Fig 2(b) Observed velocity field for aspect ratio 0.25(Sukhodolov 2002)

고정 베드의 불침투성 토양에서 흐름 패턴의 수치 시뮬레이션

NUMERICAL SIMULATION OF FLOW PATTERN IN SERIES OF IMPERMEABLE GROYNES IN FIXED BED

Kafle, Mukesh Raj1
1Asst. Professor, Department of Civil Engineering, Institute of Engineering, Pulchowk Campus, Nepal
Email: mkafle@pcampus.edu.np

Abstract

This paper presents a numerical simulation of recirculating flow patterns in groyne fields. Moreover, it entails the concept determination of proper spacing of vertical unsubmerged and impermeable groynesin seriesto control the bank erosion. Flow pattern between the groynes varies along their space. The flow in groyne field may significantly affect the flow change, bed change, bank erosion and condition of habitat. In this regard, an assessment of flow along the space of groynes will yield important data needed to diversify the object of groyne installation. So, knowledge about determination of the proper spacing of groynes in groyne field is important. Space of vertical groynes was set from 1.5 to 10 times the length of groynes. The velocity field between groynes was simulated by using Computational Fluid Dynamics (CFD) model Nays 2D. Simulated velocity field was compared with existing experimentaldata for the same parameter, which agreed satisfactorily. Based on simulated results,the optimal spacing of vertical groynes to control the bank erosion was recommended.

이 논문은 groyne 필드에서 재순환 흐름 패턴의 수치 시뮬레이션을 제공합니다. 더욱이, 그것은 제방 침식을 제어하기 위해 수직 비침수 및 불침투성 그로이네신 시리즈의 적절한 간격의 개념 결정을 수반합니다. groynes 사이의 흐름 패턴은 공간에 따라 다릅니다. groyne field의 흐름은 흐름 변화, 하상 변화, 제방 침식 및 서식지 상태에 중대한 영향을 미칠 수 있습니다. 이와 관련하여, groyne 공간을 따른 흐름의 평가는 groyne 설치 대상을 다양화하는 데 필요한 중요한 데이터를 산출할 것입니다. 따라서, groyne field에서 groyne의 적절한 간격 결정에 대한 지식이 중요합니다. 수직 여백의 간격은 여아 길이의 1.5배에서 10배 사이로 설정하였다. groyne 사이의 속도장은 CFD(Computational Fluid Dynamics) 모델 Nays 2D를 사용하여 시뮬레이션되었습니다. 시뮬레이션된 속도장은 동일한 매개변수에 대해 기존 실험 데이터와 비교되었으며 만족스럽게 일치했습니다. 모의 결과를 바탕으로 제방 침식을 억제하기 위한 최적의 수직 제방 간격을 제안하였다.

  1. Introduction
    Spur dikes or groynes are used to protect river banks from erosion and also keep the channel
    navigable.Depending upon the flow characteristics, spur-dikes may be classified as submerged and unsubmerged. Also, based on the permeability, spur dikes are further classified as permeable and
    impermeable. Herein, un-submerged !impermeable spur dikes are dealt. These structures are built from the river bank into the stream flow and usually built in group. Construction of groyne against the flow causes significant changes in flow pattern in channel. Those changes may result in scour phenomenon around groynes which may lead structure instability and changes in river morphology. Moreover, in series of groynes, spacing of groynes leads different types of recirculating flow patterns.Therefore, investigating the characteristics of flow pattern around groynes have been a great interest in river engineering. Numerous researchers like Sukhodolov et al. (2002), Hao Zhang et al.(2009), Beheshti (2010), Duan (2009), Naji(2010), Karami(2011) made a variety of experiments in order to determine the flow pattern around groynes. Most of these researchers studied effect of single groyne, while using series of groynes is more effective in protection of rivers. Besides experimental studies, variety of CFD models have been developed for computing flow pattern around hydraulic structures; like Fluent, Flow 3D, Nays 2D, Nays CUBE and SSIIM. In this study, Nays 2D numerical modelling has been used to investigate flow and recirculating pattern around a series of groynes and streamlines including components of velocities.
  1. Flow pattern in groyne fields
    Under conditions where the groynes are not submerged, the groyne fields are not really part of the wetted cross section of a river. Because of that, the flow pattern in the groyne-field is not directly the result of the discharge in the main channel. Reducing the main stream velocity has no effect on the flow pattern itself, whereas lowering the water level does (Uijttewaal et al.2001). Moreover, the flow pattern inside a groyne field may change with the change of its geometry, location along the river (inner curve, outer curve, or straight part), and/ or the groynes orientation( Przedwojski et al.1995). However, there is an indirect effect of the discharge on the flow pattern in the groyne field. Because of the flow that is diverted from the main channel into the groyne fields, water flows into the groyne field with low velocity through the downstream half of the interfacial section between the groyne field and the main channel. This water flows back to the main channel through a small width of, just downstream the upstream groyne of the groyne field ( Termes et al.1991). Flow separates on a groyne head and forms a secondary flow represented by a large scale vortex with a vertical axis of rotation called primary gyre. Deflection of the flow inside the groyne field by banks and upstream groynes leads to the development of a secondary gyre with an opposite direction of rotation to the primary gyre. Location, mutual interactions, and energy exchange between gyres are the factors that create a specific recirculation pattern, and, consequently assuming correspondence with sedimentation processes, they define deposition patterns.
  2. Model Formulation
    The CFD model selected for this study is the publically available software NAYS 2D (iRIC 2.0), which is an analytical solver for calculation of unsteady two-dimensional plane flow and riverbed deformation using boundary-fitted coordinates within general curvilinear coordinates. A numerical channel of length 8.0m and width 0.9m was created with grid size of 0.01m im stream wise and 0.03m in cross stream directions. Groynes or spur dikes of length 0.15 and width 0.01m were chosen in series. Groyne field with various aspect ratio (b/x) 0.7, 0.25, 0.17, 0.125 and 0.10, where b=length of spur dike, x=spacing of two dikes. Discharge of 0.0175 m3 /s was applied. For boundary conditions, water surface at downstream and velocity at upstream were considered as uniform flow. Relaxation coefficient for water surface calculation was considered as 0.8. For the finite-difference method, the CIP method was applied to the advection terms in equations of motion. For the turbulent field calculation, Constant eddy viscosity, Zero-equation model and k-G models were applied and compared. The model!s accuracy in predicting the velocity magnitudes is evaluated using statistical parameters- mean absolute error (MAE), mean square error(MSE), and root mean square error (RMSE). The comparison of results shows the importance of selecting an appropriate turbulence model in simulating flow field around a spur dike. From the comparison, k-I model is found superior over zero energy model and eddy viscosity model. So, k-I model is chosen as appropriate turbulence closure model.
  3. Model!s Validation
    The capability of CFD model Nays 2D to simulate the velocity field and recirculation pattern in groyne field was compared with experimental data of laboratory experiments by Sukhodolov et al. (2002). The numerical simulation was validated for aspect ratio (R=b/x=0.7) and R=0.25. For aspect ratio R=0.7, one gyre system occupies the whole area of the groyne field. The areas with lower-than-average velocity values are clearly seen in the central part of the gyre and near its corners. Velocities increase towards the margins of the gyre. For aspect ratio R=0.25, two gyre velocity fields were observed in the groyne field. In the downstream part of the groyne field a large gyre, covering two-thirds of the area is clearly visible. The left part(upstream) contains second gyre rotating much more slowly and in the direction opposed to the primary gyre. The simulated and observed velocity field pattern and gyre found satisfactorily agreed. Now, after validation, the model was used for further analysis of velocity field for various aspect ratios.
Fig 2(b) Observed velocity field for aspect ratio 0.25(Sukhodolov 2002)
Fig 2(b) Observed velocity field for aspect ratio 0.25(Sukhodolov 2002)
  1. Results and Discussions
    The calibrated model was applied to five different cases of un-submerged and impermeable groyne fields with aspect ratios R=0.70,0.25,0.17,0.125 & 0.10 and flow pattern was numerically simulated. For aspect ratio R=0.7 i.e x/b=1.5, Fig 1(a) only one lateral primary gyre was formed inside the groyne field. The circulation pattern in this case is distinguished by the main flow that is deflected outside the groyne field. The developed primary gyre prevents the main flow from penetrating the groyne field. Therefore, this pattern is desirable for navigation purposes as a continuous deep channel is maintained along the face of the groyne field. Simulated velocity pattern satisfactorily agrees with the observed velocity field Fig 1(b) for the same aspect ratio by Sukhodolov (2002). The spacing of the groyne was further increased maintaining aspect ratio R= 0.25 i. e x/b=4 Fig 2(a) and flow pattern inside the groyne field was simulated. In this case, in the downstream part of the groyne field, a primary gyre occupying almost two-third area was formed. In addition, deflection of the flow inside the groyne field by banks and upstream groynes leads to the development of a secondary gyre with an opposite direction of rotation to the primary gyre covering almost one-third part of the groyne field. Likewise in the first case, the main current is maintained deflected outside the groyne field. Simulated velocity pattern satisfactorily agrees with the observed velocity field Fig 2(b) for the same aspect ratio by Sukhodolov (2002). The spacing of the groyne was further increased maintaining aspect ratio R=0.17 i.e x/b=6. In this case the flow pattern was similar to the aspect ratio R=0.25. The spacing of the groynes was further increased maintaining aspect ratio R=0.125 i. e x/b=8. In this case, similar to the previous scenarios two longitudinal gyres but with different positions are formed. The main current is directed in to the groyne field (Fig 3) creating a much more stronger eddy near the upstream groyne and greater turbulence along the upstream face and at the groyne lower head. As the spacing between groynes increased maintaining aspect ratio R=0.10 i. e x/b=10 (Fig 4), still primary and secondary gyres are generated. The formed gyres deflect the main flow thus preventing to enter in to the groyne field in upstream part. However, in the downstream of the primary gyre and just upstream of the second groyne, the flow attacks the bank directly. The resultant velocity profiles at the deflected region y/b=3 were plotted and how the spacing of second groyne affect the result was analyzed. Spacing of groynes makes little change in upstream resultant velocity. However, in the deflected region, its effect is significant. Higher value of spacing of groyne leads higher average deviation in resultant velocity. For aspect ratio R=0.7, the average deviation estimated as 0.02%. In the case of aspect ratio R=0.25, this value was reached to 1.57%. Further increment of spacing i. e decreasing the aspect ratio R=0.17, average deviation was found 3.82%. For the aspect ratio R=0.125, that value was estimated as 4.16%.
  2. Conclusions
    Geometry of the groyne fields; width and length of the groyne field mainly cause the specific flow patterns including number and shape of eddies or gyres. Eddies developed inside the groyne field deflects the main flow preventing it entering into the dead zone. An aspect ratio close to unity gives rise to a single eddy. A smaller aspect ratio (higher spacing between groynes) gives room to two stationary eddies, a large one called primary eddy, in the downstream part of the groyne field, and a smaller secondary eddy emerges near the upstream groyne. The extreme long groyne field -case of length to width ratio of larger thaneight shows penetration of main flow into the groyne field. The two eddies remain in a relatively stable position, while the main flow zone starts to penetrate into groyne field further downstream. In all cases, there is an eddy detaches from the upstream groyne tip that travels along the main channel groyne field interface and eventually merges with the primary eddy. The simulated results indicate that the spacing of groynes or spur dikes from the controlling of bank erosion point of view should be limited within six times the length of groyne.
Fig 3 Computed velocity field for aspect ratio 0.125
Fig 3 Computed velocity field for aspect ratio 0.125
Fig 4 Computed velocity field for aspect ratio 0.10
Fig 4 Computed velocity field for aspect ratio 0.10
Fig 5 Resultant velocity profiles at y/b=3
Fig 5 Resultant velocity profiles at y/b=3
Fig 5 Resultant velocity profiles at y/b=3
Fig 5 Resultant velocity profiles at y/b=3

References

  1. Holtz, K.P  Numerical simulation of recirculating flow at groynes.Å Computer Methods in Water Resources, Vol 2, No 2 (1991).
  2. Hossein, Bassar; Abdollah, Ardeshir; Hojat, Karami.  Numerical simulation of flow pattern around spur dikes series in rigid bed.Å 9th international congress on civil engineering, May 8- 10,2012, Isfahan University of Technology (IUT) , Isfahan, Iran (2012).
  3. Kang, J.G; Yeo, H.K; Kim,S.J An experimental study on a characteristics of flow around groyne area by install conditions.Å www.SciRP.org/journal/eng(2012).
  4. Shimizu,Y; Nelson,JIntroduction of Nays solver in iRIC.Åwww.i-ric.org(2012).
  5. Sukhodolov, A. Uijttewaal, W. S. J., and Engelhardt, C. On the correspondence between morphological and hydro dynamical patterns of groyne fields.Å Earth Surf. Processes Landforms, 27(3) (2002).
  6. Uijttewall, W.S.J; Lehman,D; VanMazijk,A.  Exchange process between a river and its groyne fields-model experiments.Å Journal of Hydraulic Engineering, ASCE, 127(11) (2001).
  7. Uijttewall, W.S.J Groyne field velocity patterns determined with particle tracking
    velocimetryÅ.28th IAHR congress, Graz, Austria (1999).
  8. Yossef, Mohamed  Flow details near groynes: Experimental investigations.Å Journal of Hydraulic Engineering, ASCE, 137 (2011).
Figura 4.5 – Superfície de contorno de velocidades a 3,9 m do piso após 20 s de acionamento da motosserra.

전기톱 절단 시험실에서 배기 시스템의 CFD 시뮬레이션

CFD Simulation of an exhaust system in chainsaw cutting test room

Área de Concentração: Energia e Fenômenos de Transporte
Orientador: Prof. Diogo Elias da Vinha Andrade
Comissão de Avaliação:
Profa
. Letícia Jenisch Rodrigues
Prof. Francis Henrique Ramos França
Prof. Paulo Smith Schneider

Abstract

The objective of the present work is to improve an exhaust system for a chain saw
cutting test room through a fluid dynamic computational simulation (CFD). The purpose of the
designed system is to remove combustion gases, such as carbon monoxide (CO), which is
extremely toxic, colourless and inodorous. The current system consists of a set of exhaust fans,
a hood and an insufflation set. From experimental tests, the input data of the simulation were
collected to define the variables and boundary conditions such as volumetric flow of CO, its
temperature and density and the supply of fresh air in the room. The necessary means of
instrumentation are presented so that it is possible to obtain the correlation with the results of
the simulation and, once validated, a study of mesh refinement was carried out. With this, the
possible solutions to the problem are evaluated through a case study involving the geometry of
the hood and the exhaust and insufflation systems. By changing the hood geometry, the most
satisfactory result was obtained for the problem, as it was shown to be able to remove all CO
from the room, respecting the proposed operational limits.

현재 연구의 목적은 유체 역학 계산 시뮬레이션(CFD)을 통해 체인 톱 절단 시험실의 배기 시스템을 개선하는 것입니다. 설계된 시스템의 목적은 매우 유독하고 무색이며 냄새가 나는 일산화탄소(CO)와 같은 연소 가스를 제거하는 것입니다. 현재 시스템은 배기 팬 세트, 후드 및 흡입 세트로 구성됩니다. 실험 테스트에서 시뮬레이션의 입력 데이터는 CO의 체적 유량, 온도 및 밀도, 실내의 신선한 공기 공급과 같은 변수 및 경계 조건을 정의하기 위해 수집되었습니다. 시뮬레이션 결과와의 상관관계를 얻을 수 있도록 필요한 계측 수단을 제시하고 검증 후 메쉬 미세화 연구를 수행했습니다. 이를 통해 후드의 기하학적 구조와 배기 및 흡입 시스템과 관련된 사례 연구를 통해 문제에 대한 가능한 솔루션을 평가합니다. 후드 형상을 변경함으로써 제안된 작동 한계를 준수하면서 실내에서 모든 CO를 제거할 수 있는 것으로 나타났기 때문에 문제에 대해 가장 만족스러운 결과를 얻었습니다.

Keywords

carbon monoxide, exhaust system, CFD simulation.

Figura 3.2 – Geometria simplificada da sala de testes da primeira versão.
Figura 3.2 – Geometria simplificada da sala de testes da primeira versão.
Figura 3.4 – Velocidade nos sensores de velocidade para verificar independência de malha para cada refino após 20 s do acionamento da motosserra.
Figura 3.4 – Velocidade nos sensores de velocidade para verificar independência de malha para cada refino após 20 s do acionamento da motosserra.
Figura 3.4 – Velocidade nos sensores de velocidade para verificar independência de malha para cada refino após 20 s do acionamento da motosserra.
Figura 3.4 – Velocidade nos sensores de velocidade para verificar independência de malha para cada refino após 20 s do acionamento da motosserra.
Figura 3.5 – Vista em detalhe da coifa e os elementos que a compõe.
Figura 3.5 – Vista em detalhe da coifa e os elementos que a compõe.
Figura 3.6 – Geometrias das versões simuladas do Teste de Casos.
Figura 3.6 – Geometrias das versões simuladas do Teste de Casos.
Figura 4.1 – Concentração de CO medida pelos sensores da simulação.
Figura 4.1 – Concentração de CO medida pelos sensores da simulação.
Figura 4.2 – Plano indicando os três cortes realizados na simulação para as superfícies de contorno sendo (1) a altura do escape da máquina, (2) a altura dos detectores de CO e (3) a altura dos exaustores
Figura 4.2 – Plano indicando os três cortes realizados na simulação para as superfícies de contorno sendo (1) a altura do escape da máquina, (2) a altura dos detectores de CO e (3) a altura dos exaustores
Figura 4.3 – Superfície de contorno de velocidades a 1,3 m do piso após 20 s de acionamento da motosserra.
Figura 4.3 – Superfície de contorno de velocidades a 1,3 m do piso após 20 s de acionamento da motosserra.
Figura 4.4 – Superfície de contorno de velocidades a 1,5 m do piso após 20 s de acionamento da motosserra.
Figura 4.4 – Superfície de contorno de velocidades a 1,5 m do piso após 20 s de acionamento da motosserra.
Figura 4.5 – Superfície de contorno de velocidades a 3,9 m do piso após 20 s de acionamento da motosserra.
Figura 4.5 – Superfície de contorno de velocidades a 3,9 m do piso após 20 s de acionamento da motosserra.
Figura 4.6 – Superfície de contorno de massas específicas a 1,3 m do piso após 20 s de acionamento da motosserra.
Figura 4.6 – Superfície de contorno de massas específicas a 1,3 m do piso após 20 s de acionamento da motosserra.
Figura 4.7 – Superfície de contorno de massas específicas a 1,5 m do piso após 20 s de acionamento da motosserra.
Figura 4.7 – Superfície de contorno de massas específicas a 1,5 m do piso após 20 s de acionamento da motosserra.
Figura 4.8 – Superfície de contorno de massas específicas a 3,9 m do piso após 20 s de acionamento da motosserra.
Figura 4.8 – Superfície de contorno de massas específicas a 3,9 m do piso após 20 s de acionamento da motosserra.
Figura 4.9 – Volume total de monóxido ao longo do tempo na sala.
Figura 4.9 – Volume total de monóxido ao longo do tempo na sala.
Figura 4.9 – Vazão volumétrica de CO ao longo do tempo através da superfície de controle. As linhas contínuas representam curvas de ajuste aos dados simulados.
Figura 4.9 – Vazão volumétrica de CO ao longo do tempo através da superfície de controle. As linhas contínuas representam curvas de ajuste aos dados simulados.

REFERENCIAS

CROWL, Daniel A.; LOUVAR, Joseph F. Chemical process safety: fundamentals with applications. Second Edition, Pearson Education, 2001. BURNETT, J.; CHAN, M. Y. Criteria for air quality in enclosed car parks. Em: Proceedings of the Institution of Civil Engineers-Transport. Thomas Telford-ICE Virtual Library, 1997. Disponível em: < http://www.icevirtuallibrary.com/doi/10.1680/itran.1997.29379> SITTISAK, P.; CHARINPANITKUL T.; CHALERMSINSUWAN, B. Enhancement of carbon monoxide removal in an underground car park using ventilation system with single and twin jet fans. Em: Tunnelling and Underground Space Technology. Volume 97, 2020. VERSTEEG, H.K.; MALALASEKERA, W. Computational Fluid Dynamics: The Finite Volume Method. Second Edition, Pearson Education, 2007. BULIŃSKA, A.; POPIOŁEK, Z.; BULIŃSKI, Z.; Experimentally validated CFD analysis on sampling region determination of average indoor carbon dioxide concentration in occupied space. Em: Building and Environment. Volume 72, 2014. KARIMI, H.; RIAZI, B.; MOHHAMMADI, M. Application of Computational Fluid Dynamics in the Simulation of Carbon Monoxide Distribution, a Case Study: Sayad Underground Tunnel in Tehran. Disponível em: YAKHOT, V.; ORSZAG, S. Renormalization group analysis of turbulence. I. Basic theory. Journal of scientific computing, v. 1, n. 1, p. 3-51, 1986. VAN HOOFF, T.; BLOCKEN, B. CFD evaluation of natural ventilation of indoor environments by the concentration decay method: CO2 gas dispersion from a semi-enclosed stadium. Building and Environment, v. 61, p. 1-17, 2013. Disponível em: < https://www.sciencedirect.com/science/article/pii/S0360132312003216> YANG, L., YE, M., HE, B. CFD simulation research on residential indoor air quality. Em Science of The Total Environment. Volume 472, 2014. Disponível em: < https://www.sciencedirect.com/science/article/pii/S0048969713014228> Flow-3D. Flow-3D User’s Guide. Versão 12, 2020. LAUNDER, B. E. e SPALDING, D. B. The numerical computation of turbulent flows. Em Computer Methods in Applied Mechanics and Engineering, vol. 3, 1974. pp. 269-289 MALISKA, Clovis R. Transferência de Calor e Mecânica dos Fluidos Computacional: fundamentos e coordenadas generalizadas. Segunda Edição. Rio de Janeiro, LTC, 2004. ROACHE, P. J. Perspective: A Method for Uniform Reporting of Grid Refinement Studies, Journal of Fluids Engineering, Vol. 116, 1994; 405-413.

