류 입자 형성을 더 잘 이해할 수 있다는 점에 주목하는 것이 중요합니다. 우리의 현재 결과는 최적의 레이저 매개변수에 대한 일반적인 지침을 제공하여 최소 스트레이 그레인을 달성하고 단결정 구조를 유지합니다. 이 가이드라인은 250W 정도의 전력과 600~800mm/s의 스캔 속도로 최소 흩어진 입자에 적합한 공정 창을 제공합니다. 각 처리 매개변수를 신중하게 선택하면 과거에 스테인리스강에 대한 거의 단결정 미세 구조를 인쇄하는 데 성공했으며 이는 CMSX-4 AM 빌드에 대한 가능성을 보여줍니다. 63 ]신뢰성을 보장하기 위해 AM 수리 프로세스를 시작하기 전에 보다 엄격한 실험 테스트 및 시뮬레이션이 여전히 필요합니다. 둘 이상의 레이저 트랙 사이의 상호 작용도 고려해야 합니다. 또한 레이저, CMSX-4 분말 및 벌크 재료 간의 상호 작용이 중요하며, 수리 중에 여러 층의 CMSX-4 재료를 축적해야 하는 경우 다른 스캔 전략의 효과도 중요한 역할을 할 수 있습니다. 분말이 포함된 경우 Lopez-Galilea 등 의 연구에서 제안한 바와 같이 분말이 주로 완전히 녹지 않았을 때 추가 핵 생성 사이트를 도입하기 때문에 단순히 레이저 분말과 속도를 조작하여 흩어진 입자 형성을 완화하기 어려울 수 있습니다 . 22 ]결과적으로 CMSX-4 단결정을 수리하기 위한 레이저 AM의 가능성을 다루기 위해서는 기판 재료, 레이저 출력, 속도, 해치 간격 및 층 두께의 조합을 모두 고려해야 하며 향후 연구에서 다루어야 합니다. CFD 모델링은 2개 이상의 레이저 트랙 사이의 상호작용과 열장에 미치는 영향을 통합할 수 있으며, 이는 AM 빌드 시나리오 동안 핵 생성 조건으로 단일 비드 연구의 지식 격차를 해소할 것입니다.

    결론

    LPBF 제조의 특징적인 조건 하에서 CMSX-4 단결정 의 에피택셜(기둥형)  등축 응고 사이의 경쟁을 실험적 및 이론적으로 모두 조사했습니다. 이 연구는 고전적인 응고 개념을 도입하여 빠른 레이저 용융의 미세 구조 특징을 설명하고 응고 조건과 표유 결정 성향을 예측하기 위해 해석적 및 수치적 고충실도 CFD 열 모델 간의 비교를 설명했습니다. 본 연구로부터 다음과 같은 주요 결론을 도출할 수 있다.

    • 단일 레이저 트랙의 레이저 가공 조건은 용융 풀 형상, 레이저 흡수율, 유체 흐름 및 키홀 요동, 입자 구조 및 표류 입자 형성 민감성에 강한 영향을 미치는 것으로 밝혀졌습니다.
    • 레이저 용접을 위해 개발된 이론적인 표유 결정립 핵형성 분석이 레이저 용융 AM 조건으로 확장되었습니다. 분석 모델링 결과와 단일 레이저 트랙의 미세구조 특성화를 비교하면 예측이 전도 및 볼링 조건에서 실험적 관찰과 잘 일치하는 반면 키홀 조건에서는 예측이 약간 과소하다는 것을 알 수 있습니다. 이러한 불일치는 레이저 트랙의 대표성이 없는 섹션이나 유체 속도 필드의 변화로 인해 발생할 수 있습니다. CFD 모델에서 추출한 열장에 동일한 표유 입자 계산 파이프라인을 적용하면 연구된 모든 사례에서 과대평가가 발생하지만 분석 모델보다 연장된 용융 풀의 실험 데이터와 더 정확하게 일치합니다.
    • 이 연구에서 두 가지 표류 결정립 형성 메커니즘인 불균일 핵형성 및 수상돌기 조각화가 평가되었습니다. 우리의 결과는 불균일 핵형성이 용융 풀의 상단 중심선에서 새로운 결정립의 형성으로 이어지는 주요 메커니즘임을 시사합니다.지 /V티G/V티정권.
    • 용융 풀 경계 근처의 흩어진 입자는 깊은 키홀 모양의 용융 풀에서 독점적으로 관찰되며, 이는 강한 유체 흐름으로 인한 수상 돌기 조각화의 영향이 이러한 유형의 용융 풀에서 고려하기에 충분히 강력할 수 있음을 시사합니다.
    • 일반적으로 더 높은 레이저 스캐닝 속도와 더 낮은 전력 외에도 안정적인 키홀과 최소 유체 속도는 또한 흩어진 입자 형성을 완화하고 레이저 단일 트랙에서 에피택셜 성장을 보존합니다.

    References

    1. R.C. Reed: The Superalloys: Fundamentals and Applications, Cambridge University Press, Cambridge, 2006, pp.17–20.Book Google Scholar 
    2. A. Basak, R. Acharya, and S. Das: Metall. Mater. Trans. A, 2016, vol. 47A, pp. 3845–59.Article Google Scholar 
    3. J. Vitek: Acta Mater., 2005, vol. 53, pp. 53–67.Article CAS Google Scholar 
    4. R. Vilar and A. Almeida: J. Laser Appl., 2015, vol. 27, p. S17004.Article Google Scholar 
    5. T. Kalfhaus, M. Schneider, B. Ruttert, D. Sebold, T. Hammerschmidt, J. Frenzel, R. Drautz, W. Theisen, G. Eggeler, O. Guillon, and R. Vassen: Mater. Des., 2019, vol. 168, p. 107656.Article CAS Google Scholar 
    6. S.S. Babu, S.A. David, J.W. Park, and J.M. Vitek: Sci. Technol. Weld. Join., 2004, vol. 9, pp. 1–12.Article CAS Google Scholar 
    7. L. Felberbaum, K. Voisey, M. Gäumann, B. Viguier, and A. Mortensen: Mater. Sci. Eng. A, 2001, vol. 299, pp. 152–56.Article Google Scholar 
    8. S. Mokadem, C. Bezençon, J.M. Drezet, A. Jacot, J.D. Wagnière, and W. Kurz: TMS Annual Meeting, 2004, pp. 67–76.
    9. J.M. Vitek: ASM Proc. Int. Conf. Trends Weld. Res., vol. 2005, pp. 773–79.
    10. J.M. Vitek, S. Babu, and S. David: Process Optimization for Welding Single-Crystal Nickel-Bbased Superalloyshttps://technicalreports.ornl.gov/cppr/y2001/pres/120424.pdf
    11. J.D. Hunt: Mater. Sci. Eng., 1984, vol. 65, pp. 75–83.Article CAS Google Scholar 
    12. M. Gäumann, R. Trivedi, and W. Kurz: Mater. Sci. Eng. A, 1997, vol. 226–228, pp. 763–69.Article Google Scholar 
    13. M. Gäumann, S. Henry, F. Cléton, J.D. Wagnière, and W. Kurz: Mater. Sci. Eng. A, 1999, vol. 271, pp. 232–41.Article Google Scholar 
    14. M. Gäumann, C. Bezençon, P. Canalis, and W. Kurz: Acta Mater., 2001, vol. 49, pp. 1051–62.Article Google Scholar 
    15. J.M. Vitek, S.A. David, and S.S. Babu: Welding and Weld Repair of Single Crystal Gas Turbine Alloyshttps://www.researchgate.net/profile/Stan-David/publication/238692931_WELDING_AND_WELD_REPAIR_OF_SINGLE_CRYSTAL_GAS_TURBINE_ALLOYS/links/00b4953204ab35bbad000000/WELDING-AND-WELD-REPAIR-OF-SINGLE-CRYSTAL-GAS-TURBINE-ALLOYS.pdf
    16. B. Kianian: Wohlers Report 2017: 3D Printing and Additive Manufacturing State of the Industry, Annual Worldwide Progress Report, Wohlers Associates, Inc., Fort Collins, 2017.Google Scholar 
    17. M. Ramsperger, L. Mújica Roncery, I. Lopez-Galilea, R.F. Singer, W. Theisen, and C. Körner: Adv. Eng. Mater., 2015, vol. 17, pp. 1486–93.Article CAS Google Scholar 
    18. A.B. Parsa, M. Ramsperger, A. Kostka, C. Somsen, C. Körner, and G. Eggeler: Metals, 2016, vol. 6, pp. 258-1–17.Article Google Scholar 
    19. C. Körner, M. Ramsperger, C. Meid, D. Bürger, P. Wollgramm, M. Bartsch, and G. Eggeler: Metall. Mater. Trans. A, 2018, vol. 49A, pp. 3781–92.Article Google Scholar 
    20. D. Bürger, A. Parsa, M. Ramsperger, C. Körner, and G. Eggeler: Mater. Sci. Eng. A, 2019, vol. 762, p. 138098,Article Google Scholar 
    21. J. Pistor and C. Körner: Sci. Rep., 2021, vol. 11, p. 24482.Article CAS Google Scholar 
    22. I. Lopez-Galilea, B. Ruttert, J. He, T. Hammerschmidt, R. Drautz, B. Gault, and W. Theisen: Addit. Manuf., 2019, vol. 30, p. 100874.CAS Google Scholar 
    23. N. Lu, Z. Lei, K. Hu, X. Yu, P. Li, J. Bi, S. Wu, and Y. Chen: Addit. Manuf., 2020, vol. 34, p. 101228.CAS Google Scholar 
    24. K. Chen, R. Huang, Y. Li, S. Lin, W. Zhu, N. Tamura, J. Li, Z.W. Shan, and E. Ma: Adv. Mater., 2020, vol. 32, pp. 1–8.Google Scholar 
    25. W.J. Sames, F.A. List, S. Pannala, R.R. Dehoff, and S.S. Babu: Int. Mater. Rev., 2016, vol. 61, pp. 315–60.Article Google Scholar 
    26. A. Basak, R. Acharya, and S. Das: Addit. Manuf., 2018, vol. 22, pp. 665–71.CAS Google Scholar 
    27. R. Jiang, A. Mostafaei, J. Pauza, C. Kantzos, and A.D. Rollett: Mater. Sci. Eng. A, 2019. https://doi.org/10.1016/J.MSEA.2019.03.103.Article Google Scholar 
    28. R. Cunningham, C. Zhao, N. Parab, C. Kantzos, J. Pauza, K. Fezzaa, T. Sun, and A.D. Rollett: Science, 2019, vol. 363, pp. 849–52.Article CAS Google Scholar 
    29. B. Fotovvati, S.F. Wayne, G. Lewis, and E. Asadi: Adv. Mater. Sci. Eng., 2018, vol. 2018, p. 4920718.Article Google Scholar 
    30. P.-J. Chiang, R. Jiang, R. Cunningham, N. Parab, C. Zhao, K. Fezzaa, T. Sun, and A.D. Rollett: in Advanced Real Time Imaging II, pp. 77–85.
    31. J. Ye, S.A. Khairallah, A.M. Rubenchik, M.F. Crumb, G. Guss, J. Belak, and M.J. Matthews: Adv. Eng. Mater., 2019, vol. 21, pp. 1–9.Article Google Scholar 
    32. C. Zhao, Q. Guo, X. Li, N. Parab, K. Fezzaa, W. Tan, L. Chen, and T. Sun: Phys. Rev. X, 2019, vol. 9, p. 021052.CAS Google Scholar 
    33. S.A. Khairallah, A.T. Anderson, A. Rubenchik, and W.E. King: Acta Mater., 2016, vol. 108, pp. 36–45.Article CAS Google Scholar 
    34. N. Kouraytem, X. Li, R. Cunningham, C. Zhao, N. Parab, T. Sun, A.D. Rollett, A.D. Spear, and W. Tan: Appl. Phys. Rev., 2019, vol. 11, p. 064054.Article CAS Google Scholar 
    35. T. DebRoy, H. Wei, J. Zuback, T. Mukherjee, J. Elmer, J. Milewski, A. Beese, A. Wilson-Heid, A. De, and W. Zhang: Prog. Mater. Sci., 2018, vol. 92, pp. 112–224.Article CAS Google Scholar 
    36. J.H. Cho and S.J. Na: J. Phys. D, 2006, vol. 39, pp. 5372–78.Article CAS Google Scholar 
    37. I. Yadroitsev, A. Gusarov, I. Yadroitsava, and I. Smurov: J. Mater. Process. Technol., 2010, vol. 210, pp. 1624–31.Article CAS Google Scholar 
    38. S. Ghosh, L. Ma, L.E. Levine, R.E. Ricker, M.R. Stoudt, J.C. Heigel, and J.E. Guyer: JOM, 2018, vol. 70, pp. 1011–16.Article CAS Google Scholar 
    39. Y. He, C. Montgomery, J. Beuth, and B. Webler: Mater. Des., 2019, vol. 183, p. 108126.Article CAS Google Scholar 
    40. D. Rosenthal: Weld. J., 1941, vol. 20, pp. 220–34.Google Scholar 
    41. M. Tang, P.C. Pistorius, and J.L. Beuth: Addit. Manuf., 2017, vol. 14, pp. 39–48.CAS Google Scholar 
    42. R.E. Aune, L. Battezzati, R. Brooks, I. Egry, H.J. Fecht, J.P. Garandet, M. Hayashi, K.C. Mills, A. Passerone, P.N. Quested, E. Ricci, F. Schmidt-Hohagen, S. Seetharaman, B. Vinet, and R.K. Wunderlich: Proc. Int.Symp. Superalloys Var. Deriv., 2005, pp. 467–76.
    43. B.C. Wilson, J.A. Hickman, and G.E. Fuchs: JOM, 2003, vol. 55, pp. 35–40.Article CAS Google Scholar 
    44. J.J. Valencia and P.N. Quested: ASM Handb., 2008, vol. 15, pp. 468–81.Google Scholar 
    45. H.L. Wei, J. Mazumder, and T. DebRoy: Sci. Rep., 2015, vol. 5, pp. 1–7.Google Scholar 
    46. N. Raghavan, R. Dehoff, S. Pannala, S. Simunovic, M. Kirka, J. Turner, N. Carlson, and S.S. Babu: Acta Mater., 2016, vol. 112, pp. 303–14.Article CAS Google Scholar 
    47. R. Lin, H. Wang, F. Lu, J. Solomon, and B.E. Carlson: Int. J. Heat Mass Transf., 2017, vol. 108, pp. 244–56.Article CAS Google Scholar 
    48. M. Bayat, A. Thanki, S. Mohanty, A. Witvrouw, S. Yang, J. Thorborg, N.S. Tiedje, and J.H. Hattel: Addit. Manuf., 2019, vol. 30, p. 100835.CAS Google Scholar 
    49. K. Higuchi, H.-J. Fecht, and R.K. Wunderlich: Adv. Eng. Mater., 2007, vol. 9, pp. 349–54.Article CAS Google Scholar 
    50. Q. Guo, C. Zhao, M. Qu, L. Xiong, L.I. Escano, S.M.H. Hojjatzadeh, N.D. Parab, K. Fezzaa, W. Everhart, T. Sun, and L. Chen: Addit. Manuf., 2019, vol. 28, pp. 600–09.Google Scholar 
    51. J. Trapp, A.M. Rubenchik, G. Guss, and M.J. Matthews: Appl. Mater. Today, 2017, vol. 9, pp. 341–49.Article Google Scholar 
    52. M. Schneider, L. Berthe, R. Fabbro, and M. Muller: J. Phys. D, 2008, vol. 41, p. 155502.Article Google Scholar 
    53. Z. Gan, O.L. Kafka, N. Parab, C. Zhao, L. Fang, O. Heinonen, T. Sun, and W.K. Liu: Nat. Commun., 2021, vol. 12, p. 2379.Article CAS Google Scholar 
    54. B.J. Simonds, E.J. Garboczi, T.A. Palmer, and P.A. Williams: Appl. Phys. Rev., 2020, vol. 13, p. 024057.Article CAS Google Scholar 
    55. J. Dantzig and M. Rappaz: Solidification, 2nd ed., EPFL Press, Lausanne, 2016, pp. 483–532.Google Scholar 
    56. W. Tiller, K. Jackson, J. Rutter, and B. Chalmers: Acta Metall., 1953, vol. 1, pp. 428–37.Article CAS Google Scholar 
    57. D. Zhang, A. Prasad, M.J. Bermingham, C.J. Todaro, M.J. Benoit, M.N. Patel, D. Qiu, D.H. StJohn, M. Qian, and M.A. Easton: Metall. Mater. Trans. A, 2020, vol. 51A, pp. 4341–59.Article Google Scholar 
    58. F. Yan, W. Xiong, and E.J. Faierson: Materials, 2017, vol. 10, p. 1260.Article Google Scholar 
    59. W. Tan and Y.C. Shin: Comput. Mater. Sci., 2015, vol. 98, pp. 446–58.Article CAS Google Scholar 
    60. A. Hellawell, S. Liu, and S.Z. Lu: JOM, 1997, vol. 49, pp. 18–20.Article CAS Google Scholar 
    61. H. Ji: China Foundry, 2019, vol. 16, pp. 262–66.Article Google Scholar 
    62. J.M. Vitek, S.A. David, and L.A. Boatner: Sci. Technol. Weld. Join., 1997, vol. 2, pp. 109–18.Article CAS Google Scholar 
    63. X. Wang, J.A. Muñiz-Lerma, O. Sanchez-Mata, S.E. Atabay, M.A. Shandiz, and M. Brochu: Prog. Addit. Manuf., 2020, vol. 5, pp. 41–49.Article Google Scholar 