Computational Fluid Dynamics, 온실

CFD 사용: 유압 구조 및 농업에서의 응용

USO DE CFD COMO HERRAMIENTA PARA LA MODELACIÓN Y  PREDICCIÓN NUMÉRICA DE LOS FLUIDOS: APLICACIONES EN  ESTRUCTURAS HIDRÁULICAS Y AGRICULTURA

Cruz Ernesto Aguilar-Rodriguez1*; Candido Ramirez-Ruiz2; Erick Dante Mattos Villarroel3 

1Tecnológico Nacional de México/ITS de Los Reyes. Carretera Los Reyes-Jacona, Col. Libertad. 60300.  Los Reyes de Salgado, Michoacán. México. 

ernesto.ar@losreyes.tecnm.mx – 3541013901 (*Autor de correspondencia) 

2Instituto de Ciencias Aplicadas y Tecnología, UNAM. Cto. Exterior S/N, C.U., Coyoacán, 04510, Ciudad  de México. México.  3Riego y Drenaje. Instituto Mexicano de Tecnología del Agua. Paseo Cuauhnáhuac 8532, Progreso,  Jiutepec, Morelos, C.P. 62550. México.

Abstract

공학에서 유체의 거동은 설명하기에 광범위하고 복잡한 과정이며, 유체역학은 유체의 거동을 지배하는 방정식을 통해 유체 역학 현상을 분석할 수 있는 과학 분야이지만 이러한 방정식에는 전체 솔루션이 없습니다. . 전산유체역학(Computational Fluid Dynamics, 이하 CFD)은 수치적 기법을 통해 방정식의 해에 접근할 수 있는 도구로, 신뢰할 수 있는 계산 모델을 얻기 위해서는 물리적 모델의 실험 데이터로 평가해야 합니다. 수력구조물에서 선형 및 미로형 여수로에서 시뮬레이션을 수행하고 배출 시트의 거동과 현재의 폭기 조건을 분석했습니다. 침강기에서 유체의 특성화를 수행하고 필요한 특성에 따라 사체적, 피스톤 또는 혼합의 분수를 수정하는 것이 가능합니다. 농업에서는 온실 환경을 특성화하고 환경에 대한 재료의 디자인, 방향 및 유형 간의 관계를 찾는 데 사용할 수 있습니다. 발견된 가장 중요한 결과 중 온실의 길이와 설계가 환기율에 미칠 수 있는 영향으로 온실의 길이는 높이의 6배 미만인 것이 권장됩니다.

키워드: Computational Fluid Dynamics, 온실,

Spillway, Settler 기사: COMEII-21048 소개 

CFD는 유체 운동 문제에 대한 수치적 솔루션을 얻어 수리학적 현상을 더 잘 이해할 수 있게 함으로써 공간 시각화를 가능하게 하는 수치 도구입니다. 예를 들어, 수력 공학에서 벤츄리(Xu, Gao, Zhao, & Wang, 2014) 워터 펌핑(ȘCHEAUA, 2016) 또는 개방 채널 적용( Wu et 알., 2000). 

문헌 검토는 실험 연구에서 검증된 배수로의 흐름 거동에 대한 수리학적 분석을 위한 CFD 도구의 효율성을 보여줍니다. 이 검토는 둑의 흐름 거동에 대한 수리학적 분석을 위한 CFD의 효율성을 보여줍니다. Crookston et al. (2012)는 미로 여수로에 대해 Flow 3D로 테스트를 수행했으며, 배출 계수의 결과는 3%에서 7%까지 다양한 오류로 실험적으로 얻은 결과로 허용 가능했으며 연구 결과 측면에 저압 영역이 있음을 발견했습니다. 익사 방식으로 작업할 때 위어의 벽. Zuhair(2013)는 수치 모델링 결과를 Mandali weir 원형의 실험 데이터와 비교했습니다.  

최근 연구에서는 다양한 난류 모델을 사용하여 CFD를 적용할 가능성이 있음을 보여주었습니다. 그리고 일부만이 음용수 처리를 위한 침적자의 사례 연구를 제시했으며, 다른 설계 변수 중에서 기하학적인 대안, 수온 변화 등을 제안했습니다. 따라서 기술 개발로 인해 설계 엔지니어가 유체 거동을 분석하는 데 CFD 도구를 점점 더 많이 사용하게 되었습니다. 

보호 농업에서 CFD는 온실 환경을 모델링하고 보조 냉방 또는 난방 시스템을 통해 온실의 미기후 관리를 위한 전략을 제안하는 데 사용되는 기술이었습니다(Aguilar Rodríguez et al., 2020).  

2D 및 3D CFD 모델을 사용한 본격적인 온실 시뮬레이션은 태양 복사 모델과 현열 및 잠열 교환 하위 모델의 통합을 통해 온실의 미기후 분포를 연구하는 데 사용되었습니다(Majdoubi, Boulard, Fatnassi, & Bouirden, 2009). 마찬가지로 이 모델을 사용하여 온실 설계(Sethi, 2009), 덮개 재료(Baxevanou, Fidaros, Bartzanas, & Kittas, 2018), 시간, 연중 계절( Tong, Christopher, Li, & Wang, 2013), 환기 유형 및 구성(Bartzanas, Boulard, & Kittas, 2004). 

CFD 거래 프로그램은 사용자 친화적인 플랫폼으로 설계되어 결과를 쉽게 관리하고 이해할 수 있습니다.  

Figura 1. Distribución de presiones y velocidades en un vertedor de pared delgada.
Figura 2. Perfiles de velocidad y presión en la cresta vertedora.
Figura 3. Condiciones de aireación en vertedor tipo laberinto. (A)lámina adherida a la pared del
vertedor, (B) aireado, (C) parcialmente aireado, (D) ahogado.
Figura 4. Realización de prueba de riego.
Figura 5. Efecto de la posición y dirección de los calefactores en un invernadero a 2 m del suelo.
Figura 5. Efecto de la posición y dirección de los calefactores en un invernadero a 2 m del suelo.
Figura 6. Indicadores ambientales para medir el confort ambiental de los cultivos.
Figura 6. Indicadores ambientales para medir el confort ambiental de los cultivos.
Figura 7. Líneas de corriente dentro del sedimentador experimental en estado estacionario  (Ramirez-Ruiz, 2019).
Figura 7. Líneas de corriente dentro del sedimentador experimental en estado estacionario (Ramirez-Ruiz, 2019).

Referencias Bibliográficas

Aguilar-Rodriguez, C.; Flores-Velazquez, J.; Ojeda-Bustamante, W.; Rojano, F.; Iñiguez-
Covarrubias, M. 2020. Valuation of the energyperformance of a greenhouse with

an electric heater using numerical simulations. Processes, 8, 600.

Aguilar-Rodriguez, C.; Flores-Velazquez, J.; Rojano, F.; Ojeda-Bustamante, W.; Iñiguez-
Covarrubias, M. 2020. Estimación del ciclo de cultivo de tomate (Solanum

lycopersicum L.) en invernadero, con base en grados días calor (GDC) simulados
con CFD. Tecnología y ciencias del agua, ISSN 2007-2422, 11(4), 27-57.
Al-Sammarraee, M., y Chan, A. (2009). Large-eddy simulations of particle sedimentation
in a longitudinal sedimentation basin of a water treatment plant. Part 2: The effects
of baffles. Chemical Engineering Journal, 152(2-3), 315-321.
doi:https://doi.org/10.1016/j.cej.2009.01.052.
Bartzanas, T.; Boulard, T.; Kittas, C. 2004. Effect of vent arrangement on windward
ventilation of a tunnel greenhouse. Biosystems Engineering, 88(4).
Baxevanou, C.; Fidaros, D.; Bartzanas, T.; Kittas, C. 2018. Yearly numerical evaluation of
greenhouse cover materials. Computers and Electronics in Agriculture, 149, 54–

  1. DOI: https://doi.org/10.1016/j.compag.2017.12.006.
    Crookston, B. M., & Tullis, B. P. 2012. Labyrinth weirs: Nappe interference and local
    submergence. Journal of Irrigation and Drainage Engineering, 138(8), 757-765.
    Fernández, J. M. 2012. Técnicas numéricas en Ingeniería de Fluidos: Introducción a la
    Dinámica de Fluidos Computacional (CFD) por el Método de Volumen Finito;
    Reverté, Barcelona, pp. 98-294.
    Goula, A., Kostoglou, M., Karapantsios, T., y Zouboulis, A. (2008). The effect of influent
    temperature variations in a sedimentation tank for potable water treatment— A
    computational fluid dynamics study. Water Research, 42(13), 3405-3414.
    doi://doi.org/10.1016/j.watres.2008.05.002.
    Majdoubi, H.; Boulard, T.; Fatnassi, H.; Bouirden, L. 2009. Airflow and microclimate
    patterns in a one-hectare Canary type greenhouse: an experimental and CFD
    assisted study. Agricultural and Forest Meteorology, 149(6-7), 1050-1062.
    Ramirez-Ruiz Candido (2019). Estudio hidrodinámico de sedimentadores de alta tasa en
    plantas potabilizadoras utilizando dinámica de fluidos computacional (CFD).
    Universidad Nacional Autónoma de México. Tesis de maestría.
    Sánchez, J. M. C., & Elsitdié, L. G. C. 2011. Consideraciones del mallado aplicadas al
    cálculo de flujos bifásicos con las técnicas de dinámica de fluidos computacional.
    J. Introd. Inv. UPCT., 4, 33-35.
    Sethi, V.P. 2009. On the selection of shape and orientation of a greenhouse: Thermal
    modeling and experimental validation, Sol. Energy, 83, 21–38.
    ȘCHEAUA, F. 2016. AGRICULTURAL FIELD IRRIGATION SOLUTION BASED ON
    VENTURI NOZZLE γ 2 g γ 2 g. JOURNAL OF INDUSTRIAL DESIGN AND
    ENGINEERING GRAPHICS, 2(1), 31–35.

Tong, G.; Christopher, D.; Li, T.; Wang, T. 2013. Passive solar energy utilization: a review
of cross-section building parameter selection for Chinese solar greenhouses.
Renewable and Sustainable Energy Reviews, 26, 540-548.

Xu, Y., Gao, L., Zhao, Y., & Wang, H. 2014. Wet gas overreading characteristics of a long-
throat Venturi at high pressure based on CFD. Flow Measurement and

Instrumentation, 40, 247–255. https://doi.org/10.1016/j.flowmeasinst.2014.09.004
Wu, W., Rodi, W y Wenka, T. 2000. 3D numerical modeling of flow and sediment transport
in open channels. ASCE Journal of Hydraulic Engineering. Vol 126 Num 1.
Zuhair al zubaidy, Riyadh. 2013. Numerical Simulation of Two-Phase Flow.
En:International Journal of Structural and Civil Engineering Research. Vol 2, No 3;
13p

Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulation

Understanding dry-out mechanism in rod bundles of boiling water reactor

끓는 물 원자로 봉 다발의 건조 메커니즘 이해

Liril D.SilviaDinesh K.ChandrakercSumanaGhoshaArup KDasb
aDepartment of Chemical Engineering, Indian Institute of Technology, Roorkee, India
bDepartment of Mechanical Engineering, Indian Institute of Technology, Roorkee, India
cReactor Engineering Division, Bhabha Atomic Research Centre, Mumbai, India

Abstract

Present work reports numerical understanding of interfacial dynamics during co-flow of vapor and liquid phases of water inside a typical Boiling Water Reactor (BWR), consisting of a nuclear fuel rod bundle assembly of 7 pins in a circular array. Two representative spacings between rods in a circular array are used to carry out the simulation. In literature, flow boiling in a nuclear reactor is dealt with mechanistic models or averaged equations. Hence, in the present study using the Volume of Fluid (VOF) based multiphase model, a detailed numerical understanding of breaking and making in interfaces during flow boiling in BWR is targeted. Our work will portray near realistic vapor bubble and liquid flow dynamics in rod bundle scenario. Constant wall heat flux for fuel rod and uniform velocity of the liquid at the inlet patch is applied as a boundary condition. The saturation properties of water are taken at 30 bar pressure. Flow boiling stages involving bubble nucleation, growth, merging, local dry-out, rewetting with liquid patches, and complete dry-out are illustrated. The dry-out phenomenon with no liquid presence is numerically observed with phase fraction contours at various axial cut-sections. The quantification of the liquid phase fraction at different axial planes is plotted over time, emphasizing the progressive dry-out mechanism. A comparison of liquid-vapor distribution for inner and outer rods reveals that the inner rod’s dry-out occurs sooner than that of the outer rod. The heat transfer coefficient to identify the heat dissipation capacity of each case is also reported.

현재 작업은 원형 배열에 있는 7개의 핀으로 구성된 핵연료봉 다발 어셈블리로 구성된 일반적인 끓는 물 원자로(BWR) 내부의 물의 증기 및 액체상의 동시 흐름 동안 계면 역학에 대한 수치적 이해를 보고합니다.

원형 배열의 막대 사이에 두 개의 대표적인 간격이 시뮬레이션을 수행하는 데 사용됩니다. 문헌에서 원자로의 유동 비등은 기계론적 모델 또는 평균 방정식으로 처리됩니다.

따라서 VOF(Volume of Fluid) 기반 다상 모델을 사용하는 본 연구에서는 BWR에서 유동 비등 동안 계면의 파괴 및 생성에 대한 자세한 수치적 이해를 목표로 합니다.

우리의 작업은 막대 번들 시나리오에서 거의 사실적인 증기 기포 및 액체 흐름 역학을 묘사합니다. 연료봉에 대한 일정한 벽 열유속과 입구 패치에서 액체의 균일한 속도가 경계 조건으로 적용됩니다. 물의 포화 특성은 30bar 압력에서 취합니다.

기포 핵 생성, 성장, 병합, 국소 건조, 액체 패치로 재습윤 및 완전한 건조를 포함하는 유동 비등 단계가 설명됩니다. 액체가 존재하지 않는 건조 현상은 다양한 축 단면에서 위상 분율 윤곽으로 수치적으로 관찰됩니다.

다른 축 평면에서 액상 분율의 정량화는 점진적인 건조 메커니즘을 강조하면서 시간이 지남에 따라 표시됩니다. 내부 막대와 외부 막대의 액-증기 분포를 비교하면 내부 막대의 건조가 외부 막대보다 더 빨리 발생함을 알 수 있습니다. 각 경우의 방열 용량을 식별하기 위한 열 전달 계수도 보고됩니다.

Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulation
Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulation
Fig. 2. (a-c) dimensions and mesh configuration for G = 6 mm; (d-f) dimensions and mesh configuration for G = 0.6 mm
Fig. 2. (a-c) dimensions and mesh configuration for G = 6 mm; (d-f) dimensions and mesh configuration for G = 0.6 mm
Fig. 3. Simulating the effect of spacer (a) Spacer configuration around rod bundle (b) Mesh structure in spacer zone (c) Distribution of vapor bubbles in a rod bundle with spacer (d) Liquid phase fraction comparison for geometry with and without spacer (e,f,g) Wall temperature comparison for geometry with and without spacer; WS: With Spacer, WOS: Without Spacer; Temperature in the y-axis is in (f) and (g) is same as (e).
Fig. 3. Simulating the effect of spacer (a) Spacer configuration around rod bundle (b) Mesh structure in spacer zone (c) Distribution of vapor bubbles in a rod bundle with spacer (d) Liquid phase fraction comparison for geometry with and without spacer (e,f,g) Wall temperature comparison for geometry with and without spacer; WS: With Spacer, WOS: Without Spacer; Temperature in the y-axis is in (f) and (g) is same as (e).
Fig. 4. Validation of the present numerical model with crossflow boiling over a heated cylindrical rod [40]
Fig. 4. Validation of the present numerical model with crossflow boiling over a heated cylindrical rod [40]
Fig. 5. Grid-Independent study in terms of vapor volume in 1/4th of computational domain
Fig. 5. Grid-Independent study in terms of vapor volume in 1/4th of computational domain
Fig. 6. Interface contour for G = 6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; they are showing nucleation, growth, merging, and pseudo-steady-state condition.
Fig. 6. Interface contour for G = 6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; they are showing nucleation, growth, merging, and pseudo-steady-state condition.
Fig. 7. Interface contours for G = 0.6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; It shows dry-out at pseudo-steady-state near the exit
Fig. 7. Interface contours for G = 0.6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; It shows dry-out at pseudo-steady-state near the exit
Fig. 8. Vapor-liquid distribution across various distant cross-sections (Black color indicates liquid; Gray color indicates vapor); Magnification factor: 1 × (for a and b), 1.5 × (for c and d)
Fig. 8. Vapor-liquid distribution across various distant cross-sections (Black color indicates liquid; Gray color indicates vapor); Magnification factor: 1 × (for a and b), 1.5 × (for c and d)
Fig. 21. Two-phase flow mixture velocity (u¯z); for G = 6 mm, r = 5 means location at inner heated wall and r = 25 means location at outer adiabatic wall; for G = 0.66 mm, r = 5 means location at inner heated wall and r = 16.6 mm means location at outer adiabatic wall.
Fig. 21. Two-phase flow mixture velocity (u¯z); for G = 6 mm, r = 5 means location at inner heated wall and r = 25 means location at outer adiabatic wall; for G = 0.66 mm, r = 5 means location at inner heated wall and r = 16.6 mm means location at outer adiabatic wall.

References

[1] J. Würtz, An Experimental and Theoretical Investigation of Annular Steam-Water Flow in Tubes and Annuli at 30 to 90 Bar, Risø National Laboratory,
Roskilde, 1978.
[2] W. Tian, A. Myint, Z. Li, S. Qiu, G.H. Su, D. Jia, Experimental study on dryout point in vertical narrow annulus under low flow conditions, in: International Conference on Nuclear Engineering, 4689, 2004, pp. 643–648. Jan
1Vol.
[3] K.M. Becker, C.H. Ling, S. Hedberg, G. Strand, An experimental investigation of
post dryout heat transfer, R. Inst. Technol. (1983).
[4] K.M. Becker, A Burnout Correlation for Flow of Boiling Water in Vertical Rod
Bundles, AB Atomenergi, 1967.
[5] Jr J.R. Barbosa, G.F. Hewitt, S.M. Richardson, High-speed visualisation of nucleate boiling in vertical annular flow, Int. J. Heat Mass Transf. 46 (26) (2003)
5153–5160 1, doi:10.1016/S0017-9310(03)00255-2.
[6] Y. Mizutani, A. Tomiyama, S. Hosokawa, A. Sou, Y. Kudo, K. Mishima, Twophase flow patterns in a four by four rod bundle, J. Nucl. Sci. Technol. 44 (6)
(2007) 894–901 1, doi:10.1080/18811248.2007.9711327.
[7] S.S. Paranjape, Two-Phase Flow Interfacial Structures in a Rod Bundle Geometry, Purdue University, 2009.
[8] D. Lavicka, J. Polansky, Model of the cooling of a nuclear reactor fuel rod, Multiph. Sci. Technol. 25 (2-4) (2013), doi:10.1615/MultScienTechn.v25.i2-4.90.
[9] M. Thurgood, J. Kelly, T. Guidotti, R. Kohrt, K. Crowell, Tech. rep., Pacific Northwest National Laboratory, 1983.
[10] S. Sugawara, Droplet deposition and entrainment modeling based on the
three-fluid model, Nucl. Eng. Des. 122 (1-3) (1990) 67–84, doi:10.1016/
0029-5493(90)90197-6.
[11] C. Adamsson, J.M. Le Corre, Modeling and validation of a mechanistic tool
(MEFISTO) for the prediction of critical power in BWR fuel assemblies, Nucl.
Eng. Des. 241 (8) (2011) 2843–2858, doi:10.1016/j.nucengdes.2011.01.033.
[12] S. Talebi, H. Kazeminejad, A mathematical approach to predict dryout in a rod
bundle, Nucl. Eng. Des. 249 (2012) 348–356, doi:10.1016/j.nucengdes.2012.04.
016.
[13] H. Anglart, O. Nylund, N. Kurul, M.Z. Podowski, CFD prediction of flow and
phase distribution in fuel assemblies with spacers, Nucl. Eng. Des. 177 (1-3)
(1997) 215–228, doi:10.1016/S0029-5493(97)00195-7.
[14] H. Li, H. Anglart, CFD model of diabatic annular two-phase flow using the
Eulerian–Lagrangian approach, Ann. Nucl. Energy 77 (2015) 415–424, doi:10.
1016/j.anucene.2014.12.002.
[15] G. Sorokin, A. Sorokin, Experimental and numerical investigation of liquid metal boiling in fuel subassemblies under natural circulation conditions, Prog. Nucl. Energy 47 (1-4) (2005) 656–663, doi:10.1016/j.pnucene.2005.
05.069.
[16] W.D. Pointer, A. Tentner, T. Sofu, D. Weber, S. Lo, A. Splawski, Eulerian
two-phase computational fluid dynamics for boiling water reactor core analysis, Joint International Topical Meeting on Mathematics and Computation and
Supercomputing in Nuclear Applications (M and C± SNA), 2007.
[17] K. Podila, Y. Rao, CFD modelling of supercritical water flow and heat transfer
in a 2 × 2 fuel rod bundle, Nucl. Eng. Des. 301 (2016) 279–289, doi:10.1016/j.
nucengdes.2016.03.019.
[18] H. Pothukuchi, S. Kelm, B.S. Patnaik, B.V. Prasad, H.J. Allelein, Numerical investigation of subcooled flow boiling in an annulus under the influence of eccentricity, Appl. Therm. Eng. 129 (2018) 1604–1617, doi:10.1016/j.applthermaleng.
2017.10.105.
[19] H. Pothukuchi, S. Kelm, B.S. Patnaik, B.V. Prasad, H.J. Allelein, CFD modeling of
critical heat flux in flow boiling: validation and assessment of closure models,
Appl. Therm. Eng. 150 (2019) 651–665, doi:10.1016/j.applthermaleng.2019.01.
030.
[20] W. Fan, H. Li, H. Anglart, A study of rewetting and conjugate heat transfer
influence on dryout and post-dryout phenomena with a multi-domain coupled CFD approach, Int. J. Heat Mass Transf. 163 (2020) 120503, doi:10.1016/j.
ijheatmasstransfer.2020.120503.
[21] R. Zhang, T. Cong, G. Su, J. Wang, S. Qiu, Investigation on the critical heat
flux in typical 5 by 5 rod bundle at conditions prototypical of PWR based
on CFD methodology, Appl. Therm. Eng. 179 (2020) 115582, doi:10.1016/j.
applthermaleng.2020.115582.