    Download references

    Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

    Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

    범람으로 인한 비점착성 흙댐 붕괴에 대한 테일워터 깊이의 영향

    ShaimaaAmanaMohamedAbdelrazek RezkbRabieaNasrc

    Abstract

    본 연구에서는 범람으로 인한 토사댐 붕괴에 대한 테일워터 깊이의 영향을 실험적으로 조사하였다. 테일워터 깊이의 네 가지 다른 값을 검사합니다. 각 실험에 대해 댐 수심 측량 프로파일의 진화, 고장 기간, 침식 체적 및 유출 수위곡선을 관찰하고 기록합니다.

    결과는 tailwater 깊이를 늘리면 고장 시간이 최대 57% 감소하고 상대적으로 침식된 마루 높이가 최대 77.6% 감소한다는 것을 보여줍니다. 또한 상대 배수 깊이가 3, 4, 5인 경우 누적 침식 체적의 감소는 각각 23, 36.5 및 75%인 반면 최대 유출량의 감소는 각각 7, 14 및 17.35%입니다.

    실험 결과는 침식 과정을 복제할 때 Flow 3D 소프트웨어의 성능을 평가하는 데 활용됩니다. 수치 모델은 비응집성 흙댐의 침식 과정을 성공적으로 시뮬레이션합니다.

    The influence of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. Four different values of tailwater depths are examined. For each experiment, the evolution of the dam bathymetry profile, the duration of failure, the eroded volume, and the outflow hydrograph are observed and recorded. The results reveal that increasing the tailwater depth reduces the time of failure by up to 57% and decreases the relative eroded crest height by up to 77.6%. In addition, for relative tailwater depths equal to 3, 4, and 5, the reduction in the cumulative eroded volume is 23, 36.5, and 75%, while the reduction in peak discharge is 7, 14, and 17.35%, respectively. The experimental results are utilized to evaluate the performance of the Flow 3D software in replicating the erosion process. The numerical model successfully simulates the erosion process of non-cohesive earth dams.

    Keywords

    Earth dam, Eroded volume, Flow 3D model, Non-cohesive soil, Overtopping failure, Tailwater depth

    Notation

    d50

    Mean partical diameterWc

    Optimum water contentZo

    Dam height (cm)do

    Tailwater depth (cm)Zeroded

    Eroded height of the dam measured at distance of 0.7 m from the dam heel (cm)t

    Total time of failure (sec)t1

    Time of crest width erosion (sec)Zcrest

    The crest height (cm)Vtotal

    Total volume of the dam (m3)Veroded

    Cumulative eroded volume (m3)RMSE

    The statistical variable root- mean- square errord

    Degree of agreement indexyu.s.

    The upstream water depth (cm)yd.s

    The downstream water depth (cm)H

    Water surface elevation over sharp crested weir (cm)Q

    Outflow discharge (liter/sec)Qpeak

    Peak discharge (liter/sec)

    1. Introduction

    Earth dams are compacted structures composed of natural materials that are usually mined or quarried from local locations. The failures of the earth dams have proven to be deadly, destructive, and costly. According to People’s Daily, two earthen dams, Yong’an Dam and Xinfa Dam located in Hulun Buir City in North China’s Inner Mongolia failed on 2021, due to a surge in the water level of the Nuomin River caused by heavy rain. The dam breach affected 16,660 people, flooded 325,622 mu of farmland (21708.1 ha), and destroyed 22 bridges, 124 culverts, and 15.6 km of roadways. Also, the failure of south fork dam (earth and rock fill dam) near Johnstown on 1889 is considered the worst U.S dam disaster in terms of loss of life. The dam was overtopped and washed away due to unexpected heavy rains, releasing 20 million tons of water which destroyed Johnstown and resulted in 2209 deaths, [1][2]. Piping or shear sliding, failure due to natural factors, and failure due to overtopping are all possible causes of earth dam failure. However, overtopping failure is the most frequent cause of dam failure. According to The International Committee on Large Dams (ICOLD, 1995), and [3], more than one-third of the total known dam failures were caused by dam overtopping.

    Overtopping occurs as the result of insufficient flood design or freeboard in some cases. Extreme rainstorms can cause floods which can overtop the dam and cause it to fail. The size and geometry of the reservoir or the dam (side slopes, top width, height, etc.), the homogeneity of the material used in the construction of the dam, overtopping depth, and the presence or absence of tailwater are all elements that influence this type of failure which will be illustrated in the following literature. Overtopping failures of earth dams may be divided into several failure mechanisms based on the material composition and the inner structure of the dam. For cohesive earth dams because of low permeability, no seepage exists on the slopes. Erosion often begins at the earth dam toe during turbulent erosion and moves upstream, undercutting the slope, causing the removal of large chunks of materials. While for non-cohesive earth dams the downstream face of the dam flattens progressively and is often said to rotate around a point near the downstream toe [4][5][6] In the last few decades, the study of failures due to overtopping has gained popularity among researchers. The overtopping failure, in fact, has been widely investigated in coastal and river hydraulics and morpho dynamic. In addition, several laboratory experimental studies have been conducted in this field in order to better understand different involved factors. Also, many numerical types of research have been conducted to investigate the process of overtopping failure as well as the elements that influence this type of failure.

    Tabrizi et al. [5] conducted a series of embankment overtopping tests to find the effect of compaction on the failure of a homogenous sand embankment. A plane breach process occurred across the flume width due to the narrow flume width. They measured the downstream hydrographs and embankment surface profile for every case. They concluded that the peak discharge decreased with a high compaction level, while the time to peak increased. Kansoh et al. [6] studied experimentally the failure of compacted homogeneous non-cohesive earthen embankment due to overtopping. They investigated the influence of different shape parameters including the downstream slope, the crest width, and the height of the embankment on the erosion process. The erosion process was initiated by carving a pilot channel into the embankment crest. They evaluated the time of embankment failure for different shape parameters. They concluded that the failure time increases with increasing the downstream slope and the crest width. Zhu et al. [7] investigated experimentally the breaching of five embankments, one constructed with pure sand, and four with different sand-silt–clay mixtures. The erosion pattern was similar across the flume width. They stated that for cohesive soil mixtures the head cut erosion was the most important factor that affected the breach growth, while for non-cohesive soil the breach erosion was affected by shear erosion.