[22] L.D. Silvi, A. Saha, D.K. Chandraker, S. Ghosh, A.K. Das, Numerical analysis of
pre-dryout sequences through the route of interfacial evolution in annular gasliquid two-phase flow with phase change, Chem. Eng. Sci. 212 (2020) 115356,
doi:10.1016/j.ces.2019.115356.
[23] L.D. Silvi, D.K. Chandraker, S. Ghosh, A.K. Das, On-route to dryout through sequential interfacial dynamics in annular flow boiling around temperature and
heat flux controlled heater rod, Chem. Eng. Sci. 229 (2021) 116014, doi:10.1016/
j.ces.2020.116014.
[24] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface
tension, J. Comput. Phys. 100 (2) (1992) 335–354, doi:10.1016/0021-9991(92)
90240-Y.
[25] B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, G. Zanetti, Modelling merging
and fragmentation in multiphase flows with SURFER, J. Comput. Phys. 113 (1)
(1994) 134–147, doi:10.1006/jcph.1994.1123.
[26] I. Tanasawa, Advances in condensation heat transfer, Ad. Heat Transf. 21 (1991)
55–139 Vol, doi:10.1016/S0065-2717(08)70334-4.
[27] V.H. Del Valle, D.B. Kenning, Subcooled flow boiling at high heat flux, Int.
J. Heat Mass Transf. 28 (10) (1985) 1907–1920, doi:10.1016/0017-9310(85)
90213-3.
[28] B. Matzner, G.M. Latter, Reduced pressure drop space for boiling water reactor
fuel bundles, US Patent US5375154A, (1993)
[29] C. Unal, O. Badr, K. Tuzla, J.C. Chen, S. Neti, Pressure drop at rod-bundle spacers
in the post-CHF dispersed flow regime, Int. J. Multiphase Flow 20 (3) (1994)
515–522, doi:10.1016/0301-9322(94)90025-6.
[30] D.K. Chandraker, A.K. Nayak, V.P. Krishnan, Effect of spacer on the dryout of
BWR fuel rod assemblies, Nucl. Eng. Des. 294 (2015), doi:10.1016/j.nucengdes.
2015.09.004.
[31] S.K Verma, S.L. Sinha, D.K. Chandraker, A comprehensive review of the spacer
effect on performance of nuclear fuel bundle using computational fluid dynamics methodology, Mater. Today: Proc. 4 (2017) 100030–110034, doi:10.
1016/j.matpr.2017.06.315.
[32] S.K Verma, S.L. Sinha, D.K. Chandraker, Experimental investigation on the effect
of space on the turbulent mixing in vertical pressure tube-type boiling water
reactor, Nucl. Sci. Eng. 190 (2) (2018), doi:10.1080/00295639.2017.1413874.
[33] T. Zhang, Y. Liu, Numerical investigation of flow and heat transfer characteristics of subcooled boiling in a single rod channel with/without spacer grid,
Case Stud. Therm. Eng. 20 (2020) 100644, doi:10.1016/j.csite.2020.100644.
[34] K.M. Becker, G. Hernborg, M. Bode, O. Eriksson, Burnout data for flow of boiling water in vertical round ducts, annuli and rod clusters, AB Atomenergi
(1965).
[35] A. Saha, A.K. Das, Numerical study of boiling around wires and influence of
active or passive neighbours on vapour film dynamics, Int. J. Heat Mass Transf.
130 (2019) 440–454, doi:10.1016/j.ijheatmasstransfer.2018.10.117.
[36] M. Reimann, U. Grigull, Heat transfer with free convection and film boiling in
the critical area of water and carbon dioxide, Heat Mass Transf. 8 (1975) 229–
239, doi:10.1007/BF01002151.
[37] M.S. Plesset, S.A. Zwick, The growth of vapor bubbles in superheated liquids, J.
Appl. Phys. 25 (4) (1954) 493–500, doi:10.1063/1.1721668.
[38] N. Samkhaniani, M.R. Ansari, Numerical simulation of superheated vapor bubble rising in stagnant liquid, Heat Mass Transf. 53 (9) (2017) 2885–2899,
doi:10.1007/S00231-017-2031-6.
[39] N. Samkhaniani, M.R. Ansari, The evaluation of the diffuse interface method
for phase change simulations using OpenFOAM, Heat Transf. Asian Res. 46 (8)
(2017) 1173–1203, doi:10.1002/htj.21268.
[40] P. Goel, A.K. Nayak, M.K. Das, J.B. Joshi, Bubble departure characteristics in a
horizontal tube bundle under cross flow conditions, Int. J. Multiph. Flow 100
(2018) 143–154, doi:10.1016/j.ijmultiphaseflow.2017.12.013.
[41] K.M. Becker, J. Engstorm, B.Scholin Nylund, B. Sodequist, Analysis of the dryout
incident in the Oskarshamn 2 boiling water reactor, Int. J. Multiph. Flow 16 (6)
(1990) 959–974, doi:10.1016/0301-9322(90)90101-N.
[42] H.G. Weller, A New Approach to VOF-Based Interface Capturing Methods
for Incompressible and Compressible Flow, A New Approach to VOF-Based
Interface Capturing Methods for Incompressible and Compressible Flow, 4,
OpenCFD Ltd., 2008 Report TR/HGW.
[43] G. Boeing, Visual analysis of nonlinear dynamical systems: chaos, fractals, selfsimilarity and the limits of prediction, Systems 4 (4) (2016) 37, doi:10.3390/
systems4040037.

Fig. 5. The predicted shapes of initial breach (a) Rectangular (b) V-notch. Fig. 6. Dam breaching stages.

Investigating the peak outflow through a spatial embankment dam breach

공간적 제방댐 붕괴를 통한 최대 유출량 조사

Mahmoud T.GhonimMagdy H.MowafyMohamed N.SalemAshrafJatwaryFaculty of Engineering, Zagazig University, Zagazig 44519, Egypt

Abstract

Investigating the breach outflow hydrograph is an essential task to conduct mitigation plans and flood warnings. In the present study, the spatial dam breach is simulated by using a three-dimensional computational fluid dynamics model, FLOW-3D. The model parameters were adjusted by making a comparison with a previous experimental model. The different parameters (initial breach shape, dimensions, location, and dam slopes) are studied to investigate their effects on dam breaching. The results indicate that these parameters have a significant impact. The maximum erosion rate and peak outflow for the rectangular shape are higher than those for the V-notch by 8.85% and 5%, respectively. Increasing breach width or decreasing depth by 5% leads to increasing maximum erosion rate by 11% and 15%, respectively. Increasing the downstream slope angle by 4° leads to an increase in both peak outflow and maximum erosion rate by 2.0% and 6.0%, respectively.

유출 유출 수문곡선을 조사하는 것은 완화 계획 및 홍수 경보를 수행하는 데 필수적인 작업입니다. 본 연구에서는 3차원 전산유체역학 모델인 FLOW-3D를 사용하여 공간 댐 붕괴를 시뮬레이션합니다. 이전 실험 모델과 비교하여 모델 매개변수를 조정했습니다.

다양한 매개변수(초기 붕괴 형태, 치수, 위치 및 댐 경사)가 댐 붕괴에 미치는 영향을 조사하기 위해 연구됩니다. 결과는 이러한 매개변수가 상당한 영향을 미친다는 것을 나타냅니다. 직사각형 형태의 최대 침식율과 최대 유출량은 V-notch보다 각각 8.85%, 5% 높게 나타났습니다.

위반 폭을 늘리거나 깊이를 5% 줄이면 최대 침식률이 각각 11% 및 15% 증가합니다. 하류 경사각을 4° 증가시키면 최대 유출량과 최대 침식률이 각각 2.0% 및 6.0% 증가합니다.

Keywords

Spatial dam breach; FLOW-3D; Overtopping erosion; Computational fluid dynamics (CFD)

1. Introduction

There are many purposes for dam construction, such as protection from flood disasters, water storage, and power generationEmbankment failures may have a catastrophic impact on lives and infrastructure in the downstream regions. One of the most common causes of embankment dam failure is overtopping. Once the overtopping of the dam begins, the breach formation will start in the dam body then end with the dam failure. This failure occurs within a very short time, which threatens to be very dangerous. Therefore, understanding and modeling the embankment breaching processes is essential for conducting mitigation plans, flood warnings, and forecasting flood damage.

The analysis of the dam breaching process is implemented by different techniques: comparative methods, empirical models with dimensional and dimensionless solutions, physical-based models, and parametric models. These models were described in detail [1]Parametric modeling is commonly used to simulate breach growth as a time-dependent linear process and calculate outflow discharge from the breach using hydraulics principles [2]. Alhasan et al. [3] presented a simple one-dimensional mathematical model and a computer code to simulate the dam breaching process. These models were validated by small dams breaching during the floods in 2002 in the Czech Republic. Fread [4] developed an erosion model (BREACH) based on hydraulics principles, sediment transport, and soil mechanics to estimate breach size, time of formation, and outflow discharge. Říha et al. [5] investigated the dam break process for a cascade of small dams using a simple parametric model for piping and overtopping erosion, as well as a 2D shallow-water flow model for the flood in downstream areas. Goodarzi et al. [6] implemented mathematical and statistical methods to assess the effect of inflows and wind speeds on the dam’s overtopping failure.

Dam breaching studies can be divided into two main modes of erosion. The first mode is called “planar dam breach” where the flow overtops the whole dam width. While the second mode is called “spatial dam breach” where the flow overtops through the initial pilot channel (i.e., a channel created in the dam body). Therefore, the erosion will be in both vertical and horizontal directions [7].

The erosion process through the embankment dams occurs due to the shear stress applied by water flows. The dam breaching evolution can be divided into three stages [8][9], but Y. Yang et al. [10] divided the breach development into five stages: Stage I, the seepage erosion; Stage II, the initial breach formation; Stage III, the head erosion; Stage IV, the breach expansion; and Stage V, the re-equilibrium of the river channel through the breach. Many experimental tests have been carried out on non-cohesive embankment dams with an initial breach to examine the effect of upstream inflow discharges on the longitudinal profile evolution and the time to inflection point [11].

Zhang et al. [12] studied the effect of changing downstream slope angle, sediment grain size, and dam crest length on erosion rates. They noticed that increasing dam crest length and decreasing downstream slope angle lead to decreasing sediment transport rate. While the increase in sediment grain size leads to an increased sediment transport rate at the initial stages. Höeg et al. [13] presented a series of field tests to investigate the stability of embankment dams made of various materials. Overtopping and piping were among the failure tests carried out for the dams composed of homogeneous rock-fill, clay, or gravel with a height of up to 6.0 m. Hakimzadeh et al. [14] constructed 40 homogeneous cohesive and non-cohesive embankment dams to study the effect of changing sediment diameter and dam height on the breaching process. They also used genetic programming (GP) to estimate the breach outflow. Refaiy et al. [15] studied different scenarios for the downstream drain geometry, such as length, height, and angle, to minimize the effect of piping phenomena and therefore increase dam safety.

Zhu et al. [16] examined the effect of headcut erosion on dam breach growth, especially in the case of cohesive dams. They found that the breach growth in non-cohesive embankments is slower than cohesive embankments due to the little effect of headcut. Schmocker and Hager [7] proposed a relationship for estimating peak outflow from the dam breach process.(1)QpQin-1=1.7exp-20hc23d5013H0

where: Qp = peak outflow discharge.

Qin = inflow discharge.

hc = critical flow depth.

d50 = mean sediment diameter.

Ho = initial dam height.

Yu et al. [17] carried out an experimental study for homogeneous non-cohesive embankment dams in a 180° bending rectangular flume to determine the effect of overtopping flows on breaching formation. They found that the main factors influencing breach formation are water level, river discharge, and embankment material diameter.

Wu et al. [18] carried out a series of experiments to investigate the effect of breaching geometry on both non-cohesive and cohesive embankment dams in a U-bend flume due to overtopping flows. In the case of non-cohesive embankments, the non-symmetrical lateral expansion was noticed during the breach formation. This expansion was described by a coefficient ranging from 2.7 to 3.3.

The numerical models of the dam breach can be categorized according to different parameters, such as flow dimensions (1D, 2D, or 3D), flow governing equations, and solution methods. The 1D models are mainly used to predict the outflow hydrograph from the dam breach. Saberi et al. [19] applied the 1D Saint-Venant equation, which is solved by the finite difference method to investigate the outflow hydrograph during dam overtopping failure. Because of the ability to study dam profile evolution and breach formation, 2D models are more applicable than 1D models. Guan et al. [20] and Wu et al. [21] employed both 2D shallow water equations (SWEs) and sediment erosion equations, which are solved by the finite volume method to study the effect of the dam’s geometry parameters on outflow hydrograph and dam profile evolution. Wang et al. [22] also proposed a second-order hybrid-type of total variation diminishing (TVD) finite-difference to estimate the breach outflow by solving the 2D (SWEs). The accuracy of (SWEs) for both vertical flow contraction and surface roughness has been assessed [23]. They noted that the accuracy of (SWEs) is acceptable for milder slopes, but in the case of steeper slopes, modelers should be more careful. Generally, the accuracy of 2D models is still low, especially with velocity distribution over the flow depth, lateral momentum exchange, density-driven flows, and bottom friction [24]. Therefore, 3D models are preferred. Larocque et al. [25] and Yang et al. [26] started to use three-dimensional (3D) models that depend on the Reynolds-averaged Navier-Stokes (RANS) equations.

Previous experimental studies concluded that there is no clear relationship between the peak outflow from the dam breach and the initial breach characteristics. Some of these studies depend on the sharp-crested weir fixed at the end of the flume to determine the peak outflow from the breach, which leads to a decrease in the accuracy of outflow calculations at the microscale. The main goals of this study are to carry out a numerical simulation for a spatial dam breach due to overtopping flows by using (FLOW-3D) software to find an empirical equation for the peak outflow discharge from the breach and determine the worst-case that leads to accelerating the dam breaching process.

2. Numerical simulation

The current study for spatial dam breach is simulated by using (FLOW-3D) software [27], which is a powerful computational fluid dynamics (CFD) program.

2.1. Geometric presentations

A stereolithographic (STL) file is prepared for each change in the initial breach geometry and dimensions. The CAD program is useful for creating solid objects and converting them to STL format, as shown in Fig. 1.

2.2. Governing equations

The governing equations for water flow are three-dimensional Reynolds Averaged Navier-Stokes equations (RANS).

The continuity equation:(2)∂ui∂xi=0

The momentum equation:(3)∂ui∂t+1VFuj∂ui∂xj=1ρ∂∂xj-pδij+ν∂ui∂xj+∂uj∂xi-ρu`iu`j¯

where u is time-averaged velocity,ν is kinematic viscosity, VF is fractional volume open to flow, p is averaged pressure and -u`iu`j¯ are components of Reynold’s stress. The Volume of Fluid (VOF) technique is used to simulate the free surface profile. Hirt et al. [28] presented the VOF algorithm, which employs the function (F) to express the occupancy of each grid cell with fluid. The value of (F) varies from zero to unity. Zero value refers to no fluid in the grid cell, while the unity value refers to the grid cell being fully occupied with fluid. The free surface is formed in the grid cells having (F) values between zero and unity.(4)∂F∂t+1VF∂∂xFAxu+∂∂yFAyv+∂∂zFAzw=0

where (u, v, w) are the velocity components in (x, y, z) coordinates, respectively, and (AxAyAz) are the area fractions.

2.3. Boundary and initial conditions

To improve the accuracy of the results, the boundary conditions should be carefully determined. In this study, two mesh blocks are used to minimize the time consumed in the simulation. The boundary conditions for mesh block 1 are as follows: The inlet and sides boundaries are defined as a wall boundary condition (wall boundary condition is usually used for bound fluid by solid regions. In the case of viscous flows, no-slip means that the tangential velocity is equal to the wall velocity and the normal velocity is zero), the outlet is defined as a symmetry boundary condition (symmetry boundary condition is usually used to reduce computational effort during CFD simulation. This condition allows the flow to be transferred from one mesh block to another. No inputs are required for this boundary condition except that its location should be defined accurately), the bottom boundary is defined as a uniform flow rate boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure. The boundary conditions for mesh block 2 are as follows: The inlet is defined as a symmetry boundary condition, the outlet is defined as a free flow boundary condition, the bottom and sides boundaries are defined as a wall boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure as shown in Fig. 2. The initial conditions required to be set for the fluid (i.e., water) inside of the domain include configuration, temperature, velocities, and pressure distribution. The configuration of water depends on the dimensions and shape of the dam reservoir. While the other conditions have been assigned as follows: temperature is normal water temperature (25 °c) and pressure distribution is hydrostatic with no initial velocity.

2.4. Numerical method

FLOW-3D uses the finite volume method (FVM) to solve the governing equation (Reynolds-averaged Navier-Stokes) over the computational domain. A finite-volume method is an Eulerian approach for representing and evaluating partial differential equations in algebraic equations form [29]. At discrete points on the mesh geometry, values are determined. Finite volume expresses a small volume surrounding each node point on a mesh. In this method, the divergence theorem is used to convert volume integrals with a divergence term to surface integrals. After that, these terms are evaluated as fluxes at each finite volume’s surfaces.

2.5. Turbulent models

Turbulence is the chaotic, unstable motion of fluids that occurs when there are insufficient stabilizing viscous forces. In FLOW-3D, there are six turbulence models available: the Prandtl mixing length model, the one-equation turbulent energy model, the two-equation (k – ε) model, the Renormalization-Group (RNG) model, the two-equation (k – ω) models, and a large eddy simulation (LES) model. For simulating flow motion, the RNG model is adopted to simulate the motion behavior better than the k – ε and k – ω.

models [30]. The RNG model consists of two main equations for the turbulent kinetic energy KT and its dissipation.εT(5)∂kT∂t+1VFuAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z=PT+GT+DiffKT-εT(6)∂εT∂t+1VFuAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z=C1.εTKTPT+c3.GT+Diffε-c2εT2kT

where KT is the turbulent kinetic energy, PT is the turbulent kinetic energy production, GT is the buoyancy turbulence energy, εT is the turbulent energy dissipation rate, DiffKT and Diffε are terms of diffusion, c1, c2 and c3 are dimensionless parameters, in which c1 and c3 have a constant value of 1.42 and 0.2, respectively, c2 is computed from the turbulent kinetic energy (KT) and turbulent production (PT) terms.