    Amaral et al. [8] studied experimentally the failure by overtopping for two embankments built from silt sand material. They studied the effect of the degree of compaction of the embankment and the geometry of the pilot channel carved at the centre of the dam crest. They studied two shapes of pilot channel a rectangular shape and triangular shape. They stated that the breach development is influenced by a higher degree of compaction, however, the pilot channel geometry did not influence the breach’s final form. Bereta et al. [9] studied experimentally the breach formation of five dam models, three of them were homogenous clay soil while two were sandy-clay mixtures. The erosion process was initiated by cutting a pilot channel at the centre of the dam crest. They observed the initiation of erosion, flow shear erosion, sidewall bottom erosion, and distinguished the soil mechanical slope mass failure from the head cut vertically and laterally during these tests. Verma et al. [10] investigated experimentally a two-dimensional erosion phenomenon due to overtopping by using a wooden fuse plug model and five different soils. They concluded that the erosion process was affected mostly by cohesiveness and degree of compaction. For cohesive soils, a head cut erosion was observed, while for non-cohesive soils surface erosion occurred gradually. Also, the dimensions of fuse plug, type of fill material, reservoir capacity, and inflow were found to affect the behaviour of the overall breaching process.

    Wu and Qin [11] studied the effect of adding coarse grains to the downstream face of a non-cohesive dam as a result of tailings deposition. The process of overtopping during tailings dam failures is analyzed and its effect on delaying the dam-break process and disaster mitigation are investigated. They found that the tested protective measures decreased the breach area, the maximum breaching flow discharge and flow velocity, and the downstream inundated area. Khankandi et al. [12] studied experimentally the effect of reservoir geometry on dam break flow in case of dry and wet bed conditions. They considered four different reservoir shapes, a long reservoir, a wide, a trapezoidal shaped and one with a 90◦ bend all with identical water volume and horizontal bed. The dam break is simulated by the sudden gate removal using a pneumatic jack. They measured the variation of water level over time with ultrasonic sensors and flow velocity component with an acoustic Doppler velocimeter. Also, the experimental results of water level variation are compared with Ritters solution (1892) [13]. They stated that for dry bed condition the long and 90 bend reservoirs results are close to the analytical solution by ritter also in these two shapes a 1D flow is noticed. However, for wide and trapezoidal reservoirs a 2D effect is significant due to flow contraction at channel entrance.

    Rifai et al. [14] conducted a series of experiments to investigate the effect of tailwater depth on the outflow discharge and breach geometry during non-cohesive homogenous fluvial dikes overtopping failure. They cut an initial notch in the crest at 0.8 m from the upstream end of the dike to initiate overtopping. They compared their results to previous experiments under different main channel inflow discharges combined with a free floodplain. They divided the dike breaching process into three stages: gradual start of overtopping flow resulting in slow initiation of dike erosion, deepening and widening breach due to large flow depth and velocity, finally the flow depth starts stabilizing at its minimal level with or without sustained breach expansion. They stated that breach discharge has lower values than in free floodplain tests. Jiang [15] studied the effect of bed slope on breach parameters and peak discharge in non-cohesive embankment failure. An initial triangular breach with a depth and width of 4 cm was pre-set on one side of the dam. He stated that peak discharge increases with the increase of bed slope and then decreases.

    Ozmen-cagatay et al. [16] studied experimentally flood wave propagation resulted from a sudden dam break event. For dam-break modelling, they used a mechanism that permitted the rapid removal of a vertical plate with a thickness of 4 mm and made of rigid plastic. They conducted three tests, one with dry bed condition and two tests with tailwater depths equal 0.025 m and 0.1 m respectively. They recorded the free surface profile during initial stages of dam break by using digital image processing. Finally, they compared the experimental results with the with a commercially available VOF-based CFD program solving the Reynolds-averaged Navier –Stokes equations (RANS) with the k– Ɛ turbulence model and the shallow water equations (SWEs). They concluded that Wave breaking was delayed with increasing the tailwater depth to initial reservoir depth ratio. They also stated that the SWE approach is sufficient more to represent dam break flows for wet bed condition. Evangelista [17] investigated experimentally and numerically using a depth-integrated two-phase model, the erosion of sand dike caused by the impact of a dam break wave. The dam break is simulated by a sudden opening of an upstream reservoir gate resulting in the overtopping of a downstream trapezoidal sand dike. The evolution of the water wave caused from the gate opening and dike erosion process are recorded by using a computer-controlled camera. The experimental results demonstrated that the progression of the wave front and dike erosion have a considerable influence on each other during the process. In addition, the dike constructed from fine sands was more resistant to erosion than the one built with coarse sand. They also stated that the numerical model can is capable of accurately predicting wave front position and dike erosion. Also, Di Cristo et al. [18] studied the effect of dam break wave propagation on a sand embankment both experimentally and numerically using a two-phase shallow-water model. The evolution of free surface and of the embankment bottom are recorded and used in numerical model assessment. They stated that the model allows reasonable simulation of the experimental trends of the free surface elevation regardeless of the geofailure operator.

    Lots of numerical models have been developed over the past few years to simulate the dam break flooding problem. A one-dimensional model, such as Hec-Ras, DAMBRK and MIKE 11, ect. A two-dimensional model such as iRIC Nay2DH is used in earth embankment breach simulation. Other researchers studied the failure process numerically using (3D) computational fluid dynamics (CFD) models, such as FLOW-3D, and FLUENT. Goharnejad et al. [19] determined the outflow hydrograph which results from the embankment dam break due to overtopping. Hu et al. [20] performed a comparison between Flow-3D and MIKE3 FM numerical models in simulating a dam break event under dry and wet bed conditions with different tailwater depths. Kaurav et al. [21] simulated a planar dam breach process due to overtopping. They conducted a sensitivity analysis to find the effect of dam material, dam height, downstream slope, crest width, and inlet discharge on the erosion process and peak discharge through breach. They concluded that downstream slope has a significant influence on breaching process. Yusof et al. [22] studied the effect of embankment sediment sizes and inflow rates on breaching geometric and hydrodynamic parameters. They stated that the peak outflow hydrograph increases with increasing sediment size and inflow rates while time of failure decreases.

    In the present work, the effect of tailwater depth on earth dam failure during overtopping is studied experimentally. The relation between the eroded volume of the dam and the tailwater depth is presented. Also, the percentage of reduction in peak discharge due to tailwater existence is calculated. An assessment of Flow 3D software performance in simulating the erosion process during earth dam failure is introduced. The statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are used in model assessment.

    2. Material and methods

    The tests are conducted in a straight rectangular flume in the laboratory of Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexandria University, Egypt. The flume dimensions are 10 m long, 0.86 m wide, and 0.5 m deep. The front part of the flume is connected to a storage basin 1 m long by 0.86 m wide. The storage basin is connected to a collecting tank for water recirculation during the experiments as shown in Fig. 1Fig. 2. A sharp-crested weir is placed at a distance of 4 m downstream the constructed dam to keep a constant tailwater depth in each experiment and to measure the outflow discharge.

    To measure the eroded volume with time a rods technique is used. This technique consists of two parallel wooden plates with 10 cm distance in between and five rows of stainless-steel rods passing vertically through the wooden plates at a spacing of 20 cm distributed across flume width. Each row consists of four rods with 15 cm spacing between them. Also, a graph board is provided to measure the drop in each rod with time as shown in Fig. 3Fig. 4. After dam construction the rods are carefully rested on the dam, with the first line of rods resting in the middle of the dam crest and then a constant distance of 15 cm between rods lines is maintained.

    A soil sample is taken and tested in the laboratory of the soil mechanics to find the soil geotechnical parameters. The soil particle size distribution is also determined by sieve analysis as shown in Fig. 5. The soil mean diameter d50,equals 0.38 mm and internal friction angle equals 32.6°.

    2.1. Experimental procedures

    To investigate the effect of the tailwater depth (do), the tailwater depth is changed four times 5, 15, 20, and 25 cm on the sand dam model. The dam profile is 35 cm height, with crest width = 15 cm, the dam base width is 155 cm, and the upstream and downstream slopes are 2:1 as shown in Fig. 6. The dam dimensions are set as the flume permitted to allow observation of the dam erosion process under the available flume dimensions and conditions. All of the conducted experiments have the same dimensions and configurations.

    The optimum water content, Wc, from the standard proctor test is found to be 8 % and the maximum dry unit weight is 19.42 kN/m3. The soil and water are mixed thoroughly to ensure consistency and then placed on three horizontal layers. Each layer is compacted according to ASTM standard with 25 blows by using a rammer (27 cm × 20.5 cm) weighing 4 kg. Special attention is paid to the compaction of the soil to guarantee the repeatability of the tests.

    After placing and compacting the three layers, the dam slopes are trimmed carefully to form the trapezoidal shape of the dam. A small triangular pilot channel with 1 cm height and 1:1 side slopes is cut into the dam crest to initiate the erosion process. The position of triangular pilot channel is presented in Fig. 1. Three digital video cameras with a resolution of 1920 × 1080 pixels and a frame rate of 60 fps are placed in three different locations. One camera on one side of the flume to record the progress of the dam profile during erosion. Another to track the water level over the sharp-crested rectangular weir placed at the downstream end of the flume. And the third camera is placed above the flume at the downstream side of the dam and in front of the rods to record the drop of the tip of the rods with time as shown previously in Fig. 1.

    Before starting the experiment, the water is pumped into the storage basin by using pump with capacity 360 m3/hr, and then into the upstream section of the flume. The upstream boundary is an inflow condition. The flow discharge provided to the storage basin is kept at a constant rate of 6 L/sec for all experiments, while the downstream boundary is an outflow boundary condition.

    Also, the required tailwater depth for each experiment is filled to the desired depth. A dye container valve is opened to color the water upstream of the dam to make it easy to distinguish the dam profile from the water profile. A wooden board is placed just upstream of the dam to prevent water from overtopping the dam until the water level rises to a certain level above the dam crest and then the wooden board is removed slowly to start the experiment.

    2.2. Repeatability

    To verify the accuracy of the results, each experiment is repeated two times under the same conditions. Fig. 7 shows the relative eroded crest height, Zeroded / Zo, with time for 5 cm tailwater depth. From the Figure, it can be noticed that results for all runs are consistent, and accuracy is achieved.

    3. Numerical model

    The commercially available numerical model, Flow 3D is used to simulate the dam failure due to overtopping for the cases of 15 cm, 20 cm and 25 cm tailwater depths. For numerical model calibration, experimental results for dam surface evolution are used. The numerical model is calibrated for selection of the optimal turbulence model (RNG, K-e, and k-w) and sediment scour equations (Van Rin, Meyer- peter and Muller, and Nielsen) that produce the best results. In this, the flow field is solved by the RNG turbulence model, and the van Rijn equation is used for the sediment scour model. A geometry file is imported before applying the mesh.

    A Mesh sensitivity is analyzed and checked for various cell sizes, and it is found that decreasing the cell size significantly increases the simulation time with insignificant differences in the result. It is noticed that the most important factor influencing cell size selection is the value of the dam’s upstream and downstream slopes. For example, the slopes in the dam model are 2:1, thus the cell size ratio in X and Z directions should be 2:1 as well. The cell size in a mesh block is set to be 0.02 m, 0.025 m, and 0.01 m in X, Y and Z directions respectively.

    In the numerical computations, the boundary conditions employed are the walls for sidewalls and the channel bottom. The pressure boundary condition is applied at the top, at the air–water interface, to account for atmospheric pressure on the free surface. The upstream boundary is volume flow rate while the downstream boundary is outflow discharge.

    The initial condition is a fluid region, which is used to define fluid areas both upstream and downstream of the dam. To assess the model accuracy, the statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are calculated as(1)RMSE=1N∑i=1N(Pi-Mi)2(2)d=1-∑Mi-Pi2∑Mi-M¯+Pi-P¯2

    where N is the number of samples, Pi and Mi are the models and experimental values, P and M are the means of the model and experimental values. The best fit between the experimental and model results would have an RMSE = 0 and degree of agreement, d = 1.

    4. Results of experimental work

    The results of the total time of failure, t (defined as the time from when the water begins to overtop the dam crest until the erosion reaches a steady state, when no erosion occurs), time of crest width erosion t1, cumulative eroded volume Veroded, and peak discharge Qpeak for each experiment are listed in Table 1. The case of 5 cm tailwater depth is considered as a reference case in this work.

    Table 1. Results of experimental work.

    Tailwater depth, do (cm)Total time of failure, t (sec)Time of crest width erosion, t1 (sec)cumulative eroded volume, Veroded (m3)Peak discharge, Qpeak (liter/sec)
    5255220.2113.12
    15165300.1612.19
    20140340.1311.29
    25110390.0510.84

    5. Discussion

    5.1. Side erosion

    The evolution of the bathymetry of the erosion line recorded by the video camera1. The videos are split into frames (60 frames/sec) by the Free Video to JPG Converter v.5.063 build and then converted into an excel spreadsheet using MATLAB code as shown in Fig. 8.

    Fig. 9 shows a sample of numerical model output. Fig. 10Fig. 11Fig. 12 show a dam profile development for different time steps from both experimental and numerical model, for tailwater depths equal 15 cm, 20 cm and 25 cm. Also, the values of RMSE and d for each figure are presented. The comparison shows that the Flow 3D software can simulate the erosion process of non-cohesive earth dam during overtopping with an RMSE value equals 0.023, 0.0218, and 0.0167 and degree of agreement, d, equals 0.95, 0.968, and 0.988 for relative tailwater depths, do/(do)ref, = 3, 4 and 5, respectively. The low values of RMSE and high values of d show that the Flow 3D can effectively simulate the erosion process. From Fig. 10Fig. 11Fig. 12, it can be noticed that the model is not capable of reproducing the head cut, while it can simulate well the degradation of the crest height with a minor difference from experimental work. The reason of this could be due to inability of simulation of all physical conditions which exists in the experimental work, such as channel friction and the grain size distribution of the dam soil which is surely has a great effect on the erosion process and breach development. In the experimental work the grain size distribution is shown in Fig. 5, while the numerical model considers that the soil is uniform and exactly 50 % of the dam particles diameter are equal to the d50 value. Another reason is that the model is not considering the increased resistance of the dam due to the apparent cohesion which happens due to dam saturation [23].

    It is clear from both the experimental and numerical results that for a 5 cm tailwater depth, do/(do)ref = 1.0, erosion begins near the dam toe and continues upward on the downstream slope until it reaches the crest. After eroding the crest width, the crest is lowered, resulting in increased flow rates and the speeding up of the erosion process. While for relative tailwater depths, do/(do)ref = 3, 4, and 5 erosion starts at the point of intersection between the downstream slope and tailwater. The existence of tailwater works as an energy dissipater for the falling water which reduces the erosion process and prevents the dam from failure as shown in Fig. 13. It is found that the time of the failure decreases with increasing the tailwater depth because most of the dam height is being submerged with water which decreases the erosion process. The reduction in time of failure from the referenced case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively.

    The relation between the relative eroded crest height, Zeroded /Zo, with time is drawn as shown in Fig. 14. It is found that the relative eroded crest height decreases with increasing tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively. The time required for the erosion of the crest width, t1, is calculated for each experiment. The relation between relative tailwater depth and relative time of crest width erosion is shown in Fig. 15. It is found that the time of crest width erosion increases linearly with increasing, do /Zo. The percent of increase is 36.4, 54.5 and 77.3 % for relative tailwater depth, do /(do)ref = 3, 4 and 5, respectively.

    Crest height, Zcrest is calculated from the experimental results and the Flow 3D results for relative tailwater depths, do/(do)ref, = 3, 4, and 5. A relation between relative crest height, Zcrest/Zo with time from experimental and numerical results is presented in Fig. 16. From Fig. 16, it is seen that there is a good consistency between the results of numerical model and the experimental results in the case of tracking the erosion of the crest height with time.

    5.2. Upstream and downstream water depths

    It is noticed that at the beginning of the erosion process, both upstream and downstream water depths increase linearly with time as long as erosion of the crest height did not take place. However, when the crest height starts to lower the upstream water depth decreases with time while the downstream water depth increases. At the end of the experiment, the two depths are nearly equal. A relation between relative downstream and upstream water depths with time is drawn for each experiment as shown in Fig. 17.

    5.3. Eroded volume

    A MATLAB code is used to calculate the cumulative eroded volume every time interval for each experiment. The total volume of the dam, Vtotal is 0.256 m3. The cumulative eroded volume, Veroded is 0.21, 0.16, 0.13, and 0.05 m3 for tailwater depths, do = 5, 15, 20, and 25 cm, respectively. Fig. 18 presents the relation between cumulative eroded volume, Veroded and time. From Fig. 18, it is observed that the cumulative eroded volume decreases with increasing the tailwater depth. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative remained volume of the dam equals 0.18, 0.375, 0.492, and 0.8 for tailwater depths = 5, 15, 20, and 25 cm, respectively. Fig. 19 shows a relation between relative tailwater depth and relative cumulative eroded volume from experimental results. From that figure, it is noticed that the eroded volume decreases exponentially with increasing relative tailwater depth.

    5.4. The outflow discharge

    The inflow discharge provided to the storage tank is maintained constant for all experiments. The water surface elevation, H, over the sharp-crested weir placed at the downstream side is recorded by the video camera 2. For each experiment, the outflow discharge is then calculated by using the sharp-crested rectangular weir equation every 10 sec.

    The outflow discharge is found to increase rapidly until it reaches its peak then it decreases until it is constant. For high values of tailwater depths, the peak discharge becomes less than that in the case of small tailwater depth as shown in Fig. 20 which agrees well with the results of Rifai et al. [14] The reduction in peak discharge is 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively.

    The scenario presented in this article in which the tailwater depth rises due to unexpected heavy rainfall, is investigated to find the effect of rising tailwater depth on earth dam failure. The results revealed that rising tailwater depth positively affects the process of dam failure in terms of preventing the dam from complete failure and reducing the outflow discharge.

    6. Conclusions

    The effect of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. The study focuses on the effect of tailwater depth on side erosion, upstream and downstream water depths, eroded volume, outflow hydrograph, and duration of the failure process. The Flow 3D numerical software is used to simulate the dam failure, and a comparison is made between the experimental and numerical results to find the ability of this software to simulate the erosion process. The following are the results of the investigation:

    The existence of tailwater with high depths prevents the dam from completely collapsing thereby turning it into a broad crested weir. The failure time decreases with increasing the tailwater depth and the reduction from the reference case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The difference between the upstream and downstream water depths decreases with time till it became almost negligible at the end of the experiment. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The peak discharge decreases by 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative eroded crest height decreases linearly with increasing the tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The numerical model can reproduce the erosion process with a minor deviation from the experimental results, particularly in terms of tracking the degradation of the crest height with time.

    Declaration of Competing Interest

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

    Reference

    [1]

    D. McCullough

    The Johnstown Flood

    Simon and Schuster, NY (1968)

    Google Scholar[2]Rose AT. The influence of dam failures on dam safety laws in Pennsylvania. Association of State Dam Safety Officials Annual Conference 2013, Dam Safety 2013. 2013;1:738–56.

    Google Scholar[3]

    M. Foster, R. Fell, M. Spannagle

    The statistics of embankment dam failures and accidents

    Can Geotech J, 37 (5) (2000), pp. 1000-1024, 10.1139/t00-030 View PDF

    View Record in ScopusGoogle Scholar[4]Pickert, G., Jirka, G., Bieberstein, A., Brauns, J. Soil/water interaction during the breaching process of overtopped embankments. In: Greco, M., Carravetta, A., Morte, R.D. (Eds.), Proceedings of the Conference River-Flow 2004, Balkema.

    Google Scholar[5]

    A. Asghari Tabrizi, E. Elalfy, M. Elkholy, M.H. Chaudhry, J. Imran

    Effects of compaction on embankment breach due to overtopping

    J Hydraul Res, 55 (2) (2017), pp. 236-247, 10.1080/00221686.2016.1238014 View PDF

    View Record in ScopusGoogle Scholar[6]

    R.M. Kansoh, M. Elkholy, G. Abo-Zaid

    Effect of Shape Parameters on Failure of Earthen Embankment due to Overtopping

    KSCE J Civ Eng, 24 (5) (2020), pp. 1476-1485, 10.1007/s12205-020-1107-x View PDF

    View Record in ScopusGoogle Scholar[7]

    YongHui Zhu, P.J. Visser, J.K. Vrijling, GuangQian Wang

    Experimental investigation on breaching of embankments

    Experimental investigation on breaching of embankments, 54 (1) (2011), pp. 148-155 View PDF

    CrossRefView Record in ScopusGoogle Scholar[8]Amaral S, Jónatas R, Bento AM, Palma J, Viseu T, Cardoso R, et al. Failure by overtopping of earth dams. Quantification of the discharge hydrograph. Proceedings of the 3rd IAHR Europe Congress: 14-15 April 2014, Portugal. 2014;(1):182–93.

    Google Scholar[9]

    G. Bereta, P. Hui, H. Kai, L. Guang, P. Kefan, Y.Z. Zhao

    Experimental study of cohesive embankment dam breach formation due to overtopping

    Periodica Polytechnica Civil Engineering, 64 (1) (2020), pp. 198-211, 10.3311/PPci.14565 View PDF

    View Record in ScopusGoogle Scholar[10]

    D.K. Verma, B. Setia, V.K. Arora

    Experimental study of breaching of an earthen dam using a fuse plug model

    Int J Eng Trans A, 30 (4) (2017), pp. 479-485, 10.5829/idosi.ije.2017.30.04a.04 View PDF

    View Record in ScopusGoogle Scholar[11]Wu T, Qin J. Experimental Study of a Tailings Impoundment Dam Failure Due to Overtopping. Mine Water and the Environment [Internet]. 2018;37(2):272–80. Available from: doi: 10.1007/s10230-018-0529-x.

    Google Scholar[12]

    A. Feizi Khankandi, A. Tahershamsi, S. Soares-Frazo

    Experimental investigation of reservoir geometry effect on dam-break flow

    J Hydraul Res, 50 (4) (2012), pp. 376-387 View PDF

    CrossRefView Record in ScopusGoogle Scholar[13]

    A. Ritter

    Die Fortpflanzung der Wasserwellen (The propagation of water waves)

    Zeitschrift Verein Deutscher Ingenieure, 36 (33) (1892), pp. 947-954

    [in German]

    View Record in ScopusGoogle Scholar[14]

    I. Rifai, K. El Kadi Abderrezzak, S. Erpicum, P. Archambeau, D. Violeau, M. Pirotton, et al.

    Floodplain Backwater Effect on Overtopping Induced Fluvial Dike Failure

    Water Resour Res, 54 (11) (2018), pp. 9060-9073 View PDF

    This article is free to access.

    CrossRefView Record in ScopusGoogle Scholar[15]

    X. Jiang

    Laboratory Experiments on Breaching Characteristics of Natural Dams on Sloping Beds

    Advances in Civil Engineering, 2019 (2019), pp. 1-14

    View Record in ScopusGoogle Scholar[16]

    H. Ozmen-Cagatay, S. Kocaman

    Dam-break flows during initial stage using SWE and RANS approaches

    J Hydraul Res, 48 (5) (2010), pp. 603-611 View PDF

    CrossRefView Record in ScopusGoogle Scholar[17]

    S. Evangelista

    Experiments and numerical simulations of dike erosion due to a wave impact

    Water (Switzerland), 7 (10) (2015), pp. 5831-5848 View PDF

    CrossRefView Record in ScopusGoogle Scholar[18]

    C. Di Cristo, S. Evangelista, M. Greco, M. Iervolino, A. Leopardi, A. Vacca

    Dam-break waves over an erodible embankment: experiments and simulations

    J Hydraul Res, 56 (2) (2018), pp. 196-210 View PDF

    CrossRefView Record in ScopusGoogle Scholar[19]Goharnejad H, Sm M, Zn M, Sadeghi L, Abadi K. Numerical Modeling and Evaluation of Embankment Dam Break Phenomenon (Case Study : Taleghan Dam) ISSN : 2319-9873. 2016;5(3):104–11.