2.6. Sediment scour model

The sediment scour model available in FLOW-3D can calculate all the sediment transport processes including Entrainment transport, Bedload transport, Suspended transport, and Deposition. The erosion process starts once the water flows remove the grains from the packed bed and carry them into suspension. It happens when the applied shear stress by water flows exceeds critical shear stress. This process is represented by entrainment transport in the numerical model. After entrained, the grains carried by water flow are represented by suspended load transport. After that, some suspended grains resort to settling because of the combined effect of gravity, buoyancy, and friction. This process is described through a deposition. Finally, the grains sliding motions are represented by bedload transport in the model. For the entrainment process, the shear stress applied by the fluid motion on the packed bed surface is calculated using the standard wall function as shown in Eq.7.(7)ks,i=Cs,i∗d50

where ks,i is the Nikuradse roughness and Cs,i is a user-defined coefficient. The critical bed shear stress is defined by a dimensionless parameter called the critical shields number as expressed in Eq.8.(8)θcr,i=τcr,i‖g‖diρi-ρf

where θcr,i is the critical shields number, τcr,i is the critical bed shear stress, g is the absolute value of gravity acceleration, di is the diameter of the sediment grain, ρi is the density of the sediment species (i) and ρf is the density of the fluid. The value of the critical shields number is determined according to the Soulsby-Whitehouse equation.(9)θcr,i=0.31+1.2d∗,i+0.0551-exp-0.02d∗,i

where d∗,i is the dimensionless diameter of the sediment, given by Eq.10.(10)d∗,i=diρfρi-ρf‖g‖μf213

where μf is the fluid dynamic viscosity. For the sloping bed interface, the value of the critical shields number is modified according to Eq.11.(11)θ`cr,i=θcr,icosψsinβ+cos2βtan2φi-sin2ψsin2βtanφi

where θ`cr,i is the modified critical shields number, φi is the angle of repose for the sediment, β is the angle of bed slope and ψ is the angle between the flow and the upslope direction. The effects of the rolling, hopping, and sliding motions of grains along the packed bed surface are taken by the bedload transport process. The volumetric bedload transport rate (qb,i) per width of the bed is expressed in Eq.12.(12)qb,i=Φi‖g‖ρi-ρfρfdi312

where Φi is the dimensionless bedload transport rate is calculated by using Meyer Peter and Müller equation.(13)Φi=βMPM,iθi-θ`cr,i1.5cb,i

where βMPM,i is the Meyer Peter and Müller user-defined coefficient and cb,i is the volume fraction of species i in the bed material. The suspended load transport is calculated as shown in Eq.14.(14)∂Cs,i∂t+∇∙Cs,ius,i=∇∙∇DCs,i

where Cs,i is the suspended sediment mass concentration, D is the diffusivity, and us,i is the grain velocity of species i. Entrainment and deposition are two opposing processes that take place at the same time. The lifting and settling velocities for both entrainment and deposition processes are calculated according to Eq.15 and Eq.16, respectively.(15)ulifting,i=αid∗,i0.3θi-θ`cr,igdiρiρf-1(16)usettling,i=υfdi10.362+1.049d∗,i3-10.36

where αi is the entrainment coefficient of species i and υf is the kinematic viscosity of the fluid.

2.7. Grid type

Using simple rectangular orthogonal elements in planes and hexahedral in volumes in the (FLOW-3D) program makes the mesh generation process easier, decreases the required memory, and improves numerical accuracy. Two mesh blocks were used in a joined form with a size ratio of 2:1. The first mesh block is coarser, which contains the reservoir water, and the second mesh block is finer, which contains the dam. For achieving accuracy and efficiency in results, the mesh size is determined by using a grid convergence test. The optimum uniform cell size for the first mesh block is 0.012 m and for the second mesh block is 0.006 m.

2.8. Time step

The maximum time step size is determined by using a Courant number, which controls the distance that the flow will travel during the simulation time step. In this study, the Courant number was taken equal to 0.25 to prevent the flow from traveling through more than one cell in the time step. Based on the Courant number, a maximum time step value of 0.00075 s was determined.

2.9. Numerical model validation

The numerical model accuracy was achieved by comparing the numerical model results with previous experimental results. The experimental study of Schmocker and Hager [7] was based on 31 tests with changes in six parameters (d50, Ho, Bo, Lk, XD, and Qin). All experimental tests were conducted in a straight open glass-sided flume. The horizontal flume has a rectangular cross-section with a width of 0.4 m and a height of 0.7 m. The flume was provided with a flow straightener and an intake with a length of 0.66 m. All tested dams were inserted at various distances (XD) from the intake. Test No.1 from this experimental program was chosen to validate the numerical model. The different parameters used in test No.1 are as follows:

(1) uniform sediment with a mean diameter (d50 = 0.31 mm), (2) Ho = 0.2 m, (3) Bo = 0.2 m, (4) Lk = 0.1 m,

(5) XD = 1.0 m, (6) Qin = 6.0 lit/s, (7) Su and Sd = 2:1, (8) mass density (ρs = 2650 kg/m3(9) Homogenous and non-cohesive embankment dam. As shown in Fig. 2, the simulation is contained within a rectangular grid with dimensions: 3.56 m in the x-direction (where 0.66 m is used as inlet, 0.9 m as dam base width, and 1.0 m as outlet), in y-direction 0.2 m (dam length), and in the z-direction 0.3 m, which represents the dam height (0.2 m) with a free distance (0.1 m) above the dam. There are two main reasons that this experimental program is preferred for the validation process. The first reason is that this program deals with homogenous, non-cohesive soil, which is available in FLOW-3D. The second reason is that this program deals with small-scale models which saves time for numerical simulation. Finally, some important assumptions were considered during the validation process. The flow is assumed to be incompressible, viscous, turbulent, and three-dimensional.

By comparing dam profiles at different time instants for the experimental test with the current numerical model, it appears that the numerical model gives good agreement as shown in Fig. 3 and Fig. 4, with an average error percentage of 9% between the experimental results and the numerical model.

3. Analysis and discussions

The current model is used to study the effects of different parameters such as (initial breach shapes, dimensions, locations, upstream and downstream dam slopes) on the peak outflow discharge, QP, time of peak outflow, tP, and rate of erosion, E.

This study consists of a group of scenarios. The first scenario is changing the shapes of the initial breach according to Singh [1], the most predicted shapes are rectangular and V-notch as shown in Fig. 5. The second scenario is changing the initial breach dimensions (i.e., width and depth). While the third scenario is changing the location of the initial breach. Eventually, the last scenario is changing the upstream and downstream dam slopes.

All scenarios of this study were carried out under the same conditions such as inflow discharge value (Qin=1.0lit/s), dimensions of the tested dam, where dam height (Ho=0.20m), crest width.

(Lk=0.1m), dam length (Bo=0.20m), and homogenous & non-cohesive soil with a mean diameter (d50=0.31mm).

3.1. Dam breaching process evolution

The dam breaching process is a very complex process due to the quick changes in hydrodynamic conditions during dam failure. The dam breaching process starts once water flows reach the downstream face of the dam. During the initial stage of dam breaching, the erosion process is relatively quiet due to low velocities of flow. As water flows continuously, erosion rates increase, especially in two main zones: the crest and the downstream face. As soon as the dam crest is totally eroded, the water levels in the dam reservoir decrease rapidly, accompanied by excessive erosion in the dam body. The erosion process continues until the water levels in the dam reservoir equal the remaining height of the dam.

According to Zhou et al. [11], the breaching process consists of three main stages. The first stage starts with beginning overtopping flow, then ends when the erosion point directed upstream and reached the inflection point at the inflection time (ti). The second stage starts from the end of the stage1 until the occurrence of peak outflow discharge at the peak outflow time (tP). The third stage starts from the end of the stage2 until the value of outflow discharge becomes the same as the value of inflow discharge at the final time (tf). The outflow discharge from the dam breach increases rapidly during stage1 and stage2 because of the large dam storage capacity (i.e., the dam reservoir is totally full of water) and excessive erosion. While at stage3, the outflow values start to decrease slowly because most of the dam’s storage capacity was run out. The end of stage3 indicates that the dam storage capacity was totally run out, so the outflow equalized with the inflow discharge as shown in Fig. 6 and Fig. 7.

3.2. The effect of initial breach shape

To identify the effect of the initial breach shape on the evolution of the dam breaching process. Three tests were carried out with different cross-section areas for each shape. The initial breach is created at the center of the dam crest. Each test had an ID to make the process of arranging data easier. The rectangular shape had an ID (Rec5h & 5b), which means that its depth and width are equal to 5% of the dam height, and the V-notch shape had an ID (V-noch5h & 1:1) which means that its depth is equal to 5% of the dam height and its side slope is equal to 1:1. The comparison between rectangular and V-notch shapes is done by calculating the ratio between maximum dam height at different times (ZMax) to the initial dam height (Ho), rate of erosion, and hydrograph of outflow discharge for each test. The rectangular shape achieves maximum erosion rate and minimum inflection time, in addition to a rapid decrease in the dam reservoir levels. Therefore, the dam breaching is faster in the case of a rectangular shape than in a V-notch shape, which has the same cross-section area as shown in Fig. 8.

Also, by comparing the hydrograph for each test, the peak outflow discharge value in the case of a rectangular shape is higher than the V-notch shape by 5% and the time of peak outflow for the rectangular shape is shorter than the V-notch shape by 9% as shown in Fig. 9.

3.3. The effect of initial breach dimensions

The results of the comparison between the different initial breach shapes indicate that the worst initial breach shape is rectangular, so the second scenario from this study concentrated on studying the effect of a change in the initial rectangular breach dimensions. Groups of tests were carried out with different depths and widths for the rectangular initial breach. The first group had a depth of 5% from the dam height and with three different widths of 5,10, and 15% from the dam height, the second group had a depth of 10% with three different widths of 5,10, and 15%, the third group had a depth of 15% with three different widths of 5,10, and 15% and the final group had a width of 15% with three different heights of 5, 10, and 15% for a rectangular breach shape. The comparison was made as in the previous section to determine the worst case that leads to the quick dam failure as shown in Fig. 10.

The results show that the (Rec 5 h&15b) test achieves a maximum erosion rate for a shorter period of time and a minimum ratio for (Zmax / Ho) as shown in Fig. 10, which leads to accelerating the dam failure process. The dam breaching process is faster with the minimum initial breach depth and maximum initial breach width. In the case of a minimum initial breach depth, the retained head of water in the dam reservoir is high and the crest width at the bottom of the initial breach (L`K) is small, so the erosion point reaches the inflection point rapidly. While in the case of the maximum initial breach width, the erosion perimeter is large.

3.4. The effect of initial breach location

The results of the comparison between the different initial rectangular breach dimensions indicate that the worst initial breach dimension is (Rec 5 h&15b), so the third scenario from this study concentrated on studying the effect of a change in the initial breach location. Three locations were checked to determine the worst case for the dam failure process. The first location is at the center of the dam crest, which was named “Center”, the second location is at mid-distance between the dam center and dam edge, which was named “Mid”, and the third location is at the dam edge, which was named “Edge” as shown in Fig. 11. According to this scenario, the results indicate that the time of peak outflow discharge (tP) is the same in the three cases, but the maximum value of the peak outflow discharge occurs at the center location. The difference in the peak outflow values between the three cases is relatively small as shown in Fig. 12.

The rates of erosion were also studied for the three cases. The results show that the maximum erosion rate occurs at the center location as shown in Fig. 13. By making a comparison between the three cases for the dam storage volume. The results show that the center location had the minimum values for the dam storage volume, which means that a large amount of water has passed to the downstream area as shown in Fig. 14. According to these results, the center location leads to increased erosion rate and accelerated dam failure process compared with the two other cases. Because the erosion occurs on both sides, but in the case of edge location, the erosion occurs on one side.

3.5. The effect of upstream and downstream dam slopes

The results of the comparison between the different initial rectangular breach locations indicate that the worst initial breach location is the center location, so the fourth scenario from this study concentrated on studying the effect of a change in the upstream (Su) and downstream (Sd) dam slopes. Three slopes were checked individually for both upstream and downstream slopes to determine the worst case for the dam failure process. The first slope value is (2H:1V), the second slope value is (2.5H:1V), and the third slope value is (3H:1V). According to this scenario, the results show that the decreasing downstream slope angle leads to increasing time of peak outflow discharge (tP) and decreasing value of peak outflow discharge. The difference in the peak outflow values between the three cases for the downstream slope is 2%, as shown in Fig. 15, but changing the upstream slope has a negligible impact on the peak outflow discharge and its time as shown in Fig. 16.

The rates of erosion were also studied in the three cases for both upstream and downstream slopes. The results show that the maximum erosion rate increases by 6.0% with an increasing downstream slope angle by 4°, as shown in Fig. 17. The results also indicate that the erosion rates aren’t affected by increasing or decreasing the upstream slope angle, as shown in Fig. 18. According to these results, increasing the downstream slope angle leads to increased erosion rate and accelerated dam failure process compared with the upstream slope angle. Because of increasing shear stress applied by water flows in case of increasing downstream slope.

According to all previous scenarios, the dimensionless peak outflow discharge QPQin is presented for a fixed dam height (Ho) and inflow discharge (Qin). Fig. 19 illustrates the relationship between QP∗=QPQin and.

Lr=ho2/3∗bo2/3Ho. The deduced relationship achieves R2=0.96.(17)QP∗=2.2807exp-2.804∗Lr

4. Conclusions

A spatial dam breaching process was simulated by using FLOW-3D Software. The validation process was performed by making a comparison between the simulated results of dam profiles and the dam profiles obtained by Schmocker and Hager [7] in their experimental study. And also, the peak outflow value recorded an error percentage of 12% between the numerical model and the experimental study. This model was used to study the effect of initial breach shape, dimensions, location, and dam slopes on peak outflow discharge, time of peak outflow, and the erosion process. By using the parameters obtained from the validation process, the results of this study can be summarized in eight points as follows.1.

The rectangular initial breach shape leads to an accelerating dam failure process compared with the V-notch.2.

The value of peak outflow discharge in the case of a rectangular initial breach is higher than the V-notch shape by 5%.3.

The time of peak outflow discharge for a rectangular initial breach is shorter than the V-notch shape by 9%.4.

The minimum depth and maximum width for the initial breach achieve maximum erosion rates (increasing breach width, b0, or decreasing breach depth, h0, by 5% from the dam height leads to an increase in the maximum rate of erosion by 11% and 15%, respectively), so the dam failure is rapid.5.

The center location of the initial breach leads to an accelerating dam failure compared with the edge location.6.

The initial breach location has a negligible effect on the peak outflow discharge value and its time.7.

Increasing the downstream slope angle by 4° leads to an increase in both peak outflow discharge and maximum rate of erosion by 2.0% and 6.0%, respectively.8.

The upstream slope has a negligible effect on the dam breaching process.

References

[1]V. SinghDam breach modeling technologySpringer Science & Business Media (1996)Google Scholar[2]Wahl TL. Prediction of embankment dam breach parameters: a literature review and needs assessment. 1998.Google Scholar[3]Z. Alhasan, J. Jandora, J. ŘíhaStudy of dam-break due to overtopping of four small dams in the Czech RepublicActa Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 63 (3) (2015), pp. 717-729 View PDFCrossRefView Record in ScopusGoogle Scholar[4]D. FreadBREACH, an erosion model for earthen dam failures: Hydrologic Research LaboratoryNOAA, National Weather Service (1988)Google Scholar[5]J. Říha, S. Kotaška, L. PetrulaDam Break Modeling in a Cascade of Small Earthen Dams: Case Study of the Čižina River in the Czech RepublicWater, 12 (8) (2020), p. 2309, 10.3390/w12082309 View PDFView Record in ScopusGoogle Scholar[6]E. Goodarzi, L. Teang Shui, M. ZiaeiDam overtopping risk using probabilistic concepts–Case study: The Meijaran DamIran Ain Shams Eng J, 4 (2) (2013), pp. 185-197ArticleDownload PDFView Record in ScopusGoogle Scholar[7]L. Schmocker, W.H. HagerPlane dike-breach due to overtopping: effects of sediment, dike height and dischargeJ Hydraul Res, 50 (6) (2012), pp. 576-586 View PDFCrossRefView Record in ScopusGoogle Scholar[8]J.S. Walder, R.M. Iverson, J.W. Godt, M. Logan, S.A. SolovitzControls on the breach geometry and flood hydrograph during overtopping of noncohesive earthen damsWater Resour Res, 51 (8) (2015), pp. 6701-6724View Record in ScopusGoogle Scholar[9]H. Wei, M. Yu, D. Wang, Y. LiOvertopping breaching of river levees constructed with cohesive sedimentsNat Hazards Earth Syst Sci, 16 (7) (2016), pp. 1541-1551 View PDFCrossRefView Record in ScopusGoogle Scholar[10]Y. Yang, S.-Y. Cao, K.-J. Yang, W.-P. LiYang K-j, Li W-p. Experimental study of breach process of landslide dams by overtopping and its initiation mechanismsJ Hydrodynamics, 27 (6) (2015), pp. 872-883ArticleDownload PDFCrossRefView Record in ScopusGoogle Scholar[11]G.G.D. Zhou, M. Zhou, M.S. Shrestha, D. Song, C.E. Choi, K.F.E. Cui, et al.Experimental investigation on the longitudinal evolution of landslide dam breaching and outburst floodsGeomorphology, 334 (2019), pp. 29-43ArticleDownload PDFView Record in ScopusGoogle Scholar[12]J. Zhang, Z.-x. Guo, S.-y. CaoYang F-g. Experimental study on scour and erosion of blocked damWater Sci Eng, 5 (2012), pp. 219-229ArticleDownload PDFView Record in ScopusGoogle Scholar[13]K. Höeg, A. Løvoll, K. VaskinnStability and breaching of embankment dams: Field tests on 6 m high damsInt J Hydropower Dams, 11 (2004), pp. 88-92View Record in ScopusGoogle Scholar[14]H. Hakimzadeh, V. Nourani, A.B. AminiGenetic programming simulation of dam breach hydrograph and peak outflow dischargeJ Hydrol Eng, 19 (4) (2014), pp. 757-768View Record in ScopusGoogle Scholar[15]A.R. Refaiy, N.M. AboulAtta, N.Y. Saad, D.A. El-MollaModeling the effect of downstream drain geometry on seepage through earth damsAin Shams Eng J, 12 (3) (2021), pp. 2511-2531ArticleDownload PDFView Record in ScopusGoogle Scholar[16]Y. Zhu, P.J. Visser, J.K. Vrijling, G. WangExperimental investigation on breaching of embankmentsScience China Technological Sci, 54 (1) (2011), pp. 148-155 View PDFCrossRefView Record in ScopusGoogle Scholar[17]M.-H. Yu, H.-Y. Wei, Y.-J. Liang, Y. ZhaoInvestigation of non-cohesive levee breach by overtopping flowJ Hydrodyn, 25 (4) (2013), pp. 572-579ArticleDownload PDFCrossRefView Record in ScopusGoogle Scholar[18]S. Wu, M. Yu, H. Wei, Y. Liang, J. ZengNon-symmetrical levee breaching processes in a channel bend due to overtoppingInt J Sedim Res, 33 (2) (2018), pp. 208-215ArticleDownload PDFView Record in ScopusGoogle Scholar[19]O. Saberi, G. ZenzNumerical investigation on 1D and 2D embankment dams failure due to overtopping flowInt J Hydraulic Engineering, 5 (2016), pp. 9-18View Record in ScopusGoogle Scholar[20]M. Guan, N.G. Wright, P.A. Sleigh2D Process-Based Morphodynamic Model for Flooding by Noncohesive Dyke BreachJ Hydraul Eng, 140 (7) (2014), p. 04014022, 10.1061/(ASCE)HY.1943-7900.0000861 View PDFView Record in ScopusGoogle Scholar[21]W. Wu, R. Marsooli, Z. HeDepth-Averaged Two-Dimensional Model of Unsteady Flow and Sediment Transport due to Noncohesive Embankment Break/BreachingJ Hydraul Eng, 138 (6) (2012), pp. 503-516View Record in ScopusGoogle Scholar[22]Z. Wang, D.S. BowlesThree-dimensional non-cohesive earthen dam breach model. Part 1: Theory and methodologyAdv Water Resour, 29 (10) (2006), pp. 1528-1545ArticleDownload PDFView Record in ScopusGoogle Scholar[23]Říha J, Duchan D, Zachoval Z, Erpicum S, Archambeau P, Pirotton M, et al. Performance of a shallow-water model for simulating flow over trapezoidal broad-crested weirs. J Hydrology Hydromechanics. 2019;67:322-8.Google Scholar[24]C.B. VreugdenhilNumerical methods for shallow-water flowSpringer Science & Business Media (1994)Google Scholar[25]L.A. Larocque, J. Imran, M.H. Chaudhry3D numerical simulation of partial breach dam-break flow using the LES and k–∊ turbulence modelsJ Hydraul Res, 51 (2) (2013), pp. 145-157 View PDFCrossRefView Record in ScopusGoogle Scholar[26]C. Yang, B. Lin, C. Jiang, Y. LiuPredicting near-field dam-break flow and impact force using a 3D modelJ Hydraul Res, 48 (6) (2010), pp. 784-792 View PDFCrossRefView Record in ScopusGoogle Scholar[27]FLOW-3D. Version 11.1.1 Flow Science, Inc., Santa Fe, NM. https://wwwflow3dcom.Google Scholar[28]C.W. Hirt, B.D. NicholsVolume of fluid (VOF) method for the dynamics of free boundariesJ Comput Phys, 39 (1) (1981), pp. 201-225ArticleDownload PDFGoogle Scholar[29]S.V. PatankarNumerical heat transfer and fluid flow, Hemisphere PublCorp, New York, 58 (1980), p. 288View Record in ScopusGoogle Scholar[30]M. Alemi, R. MaiaNumerical simulation of the flow and local scour process around single and complex bridge piersInt J Civil Eng, 16 (5) (2018), pp. 475-487 View PDFCrossRefView Record in ScopusGoogle Scholar

Figure 2: Temperature contours and melt pool border lines at different times for the 50 % duty cycle case: (a) - (c) Δtcycle = 400 μs, (d) – (f) Δtcycle = 1000 μs and (g) – (i) Δtcycle = 3000 μs.

MULTIPHYSICS SIMULATION OF THEMRAL AND FLUID DYNAMICS PHENOMENA DURING THE PULSED LASER POWDER BED FUSION PROCESS OF 316-L STEEL

M. Bayat* , V. K. Nadimpalli, J. H. Hattel
1Department of Mechanical Engineering, Technical University of Denmark (DTU), Produktionstorvet
425, Kgs. 2800, Lyngby, Denmark

ABSTRACT

L-PBF(Laser Powder Bed Fusion)는 다양한 산업 분야에서 많은 관심을 받았으며, 주로 기존 제조 기술을 사용하여 만들 수 없었던 복잡한 토폴로지 최적화 구성 요소를 구현하는 잘 알려진 능력 덕분입니다. . 펄스 L-PBF(PL-PBF)에서 레이저의 시간적 프로파일은 주기 지속 시간과 듀티 주기 중 하나 또는 둘 다를 수정하여 변조할 수 있습니다. 따라서 레이저의 시간적 프로파일은 향후 적용을 위해 이 프로세스를 더 잘 제어할 수 있는 길을 열어주는 새로운 프로세스 매개변수로 간주될 수 있습니다. 따라서 이 작업에서 우리는 레이저의 시간적 프로파일을 변경하는 것이 PL-PBF 공정에서 용융 풀 조건과 트랙의 최종 모양 및 형상에 어떻게 영향을 미칠 수 있는지 조사하는 것을 목표로 합니다. 이와 관련하여 본 논문에서는 CFD(Computational Fluid Dynamics) 소프트웨어 패키지인 Flow-3D를 기반으로 하는 316-L 스테인리스강 PL-PBF 공정의 다중물리 수치 모델을 개발하고 이 모델을 사용하여 열과 유체를 시뮬레이션합니다. 다양한 펄스 모드에서 공정 과정 중 용융 풀 내부에서 발생하는 유동 조건. 따라서 고정된 레이저 듀티 사이클(50%)이 있는 레이저 주기 지속 시간이 용융 풀의 모양과 크기 및 최종 트랙 형태에 미치는 영향을 연구하기 위해 매개변수 연구가 수행됩니다. 더 긴 주기 기간에서 더 많은 재료가 더 큰 용융 풀 내에서 변위됨에 따라 용융 풀의 후류에 더 눈에 띄는 혹이 형성되며, 동시에 더 심각한 반동 압력을 받습니다. 또한 시뮬레이션에서 50% 듀티 사이클에서 1000μs에서 형성된 보다 대칭적인 용융 풀과 비교하여 400μs 사이클 주기에서 더 긴 용융 풀이 형성된다는 것이 관찰되었습니다. 풀 볼륨은 1000μs의 경우 더 큽니다. 매개변수 연구는 연속 트랙과 파손된 트랙 PL-PBF 사이의 경계를 설명하며, 여기서 연속 트랙은 항상 소량의 용융 재료를 유지함으로써 유지됩니다.

English Abstract

Laser Powder Bed Fusion (L-PBF) has attracted a lot of attention from various industrial sectors and mainly thanks to its well-proven well-known capacity of realizing complex topology-optimized components that have so far been impossible to make using conventional manufacturing techniques. In Pulsed L-PBF (PL-PBF), the laser’s temporal profile can be modulated via modifying either or both the cycle duration and the duty cycle. Thus, the laser’s temporal profile could be considered as a new process parameter that paves the way for a better control of this process for future applications. Therefore, in this work we aim to investigate how changing the laser’s temporal profile can affect the melt pool conditions and the final shape and geometry of a track in the PL-PBF process. In this respect, in this paper a multiphysics numerical model of the PL-PBF process of 316-L stainless steel is developed based on the computational fluid dynamics (CFD) software package Flow-3D and the model is used to simulate the heat and fluid flow conditions occurring inside the melt pool during the course of the process at different pulsing modes. Thus, a parametric study is carried out to study the influence of the laser’s cycle duration with a fixed laser duty cycle (50 %) on the shape and size of the melt pool and the final track morphology. It is noticed that at longer cycle periods, more noticeable humps form at the wake of the melt pool as more material is displaced within bigger melt pools, which are at the same time subjected to more significant recoil pressures. It is also observed in the simulations that at 50 % duty cycle, longer melt pools form at 400 μs cycle period compared to the more symmetrical melt pools formed at 1000 μs, primarily because of shorter laser off-times in the former, even though melt pool volume is bigger for the 1000 μs case. The parameteric study illustrates the boundary between a continuous track and a broken track PL-PBF wherein the continuous track is retained by always maintaining a small volume of molten material.

Figure 1: Front and side views of the computational domain. Note that the region along z and from -100 μm to +50 μm is void.
Figure 1: Front and side views of the computational domain. Note that the region along z and from -100 μm to +50 μm is void.
Figure 2: Temperature contours and melt pool border lines at different times for the 50 % duty cycle case: (a) - (c) Δtcycle = 400 μs, (d) – (f) Δtcycle = 1000 μs and (g) – (i) Δtcycle = 3000 μs.
Figure 2: Temperature contours and melt pool border lines at different times for the 50 % duty cycle case: (a) – (c) Δtcycle = 400 μs, (d) – (f) Δtcycle = 1000 μs and (g) – (i) Δtcycle = 3000 μs.
Figure 3: Plot of melt pool volume versus time for four cases including continuous wave laser as well as 50 % duty cycle at 400 μs, 1000 μs and 3000 μs.
Figure 3: Plot of melt pool volume versus time for four cases including continuous wave laser as well as 50 % duty cycle at 400 μs, 1000 μs and 3000 μs.

CONCLUSIONS

In this work a CFD model of the modulated PL-PBF process of stainless steel 316-L is developed in the commercial software package Flow-3D. The model involves physics such as solidification, melting, evaporation, convection, laser-material interaction, capillarity, Marangoni effect and the recoil pressure effect. In the current study, a parametric study is carried out to understand how the change in the cycle period duration affects the melt pool’s thermo-fluid conditions during the modulated PL-PBF process. It is observed that at the pulse mode with 50 % duty cycle and 400 μs cycle period, an overlapped chain of humps form at the wake of the melt pool and at a spatial frequency of occurrence of about 78 μm. Furthermore and as expected, it is noted that the melt pool volume, the size of the hump as well as the crater size at the end of the track, increase with increase in the cycle period duration, as more material is re-deposited at the back of the melt pool and that itself is caused by more pronounced recoil pressures. Moreover, it is noticed that due to the short off-time period of the laser in the 400 μs cycle period case, there is always an amount of liquid metal left from the previous cycle, at the time the new cycle starts. This is found to be the main reason why longer and elongated melt pools form at 400 μs cycle period, compared to the bigger, shorter and more symmetrical-like melt pools forming at the 1000 μs case. In this study PL-PBF single tracks including the broken track and the continuous track examples were studied to illustrate the boundary of this transition at a given laser scan parameter setting. At higher scan speeds, it is expected that the Plateau–Rayleigh instability will compete with the pulsing behavior to change the transition boundary between a broken and continuous track, which is suggested as future work from this study.

REFERENCES

[1] T. Craeghs, L. Thijs, F. Verhaeghe, J.-P. Kruth, J. Van Humbeeck, A study of the microstructural
evolution during selective laser melting of Ti–6Al–4V, Acta Mater. 58 (2010) 3303–3312.
https://doi.org/10.1016/j.actamat.2010.02.004.
[2] J. Liu, A.T. Gaynor, S. Chen, Z. Kang, K. Suresh, A. Takezawa, L. Li, J. Kato, J. Tang, C.C.L. Wang, L.
Cheng, X. Liang, A.C. To, Current and future trends in topology optimization for additive manufacturing,
(2018) 2457–2483.
[3] M. Bayat, W. Dong, J. Thorborg, A.C. To, J.H. Hattel, A review of multi-scale and multi-physics
simulations of metal additive manufacturing processes with focus on modeling strategies, Addit. Manuf.
47 (2021). https://doi.org/10.1016/j.addma.2021.102278.
[4] A. Foroozmehr, M. Badrossamay, E. Foroozmehr, S. Golabi, Finite Element Simulation of Selective Laser
Melting process considering Optical Penetration Depth of laser in powder bed, Mater. Des. 89 (2016)
255–263. https://doi.org/10.1016/j.matdes.2015.10.002.
[5] Y.S. Lee, W. Zhang, Modeling of heat transfer, fluid flow and solidification microstructure of nickel-base
superalloy fabricated by laser powder bed fusion, Addit. Manuf. 12 (2016) 178–188.
https://doi.org/10.1016/j.addma.2016.05.003.
[6] S.A. Khairallah, A.T. Anderson, A. Rubenchik, W.E. King, Laser powder-bed fusion additive
manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation
zones, Acta Mater. 108 (2016) 36–45. https://doi.org/10.1016/j.actamat.2016.02.014.
[7] M. Bayat, A. Thanki, S. Mohanty, A. Witvrouw, S. Yang, J. Thorborg, N.S. Tiedje, J.H. Hattel, Keyholeinduced porosities in Laser-based Powder Bed Fusion (L-PBF) of Ti6Al4V: High-fidelity modelling and
experimental validation, Addit. Manuf. 30 (2019). https://doi.org/10.1016/j.addma.2019.100835.
[8] A. Charles, M. Bayat, A. Elkaseer, L. Thijs, J.H. Hattel, S. Scholz, Elucidation of dross formation in laser
powder bed fusion at down-facing surfaces: phenomenon-oriented multiphysics simulation and
experimental validation, Addit. Manuf. Under revi (2021).
[9] M. Bayat, V.K. Nadimpalli, D.B. Pedersen, J.H. Hattel, A fundamental investigation of thermo-capillarity
in laser powder bed fusion of metals and alloys, Int. J. Heat Mass Transf. 166 (2021) 120766.
https://doi.org/10.1016/j.ijheatmasstransfer.2020.120766.
[10] J.D. Roehling, S.A. Khairallah, Y. Shen, A. Bayramian, C.D. Boley, A.M. Rubenchik, J. Demuth, N.
Duanmu, M.J. Matthews, Physics of large-area pulsed laser powder bed fusion, Addit. Manuf. 46 (2021) https://doi.org/10.1016/j.addma.2021.102186.
[11] M. Zheng, L. Wei, J. Chen, Q. Zhang, J. Li, S. Sui, G. Wang, W. Huang, Surface morphology evolution
during pulsed selective laser melting: Numerical and experimental investigations, Appl. Surf. Sci. 496
(2019) 143649. https://doi.org/10.1016/j.apsusc.2019.143649.
[12] M. Bayat, V.K. Nadimpalli, D.B. Pedersen, J.H. Hattel, A fundamental investigation of thermo-capillarity
in laser powder bed fusion of metals and alloys, Int. J. Heat Mass Transf. 166 (2021).
https://doi.org/10.1016/j.ijheatmasstransfer.2020.120766.

Effect of roughness on separation zone dimensions.

Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

조도 계수 및 역전 수준 변화가 개선된 90도 측면 분출구에서의 유동에 대한 실험적 및 수치적 연구

Maryam BagheriSeyed M. Ali ZomorodianMasih ZolghadrH. Md. AzamathullaC. Venkata Siva Rama Prasad

Abstract

측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 출력 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다. 본 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 7가지 유형의 거칠기 요소를 분기구 입구에 설치하고 4가지 다른 배출(총 84번의 실험을 수행)과 함께 3개의 서로 다른 베드 반전 레벨을 조사했습니다. 또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면, 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 가지 방법을 결합하면 분리 영역 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%.

HIGHLIGHTS

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  • Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance.
  • Installation of 7 types of roughening elements at the turnout entrance and 3 different bed level inverts were investigated.
  • Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow.
  • Combining both methods can reduce the separation zone dimensions by up to 63%.
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

Keywords

discharge ratioflow separation zoneintakethree dimensional simulation

INTRODUCTION

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Turnouts or intakes are amongst the oldest and most widely used hydraulic structures in irrigation networks. Turnouts are also used in water distribution, transmission networks, power generation facilities, and waste water treatment plants etc. The flows that enter a turnout have a strong momentum in the direction of the main waterway and that is why flow separation occurs inside the turnout. The horizontal vortex formed in the separation area is a suitable place for accumulation and deposition of sediments. The separation zone is a vulnerable area for sedimentation and for reduction of effective flow due to a contracted flow region in the lateral channel. Sedimentaion in the entrance of the intake can gradually be transfered into the lateral channel and decrease the capacity of the higher order channels over time (Jalili et al. 2011). On the other hand, the existence of coarse-grained materials causes erosion and destruction of the waterway side walls and bottom. In addition, sedimentation creates conditions for vegetation to take root and damage the waterway cover, which causes water to leak from its perimeter. Therefore, it is important to investigate the pattern of the flow separation area in turnouts and provide solutions to reduce the dimensions of this area.

The three-dimensional flow structure at turnouts is quite complex. In an experimental study by Neary & Odgaard (1993) in a 90-degree water turnout it was found that the secondary currents and separation zone varies from the bed to the water surface. They also found that at a 90-degree water turnout, the bed roughness and discharge ratio play a critical role in flow structure. They asserted that an explanation of sediment behavior at a diversion entrance requires a comprehensive understanding of 3D flow patterns around the lateral-channel entrance. In addition, they suggested that there is a strong similarity between flow in a channel bend and a diversion channel, and that this similarity can rationalize the use of bend flow models for estimation of 3D flow structures in diversion channels.

Some of the distinctive characteristics of dividing flow in a turnout include a zone of separation immediately near the entrance of the lateral turnout (separation zone), a contracted flow region in the branch channel (contracted flow), and a stagnation point near the downstream corner of the junction (stagnation zone). In the region downstream of the junction, along the continuous far wall, separation due to flow expansion may occur (Ramamurthy et al. 2007), that is, a separation zone. This can both reduce the turnout efficiency and the effective width of flow while increasing the sediment deposition in the turnout entrance (Jalili et al. 2011). Installation of submerged vanes in the turnout entrance is a method which is already applied to reduce the size of flow separation zones. The separation zone draws sediments and floating materials into themselves. This reduces effective cross-section area and reduces transmission capacity. These results have also been obtained in past studies, including by Ramamurthy et al. (2007) and in Jalili et al. (2011). Submerged vanes (Iowa vanes) are designed in order to modify the near-bed flow pattern and bed-sediment motion in the transverse direction of the river. The vanes are installed vertically on the channel bed, at an angle of attack which is usually oriented at 10–25 degrees to the local primary flow direction. Vane height is typically 0.2–0.5 times the local water depth during design flow conditions and vane length is 2–3 times its height (Odgaard & Wang 1991). They are vortex-generating devices that generate secondary circulation, thereby redistributing sediment within the channel cross section. Several factors affect the flow separation zone such as the ratio of lateral turnout discharge to main channel discharge, angle of lateral channel with respect to the main channel flow direction and size of applied submerged vanes. Nakato et al. (1990) found that sediment management using submerged vanes in the turnout entrance to Station 3 of the Council Bluffs plant, located on the Missouri River, is applicable and efficient. The results show submerged vanes are an appropriate solution for reduction of sediment deposition in a turnout entrance. The flow was treated as 3D and tests results were obtained for the flow characteristics of dividing flows in a 90-degree sharp-edged, junction. The main and lateral channel were rectangular with the same dimensions (Ramamurthy et al., 2007).

Keshavarzi & Habibi (2005) carried out experiments on intake with angles of 45, 67, 79 and 90 degrees in different discharge ratios and reported the optimum angle for inlet flow with the lowest flow separation area to be about 55 degrees. The predicted flow characteristics were validated using experimental data. The results indicated that the width and length of the separation zone increases with the increase in the discharge ratio Qr (ratio of outflow per unit width in the turnout to inflow per unit width in the main channel).

Abbasi et al. (2004) performed experiments to investigate the dimensions of the flow separation zone at a lateral turnout entrance. They demonstrated that the length and width of the separation zone decreases with the increasing ratio of lateral turn-out discharge. They also found that with a reducing angle of lateral turnout, the length of the separation zone scales up and width of separation zone reduces. Then they compared their observations with results of Kasthuri & Pundarikanthan (1987) who conducted some experiments in an open-channel junction formed by channels of equal width and an angle of lateral 90 degree turnout, which showed the dimensions of the separation zone in their experiments to be smaller than in previous studies. Kasthuri & Pundarikanthan (1987) studied vortex and flow separation dimensions at the entrance of a 90 degree channel. Results showed that increasing the diversion discharge ratio can reduce the length and width of the vortex area. They also showed that the length and width of the vortex area remain constant at diversion ratios greater than 0.7. Karami Moghaddam & Keshavarzi (2007) analyzed the flow characteristics in turnouts with angles of 55 and 90 degrees. They reported that the dimensions of the separation zone decrease by increasing the discharge ratio and reducing the turnout angle with respect to the main channel. Studies about flow separation zone can be found in Jalili et al. (2011)Nikbin & Borghei (2011)Seyedian et al. (2008).

Jamshidi et al. (2016) measured the dimensions of a flow separation zone in the presence of submerged vanes with five arrangements (parallel, stagger, compound, piney and butterflies). Results showed that the ratio of the width to the length of the separation zone (shape index) was between 0.2 and 0.28 for all arrangements.

Karami et al. (2017) developed a 3D computational fluid dynamic (CFD) code which was calibrated by measured data. They used the model to evaluate flow pattern, diversion ratio of discharge, strength of the secondary flow, and dimensions of the vortex inside the channel in various dikes and submerged vane installation scenarios. Results showed that the diversion ratio of discharge in the diversion channel is dependent on the width of the flow separation area in the main channel. A dike, perpendicular to the flow, doubles the ratio of diverted discharge and reduces the suspended sediment load compared with the base-line situation by creating outer arch conditions. In addition, increasing the longitudinal distance between vanes increases the velocity gradient between the vanes and leads to a more severe erosion of the bed near the vanes.Figure 1VIEW LARGEDOWNLOAD SLIDE

Laboratory channel dimensions.

Al-Zubaidy & Hilo (2021) used the Navier–Stokes equation to study the flow of incompressible fluids. Using the CFD software ANSYS Fluent 19.2, 3D flow patterns were simulated at a diversion channel. Their results showed good agreement using the comparison between the experimental and numerical results when the k-omega turbulence viscous model was employed. Simulation of the flow pattern was then done at the lateral channel junction using a variety of geometry designs. These improvements included changing the intake’s inclination angle and chamfering and rounding the inner corner of the intake mouth instead of the sharp edge. Flow parameters at the diversion including velocity streamlines, bed shear stress, and separation zone dimensions were computed in their study. The findings demonstrated that changing the 90° lateral intake geometry can improve the flow pattern and bed shear stress at the intake junction. Consequently, sedimentation and erosion problems are reduced. According to the conclusions of their study, a branching angle of 30° to 45° is the best configuration for increasing branching channel discharge, lowering branching channel sediment concentration.

The review of the literature shows that most of the studies deal with turnout angle, discharge ratio and implementation of vanes as techniques to reduce the area of the separation zone. This study examines the effect of roughness coefficient and drop implementation at the entrance of a 90-degree lateral turnout on the dimensions of the separation zone. As far as the authors are aware, these two variables have never been studied as a remedy to decrease the separation zone dimensions whilst enhancing turnout efficiency. Additionally, a three-dimensional numerical model is applied to simulate the flow pattern around the turnout. The numerical results are verified against experimental data.

METHOD

Experimental setup

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The experiments were conducted in a 90 degree dividing flow laboratory channel. The main channel is 15 m long, 0.5 m wide and 0.4 m high and the branch channel is 3 m long, 0.35 m wide and 0.4 m high, as shown in Figure 1. The tests were carried out at 9.65 m from the beginning of the flume and were far enough from the inlet, so we were sure that the flow was fully developed. According to Kirkgöz & Ardiçlioğlu (1997) the length of the developing region would be approximantly 65 and 72 times the flow depth. In this study, the depth is 9 cm, which makes this condition.