    Google Scholar[20]Hu H, Zhang J, Li T. Dam-Break Flows : Comparison between Flow-3D , MIKE 3 FM , and Analytical Solutions with Experimental Data. 2018;1–24. doi: 10.3390/app8122456.

    Google Scholar[21]

    R. Kaurav, P.K. Mohapatra, D. Ph

    Studying the Peak Discharge through a Planar Dam Breach, 145 (6) (2019), pp. 1-8 View PDF

    CrossRef[22]

    Z.M. Yusof, Z.A.L. Shirling, A.K.A. Wahab, Z. Ismail, S. Amerudin

    A hydrodynamic model of an embankment breaching due to overtopping flow using FLOW-3D

    IOP Conference Series: Earth and Environmental Science, 920 (1) (2021)

    Google Scholar[23]

    G. Pickert, V. Weitbrecht, A. Bieberstein

    Breaching of overtopped river embankments controlled by apparent cohesion

    J Hydraul Res, 49 (2) (Apr. 2011), pp. 143-156, 10.1080/00221686.2011.552468 View PDF

    View Record in ScopusGoogle Scholar

    Cited by (0)

    My name is Shaimaa Ibrahim Mohamed Aman and I am a teaching assistant in Irrigation and Hydraulics department, Faculty of Engineering, Alexandria University. I graduated from the Faculty of Engineering, Alexandria University in 2013. I had my MSc in Irrigation and Hydraulic Engineering in 2017. My research interests lie in the area of earth dam Failures.

    Peer review under responsibility of Ain Shams University.

    © 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.

    Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

    영국 Dawlish의 방파제에 대한 온대 저기압 피해: 목격자 설명, 해수면 분석 및 수치 모델링

    Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

    Natural Hazards (2022)Cite this article

    Abstract

    2014년 2월 영국 해협(영국)과 특히 Dawlish에 영향을 미친 온대 저기압 폭풍 사슬은 남서부 지역과 영국의 나머지 지역을 연결하는 주요 철도에 심각한 피해를 입혔습니다.

    이 사건으로 라인이 두 달 동안 폐쇄되어 5천만 파운드의 피해와 12억 파운드의 경제적 손실이 발생했습니다. 이 연구에서는 폭풍의 파괴력을 해독하기 위해 목격자 계정을 수집하고 해수면 데이터를 분석하며 수치 모델링을 수행합니다.

    우리의 분석에 따르면 이벤트의 재난 관리는 성공적이고 효율적이었으며 폭풍 전과 도중에 인명과 재산을 구하기 위해 즉각적인 조치를 취했습니다. 파도 부이 분석에 따르면 주기가 4–8, 8–12 및 20–25초인 복잡한 삼중 봉우리 바다 상태가 존재하는 반면, 조위계 기록에 따르면 최대 0.8m의 상당한 파도와 최대 1.5m의 파도 성분이 나타났습니다.

    이벤트에서 가능한 기여 요인으로 결합된 진폭. 최대 286 KN의 상당한 임펄스 파동이 손상의 시작 원인일 가능성이 가장 높았습니다. 수직 벽의 반사는 파동 진폭의 보강 간섭을 일으켜 파고가 증가하고 최대 16.1m3/s/m(벽의 미터 너비당)의 상당한 오버탑핑을 초래했습니다.

    이 정보와 우리의 공학적 판단을 통해 우리는 이 사고 동안 다중 위험 계단식 실패의 가장 가능성 있는 순서는 다음과 같다고 결론을 내립니다. 조적 파괴로 이어지는 파도 충격력, 충전물 손실 및 연속적인 조수에 따른 구조물 파괴.

    The February 2014 extratropical cyclonic storm chain, which impacted the English Channel (UK) and Dawlish in particular, caused significant damage to the main railway connecting the south-west region to the rest of the UK. The incident caused the line to be closed for two months, £50 million of damage and an estimated £1.2bn of economic loss. In this study, we collate eyewitness accounts, analyse sea level data and conduct numerical modelling in order to decipher the destructive forces of the storm. Our analysis reveals that the disaster management of the event was successful and efficient with immediate actions taken to save lives and property before and during the storm. Wave buoy analysis showed that a complex triple peak sea state with periods at 4–8, 8–12 and 20–25 s was present, while tide gauge records indicated that significant surge of up to 0.8 m and wave components of up to 1.5 m amplitude combined as likely contributing factors in the event. Significant impulsive wave force of up to 286 KN was the most likely initiating cause of the damage. Reflections off the vertical wall caused constructive interference of the wave amplitudes that led to increased wave height and significant overtopping of up to 16.1 m3/s/m (per metre width of wall). With this information and our engineering judgement, we conclude that the most probable sequence of multi-hazard cascading failure during this incident was: wave impact force leading to masonry failure, loss of infill and failure of the structure following successive tides.

    Introduction

    The progress of climate change and increasing sea levels has started to have wide ranging effects on critical engineering infrastructure (Shakou et al. 2019). The meteorological effects of increased atmospheric instability linked to warming seas mean we may be experiencing more frequent extreme storm events and more frequent series or chains of events, as well as an increase in the force of these events, a phenomenon called storminess (Mölter et al. 2016; Feser et al. 2014). Features of more extreme weather events in extratropical latitudes (30°–60°, north and south of the equator) include increased gusting winds, more frequent storm squalls, increased prolonged precipitation and rapid changes in atmospheric pressure and more frequent and significant storm surges (Dacre and Pinto 2020). A recent example of these events impacting the UK with simultaneous significant damage to coastal infrastructure was the extratropical cyclonic storm chain of winter 2013/2014 (Masselink et al. 2016; Adams and Heidarzadeh 2021). The cluster of storms had a profound effect on both coastal and inland infrastructure, bringing widespread flooding events and large insurance claims (RMS 2014).

    The extreme storms of February 2014, which had a catastrophic effect on the seawall of the south Devon stretch of the UK’s south-west mainline, caused a two-month closure of the line and significant disruption to the local and regional economy (Fig. 1b) (Network Rail 2014; Dawson et al. 2016; Adams and Heidarzadeh 2021). Restoration costs were £35 m, and economic effects to the south-west region of England were estimated up to £1.2bn (Peninsula Rail Taskforce 2016). Adams and Heidarzadeh (2021) investigated the disparate cascading failure mechanisms which played a part in the failure of the railway through Dawlish and attempted to put these in the context of the historical records of infrastructure damage on the line. Subsequent severe storms in 2016 in the region have continued to cause damage and disruption to the line in the years since 2014 (Met Office 2016). Following the events of 2014, Network Rail Footnote1 who owns the network has undertaken a resilience study. As a result, it has proposed a £400 m refurbishment of the civil engineering assets that support the railway (Fig. 1) (Network Rail 2014). The new seawall structure (Fig. 1a,c), which is constructed of pre-cast concrete sections, encases the existing Brunel seawall (named after the project lead engineer, Isambard Kingdom Brunel) and has been improved with piled reinforced concrete foundations. It is now over 2 m taller to increase the available crest freeboard and incorporates wave return features to minimise wave overtopping. The project aims to increase both the resilience of the assets to extreme weather events as well as maintain or improve amenity value of the coastline for residents and visitors.

    figure 1
    Fig. 1

    In this work, we return to the Brunel seawall and the damage it sustained during the 2014 storms which affected the assets on the evening of the 4th and daytime of the 5th of February and eventually resulted in a prolonged closure of the line. The motivation for this research is to analyse and model the damage made to the seawall and explain the damage mechanisms in order to improve the resilience of many similar coastal structures in the UK and worldwide. The innovation of this work is the multidisciplinary approach that we take comprising a combination of analysis of eyewitness accounts (social science), sea level and wave data analysis (physical science) as well as numerical modelling and engineering judgement (engineering sciences). We investigate the contemporary wave climate and sea levels by interrogating the real-time tide gauge and wave buoys installed along the south-west coast of the English Channel. We then model a typical masonry seawall (Fig. 2), applying the computational fluid dynamics package FLOW3D-Hydro,Footnote2 to quantify the magnitude of impact forces that the seawall would have experienced leading to its failure. We triangulate this information to determine the probable sequence of failures that led to the disaster in 2014.

    figure 2
    Fig. 2

    Data and methods

    Our data comprise eyewitness accounts, sea level records from coastal tide gauges and offshore wave buoys as well as structural details of the seawall. As for methodology, we analyse eyewitness data, process and investigate sea level records through Fourier transform and conduct numerical simulations using the Flow3D-Hydro package (Flow Science 2022). Details of the data and methodology are provided in the following.

    Eyewitness data

    The scale of damage to the seawall and its effects led the local community to document the first-hand accounts of those most closely affected by the storms including residents, local businesses, emergency responders, politicians and engineering contractors involved in the post-storm restoration work. These records now form a permanent exhibition in the local museum in DawlishFootnote3, and some of these accounts have been transcribed into a DVD account of the disaster (Dawlish Museum 2015). We have gathered data from the Dawlish Museum, national and international news reports, social media tweets and videos. Table 1 provides a summary of the eyewitness accounts. Overall, 26 entries have been collected around the time of the incident. Our analysis of the eyewitness data is provided in the third column of Table 1 and is expanded in Sect. 3.Table 1 Eyewitness accounts of damage to the Dawlish railway due to the February 2014 storm and our interpretations

    Full size table

    Sea level data and wave environment

    Our sea level data are a collection of three tide gauge stations (Newlyn, Devonport and Swanage Pier—Fig. 5a) owned and operated by the UK National Tide and Sea Level FacilityFootnote4 for the Environment Agency and four offshore wave buoys (Dawlish, West Bay, Torbay and Chesil Beach—Fig. 6a). The tide gauge sites are all fitted with POL-EKO (www.pol-eko.com.pl) data loggers. Newlyn has a Munro float gauge with one full tide and one mid-tide pneumatic bubbler system. Devonport has a three-channel data pneumatic bubbler system, and Swanage Pier consists of a pneumatic gauge. Each has a sampling interval of 15 min, except for Swanage Pier which has a sampling interval of 10 min. The tide gauges are located within the port areas, whereas the offshore wave buoys are situated approximately 2—3.3 km from the coast at water depths of 10–15 m. The wave buoys are all Datawell Wavemaker Mk III unitsFootnote5 and come with sampling interval of 0.78 s. The buoys have a maximum saturation amplitude of 20.5 m for recording the incident waves which implies that every wave larger than this threshold will be recorded at 20.5 m. The data are provided by the British Oceanographic Data CentreFootnote6 for tide gauges and the Channel Coastal ObservatoryFootnote7 for wave buoys.

    Sea level analysis

    The sea level data underwent quality control to remove outliers and spikes as well as gaps in data (e.g. Heidarzadeh et al. 2022; Heidarzadeh and Satake 2015). We processed the time series of the sea level data using the Matlab signal processing tool (MathWorks 2018). For calculations of the tidal signals, we applied the tidal package TIDALFIT (Grinsted 2008), which is based on fitting tidal harmonics to the observed sea level data. To calculate the surge signals, we applied a 30-min moving average filter to the de-tided data in order to remove all wind, swell and infra-gravity waves from the time series. Based on the surge analysis and the variations of the surge component before the time period of the incident, an error margin of approximately ± 10 cm is identified for our surge analysis. Spectral analysis of the wave buoy data is performed using the fast Fourier transform (FFT) of Matlab package (Mathworks 2018).