Both the main and lateral channel had a slope of 0.0003 with side walls of concrete. A 100 hp pump discharged the water into a stilling basin at the entrance of the main flume. The discharge was measured using an ultrasonic discharge meter around the discharge pipe. Eighty-four experiments in total were carried out at range of 0.1<Fr<0.4 (Froude numbers in main channel and upstream of turnout). The depth of water in the main channel in the experiments was 9 cm, in which case the effect of surface tension can be considered; according to research by Zolghadr & Shafai Bejestan (2020) and Zolghadr et al. (2021), when the water depth is more than 6 cm, the effect of surface tension is reduced and can be ignored given that the separation phenomenon occurs in the boundary layer, the height of the roughness creates disturbances in growth and development of the boundary layer and, as a result, separation growth is also faced with disruption and its dimensions grow less compared to smooth surfaces. Similar conditions occur in case of drop implementation. A disturbance occurs in the growth of the boundary layer and as a result the separation zone dimensions decrease. In order to investigate the effect of roughness coefficient and drop implementation on the separation zone dimensions, four different discharges (16, 18, 21, 23 l/s) in subcritical conditions, seven Manning (Strickler) roughness coefficients (0.009, 0.011, 0.017, 0.023, 0.028, 0.030, 0.032) as shown in Figure 2 and three invert elevation differences between the main channel and lateral turnout invert (0, 5 and 10 cm) at the entrance of the turnout were considered. The Manning roughness coefficient values were selected based on available and feasible values for real conditions, so that 0.009 is equivalent to galvanized sheet roughness and selected for the baseline tests. 0.011 is for concrete with neat surface, 0.017 and 0.023 are for unfinished and gunite concrete respectively. 0.030 and 0.032 values are for concrete on irregular excavated rock (Chow 1959). The roughness coefficients were created by gluing sediment particles on a thin galvanized sheet which was installed at the upstream side of the lateral turnout. The values of roughness coefficients were calculated based on the Manning-Strickler formula. For this purpose, some uniformly graded sediment samples were prepared and the Manning roughness coefficient of each sample was determined with respect to the median size (D50) value pasted into the Manning-Strickler formula. Some KMnO4 was sifted in the main channel upstream to visualize and measure the dimensions of the separation zone. Consequently, when KMnO4 approached the lateral turnout a photo of the separation zone was taken from a top view. All the experiments were recorded and several photos were taken during the experiment after stablishment of steady flow conditions. The photos were then imported to AutoCAD to measure the separation zone dimensions. Because all the shooting was done with a high-definition camera and it was possible to zoom in, the results are very accurate.Figure 2VIEW LARGEDOWNLOAD SLIDE

Roughness plates.

The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in transverse direction (perpendicular to the flow direction).

The water level was also measured by depth gauges with a accuracy of 0.1 mm, and velocity in one direction with a single-dimensional KENEK LP 1100 with an accuracy of ±0.02 m/s (0–1 m/s), ± 0.04 m/s (1–2 m/s), ± 0.08 m/s (2–4 m/s), ±0.10 m/s (4–5 m/s).

Numerical simulation

ListenA FLOW-3D numerical model was utilized as a solver of the Navier-Stokes equation to simulate the three-dimensional flow field at the entrance of the turnout. The governing equations included continuity momentum equations. The continuity equation, regardless of the density of the fluid in the form of Cartesian coordinates x, y, and z, is as follows:

formula

(1)where uv, and w represent the velocity components in the x, y, and z directions, respectively; AxAy, and Az are the surface flow fractions in the xy, and z directions, respectively; VF denotes flow volume fraction; r is the density of the fluid; t is time; and Rsor refers to the source of the mass. Equations (2)–(4) show momentum equations in xy and z dimensions respectively :

formula

(2)

formula

(3)

formula

(4)where GxGy, and Gz are the accelerations caused by gravity in the xy, and z directions, respectively; and fxfy, and fz are the accelerations caused by viscosity in the xy, and z directions, respectively.

The turbulence models used in this study were the renormalized group (RNG) models. Evaluation of the concordance of the mentioned models with experimental studies showed that the RNG model provides more accurate results.

Two blocks of mesh were used to simulate the main channels and lateral turnout. The meshes were denser in the vicinity of the entrance of the turnout in order to increase the accuracy of computations. Boundary conditions for the main mesh block included inflow for the channel entrance (volumetric flow rate), outflow for the channel exit, ‘wall’ for the bed and the right boundary and ‘symmetry’ for the top (free surface) and left boundaries (turnout). The side wall roughness coefficient was given to the software as the Manning number in surface roughness of any component. Considering the restrictions in the available processor, a main mesh block with appropriate mesh size was defined to simulate the main flow field in the channel, while the nested mesh-block technique was utilized to create a very dense solution field near the roughness plate in order to provide accurate results around the plates and near the entrance of the lateral turnout. This technique reduced the number of required mesh elements by up to 60% in comparison with the method in which the mesh size of the main solution field was decreased to the required extent.

The numerical outputs are verified against experimental data. The hydraulic characteristics of the experiment are shown in Table 1.Table 1

Hydraulic conditions of the flow

Q(L/s)FrY1 (m)Q2/Q1
16 0.449 0.09 0.22 
18 0.335 0.09 0.61 
21 0.242 0.09 0.71 
23 0.180 0.09 1.04 

RESULTS AND DISCUSSION

Experimental results

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During the experiments, the dimensions of the separation zone were recorded with an HD camera. Some photos were imported to AutoCad software. Then, the separation zones dimensions were measured and compared in different scenarios.

At the beginning, the flow pattern in the separation zone for four different hydraulic conditions was studied for seven different Manning roughness coefficients from 0.009 to 0.032. To compare the obtained results, roughness of 0.009 was considered as the base line. The percentage of reduction in separation zone area in different roughness coefficients is shown in Figure 3. According to this figure, by increasing the roughness of the turnout side wall, the separation zone area ratio reduces (ratio of separation zone area to turnout area). In other words, in any desired Froud number, the highest dimensions of the separation zone area are related to the lowest roughness coefficients. In Figure 3, ‘A’ is the area of the separation zone and ‘Ai’ represents the total area of the turnout.Figure 3VIEW LARGEDOWNLOAD SLIDE

Effect of roughness on separation zone dimensions.Figure 4VIEW LARGEDOWNLOAD SLIDE

Effect of roughness on separation zone dimensions.

It should be mentioned that the separation zone dimensions change with depth, so that the area is larger at the surface than near the bed. This study measured the dimensions of this area at the surface. Figure 4 show exactly where the roughness elements were located.Figure 5VIEW LARGEDOWNLOAD SLIDE

Comparison of separation zone for n=0.023 and n=0.032.

Figure 5 shows images of the separation zone at n=0.023 and n=0.032 as examples, and show that the separation area at n=0.032 is smaller than that of n=0.023.

The difference between the effect of the two 0.032 and 0.030 roughnesses is minor. In other words, the dimensions of the separation zone decreased by increasing roughness up to 0.030 and then remained with negligable changes.

In the next step, the effect of intake invert relative to the main stream (drop) on the dimensions of the separation zone was investigated. To do this, three different invert levels were considered: (1) without drop; (2) a 5 cm drop between the main canal and intake canal; and (3) a 10 cm drop between the main canal and intake canal. The without drop mode was considered as the control state. Figure 6 shows the effect of drop implementation on separation zone dimensions. Tables 2 and 3 show the reduced percentage of separation zone areas in 5 and 10 cm drop compared to no drop conditions as the base line. It was found that the best results were obtained when a 10 cm drop was implemented.Table 2

Decrease percentage of separation zone area in 5 cm drop

Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
0.08 10.56 11.06 25.27 33.03 35.57 36.5 
0.121 7.66 11.14 11.88 15.93 34.59 36.25 
0.353 1.38 2.63 8.17 14.39 31.20 31.29 
0.362 11.54 19.56 25.73 37.89 38.31 

Table 3

Decrease percentage of separation zone area in 10 cm drop

Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
0.047 4.30 8.75 23.47 31.22 34.96 35.13 
0.119 11.01 13.16 15.02 21.48 39.45 40.68 
0.348 3.89 5.71 9.82 16.09 29 30.96 
0.354 2.84 10.44 18.42 25.45 35.68 35.76 

Figure 6VIEW LARGEDOWNLOAD SLIDE

Effect of drop implementation on separation zone dimensions.

The combined effect of drop and roughness is shown in Figure 7. According to this figure, by installing a drop structure at the entrance of the intake, the dimensions of the separation zone scales down in any desired roughness coefficient. Results indicated that by increasing the roughness coefficient or drop implementation individually, the separation zone area decreases up to 38 and 25% respectively. However, employing both techniques simultaneously can reduce the separation zone area up to 63% (Table 4). The reason for the reduction of the dimensions of the separation zone area by drop implementation can be attributed to the increase of discharge ratio. This reduces the dimensions of the separation zone area.Table 4

Reduction in percentage of combined effect of roughness and 10 cm drop

Qin=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
16 32.3 35.07 37.2 45.7 58.01 59.1 
18 44.5 34.15 36.18 48.13 54.2 56.18 
21 43.18 32.33 42.30 37.79 57.16 63.2 
23 40.56 34.5 34.09 46.25 50.12 57.2 

Figure 7VIEW LARGEDOWNLOAD SLIDE

Combined effect of roughness and drop on separation zone dimensions.

This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Some other researchers reported that increasing the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007Ramamurthy et al. 2007). However, these researchers employed other methods to enhance the discharge ratio. Drop implementation is simple and applicable in practice, since there is normally an elevation difference between the main and lateral canal in irrigation networks to ensure gravity flow occurance.

Table 4 depicts the decrease in percentage of the separation zone compared to base line conditions in different arrangements of the combined tests.Figure 8VIEW LARGEDOWNLOAD SLIDE

Velocity profiles for various roughness coefficients along turnout width.

A comparison between the proposed methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. Figure 8 shows the comparison of the results. The comparison shows that the new techniques can be highly influential and still practical. In this research, with no change in structural geometry (enhancement of roughness coefficient) or minor changes with respect to drop implementation, the dimensions of the separation zone are decreased noticeably. The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in a transverse direction (perpendicular to the flow direction). The results are shown in Figure 9.Figure 9VIEW LARGEDOWNLOAD SLIDE

Effect of roughness on separation zone dimensions in numerical study.

Numerical results

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This study examined the flow patterns around the entrance of a diversion channel due to various wall roughnesses in the diversion channel. Results indicated that increasing the discharge ratio in the main channel and diversion channel reduces the area of the separation zone in the diversion channel.Figure 10VIEW LARGEDOWNLOAD SLIDE

Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).A laboratory and numerical error rate of 0.2605 was calculated from the following formula,

formula

where Uexp is the experimental result, Unum is the numerical result, and N is the number of data.

Figure 9 shows the effect of roughness on separation zone dimensions in numerical study. Figure 10 compares the vortex area (software output) for three roughnesses, 0.009, 0.023 and 0.032 and Figure 11 shows the flow lines (tecplot output) that indicate the effect of roughness on flow in the separation zone. Numerical analysis shows that by increasing the roughness coefficient, the dimensions of the separation zone area decrease, as shown in Figure 10 where the separation zone area at n=0.032 is less than the separation zone area at n=0.009.Figure 11VIEW LARGEDOWNLOAD SLIDE

Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.Figure 12VIEW LARGEDOWNLOAD SLIDE

Velocity vector for flow condition Q1/422 l/s, near surface.

The velocities intensified moving midway toward the turnout showing that the effective area is scaled down. The velocity values were almost equal to zero near the side walls as expected. As shown in Figure 12 the approach vortex area velocity decreases. Experimental and numerical measured velocity at x=0.15 m of the diversion channel compared in Figure 13 shows that away from the separation zone area, the velocity increases. All longitudinal velocity contours near the vortex area are distinctly different between different roughnesses. The separation zone is larger at less roughness both in length and width.Figure 13VIEW LARGEDOWNLOAD SLIDE

Exprimental and numerical measured velocity.

CONCLUSION

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This study introduces practical and feasible methods for enhancing turnout efficiency by reducing the separation zone dimensions. Increasing the roughness coefficient and implementation of inlet drop were considered as remedies for reduction of separation zone dimensions. A data set has been compiled that fully describes the complex, 3D flow conditions present in a 90 degree turnout channel for selected flow conditions. The aim of this numerical model was to compare the results of a laboratory model in the area of the separation zone and velocity. Results showed that enhancing roughness coefficient reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%. Further research is proposed to investigate the effect of roughness and drop implementation on sedimentation pattern at lateral turnouts. The dimensions of the separation zone decreases with the increase of the non-dimensional parameter, due to the reduction ratio of turnout discharge increasing in all the experiments.

This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Other researchers have reported that intensifying the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007Ramamurthy et al. 2007). However, they employed other methods to enhance the discharge ratio. Employing both techniques simultaneously can decrease the separation zone dimensions up to 63%. A comparison between the new methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. The comparison shows that the new techniques can be highly influential and still practical. The numerical and laboratory models are in good agreement and show that the method used in this study has been effective in reducing the separation area. This method is simple, economical and can prevent sediment deposition in the intake canal. Results show that CFD prediction of the fluid through the separation zone at the canal intake can be predicted reasonably well and the RNG model offers the best results in terms of predictability.

DATA AVAILABILITY STATEMENT

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All relevant data are included in the paper or its Supplementary Information.

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).Google Scholar 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.Google Scholar 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).Google Scholar 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.Google Scholar 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).Google Scholar 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.Google ScholarCrossref  Kasthuri B. & Pundarikanthan N. V. 1987 Discussion on separation zone at open- channel junction. Journal of Hydraulic Engineering 113 (4), 543–548.Google ScholarCrossref  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.Google ScholarCrossref  Kirkgöz M. S. & Ardiçlioğlu 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).Google Scholar 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).Google Scholar 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).Google ScholarCrossref  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.Google Scholar Odgaard J. A. & Wang Y. 1991 Sediment management with submerged vanes, I: theory. Journal of Hydraulic Engineering 117 (3), 267–283.Google ScholarCrossref  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).Google Scholar 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.Google Scholar 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.Google Scholar Zolghadr M., Zomorodian S. M. A., Shabani R. & Azamatulla H.Md. 2021 Migration of sand mining pit in rivers: an experimental, numerical and case study. Measurement. https://doi.org/10.1016/j.measurement.2020.108944.Google Scholar © 2022 The AuthorsThis is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY-NC-ND 4.0), which permits copying and redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition

Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition

Xiang WangLin-Jie ZhangJie Ning, and Suck-Joo Na
Published Online:8 Apr 2022https://doi.org/10.1089/3dp.2021.0159

Abstract

A 3D numerical model of heat transfer and fluid flow of molten pool in the process of laser wire deposition was presented by computational fluid dynamics technique. The simulation results of the deposition morphology were also compared with the experimental results under the condition of liquid bridge transfer mode. Moreover, they showed a good agreement. Considering the effect of recoil pressure, the morphology of the deposit metal obtained by the simulation was similar to the experiment result. Molten metal at the wire tip was peeled off and flowed into the molten pool, and then spread to both sides of the deposition layer under the recoil pressure. In addition, the results of simulation and high-speed charge-coupled device presented that a wedge transition zone, with a length of ∼6 mm, was formed behind the keyhole in the liquid bridge transfer process, where the height of deposited metal decreased gradually. After solidification, metal in the transition zone retained the original melt morphology, resulting in a decrease in the height of the tail of the deposition layer.

Keywords

LWD, CFD, liquid bridge transfer, fluid dynamics, wedge transition zone

Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition
Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition
Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition
Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition

References

1. Matthews MJ, Guss G, Khairallah SA, et al. Denudation of metal powder layers in laser powder bed fusion processes. Acta Mater 2016;114:33–42. CrossrefGoogle Scholar

2. Ge WJ, Han SW, Fang YC, et al. Mechanism of surface morphology in electron beam melting of Ti6Al4V based on computational flow patterns. Appl Surf Sci 2017;419:150–158. CrossrefGoogle Scholar

3. Bai XW, Colegrove P, Ding JL, et al. Numerical analyswas of heat transfer and fluid flow in multilayer deposition of PAW-based wire and arc additive manufacturing. Int J Heat Mass Transf 2018;124:504–516. CrossrefGoogle Scholar

4. Torkamany MJ, Kaplan AFH, Ghaini FM. Wire deposition by a laser-induced boiling front. Opt Laser Technol 2015;69:104–112. CrossrefGoogle Scholar

5. Yu Y, Huang W, Wang G. Investigation of melting dynamics of filler wire during wire feed laser welding. J Mec Sci Technol 2013;27:1097–1108. CrossrefGoogle Scholar

6. Ma G, Li L, Chen Y. Effects of beam confgurations on wire melting and transfer behaviors in dual beam laser welding with fller wire. Opt Laser Technol 2017;91:138–148. CrossrefGoogle Scholar

7. Abioye TE, Folkes J, Clare AT. A parametric study of Inconel 625 wire laser deposition. J Mater Process Tech 2013;213:2145–2151. CrossrefGoogle Scholar

8. Wei S, Wang G, Shin YC, et al. Comprehensive modeling of transport phenomena in laser hot-wire deposition process. Int J Heat Mass Transf 2018;125:1356–1368. CrossrefGoogle Scholar

9. Gu H, Li L. Computational fluid dynamic simulation of gravity and pressure effects in laser metal deposition for potential additive manufacturing in space. Int J Heat Mass Transf 2019;140:51–65. CrossrefGoogle Scholar

10. Hu R, Luo M, Liu T, et al. Thermal fluid dynamics of liquid bridge transfer in laser wire deposition 3D printing. Sci Technolf Weld Join 2019;24:1–11. Google Scholar

11. Chatterjee D, Chakraborty S. A hybrid lattice Boltzmann model for solid–liquid phase transition in presence of fluid flow. Phys Lett A 2006;351:359–367. CrossrefGoogle Scholar

12. Wu L, Cheon J, Kiran DV, et al. CFD simulations of GMA welding of horizontal fillet joints based on coordinate rotation of arc models. J Mater Process Tech 2016;231:221–238. CrossrefGoogle Scholar

13. Gerhard W, Boyer RR, Collings EW. Materials Properties Handbook: Titanium Alloys. ASM International: Almere, The Netherlands, 1994. Google Scholar

14. Colegrove P, Simiand PE, Varughese A, et al. Evaluation of a drilling model approach to represent laser spot microwelding. In: ASM Proceedings of the international conference: trends in welding research; 2009. Google Scholar

15. Boivineau M, Cagran C, Doytier D, et al. Thermophysical properties of solid and liquid Ti-6Al-4V (TA6V) alloy. Int J Thermophys 2006;27:507–529. CrossrefGoogle Scholar

16. Shejndlin AE, Kenisarin MM, Chekhovskoj VY. Melting point of yttrium oxide. AN SSSR 1974;216:582–584. Google Scholar

17. Cho JH, Na SJ. Teflection and Fresnel absorption of laser beam in keyhole. J Phys D Appl Phys 2006;39:5372–5378. CrossrefGoogle Scholar

18. Han SW, Ahn J, Na SJ. A study on ray tracing method for CFD simulations of laser keyhole welding: Progressive search method. Weld World 2016;60:247–258. CrossrefGoogle Scholar

19. Allmen MV. Laser-Beam Interactions with Materials. Springer, Berlin-Heidelberg, 1995. Google Scholar

20. Dobson PJ. Absorption and scattering of light by small particles. Phys Bull 1984;35:104. CrossrefGoogle Scholar

21. Greses J, Hilton PA, Barlow CY. Plume attenuation under high power Nd:yttritium aluminum garnet laser welding. J Laser Appl 2004;16:9–15. CrossrefGoogle Scholar

22. Shcheglov PY, Uspenskiy SA, Gumenyuk AV, et al. Plume attenuation of laser radiation during high power fiber laser welding. Laser Phys Lett 2011;8:475–480. CrossrefGoogle Scholar

23. Yang P, Liou KN. Effective refractive index for determining ray propagation in an absorbing dielectric particle. J Quant Spectrosc Radiat Transf 2009;110:300–306. CrossrefGoogle Scholar

24. Barber PW. Absorption and scattering of light by small particles. J Colloid Interface Sci 1984;98:290–291. Google Scholar

25. Hu ZR, Chen X, Yang G, et al. Metal transfer in wire feeding-based electron beam 3D printing: Modes, dynamics, and transition criterion. Int J Heat Mass Transf 2018;126:877–887. CrossrefGoogle Scholar

26. David SA, Babu SS, Vitek JM. Welding: Solidification and microstructure. JOM 2013;55:14–20. CrossrefGoogle Scholar

27. Zhong ML, Liu W. Laser surface cladding: The state of the art and challenges. Proc Inst Mech Eng Part C J Mech Eng Sci 2010;224:1041–1060. CrossrefGoogle Scholar

28. Kobryn PA, Semiatin S. Microstructure and texture evolution during solidification processing of Ti-6Al-4V. J Mater Process Technol 2003;135:330–339. CrossrefGoogle Scholar

29. Debroy T, David S. Physical processes in fusion welding. Rev Mod Phys 1995;67:85–112. CrossrefGoogle Scholar

30. Lee YS, Nordin M, Babu SS, et al. Effect of fluid convection on dendrite arm spacing in laser deposition. Metall Trans B 2014;45:1520–1528. CrossrefGoogle Scholar

31. Rappaz M, David SA, Vitek JM, et al. Development of microstructures in Fe15Ni15Cr single crystal electron beam welds. Metall Trans A 1989;20:1125–1138. CrossrefGoogle Scholar

Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.

Hybrid modeling on 3D hydraulic features of a step-pool unit

Chendi Zhang1
, Yuncheng Xu1,2, Marwan A Hassan3
, Mengzhen Xu1
, Pukang He1
1State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, China. 2
College of Water Resources and Civil Engineering, China Agricultural University, Beijing, 100081, China.
5 3Department of Geography, University of British Columbia, 1984 West Mall, Vancouver BC, V6T1Z2, Canada.
Correspondence to: Chendi Zhang (chendinorthwest@163.com) and Mengzhen Xu (mzxu@mail.tsinghua.edu.cn)

Abstract

스텝 풀 시스템은 계류의 일반적인 기반이며 전 세계의 하천 복원 프로젝트에 활용되었습니다. 스텝 풀 장치는 스텝 풀 기능의 형태학적 진화 및 안정성과 밀접하게 상호 작용하는 것으로 보고된 매우 균일하지 않은 수력 특성을 나타냅니다.