    Numerical modelling

    Numerical modelling of wave-structure interaction is conducted using the computational fluid dynamics package Flow3D-Hydro version 1.1 (Flow Science 2022). Flow3D-Hydro solves the transient Navier–Stokes equations of conservation of mass and momentum using a finite difference method and on Eulerian and Lagrangian frameworks (Flow Science 2022). The aforementioned governing equations are:

    ∇.u=0∇.u=0

    (1)

    ∂u∂t+u.∇u=−∇Pρ+υ∇2u+g∂u∂t+u.∇u=−∇Pρ+υ∇2u+g

    (2)

    where uu is the velocity vector, PP is the pressure, ρρ is the water density, υυ is the kinematic viscosity and gg is the gravitational acceleration. A Fractional Area/Volume Obstacle Representation (FAVOR) is adapted in Flow3D-Hydro, which applies solid boundaries within the Eulerian grid and calculates the fraction of areas and volume in partially blocked volume in order to compute flows on corresponding boundaries (Hirt and Nichols 1981). We validated the numerical modelling through comparing the results with Sainflou’s analytical equation for the design of vertical seawalls (Sainflou 1928; Ackhurst 2020), which is as follows:

    pd=ρgHcoshk(d+z)coshkdcosσtpd=ρgHcoshk(d+z)coshkdcosσt

    (3)

    where pdpd is the hydrodynamic pressure, ρρ is the water density, gg is the gravitational acceleration, HH is the wave height, dd is the water depth, kk is the wavenumber, zz is the difference in still water level and mean water level, σσ is the angular frequency and tt is the time. The Sainflou’s equation (Eq. 3) is used to calculate the dynamic pressure from wave action, which is combined with static pressure on the seawall.

    Using Flow3D-Hydro, a model of the Dawlish seawall was made with a computational domain which is 250.0 m in length, 15.0 m in height and 0.375 m in width (Fig. 3a). The computational domain was discretised using a single uniform grid with a mesh size of 0.125 m. The model has a wave boundary at the left side of the domain (x-min), an outflow boundary on the right side (x-max), a symmetry boundary at the bottom (z-min) and a wall boundary at the top (z-max). A wall boundary implies that water or waves are unable to pass through the boundary, whereas a symmetry boundary means that the two edges of the boundary are identical and therefore there is no flow through it. The water is considered incompressible in our model. For volume of fluid advection for the wave boundary (i.e. the left-side boundary) in our simulations, we utilised the “Split Lagrangian Method”, which guarantees the best accuracy (Flow Science, 2022).

    figure 3
    Fig. 3

    The stability of the numerical scheme is controlled and maintained through checking the Courant number (CC) as given in the following:

    C=VΔtΔxC=VΔtΔx

    (4)

    where VV is the velocity of the flow, ΔtΔt is the time step and ΔxΔx is the spatial step (i.e. grid size). For stability and convergence of the numerical simulations, the Courant number must be sufficiently below one (Courant et al. 1928). This is maintained by a careful adjustment of the ΔxΔx and ΔtΔt selections. Flow3D-Hydro applies a dynamic Courant number, meaning the program adjusts the value of time step (ΔtΔt) during the simulations to achieve a balance between accuracy of results and speed of simulation. In our simulation, the time step was in the range ΔtΔt = 0.0051—0.051 s.

    In order to achieve the most efficient mesh resolution, we varied cell size for five values of ΔxΔx = 0.1 m, 0.125 m, 0.15 m, 0.175 m and 0.20 m. Simulations were performed for all mesh sizes, and the results were compared in terms of convergence, stability and speed of simulation (Fig. 3). A linear wave with an amplitude of 1.5 m and a period of 6 s was used for these optimisation simulations. We considered wave time histories at two gauges A and B and recorded the waves from simulations using different mesh sizes (Fig. 3). Although the results are close (Fig. 3), some limited deviations are observed for larger mesh sizes of 0.20 m and 0.175 m. We therefore selected mesh size of 0.125 m as the optimum, giving an extra safety margin as a conservative solution.

    The pressure from the incident waves on the vertical wall is validated in our model by comparing them with the analytical equation of Sainflou (1928), Eq. (3), which is one of the most common set of equations for design of coastal structures (Fig. 4). The model was tested by running a linear wave of period 6 s and wave amplitude of 1.5 m against the wall, with a still water level of 4.5 m. It can be seen that the model results are very close to those from analytical equations of Sainflou (1928), indicating that our numerical model is accurately modelling the wave-structure interaction (Fig. 4).

    figure 4
    Fig. 4

    Eyewitness account analysis

    Contemporary reporting of the 4th and 5th February 2014 storms by the main national news outlets in the UK highlights the extreme nature of the events and the significant damage and disruption they were likely to have on the communities of the south-west of England. In interviews, this was reinforced by Network Rail engineers who, even at this early stage, were forecasting remedial engineering works to last for at least 6 weeks. One week later, following subsequent storms the cascading nature of the events was obvious. Multiple breaches of the seawall had taken place with up to 35 separate landslide events and significant damage to parapet walls along the coastal route also were reported. Residents of the area reported extreme effects of the storm, one likening it to an earthquake and reporting water ingress through doors windows and even through vertical chimneys (Table 1). This suggests extreme wave overtopping volumes and large wave impact forces. One resident described the structural effects as: “the house was jumping up and down on its footings”.

    Disaster management plans were quickly and effectively put into action by the local council, police service and National Rail. A major incident was declared, and decisions regarding evacuation of the residents under threat were taken around 2100 h on the night of 4th February when reports of initial damage to the seawall were received (Table 1). Local hotels were asked to provide short-term refuge to residents while local leisure facilities were prepared to accept residents later that evening. Initial repair work to the railway line was hampered by successive high spring tides and storms in the following days although significant progress was still made when weather conditions permitted (Table 1).

    Sea level observations and spectral analysis

    The results of surge and wave analyses are presented in Figs. 5 and 6. A surge height of up to 0.8 m was recorded in the examined tide gauge stations (Fig. 5b-d). Two main episodes of high surge heights are identified: the first surge started on 3rd February 2014 at 03:00 (UTC) and lasted until 4th of February 2014 at 00:00; the second event occurred in the period 4th February 2014 15:00 to 5th February 2014 at 17:00 (Fig. 5b-d). These data imply surge durations of 21 h and 26 h for the first and the second events, respectively. Based on the surge data in Fig. 5, we note that the storm event of early February 2014 and the associated surges was a relatively powerful one, which impacted at least 230 km of the south coast of England, from Land’s End to Weymouth, with large surge heights.

    figure 5
    Fig. 5
    figure 6
    Fig. 6

    Based on wave buoy records, the maximum recorded amplitudes are at least 20.5 m in Dawlish and West Bay, 1.9 m in Tor Bay and 4.9 m in Chesil (Fig. 6a-b). The buoys at Tor Bay and Chesil recorded dual peak period bands of 4–8 and 8–12 s, whereas at Dawlish and West Bay registered triple peak period bands at 4–8, 8–12 and 20–25 s (Fig. 6c, d). It is important to note that the long-period waves at 20–25 s occur with short durations (approximately 2 min) while the waves at the other two bands of 4–8 and 8–12 s appear to be present at all times during the storm event.

    The wave component at the period band of 4–8 s can be most likely attributed to normal coastal waves while the one at 8–12 s, which is longer, is most likely the swell component of the storm. Regarding the third component of the waves with long period of 20 -25 s, which occurs with short durations of 2 min, there are two hypotheses; it is either the result of a local (port and harbour) and regional (the Lyme Bay) oscillations (eg. Rabinovich 1997; Heidarzadeh and Satake 2014; Wang et al. 1992), or due to an abnormally long swell. To test the first hypothesis, we consider various water bodies such as Lyme Bay (approximate dimensions of 70 km × 20 km with an average water depth of 30 m; Fig. 6), several local bays (approximate dimensions of 3.6 km × 0.6 km with an average water depth of 6 m) and harbours (approximate dimensions of 0.5 km × 0.5 km with an average water depth of 4 m). Their water depths are based on the online Marine navigation website.Footnote8 According to Rabinovich (2010), the oscillation modes of a semi-enclosed rectangle basin are given by the following equation:

    Tmn=2gd−−√[(m2L)2+(nW)2]−1/2Tmn=2gd[(m2L)2+(nW)2]−1/2

    (5)

    where TmnTmn is the oscillation period, gg is the gravitational acceleration, dd is the water depth, LL is the length of the basin, WW is the width of the basin, m=1,2,3,…m=1,2,3,… and n=0,1,2,3,…n=0,1,2,3,…; mm and nn are the counters of the different modes. Applying Eq. (5) to the aforementioned water bodies results in oscillation modes of at least 5 min, which is far longer than the observed period of 20–25 s. Therefore, we rule out the first hypothesis and infer that the long period of 20–25 s is most likely a long swell wave coming from distant sources. As discussed by Rabinovich (1997) and Wang et al. (2022), comparison between sea level spectra before and after the incident is a useful method to distinguish the spectrum of the weather event. A visual inspection of Fig. 6 reveals that the forcing at the period band of 20–25 s is non-existent before the incident.

    Numerical simulations of wave loading and overtopping

    Based on the results of sea level data analyses in the previous section (Fig. 6), we use a dual peak wave spectrum with peak periods of 10.0 s and 25.0 s for numerical simulations because such a wave would be comprised of the most energetic signals of the storm. For variations of water depth (2.0–4.0 m), coastal wave amplitude (0.5–1.5 m) (Fig. 7) and storm surge height (0.5–0.8 m) (Fig. 5), we developed 20 scenarios (Scn) which we used in numerical simulations (Table 2). Data during the incident indicated that water depth was up to the crest level of the seawall (approximately 4 m water depth); therefore, we varied water depth from 2 to 4 m in our simulation scenarios. Regarding wave amplitudes, we referred to the variations at a nearby tide gauge station (West Bay) which showed wave amplitude up to 1.2 m (Fig. 7). Therefore, wave amplitude was varied from 0.5 m to 1.5 m by considering a factor a safety of 25% for the maximum wave amplitude. As for the storm surge component, time series of storm surges calculated at three coastal stations adjacent to Dawlish showed that it was in the range of 0.5 m to 0.8 m (Fig. 5). These 20 scenarios would help to study uncertainties associated with wave amplitudes and pressures. Figure 8 shows snapshots of wave propagation and impacts on the seawall at different times.

    figure 7
    Fig. 7

    Table 2 The 20 scenarios considered for numerical simulations in this study

    Full size table

    figure 8
    Fig. 8

    Results of wave amplitude simulations

    Large wave amplitudes can induce significant wave forcing on the structure and cause overtopping of the seawall, which could eventually cascade to other hazards such as erosion of the backfill and scour (Adams and Heidarzadeh, 2021). The first 10 scenarios of our modelling efforts are for the same incident wave amplitudes of 0.5 m, which occur at different water depths (2.0–4.0 m) and storm surge heights (0.5–0.8 m) (Table 2 and Fig. 9). This is because we aim at studying the impacts of effective water depth (deff—the sum of mean sea level and surge height) on the time histories of wave amplitudes as the storm evolves. As seen in Fig. 9a, by decreasing effective water depth, wave amplitude increases. For example, for Scn-1 with effective depth of 4.5 m, the maximum amplitude of the first wave is 1.6 m, whereas it is 2.9 m for Scn-2 with effective depth of 3.5 m. However, due to intensive reflections and interferences of the waves in front of the vertical seawall, such a relationship is barely seen for the second and the third wave peaks. It is important to note that the later peaks (second or third) produce the largest waves rather than the first wave. Extraordinary wave amplifications are seen for the Scn-2 (deff = 3.5 m) and Scn-7 (deff = 3.3 m), where the corresponding wave amplitudes are 4.5 m and 3.7 m, respectively. This may indicate that the effective water depth of deff = 3.3–3.5 m is possibly a critical water depth for this structure resulting in maximum wave amplitudes under similar storms. In the second wave impact, the combined wave height (i.e. the wave amplitude plus the effective water depth), which is ultimately an indicator of wave overtopping, shows that the largest wave heights are generated by Scn-2, 7 and 8 (Fig. 9a) with effective water depths of 3.5 m, 3.3 m and 3.8 m and combined heights of 8.0 m, 7.0 m and 6.9 m (Fig. 9b). Since the height of seawall is 5.4 m, the combined wave heights for Scn-2, 7 and 8 are greater than the crest height of the seawall by 2.6 m, 1.6 m and 1.5 m, respectively, which indicates wave overtopping.

    figure 9
    Fig. 9

    For scenarios 11–20 (Fig. 10), with incident wave amplitudes of 1.5 m (Table 2), the largest wave amplitudes are produced by Scn-17 (deff = 3.3 m), Scn-13 (deff = 2.5 m) and Scn-12 (deff = 3.5 m), which are 5.6 m, 5.1 m and 4.5 m. The maximum combined wave heights belong to Scn-11 (deff = 4.5 m) and Scn-17 (deff = 3.3 m), with combined wave heights of 9.0 m and 8.9 m (Fig. 10b), which are greater than the crest height of the seawall by 4.6 m and 3.5 m, respectively.

    figure 10
    Fig. 10

    Our simulations for all 20 scenarios reveal that the first wave is not always the largest and wave interactions, reflections and interferences play major roles in amplifying the waves in front of the seawall. This is primarily because the wall is fully vertical and therefore has a reflection coefficient of close to one (i.e. full reflection). Simulations show that the combined wave height is up to 4.6 m higher than the crest height of the wall, implying that severe overtopping would be expected.

    Results of wave loading calculations

    The pressure calculations for scenarios 1–10 are given in Fig. 11 and those of scenarios 11–20 in Fig. 12. The total pressure distribution in Figs. 1112 mostly follows a triangular shape with maximum pressure at the seafloor as expected from the Sainflou (1928) design equations. These pressure plots comprise both static (due to mean sea level in front of the wall) and dynamic (combined effects of surge and wave) pressures. For incident wave amplitudes of 0.5 m (Fig. 11), the maximum wave pressure varies in the range of 35–63 kPa. At the sea surface, it is in the range of 4–20 kPa (Fig. 11). For some scenarios (Scn-2 and 7), the pressure distribution deviates from a triangular shape and shows larger pressures at the top, which is attributed to the wave impacts and partial breaking at the sea surface. This adds an additional triangle-shaped pressure distribution at the sea surface elevation consistent with the design procedure developed by Goda (2000) for braking waves. The maximum force on the seawall due to scenarios 1–10, which is calculated by integrating the maximum pressure distribution over the wave-facing surface of the seawall, is in the range of 92–190 KN (Table 2).

    figure 11
    Fig. 11
    figure 12
    Fig. 12

    For scenarios 11–20, with incident wave amplitude of 1.5 m, wave pressures of 45–78 kPa and 7–120 kPa, for  the bottom and top of the wall, respectively, were observed (Fig. 12). Most of the plots show a triangular pressure distribution, except for Scn-11 and 15. A significant increase in wave impact pressure is seen for Scn-15 at the top of the structure, where a maximum pressure of approximately 120 kPa is produced while other scenarios give a pressure of 7–32 kPa for the sea surface. In other words, the pressure from Scn-15 is approximately four times larger than the other scenarios. Such a significant increase of the pressure at the top is most likely attributed to the breaking wave impact loads as detailed by Goda (2000) and Cuomo et al. (2010). The wave simulation snapshots in Fig. 8 show that the wave breaks before reaching the wall. The maximum force due to scenarios 11–20 is 120–286 KN.

    The breaking wave impacts peaking at 286 KN in our simulations suggest destabilisation of the upper masonry blocks, probably by grout malfunction. This significant impact force initiated the failure of the seawall which in turn caused extensive ballast erosion. Wave impact damage was proposed by Adams and Heidarzadeh (2021) as one of the primary mechanisms in the 2014 Dawlish disaster. In the multi-hazard risk model proposed by these authors, damage mechanism III (failure pathway 5 in Adams and Heidarzadeh, 2021) was characterised by wave impact force causing damage to the masonry elements, leading to failure of the upper sections of the seawall and loss of infill material. As blocks were removed, access to the track bed was increased for inbound waves allowing infill material from behind the seawall to be fluidised and subsequently removed by backwash. The loss of infill material critically compromised the stability of the seawall and directly led to structural failure. In parallel, significant wave overtopping (discussed in the next section) led to ballast washout and cascaded, in combination with masonry damage, to catastrophic failure of the wall and suspension of the rails in mid-air (Fig. 1b), leaving the railway inoperable for two months.

    Wave Overtopping

    The two most important factors contributing to the 2014 Dawlish railway catastrophe were wave impact forces and overtopping. Figure 13 gives the instantaneous overtopping rates for different scenarios, which experienced overtopping. It can be seen that the overtopping rates range from 0.5 m3/s/m to 16.1 m3/s/m (Fig. 13). Time histories of the wave overtopping rates show that the phenomenon occurs intermittently, and each time lasts 1.0–7.0 s. It is clear that the longer the overtopping time, the larger the volume of the water poured on the structure. The largest wave overtopping rates of 16.1 m3/s/m and 14.4 m3/s/m belong to Scn-20 and 11, respectively. These are the two scenarios that also give the largest combined wave heights (Fig. 10b).

    figure 13
    Fig. 13

    The cumulative overtopping curves (Figs. 1415) show the total water volume overtopped the structure during the entire simulation time. This is an important hazard factor as it determines the level of soil saturation, water pore pressure in the soil and soil erosion (Van der Meer et al. 2018). The maximum volume belongs to Scn-20, which is 65.0 m3/m (m-cubed of water per metre length of the wall). The overtopping volumes are 42.7 m3/m for Scn-11 and 28.8 m3/m for Scn-19. The overtopping volume is in the range of 0.7–65.0 m3/m for all scenarios.

    figure 14
    Fig. 14
    figure 15
    Fig. 15

    For comparison, we compare our modelling results with those estimated using empirical equations. For the case of the Dawlish seawall, we apply the equation proposed by Van Der Meer et al. (2018) to estimate wave overtopping rates, based on a set of decision criteria which are the influence of foreshore, vertical wall, possible breaking waves and low freeboard:

    qgH3m−−−−√=0.0155(Hmhs)12e(−2.2RcHm)qgHm3=0.0155(Hmhs)12e(−2.2RcHm)

    (6)

    where qq is the mean overtopping rate per metre length of the seawall (m3/s/m), gg is the acceleration due to gravity, HmHm is the incident wave height at the toe of the structure, RcRc is the wall crest height above mean sea level, hshs is the deep-water significant wave height and e(x)e(x) is the exponential function. It is noted that Eq. (6) is valid for 0.1<RcHm<1.350.1<RcHm<1.35. For the case of the Dawlish seawall and considering the scenarios with larger incident wave amplitude of 1.5 m (hshs= 1.5 m), the incident wave height at the toe of the structure is HmHm = 2.2—5.6 m, and the wall crest height above mean sea level is RcRc = 0.6–2.9 m. As a result, Eq. (6) gives mean overtopping rates up to approximately 2.9 m3/s/m. A visual inspection of simulated overtopping rates in Fig. 13 for Scn 11–20 shows that the mean value of the simulated overtopping rates (Fig. 13) is close to estimates using Eq. (6).

    Discussion and conclusions

    We applied a combination of eyewitness account analysis, sea level data analysis and numerical modelling in combination with our engineering judgement to explain the damage to the Dawlish railway seawall in February 2014. Main findings are:

    • Eyewitness data analysis showed that the extreme nature of the event was well forecasted in the hours prior to the storm impact; however, the magnitude of the risks to the structures was not well understood. Multiple hazards were activated simultaneously, and the effects cascaded to amplify the damage. Disaster management was effective, exemplified by the establishment of an emergency rendezvous point and temporary evacuation centre during the storm, indicating a high level of hazard awareness and preparedness.
    • Based on sea level data analysis, we identified triple peak period bands at 4–8, 8–12 and 20–25 s in the sea level data. Storm surge heights and wave oscillations were up to 0.8 m and 1.5 m, respectively.
    • Based on the numerical simulations of 20 scenarios with different water depths, incident wave amplitudes, surge heights and peak periods, we found that the wave oscillations at the foot of the seawall result in multiple wave interactions and interferences. Consequently, large wave amplitudes, up to 4.6 m higher than the height of the seawall, were generated and overtopped the wall. Extreme impulsive wave impact forces of up to 286 KN were generated by the waves interacting with the seawall.
    • We measured maximum wave overtopping rates of 0.5–16.1 m3/s/m for our scenarios. The cumulative overtopping water volumes per metre length of the wall were 0.7–65.0 m3/m.
    • Analysis of all the evidence combined with our engineering judgement suggests that the most likely initiating cause of the failure was impulsive wave impact forces destabilising one or more grouted joints between adjacent masonry blocks in the wall. Maximum observed pressures of 286 KN in our simulations are four times greater in magnitude than background pressures leading to block removal and initiating failure. Therefore, the sequence of cascading events was :1) impulsive wave impact force causing damage to masonry, 2) failure of the upper sections of the seawall, 3) loss of infill resulting in a reduction of structural strength in the landward direction, 4) ballast washout as wave overtopping and inbound wave activity increased and 5) progressive structural failure following successive tides.

    From a risk mitigation point of view, the stability of the seawall in the face of future energetic cyclonic storm events and sea level rise will become a critical factor in protecting the rail network. Mitigation efforts will involve significant infrastructure investment to strengthen the civil engineering assets combined with improved hazard warning systems consisting of meteorological forecasting and real-time wave observations and instrumentation. These efforts must take into account the amenity value of coastal railway infrastructure to local communities and the significant number of tourists who visit every year. In this regard, public awareness and active engagement in the planning and execution of the project will be crucial in order to secure local stakeholder support for the significant infrastructure project that will be required for future resilience.

    Notes

    1. https://www.networkrail.co.uk/..
    2. https://www.flow3d.com/products/flow-3d-hydro/.
    3. https://www.devonmuseums.net/Dawlish-Museum/Devon-Museums/.
    4. https://ntslf.org/.
    5. https://www.datawell.nl/Products/Buoys/DirectionalWaveriderMkIII.aspx.
    6. https://www.bodc.ac.uk/.
    7. https://coastalmonitoring.org/cco/.
    8. https://webapp.navionics.com/#boating@8&key=iactHlwfP.

    References

    Download references

    Acknowledgements

    We are grateful to Brunel University London for administering the scholarship awarded to KA. The Flow3D-Hydro used in this research for numerical modelling is licenced to Brunel University London through an academic programme contract. We sincerely thank Prof Harsh Gupta (Editor-in-Chief) and two anonymous reviewers for their constructive review comments.

    Funding

    This project was funded by the UK Engineering and Physical Sciences Research Council (EPSRC) through a PhD scholarship to Keith Adams.

    Author information

    Authors and Affiliations

    1. Department of Civil and Environmental Engineering, Brunel University London, Uxbridge, UB8 3PH, UKKeith Adams
    2. Department of Architecture and Civil Engineering, University of Bath, Bath, BA2 7AY, UKMohammad Heidarzadeh

    Corresponding author

    Correspondence to Keith Adams.

    Ethics declarations

    Conflict of interest

    The authors have no relevant financial or non-financial interests to disclose.

    Availability of data

    All data used in this study are provided in the body of the article.