그러나 스텝 풀 형태에 대한 3차원 수리학의 자세한 정보는 측정의 어려움으로 인해 부족했습니다. 이러한 지식 격차를 메우기 위해 SfM(Structure from Motion) 및 CFD(Computational Fluid Dynamics) 기술을 기반으로 하이브리드 모델을 구축했습니다. 이 모델은 CFD 시뮬레이션을 위한 입력으로 6가지 유속의 자연석으로 만든 인공 스텝 풀 장치가 있는 침대 표면의 3D 재구성을 사용했습니다.

하이브리드 모델은 스텝 풀 장치에 대한 3D 흐름 구조의 고해상도 시각화를 제공하는 데 성공했습니다. 결과는 계단 아래의 흐름 영역의 분할, 즉 수면에서의 통합 점프, 침대 근처의 줄무늬 후류 및 그 사이의 고속 제트를 보여줍니다.

수영장에서 난류 에너지의 매우 불균일한 분포가 밝혀졌으며 비슷한 용량을 가진 두 개의 에너지 소산기가 수영장에 공존하는 것으로 나타났습니다. 흐름 증가에 따른 풀 세굴 개발은 점프 및 후류 와류의 확장으로 이어지지만 이러한 증가는 스텝 풀 실패에 대한 임계 조건에 가까운 높은 흐름에서 점프에 대해 멈춥니다.

음의 경사면에서 발달된 곡물 20 클러스터와 같은 미세 지반은 국부 수력학에 상당한 영향을 주지만 이러한 영향은 수영장 바닥에서 억제됩니다. 스텝 스톤의 항력은 가장 높은 흐름이 사용되기 전에 배출과 함께 증가하는 반면 양력은 더 큰 크기와 더 넓은 범위를 갖습니다. 우리의 결과는 계단 풀 형태의 복잡한 흐름 특성을 조사할 때 물리적 및 수치적 모델링을 결합한 하이브리드 모델 접근 방식의 가능성과 큰 잠재력을 강조합니다.

Step-pool systems are common bedforms in mountain streams and have been utilized in river restoration projects around the world. Step-pool units exhibit highly non-uniform hydraulic characteristics which have been reported to closely 10 interact with the morphological evolution and stability of step-pool features. However, detailed information of the threedimensional hydraulics for step-pool morphology has been scarce due to the difficulty of measurement. To fill in this knowledge gap, we established a hybrid model based on the technologies of Structure from Motion (SfM) and computational fluid dynamics (CFD). The model used 3D reconstructions of bed surfaces with an artificial step-pool unit built by natural stones at six flow rates as inputs for CFD simulations. The hybrid model succeeded in providing high-resolution visualization 15 of 3D flow structures for the step-pool unit. The results illustrate the segmentation of flow regimes below the step, i.e., the integral jump at the water surface, streaky wake vortexes near the bed, and high-speed jets in between. The highly non-uniform distribution of turbulence energy in the pool has been revealed and two energy dissipaters with comparable capacity are found to co-exist in the pool. Pool scour development under flow increase leads to the expansion of the jump and wake vortexes but this increase stops for the jump at high flows close to the critical condition for step-pool failure. The micro-bedforms as grain 20 clusters developed on the negative slope affect the local hydraulics significantly but this influence is suppressed at pool bottom. The drag forces on the step stones increase with discharge before the highest flow is used while the lift force has a larger magnitude and wider varying range. Our results highlight the feasibility and great potential of the hybrid model approach combining physical and numerical modeling in investigating the complex flow characteristics of step-pool morphology.

Figure 1: Workflow of the hybrid modeling. SfM-MVS refers to the technology of Structure from Motion with Multi View Stereo. DSM is short for digital surface model. RNG-VOF is short for Renormalized Group (RNG) k-ε turbulence model coupled with Volume of Fluid method.
Figure 1: Workflow of the hybrid modeling. SfM-MVS refers to the technology of Structure from Motion with Multi View Stereo. DSM is short for digital surface model. RNG-VOF is short for Renormalized Group (RNG) k-ε turbulence model coupled with Volume of Fluid method.
Figure 2: Flume experiment settings in Zhang et al., (2020): (a) the artificially built-up step-pool model using natural stones, with stone number labelled; (b) the unsteady hydrograph of the run of CIFR (continually-increasing-flow-rate) T2 used in this study.
Figure 2: Flume experiment settings in Zhang et al., (2020): (a) the artificially built-up step-pool model using natural stones, with stone number labelled; (b) the unsteady hydrograph of the run of CIFR (continually-increasing-flow-rate) T2 used in this study.
Figure 3: Setup of the CFD model: (a) three-dimensional digital surface model (DSM) of the step-pool unit by structure from motion with multi view stereo (SfM-MVS) method as the input to the 3D computational fluid dynamics (CFD) modeling; (b) extruded bed 160 surface model connected to the extra downstream component (in purple blue) and rectangular columns to fill leaks (in green), with the boundary conditions shown on mesh planes; (c) recognized geometry with mesh grids of two mesh blocks shown where MS is short for mesh size; (d) sampling volumes to capture the flow forces acting on each step stone at X, Y, and Z directions; and (e) an example for the simulated 3D flow over the step-pool unit colored by velocity magnitude at the discharge of 49.9 L/s. The abbreviations for boundary conditions in (b) are: V for specified velocity; C for continuative; P for specific pressure; and W for wall 165 condition. The contraction section in Figure (e) refers to the edge between the jet and jump at water surface.
Figure 3: Setup of the CFD model: (a) three-dimensional digital surface model (DSM) of the step-pool unit by structure from motion with multi view stereo (SfM-MVS) method as the input to the 3D computational fluid dynamics (CFD) modeling; (b) extruded bed 160 surface model connected to the extra downstream component (in purple blue) and rectangular columns to fill leaks (in green), with the boundary conditions shown on mesh planes; (c) recognized geometry with mesh grids of two mesh blocks shown where MS is short for mesh size; (d) sampling volumes to capture the flow forces acting on each step stone at X, Y, and Z directions; and (e) an example for the simulated 3D flow over the step-pool unit colored by velocity magnitude at the discharge of 49.9 L/s. The abbreviations for boundary conditions in (b) are: V for specified velocity; C for continuative; P for specific pressure; and W for wall 165 condition. The contraction section in Figure (e) refers to the edge between the jet and jump at water surface.
Figure 4: Distribution of time-averaged velocity magnitude (VM_mean) and vectors in three longitudinal sections. The section at Y = 0 cm goes across the keystone while the other two (Y = -18 and 13.5 cm) are located at the step stones beside the keystone with 265 lower top elevations. Q refers to the discharge at the inlet of the computational domain. The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 4: Distribution of time-averaged velocity magnitude (VM_mean) and vectors in three longitudinal sections. The section at Y = 0 cm goes across the keystone while the other two (Y = -18 and 13.5 cm) are located at the step stones beside the keystone with lower top elevations. Q refers to the discharge at the inlet of the computational domain. The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 5: Distribution of time-averaged flow velocity at five cross sections which are set according to the reference section (x0). The reference cross section x0 is located at the downstream end of the keystone (KS). The five sections are located at 18 cm and 6 cm upstream of the reference section (x0-18 and x0-6), and 2 cm, 15 cm and 40 cm downstream of the reference section (x0+2, x0+15, x0+40). The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 5: Distribution of time-averaged flow velocity at five cross sections which are set according to the reference section (x0). The reference cross section x0 is located at the downstream end of the keystone (KS). The five sections are located at 18 cm and 6 cm upstream of the reference section (x0-18 and x0-6), and 2 cm, 15 cm and 40 cm downstream of the reference section (x0+2, x0+15, x0+40). The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 6: Distribution of the time-averaged turbulence kinetic energy (TKE) at the five cross sections same with Figure 3.
Figure 6: Distribution of the time-averaged turbulence kinetic energy (TKE) at the five cross sections same with Figure 3.
Figure 7: Boxplots for the distributions of the mass-averaged flow kinetic energy (KE, panels a-f), turbulence kinetic energy (TKE, panels g-l), and turbulent dissipation (εT, panels m-r) in the pool for all the six tested discharges (the plots at the same discharge are in the same row). The mass-averaged values were calculated every 2 cm in the streamwise direction. The flow direction is from left to right in all the plots. The general locations of the contraction section for all the flow rates are marked by the dashed lines, except for Q = 5 L/s when the jump is located too close to the step. The longitudinal distance taken up by negative slope in the pool for the inspected range is shown by shaded area in each plot.
Figure 7: Boxplots for the distributions of the mass-averaged flow kinetic energy (KE, panels a-f), turbulence kinetic energy (TKE, panels g-l), and turbulent dissipation (εT, panels m-r) in the pool for all the six tested discharges (the plots at the same discharge are in the same row). The mass-averaged values were calculated every 2 cm in the streamwise direction. The flow direction is from left to right in all the plots. The general locations of the contraction section for all the flow rates are marked by the dashed lines, except for Q = 5 L/s when the jump is located too close to the step. The longitudinal distance taken up by negative slope in the pool for the inspected range is shown by shaded area in each plot.
Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.
Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.
Figure 9: Time-averaged dynamic pressure (DP_mean) on the bed surface in the step-pool model under the two highest discharges, with the step numbers marked. The negative values in the plots result from the setting of standard atmospheric pressure = 0 Pa, whose absolute value is 1.013×105 Pa.
Figure 9: Time-averaged dynamic pressure (DP_mean) on the bed surface in the step-pool model under the two highest discharges, with the step numbers marked. The negative values in the plots result from the setting of standard atmospheric pressure = 0 Pa, whose absolute value is 1.013×105 Pa.
Figure 10: Time-averaged shear stress (SS_mean) on bed surface in the step-pool model, with the step numbers marked. The standard atmospheric pressure is set as 0 Pa.
Figure 10: Time-averaged shear stress (SS_mean) on bed surface in the step-pool model, with the step numbers marked. The standard atmospheric pressure is set as 0 Pa.
Figure 11: Variation of fluid force components and magnitude of resultant flow force acting on step stones with flow rate. The stone 4 is the keystone. Stone numbers are consistent with those in Fig. 9-10. The upper limit of the sampling volumes for flow force calculation is higher than water surface while the lower limit is set at 3 cm lower than the keystone crest.
Figure 11: Variation of fluid force components and magnitude of resultant flow force acting on step stones with flow rate. The stone 4 is the keystone. Stone numbers are consistent with those in Fig. 9-10. The upper limit of the sampling volumes for flow force calculation is higher than water surface while the lower limit is set at 3 cm lower than the keystone crest.
Figure 12: Variation of drag (CD) and lift (CL) coefficient of the step stones along with flow rate. Stone numbers are consistent with those in Fig. 8-9. KS is short for keystone. The negative values of CD correspond to the drag forces towards the upstream while the negative values of CL correspond to lift forces pointing downwards.
Figure 12: Variation of drag (CD) and lift (CL) coefficient of the step stones along with flow rate. Stone numbers are consistent with those in Fig. 8-9. KS is short for keystone. The negative values of CD correspond to the drag forces towards the upstream while the negative values of CL correspond to lift forces pointing downwards.
Figure 13: Longitudinal distributions of section-averaged and -integral turbulent kinetic energy (TKE) for the jump and wake vortexes at the largest three discharges. The flow direction is from left to right in all the plots. The general locations of the contraction sections under the three flow rates are marked by dashed lines in figures (d) to (f).
Figure 13: Longitudinal distributions of section-averaged and -integral turbulent kinetic energy (TKE) for the jump and wake vortexes at the largest three discharges. The flow direction is from left to right in all the plots. The general locations of the contraction sections under the three flow rates are marked by dashed lines in figures (d) to (f).
Figure A1: Water surface profiles of the simulations with different mesh sizes at the discharge of 43.6 L/s at the longitudinal sections at: (a) Y = 24.5 cm (left boundary); (b) Y = 0.3 cm (middle section); (c) Y = -24.5 cm (right boundary). MS is short for mesh size. The flow direction is from left to right in each plot.
Figure A1: Water surface profiles of the simulations with different mesh sizes at the discharge of 43.6 L/s at the longitudinal sections at: (a) Y = 24.5 cm (left boundary); (b) Y = 0.3 cm (middle section); (c) Y = -24.5 cm (right boundary). MS is short for mesh size. The flow direction is from left to right in each plot.
Figure A2: Contours of velocity magnitude in the longitudinal section at Y = 0 cm at different mesh sizes (MSs) under the flow condition with the discharge of 43.6 L/s: (a) 0.50 cm; (b) 0.375 cm; (c) 0.30 cm; (d) 0.27 cm; (e) 0.25 cm; (f) 0.24 cm. The flow direction is from left to right.
Figure A2: Contours of velocity magnitude in the longitudinal section at Y = 0 cm at different mesh sizes (MSs) under the flow condition with the discharge of 43.6 L/s: (a) 0.50 cm; (b) 0.375 cm; (c) 0.30 cm; (d) 0.27 cm; (e) 0.25 cm; (f) 0.24 cm. The flow direction is from left to right.
Figure A3: Measurements of water surfaces (orange lines) used in model verification: (a) water surface profiles from both sides of the flume; (b) upstream edge of the jump regime from top view. KS refers to keystone in figure (b).
Figure A3: Measurements of water surfaces (orange lines) used in model verification: (a) water surface profiles from both sides of the flume; (b) upstream edge of the jump regime from top view. KS refers to keystone in figure (b).
Figure A15. Figure (a) shows the locations of the cross sections and target coarse grains at Q = 49.9 L/s. Figures (b) to (e) show the distribution of velocity magnitude (VM_mean) in the four chosen cross sections: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5. G1 to G6 refer to 6 protruding grains in the micro-bedforms in the pool.
Figure A15. Figure (a) shows the locations of the cross sections and target coarse grains at Q = 49.9 L/s. Figures (b) to (e) show the distribution of velocity magnitude (VM_mean) in the four chosen cross sections: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5. G1 to G6 refer to 6 protruding grains in the micro-bedforms in the pool.
Figure A16. The distribution of turbulent kinetic energy (TKE) in the same cross sections as in figure S15: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5.
Figure A16. The distribution of turbulent kinetic energy (TKE) in the same cross sections as in figure S15: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5.

References

720 Aberle, J. and Smart, G. M: The influence of roughness structure on flow resistance on steep slopes, J. Hydraul. Res., 41(3),
259-269, https://doi.org/10.1080/00221680309499971, 2003.
Abrahams, A. D., Li, G., and Atkinson, J. F.: Step-pool streams: Adjustment to maximum flow resistance. Water Resour. Res.,
31(10), 2593-2602, https://doi.org/10.1029/95WR01957, 1995.
Adrian, R. J.: Twenty years of particle image velocimetry. Exp. Fluids, 39(2), 159-169, https://doi.org/10.1007/s00348-005-
725 0991-7 2005.
Chanson, H.: Hydraulic design of stepped spillways and downstream energy dissipators. Dam Eng., 11(4), 205-242, 2001.
Chartrand, S. M., Jellinek, M., Whiting, P. J., and Stamm, J.: Geometric scaling of step-pools in mountain streams:
Observations and implications, Geomorphology, 129(1-2), 141-151, https://doi.org/10.1016/j.geomorph.2011.01.020,
2011.
730 Chen, Y., DiBiase, R. A., McCarroll, N., and Liu, X.: Quantifying flow resistance in mountain streams using computational
fluid dynamics modeling over structure‐from‐motion photogrammetry‐derived microtopography, Earth Surf. Proc.
Land., 44(10), 1973-1987, https://doi.org/10.1002/esp.4624, 2019.
Church, M. and Zimmermann, A.: Form and stability of step‐pool channels: Research progress, Water Resour. Res., 43(3),
W03415, https://doi.org/10.1029/2006WR005037, 2007.
735 Cignoni, P., Callieri, M., Corsini, M., Dellepiane, M., Ganovelli, F., and Ranzuglia, G.: Meshlab: an open-source mesh
processing tool, in: Eurographics Italian chapter conference, Salerno, Italy, 2-4 July 2008, 129-136, 2008.

Comiti, F., Andreoli, A., and Lenzi, M. A.: Morphological effects of local scouring in step-pool streams, Earth Surf. Proc.
Land., 30(12), 1567-1581, https://doi.org/10.1002/esp.1217, 2005.
Comiti, F., Cadol, D., and Wohl, E.: Flow regimes, bed morphology, and flow resistance in self‐formed step-pool
740 channels, Water Resour. Res., 45(4), 546-550, https://doi.org/10.1029/2008WR007259, 2009.
Dudunake, T., Tonina, D., Reeder, W. J., and Monsalve, A.: Local and reach‐scale hyporheic flow response from boulder ‐
induced geomorphic changes, Water Resour. Res., 56, e2020WR027719, https://doi.org/10.1029/2020WR027719, 2020.
Flow Science.: Flow-3D Version 11.2 User Manual, Flow Science, Inc., Los Alamos, 2016.
Gibson, S., Heath, R., Abraham, D., and Schoellhamer, D.: Visualization and analysis of temporal trends of sand infiltration
745 into a gravel bed, Water Resour. Res., 47(12), W12601, https://doi.org/10.1029/2011WR010486, 2011.
Hassan, M. A., Tonina, D., Beckie, R. D., and Kinnear, M.: The effects of discharge and slope on hyporheic flow in step‐pool
morphologies, Hydrol. Process., 29(3), 419-433, https://doi.org/10.1002/hyp.10155, 2015.
Hirt, C. W. and Nichols, B. D.: Volume of Fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys., 39,
201-225, https://doi.org/10.1016/0021-9991(81)90145-5, 1981.
750 Javernick L., Brasington J., and Caruso B.: Modeling the topography of shallow braided rivers using structure-from-motion
photogrammetry, Geomorphology, 213(4), 166-182, https://doi.org/10.1016/j.geomorph.2014.01.006, 2014.
Lai, Y. G., Smith, D. L., Bandrowski, D. J., Xu, Y., Woodley, C. M., and Schnell, K.: Development of a CFD model and
procedure for flows through in-stream structures, J. Appl. Water Eng. Res., 1-15,
https://doi.org/10.1080/23249676.2021.1964388, 2021.
755 Lenzi, M. A.: Step-pool evolution in the Rio Cordon, northeastern Italy, Earth Surf. Proc. Land., 26(9), 991-1008,
https://doi.org/10.1002/esp.239, 2001.
Lenzi, M. A.: Stream bed stabilization using boulder check dams that mimic step-pool morphology features in Northern
Italy, Geomorphology, 45(3-4), 243-260, https://doi.org/10.1016/S0169-555X(01)00157-X, 2002.
Lenzi, M. A., Marion, A., and Comiti, F.: Local scouring at grade‐control structures in alluvial mountain rivers, Water Resour.
760 Res., 39(7), 1176, https://doi:10.1029/2002WR001815, 2003.
Li, W., Wang Z., Li, Z., Zhang, C., and Lv, L.: Study on hydraulic characteristics of step-pool system, Adv. Water Sci., 25(3),
374-382, https://doi.org/10.14042/j.cnki.32.1309.2014.03.012, 2014. (In Chinese with English abstract)
Maas, H. G., Gruen, A., and Papantoniou, D.: Particle tracking velocimetry in three-dimensional flows, Exp. Fluids, 15(2),
133-146. https://doi.org/10.1007/BF00223406, 1993.