    Additional information

    Publisher’s Note

    Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

    Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

    Reprints and Permissions

    About this article

    Cite this article

    Adams, K., Heidarzadeh, M. Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling. Nat Hazards (2022). https://doi.org/10.1007/s11069-022-05692-2

    Download citation

    • Received17 May 2022
    • Accepted17 October 2022
    • Published14 November 2022
    • DOIhttps://doi.org/10.1007/s11069-022-05692-2

    Share this article

    Anyone you share the following link with will be able to read this content:Get shareable link

    Provided by the Springer Nature SharedIt content-sharing initiative

    Keywords

    • Storm surge
    • Cyclone
    • Railway
    • Climate change
    • Infrastructure
    • Resilience
    Dissipating Culvert End Design for Erosion Control Using CFD Platform FLOW-3D Numerical Simulation Modeling

    CFD 플랫폼 FLOW-3D 수치 시뮬레이션 모델링을 사용한 침식 제어를 위한 분산 암거 종단 설계

    Dissipating Culvert End Design for Erosion Control Using CFD Platform FLOW-3D Numerical Simulation Modeling

    Saman Mostafazadeh-Fard

    Graduate Research Assistant, Dept. of Civil Engineering, New Mexico State Univ., P.O. Box 30001, MSC 3CE, Las Cruces, NM 88003-8001 (corresponding author). Email: samanmzf@nmsu.edu

    Zohrab Samani

    Professor, Dept. of Civil Engineering, New Mexico State Univ., P.O. Box 30001, MSC 3CE, Las Cruces, NM 88003-8001. Email: zsamani@nmsu.edu

    Abstract

    추상적인
    암거 끝에서 나오는 고속 흐름으로 인한 하류 침식 및 세굴은 수력 엔지니어가 직면한 주요 문제 중 하나입니다. 본 논문의 주요 목적은 일반적인 암거 단부에서 나오는 고속 흐름으로 인한 하류 침식 및 세굴의 위험을 줄일 수 있는 분산 암거 단부 설계를 개발하는 것이었습니다. 이를 위해 전산 유체 역학(CFD) 플랫폼 FLOW-3D 버전 11.1.0 코드를 실험 실행[결정 계수 R2>0.90 및 평균 제곱근 오차(RMSE)<1.9 cm]을 기반으로 보정 및 검증했습니다. 그런 다음 코드를 사용하여 두 가지 대안적인 소멸 암거 끝 설계(ALT 1 및 ALT 2)를 개발하고 하류 침식 및 세굴 완화 가능성을 분석했습니다. 각각의 출수유속과 운동에너지를 측정하여 전형적인 암거단부(대조)유량과 비교하였다. 결과에 따르면 제어 흐름에서의 질량 평균 유체 평균 운동 에너지는 1.37 j/kg2로 기록되었으며, ALT 1 및 ALT 2 흐름에서 각각 0.83 및 0.73 j/kg2로 측정되었습니다. 따라서 제어 흐름 하에서 하류 샌드박스 매스의 제거는 ALT 1 및 ALT 2 흐름에 비해 각각 약 11.1% 및 4.2% 더 높았습니다. FLOW-3D 코드는 암거 끝 흐름과 하류 침식을 예측하고 하류 침식을 줄일 수 있는 잠재적 소산 암거 끝을 설계하는 데 사용할 수 있습니다.

    Downstream erosion and scouring caused by high-velocity flow issuing from culvert ends are one of the main problems faced by hydraulic engineers. The main objective of this paper was to develop a dissipating culvert end design that can reduce the risk of downstream erosion and scour caused by high-velocity flow issuing from typical culvert ends. For this purpose, the computational fluid dynamics (CFD) platform FLOW-3D version 11.1.0 code was calibrated and validated based on the experimental runs [coefficient of determination R2>0.90R2>0.90 and root mean square error (RMSE)<1.9  cm(RMSE)<1.9  cm]. Two alternative dissipating culvert end designs (ALT 1 and ALT 2) were then developed using the code, and their potential in mitigation of downstream erosion and scouring was analyzed. The issuing flow velocity and kinetic energy for each were measured and compared with typical culvert end (control) flow. According to the results, mass averaged fluid mean kinetic energy in the control flow was recorded at 1.37  j/kg21.37  j/kg2 and was measured at 0.83 and 0.73  j/kg20.73  j/kg2 in ALT 1 and ALT 2 flows, respectively. Accordingly, the removal of downstream sandbox mass under control flow was approximately 11.1% and 4.2% higher compared with ALT 1 and ALT 2 flows, respectively. FLOW-3D code can be used to predict culvert end flow and downstream erosion and to design potential dissipating culvert ends that can reduce downstream erosion.

    Dissipating Culvert End Design for Erosion Control Using CFD Platform FLOW-3D Numerical Simulation Modeling
    Dissipating Culvert End Design for Erosion Control Using CFD Platform FLOW-3D Numerical Simulation Modeling
    Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.

    316-L 스테인리스강의 레이저 분말 베드 융합 중 콜드 스패터 형성의 충실도 높은 수치 모델링

    316-L 스테인리스강의 레이저 분말 베드 융합 중 콜드 스패터 형성의 충실도 높은 수치 모델링

    M. BAYAT1,* , AND J. H. HATTEL1

    • Corresponding author
      1 Technical University of Denmark (DTU), Building 425, Kgs. 2800 Lyngby, Denmark

    ABSTRACT

    Spatter and denudation are two very well-known phenomena occurring mainly during the laser powder bed fusion process and are defined as ejection and displacement of powder particles, respectively. The main driver of this phenomenon is the formation of a vapor plume jet that is caused by the vaporization of the melt pool which is subjected to the laser beam. In this work, a 3-dimensional transient turbulent computational fluid dynamics model coupled with a discrete element model is developed in the finite volume-based commercial software package Flow-3D AM to simulate the spatter phenomenon. The numerical results show that a localized low-pressure zone forms at the bottom side of the plume jet and this leads to a pseudo-Bernoulli effect that drags nearby powder particles into the area of influence of the vapor plume jet. As a result, the vapor plume acts like a momentum sink and therefore all nearby particles point are dragged towards this region. Furthermore, it is noted that due to the jet’s attenuation, powder particles start diverging from the central core region of the vapor plume as they move vertically upwards. It is moreover observed that only particles which are in the very central core region of the plume jet get sufficiently accelerated to depart the computational domain, while the rest of the dragged particles, especially those which undergo an early divergence from the jet axis, get stalled pretty fast as they come in contact with the resting fluid. In the last part of the work, two simulations with two different scanning speeds are carried out, where it is clearly observed that the angle between the departing powder particles and the vertical axis of the plume jet increases with increasing scanning speed.

    스패터와 denudation은 주로 레이저 분말 베드 융합 과정에서 발생하는 매우 잘 알려진 두 가지 현상으로 각각 분말 입자의 배출 및 변위로 정의됩니다.

    이 현상의 주요 동인은 레이저 빔을 받는 용융 풀의 기화로 인해 발생하는 증기 기둥 제트의 형성입니다. 이 작업에서 이산 요소 모델과 결합된 3차원 과도 난류 ​​전산 유체 역학 모델은 스패터 현상을 시뮬레이션하기 위해 유한 체적 기반 상용 소프트웨어 패키지 Flow-3D AM에서 개발되었습니다.

    수치적 결과는 플룸 제트의 바닥면에 국부적인 저압 영역이 형성되고, 이는 근처의 분말 입자를 증기 플룸 제트의 영향 영역으로 끌어들이는 의사-베르누이 효과로 이어진다는 것을 보여줍니다.

    결과적으로 증기 기둥은 운동량 흡수원처럼 작용하므로 근처의 모든 입자 지점이 이 영역으로 끌립니다. 또한 제트의 감쇠로 인해 분말 입자가 수직으로 위쪽으로 이동할 때 증기 기둥의 중심 코어 영역에서 발산하기 시작합니다.

    더욱이 플룸 제트의 가장 중심 코어 영역에 있는 입자만 계산 영역을 벗어날 만큼 충분히 가속되는 반면, 드래그된 나머지 입자, 특히 제트 축에서 초기 발산을 겪는 입자는 정체되는 것으로 관찰됩니다. 그들은 휴식 유체와 접촉하기 때문에 꽤 빠릅니다.

    작업의 마지막 부분에서 두 가지 다른 스캔 속도를 가진 두 가지 시뮬레이션이 수행되었으며, 여기서 출발하는 분말 입자와 연기 제트의 수직 축 사이의 각도가 스캔 속도가 증가함에 따라 증가하는 것이 명확하게 관찰되었습니다.

    Fig 1. Two different views of the computational domain for the fluid domain. The vapor plume is simulated by a moving momentum source with a prescribed temperature of 3000 K.
    Fig 1. Two different views of the computational domain for the fluid domain. The vapor plume is simulated by a moving momentum source with a prescribed temperature of 3000 K.
    Fig 2. (a) and (b) are two snapshots taken at an x-y plane parallel to the powder layer plane before and 0.008 seconds after the start of the scanning process. (c) Shows a magnified view of (b) where detailed powder particles' movement along with their velocity magnitude and directions are shown.
    Fig 2. (a) and (b) are two snapshots taken at an x-y plane parallel to the powder layer plane before and 0.008 seconds after the start of the scanning process. (c) Shows a magnified view of (b) where detailed powder particles’ movement along with their velocity magnitude and directions are shown.
    Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.
    Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.

    References

    [1] T. DebRoy et al., “Additive manufacturing of metallic components – Process, structure
    and properties,” Prog. Mater. Sci., vol. 92, pp. 112–224, 2018, doi:
    10.1016/j.pmatsci.2017.10.001.
    [2] M. Markl and C. Körner, “Multiscale Modeling of Powder Bed–Based Additive
    Manufacturing,” Annu. Rev. Mater. Res., vol. 46, no. 1, pp. 93–123, 2016, doi:
    10.1146/annurev-matsci-070115-032158.
    [3] A. Zinoviev, O. Zinovieva, V. Ploshikhin, V. Romanova, and R. Balokhonov, “Evolution
    of grain structure during laser additive manufacturing. Simulation by a cellular automata
    method,” Mater. Des., vol. 106, pp. 321–329, 2016, doi: 10.1016/j.matdes.2016.05.125.
    [4] Y. Zhang and J. Zhang, “Modeling of solidification microstructure evolution in laser
    powder bed fusion fabricated 316L stainless steel using combined computational fluid
    dynamics and cellular automata,” Addit. Manuf., vol. 28, no. July 2018, pp. 750–765,
    2019, doi: 10.1016/j.addma.2019.06.024.
    [5] A. A. Martin et al., “Ultrafast dynamics of laser-metal interactions in additive
    manufacturing alloys captured by in situ X-ray imaging,” Mater. Today Adv., vol. 1, p.
    100002, 2019, doi: 10.1016/j.mtadv.2019.01.001.
    [6] Y. C. Wu et al., “Numerical modeling of melt-pool behavior in selective laser melting
    with random powder distribution and experimental validation,” J. Mater. Process.
    Technol., vol. 254, no. July 2017, pp. 72–78, 2018, doi:
    10.1016/j.jmatprotec.2017.11.032.
    [7] W. Gao, S. Zhao, Y. Wang, Z. Zhang, F. Liu, and X. Lin, “Numerical simulation of
    thermal field and Fe-based coating doped Ti,” Int. J. Heat Mass Transf., vol. 92, pp. 83–
    90, 2016, doi: 10.1016/j.ijheatmasstransfer.2015.08.082.
    [8] A. Charles, M. Bayat, A. Elkaseer, L. Thijs, J. H. Hattel, and S. Scholz, “Elucidation of
    dross formation in laser powder bed fusion at down-facing surfaces: Phenomenonoriented multiphysics simulation and experimental validation,” Addit. Manuf., vol. 50,
    2022, doi: 10.1016/j.addma.2021.102551.
    [9] C. Meier, R. W. Penny, Y. Zou, J. S. Gibbs, and A. J. Hart, “Thermophysical phenomena
    in metal additive manufacturing by selective laser melting: Fundamentals, modeling,
    simulation and experimentation,” arXiv, 2017, doi:
    10.1615/annualrevheattransfer.2018019042.
    [10] W. King, A. T. Anderson, R. M. Ferencz, N. E. Hodge, C. Kamath, and S. A. Khairallah,
    “Overview of modelling and simulation of metal powder bed fusion process at Lawrence
    Livermore National Laboratory,” Mater. Sci. Technol. (United Kingdom), vol. 31, no. 8,
    pp. 957–968, 2015, doi: 10.1179/1743284714Y.0000000728.