765 Montgomery, D. R. and Buffington, J. M.: Channel-reach morphology in mountain drainage basins, Geol. Soc. Am. Bul., 109(5), 596-611, https://doi.org/10.1130/0016-7606(1997)109<0596:CRMIMD>2.3.CO;2, 1997. Morgan J. A., Brogan D. J., and Nelson P. A.: Application of structure-from-motion photogrammetry in laboratory flumes, Geomorphology, 276(1), 125-143, https://doi.org/10.1016/j.geomorph.2016.10.021, 2017. Recking, A., Leduc, P., Liébault, F., and Church, M.: A field investigation of the influence of sediment supply on step-pool 770 morphology and stability. Geomorphology, 139, 53-66, https://doi.org/10.1016/j.geomorph.2011.09.024, 2012. Roth, M. S., Jähnel, C., Stamm, J., and Schneider, L. K.: Turbulent eddy identification of a meander and vertical-slot fishways in numerical models applying the IPOS-framework, J. Ecohydraulics, 1-20, https://doi.org/10.1080/24705357.2020.1869916, 2020. Saletti, M. and Hassan, M. A.: Width variations control the development of grain structuring in steep step‐pool dominated 775 streams: insight from flume experiments, Earth Surf. Proc. Land., 45(6), 1430-1440, https://doi.org/10.1002/esp.4815, 2020. Smith, D. P., Kortman, S. R., Caudillo, A. M., Kwan‐Davis, R. L., Wandke, J. J., Klein, J. W., Gennaro, M. C. S., Bogdan, M. A., and Vannerus, P. A.: Controls on large boulder mobility in an ‘auto-naturalized’ constructed step-pool river: San Clemente Reroute and Dam Removal Project, Carmel River, California, USA, Earth Surf. Proc. Land., 45(9), 1990-2003, 780 https://doi.org/10.1002/esp.4860, 2020. Thappeta, S. K., Bhallamudi, S. M., Fiener, P., and Narasimhan, B.: Resistance in Steep Open Channels due to Randomly Distributed Macroroughness Elements at Large Froude Numbers, J. Hydraul. Eng., 22(12), 04017052, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001587, 2017. Thappeta, S. K., Bhallamudi, S. M., Chandra, V., Fiener, P., and Baki, A. B. M.: Energy loss in steep open channels with step785 pools, Water, 13(1), 72, https://doi.org/10.3390/w13010072, 2021. Turowski, J. M., Yager, E. M., Badoux, A., Rickenmann, D., and Molnar, P.: The impact of exceptional events on erosion, bedload transport and channel stability in a step-pool channel, Earth Surf. Proc. Land., 34(12), 1661-1673, https://doi.org/10.1002/esp.1855, 2009. Vallé, B. L. and Pasternack, G. B.: Air concentrations of submerged and unsubmerged hydraulic jumps in a bedrock step‐pool 790 channel, J. Geophys. Res.-Earth, 111(F3), F03016. https://doi:10.1029/2004JF000140, 2006. Waldon, M. G.: Estimation of average stream velocity, J. Hydraul. Eng., 130(11), 1119-1122. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:11(1119), 2004. Wang, Z., Melching, C., Duan, X., and Yu, G.: Ecological and hydraulic studies of step-pool systems, J. Hydraul. Eng., 135(9), 705-717, https://doi.org/10.1061/(ASCE)0733-9429(2009)135:9(705), 2009

795 Wang, Z., Qi, L., and Wang, X.: A prototype experiment of debris flow control with energy dissipation structures, Nat. Hazards, 60(3), 971-989, https://doi.org/10.1007/s11069-011-9878-5, 2012. Weichert, R. B.: Bed Morphology and Stability in Steep Open Channels, Ph.D. Dissertation, No. 16316. ETH Zurich, Switzerland, 247pp., 2005. Wilcox, A. C., Wohl, E. E., Comiti, F., and Mao, L.: Hydraulics, morphology, and energy dissipation in an alpine step‐pool 800 channel, Water Resour. Res., 47(7), W07514, https://doi.org/10.1029/2010WR010192, 2011. Wohl, E. E. and Thompson, D. M.: Velocity characteristics along a small step–pool channel. Earth Surf. Proc. Land., 25(4), 353-367, https://doi.org/10.1002/(SICI)1096-9837(200004)25:4<353::AID-ESP59>3.0.CO;2-5, 2000. Wu, S. and Rajaratnam, N.: Impinging jet and surface flow regimes at drop. J. Hydraul. Res., 36(1), 69-74, https://doi.org/10.1080/00221689809498378, 1998. 805 Xu, Y. and Liu, X.: 3D computational modeling of stream flow resistance due to large woody debris, in: Proceedings of the 8th International Conference on Fluvial Hydraulics, St. Louis, USA, 11-14, Jul, 2346-2353, 2016. Xu, Y. and Liu, X.: Effects of different in-stream structure representations in computational fluid dynamics models—Taking engineered log jams (ELJ) as an example, Water, 9(2), 110, https://doi.org/10.3390/w9020110, 2017. Zeng, Y. X., Ismail, H., and Liu, X.: Flow Decomposition Method Based on Computational Fluid Dynamics for Rock Weir 810 Head-Discharge Relationship. J. Irrig. Drain. Eng., 147(8), 04021030, https://doi.org/10.1061/(ASCE)IR.1943- 4774.0001584, 2021. Zhang, C., Wang, Z., and Li, Z.: A physically-based model of individual step-pool stability in mountain streams, in: Proceedings of the 13th International Symposium on River Sedimentation, Stuttgart, Germany, 801-809, 2016. Zhang, C., Xu, M., Hassan, M. A., Chartrand, S. M., and Wang, Z.: Experimental study on the stability and failure of individual 815 step-pool, Geomorphology, 311, 51-62, https://doi.org/10.1016/j.geomorph.2018.03.023, 2018. Zhang, C., Xu, M., Hassan, M. A., Chartrand, S. M., Wang, Z., and Ma, Z.: Experiment on morphological and hydraulic adjustments of step‐pool unit to flow increase, Earth Surf. Proc. Land., 45(2), 280-294, https://doi.org/10.1002/esp.4722, 2020. Zimmermann A., E.: Flow resistance in steep streams: An experimental study, Water Resour. Res., 46, W09536, 820 https://doi.org/10.1029/2009WR007913, 2010. Zimmermann A. E., Salleti M., Zhang C., Hassan M. A.: Step-pool Channel Features, in: Treatise on Geomorphology (2nd Edition), vol. 9, Fluvial Geomorphology, edited by: Shroder, J. (Editor in Chief), Wohl, E. (Ed.), Elsevier, Amsterdam, Netherlands, https://doi.org/10.1016/B978-0-12-818234-5.00004-3, 2020.

Figure 13 | Velocity vector for flow condition Q¼22 l/s, Near surface.

Experimental and numerical study of flow at a 90 degree lateral turn-out with enhanced roughness coefficient and invert elevation changes

조도 계수 및 역 고도 변화가 향상된 90도 측면 회전에서 유동의 실험 및 수치 연구

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

Flow separation at the upstream side of the lateral turnouts (intakes) is a critical issue causing eddy currents at the turn-out entrance. It reduces the effective width of flow, turn-out 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 turn-out entrance and 3 different bed level inverts, with 4 different discharges (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%.

측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 턴아웃 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다.

이 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 4가지 다른 배출(총 84개 실험)과 함께 7가지 유형의 조면화 요소를 출구 입구에 설치하고 3가지 서로 다른 베드 레벨 반전 장치를 조사했습니다.

또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다.

두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.

Key words

discharge ratio, flow separation zone, intake, three dimensional simulation

Experimental and numerical study of flow at a 90 degree lateral turn-out with enhanced roughness coefficient and invert elevation changes
Experimental and numerical study of flow at a 90 degree lateral turn-out with enhanced roughness coefficient and invert elevation changes
Figure 2 | Roughness plates.
Figure 2 | Roughness plates.
Figure 3 | Effect of roughness on separation zone dimensions
Figure 3 | Effect of roughness on separation zone dimensions
Figure 4 | Effect of roughness on separation zone dimensions.
Figure 4 | Effect of roughness on separation zone dimensions.
Figure 5 | Comparison of separation zone for n¼0.023 and n¼0.032.
Figure 5 | Comparison of separation zone for n¼0.023 and n¼0.032.
Figure 6 | Effect of drop implementation on separation zone dimensions
Figure 6 | Effect of drop implementation on separation zone dimensions
Figure 7 | Combined effect of roughness and drop on separation zone dimensions
Figure 7 | Combined effect of roughness and drop on separation zone dimensions
Figure 8 | Non- dimensional Length of separation zone (Lr) variations against relative unit discharge per width (qr) in present study compared with other methods.
Figure 8 | Non- dimensional Length of separation zone (Lr) variations against relative unit discharge per width (qr) in present study compared with other methods.
Figure 9 | Velocity profiles for various roughness coefficients along turn-out width.
Figure 9 | Velocity profiles for various roughness coefficients along turn-out width.
Figure 10 | Effect of roughness on sepration zone dimensions in numerical study
Figure 10 | Effect of roughness on sepration zone dimensions in numerical study
Figure 11 | Comparision of the vortex area (software output) with three roughness (0.009, 0.023 and 0.032).
Figure 11 | Comparision of the vortex area (software output) with three roughness (0.009, 0.023 and 0.032).
Figure 12 | Comparison of vortex area in 3D mode (tecplot output) with two roughness (a) 0.009 and (b) 0.032
Figure 12 | Comparison of vortex area in 3D mode (tecplot output) with two roughness (a) 0.009 and (b) 0.032
Figure 13 | Velocity vector for flow condition Q¼22 l/s, Near surface.
Figure 13 | Velocity vector for flow condition Q¼22 l/s, Near surface.
Figure 14 | Exprimental and numerical measured velocity.
Figure 14 | Exprimental and numerical measured velocity.

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 (in Persian) 62, 38–44.
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.
Jalili, H., Hosseinzadeh Dalir, A. & Farsadizadeh, D. 2011 Effect of intake geometry on the sediment transport and flow pattern at lateral.
Iranian Water Research Journal(InPersian) 5 (9), 1–10.
Jamshidi, A., Farsadizadeh, D. & Hosseinzadeh Dalir, A. 2016 Variations of flow separation zone at lateral intakes 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 55° and 900
° with rounded entrance edge.
In: 03 National Congress on Civil Engineering University of Tabriz. (In Persian). Available from: https://civilica.com/doc/16317.
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., Sotiropoulos, F. & Odgaard, A. J. 1999 Three-dimensional numerical model of lateral-intake in flows. Journal of Hydraulic
Engineering. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:2(126).
Nikbin, S. & Borghei, S. M. 2011 Experimental investigation of submerged vanes effect on dimensions of flow separation zone at 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.
Ouyang, H. T. 2009 Investigation on the dimensions and shape of a submerged vane for sediment management in alluvial channels. Journal of
Hydraulic Engineering. https://doi.org/10.1061/(ASCE)0733-9429(2009)135:3(209).
Ramamurthy, A. S., Junying, Q. & Diep, V. 2007 Numerical and experimental study of dividing open-channel flows. Journal of Hydraulic
Engineering. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:10(1135).
Samimi Behbahan, T. 2011 Laboratory investigation of submerged vane shapes effect on river banks protection. Australian Journal of Basic
and Applied Sciences 5 (12), 1402–1407.
Seyedian, S., Karami Moghaddam, K. & Shafai Begestan, M. 2008 Determine the optimal radius in lateral intakes 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. 2020 Migration of sand mining pit in rivers: an experimental,
numerical and case study. Measurement. https://doi.org/10.1016/j.measurement.2020.108944.

Figura 1. Parámetros del medidor Palmer-Bowlus

Three-Dimensional Numerical Modeling of the Palmer-Bowlus Measuring Flume Applying the FLOW-3D Software.

TOAPAXI-ALVAREZ*, JorgeSILA-BASTIDA, Roberto    TORRES-JACOBOWITZ, Cristina.

The Palmer-Bowlus flume was developed in 1936, as an adaptation of the Venturi flume for the use in sewer systems, due to the difficulty in modifying the pipe invert. There are commercially available single-body Palmer-Bowlus flume with their respective discharge curves, which increase the cost of sewer projects. Based on the physical model of the Palmer-Bowlus flume (Torres & Vásquez, 2010), the aim of this research was to carry out the three-dimensional numerical modeling of these flow meters, considering four pipe diameters: 160 mm, 200 mm, 250 mm and 400 mm; the selected diameters are the most used ones, according to the information provided by the Empresa Pública Metropolitana de Agua Potable y Saneamiento de Quito (EPMAPS). The discharge curves were calibrated and validated using the FLOW-3D program. Meshing had a great influence on the quality results and duration of the numerical simulation; in contrast, the roughness and turbulence models (RNG y k-e) had little influence. The discharge curves obtained in the numerical modeling have good approximation to those obtained in the physical model.

Palmer-Bowlus 수로는 1936년에 하수도 시스템에 사용하기 위해 Venturi 수로를 개조한 것으로 파이프 인버트를 수정하는 것이 어렵기 때문에 개발되었습니다. 각각의 배출 곡선이 있는 시판되는 단일 몸체 Palmer-Bowlus 수로가 있으며, 이는 하수도 프로젝트 비용을 증가시킵니다.

Palmer-Bowlus 수로의 물리적 모델을 기반으로(Torres & Vásquez, 2010), 이 연구의 목적은 160mm, 200mm, 4개의 파이프 직경을 고려하여 이러한 유량계의 3차원 수치 모델링을 수행하는 것이었습니다. 250mm 및 400mm; Empresa Pública Metropolitana de Agua Potable y Sanaeamiento de Quito(EPMAPS)에서 제공한 정보에 따르면 선택한 지름이 가장 많이 사용되는 지름입니다.

방전 곡선은 FLOW-3D 프로그램을 사용하여 보정 및 검증되었습니다. 메싱은 수치 시뮬레이션의 품질 결과와 기간에 큰 영향을 미쳤습니다. 대조적으로, 거칠기 및 난류 모델(RNG y k-e)은 거의 영향을 미치지 않았습니다. 수치 모델링에서 얻은 방전 곡선은 물리적 모델에서 얻은 것과 유사합니다.

Figura 1. Parámetros del medidor Palmer-Bowlus
Figura 1. Parámetros del medidor Palmer-Bowlus
Figura 2. Diagrama de flujo de la modelación del medidor Palmer-Bowlus en FLOW-3D
Figura 2. Diagrama de flujo de la modelación del medidor Palmer-Bowlus en FLOW-3D
Figura 3. Captura de pantalla del modelo numérico Q=22.047( 𝑙 𝑠 ), Ho=20.038 cm
Figura 3. Captura de pantalla del modelo numérico Q=22.047( 𝑙 𝑠 ), Ho=20.038 cm

REFERENCIAS

Aulestia, C. (2017). Modelación numérica en tres dimensiones de flujo en
las compuertas de la captación del Proyecto Toachi – Pilatón
aplicando dinámica de fluidos computacional (CFD). [Tesis
Maestría]. Quito, Ecuador: Escuela Politécnica Nacional.
Casa, E. (2016). Modelación numérica del flujo rasante en una rápida
escalonada aplicando la dinámica de fluidos computacional
(CFD) Programa FLOW-3D. [Tesis maestría]. Quito, Ecuador:
Escuela Politécnica Nacional.
Chow, V. T. (2004). Hidráulica de canales abiertos (Primera ed.). (J.
Saldarriaga, Trad.) Santafé de Bogotá, Colombia: McGrawHill.
Domínguez, F. (1999). Hidráulica (Sexta Edición ed.). Santiango de Chile,
Chile: Editorial Universitaria.
Fernández, J. (2012). Introducción a la dinámica de fluidos computacional
(CFD) por el método de volúmenes finitos. Barcelona: Editorial
Reverté, S.A.
Flow Science, Inc. (2016). Flow-3D v11.2 Documentation. Flow Science,
Inc. Santa Fe: Flow Science.
Ludwig, J., & Ludwig, R. (1951). Design of Palmer-Bowlus Flumes.
Sewafe and Insdustrial Wastes, 23(9), 1096-1107. Obtenido de
https://www.jstor.org/stable/25031687
Recasens, J. (2014). Modelación tridimensional del glujo de entrada en un
sumidero. Barcelona: UPC BARCELONATECH.
Sotelo, G. (1997). Hidráulica General Vol. 1. México D.F.: LIMUSA S.A.
Torres, C., & Vásquez, E. (2010). Análisis de medidores de caudal para
flujo subcrítico en sistemas de alcantarillado. [Tesis
ingeniería]. Quito, Ecuador: Escuela Politécnica Nacional.
Versteeg, H. K., & Malalasekera, W. (1995). An Introduction to
computational fluid dynamics – The finite volume method. New
York: John Wiley & Sons.

Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and (h) Juam-3.

Interference of Dual Spillways Operations

Jai Hong Lee, Ph.D., P.E., M.ASCE; Pierre Y. Julien, Ph.D., M.ASCE; and Christopher I. Thornton, Ph.D., P.E., M.ASCE

Abstract

이중 여수로 간섭은 여수로가 서로 가깝게 배치될 때 수압 성능의 손실을 나타냅니다. 배수로 간섭은 물리적 실험과 수치 시뮬레이션을 모두 사용하여 조사됩니다.

이중 여수로 구성의 4개 물리적 모델의 단계 및 배출 측정값을 한국의 4개 댐 부지에서 Flow-3D 계산 결과와 비교합니다.

두 개의 배수로를 함께 사용하는 것을 각 배수로의 단일 작동과 비교합니다. 두 여수로를 동시에 운영할 경우 두 여수로를 통한 총 유량은 최대 7.6%까지 감소합니다.

간섭 계수는 단계 He가 설계 단계 Hd를 초과하고 두 배수로를 분리하는 거리 D가 배수로 너비 W에 비해 짧을 때 가장 중요합니다. 매개변수 DHd/WHe는 계산 및 측정된 간섭 계수와 매우 잘 관련됩니다.

안동댐 설계방류에 대한 홍수경로 예시는 간섭계수를 적용한 경우와 적용하지 않은 경우 저수지 수위의 차이가 42cm임을 보여줍니다. 결과적으로 댐 안전을 위해 추가 여수로의 너비(간섭 계수 포함)를 늘려야 합니다.

Dual spillway interference refers to the loss of hydraulic performance of spillways when they are placed close together. Spillway interference is examined using both physical experiments and numerical simulations. Stage and discharge measurements from four physical models with dual spillways configurations are compared to the Flow-3D computational results at four dam sites in South Korea. The conjunctive use of two spillways is compared with the singular operation of each spillway. When both spillways are operated at the same time, the total flow rate through the two spillways is reduced by up to 7.6%. Interference coefficients are most significant when the stage He exceeds the design stage Hd and when the distance D separating two spillways is short compared to the spillway width W. The parameter DHd/WHecorrelates very well with the calculated and measured interference coefficients. A flood routing example for the design discharge at Andong dam shows a 42 cm difference in reservoir water level with and without application of the interference coefficient. Consequently, the width of additional spillways (including the interference coefficient) should be increased for dam safety.

Fig. 1. Definition sketch for dual spillways
Fig. 1. Definition sketch for dual spillways
Fig. 2. Stage-discharge rating curves for dual spillway operations.
Fig. 2. Stage-discharge rating curves for dual spillway operations.
Fig. 3. Physical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; and (d) Juam-1
Fig. 3. Physical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; and (d) Juam-1
Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and (h) Juam-3.
Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and (h) Juam-3.
Fig. 4. (Continued.)
Fig. 4. (Continued.)
Fig. 5. Meshes and calculation domain for numerical modeling of Andong dam.
Fig. 5. Meshes and calculation domain for numerical modeling of Andong dam.
Fig. 6. Stage-discharge rating curve for existing and additional spillways (Andong-1): (a) existing spillway; (b) additional spillway; and (c) dual spillway simulations.
Fig. 6. Stage-discharge rating curve for existing and additional spillways (Andong-1): (a) existing spillway; (b) additional spillway; and (c) dual spillway simulations.
Fig. 7. Discharge comparison of physical experiments and numerical simulations. The upper panel is the comparative result for the existing spillway (ES) and the lower panel is for the additional spillway (AS) at four dams.
Fig. 7. Discharge comparison of physical experiments and numerical simulations. The upper panel is the comparative result for the existing spillway (ES) and the lower panel is for the additional spillway (AS) at four dams.
Fig. 8. Interference coefficients for dual spillways simulations with various scenarios.
Fig. 8. Interference coefficients for dual spillways simulations with various scenarios.
Fig. 9. Regression model for the distance-width ratio (D=W) and head ratio (Hd=He) by dual spillway simulations
Fig. 9. Regression model for the distance-width ratio (D=W) and head ratio (Hd=He) by dual spillway simulations
Fig. 10. Physical and numerical model validation: (a) numerical modeling; (b) solids of overflow weir of the spillway; and (c) physical models of reservoir and spillway
Fig. 10. Physical and numerical model validation: (a) numerical modeling; (b) solids of overflow weir of the spillway; and (c) physical models of reservoir and spillway
Fig. 11. Interference coefficients for dual spillways operations with various scenarios. The dashed lines indicate the results of the validation model with dual conditions of 1 þ 2, 1 þ 4, 1 þ 6, 3 þ 4, and 4 þ 5.
Fig. 11. Interference coefficients for dual spillways operations with various scenarios. The dashed lines indicate the results of the validation model with dual conditions of 1 þ 2, 1 þ 4, 1 þ 6, 3 þ 4, and 4 þ 5.
Fig. 12. Results of reservoir operations under the PMF at Andong dam.
Fig. 12. Results of reservoir operations under the PMF at Andong dam.

References

Cassidy, J. J. 1965. “Irrotational flow over spillways of finite height.”
J. Eng. Mech. Div. 91 (6): 155–173.
Chanel, P., and J. Doering. 2008. “Assessment of spillway modeling using
computational fluid dynamics.” Can. J. Civ. Eng. 35 (12): 1481–1485.
https://doi.org/10.1139/L08-094.
Chow, V. T. 1959. Open-channel hydraulics, 365–380. New York:
McGraw-Hill.
Ho, D., B. Cooper, K. Riddette, and S. Donohoo. 2006. “Application of
numerical modelling to spillways in Australia.” In Proc., Int. Symp.
on Dams in the Societies of the 21st Century, 22nd Int. Congress on
Large Dams (ICOLD), edited by L. Berga, et al. London: Taylor &
Francis.
Huff, F. A. 1967. “Time distribution of rainfall in heavy storms.” Water
Resour. Res. 3 (4): 1007–1019. https://doi.org/10.1029/WR003i004
p01007.
Kim, D. G., and J. H. Park. 2005. “Analysis of flow structure over ogeespillway in consideration of scale and roughness effects by using CFD
model.” KSCE J. Civ. Eng. 9 (2): 161–169. https://doi.org/10.1007
/BF02829067.
Koutsunis, N. A. 2015. “Impact of climatic changes on downstream hydraulic geometry and its influence on flood hydrograph
routing—Applied to the bluestone dam watershed.” M.S. degree,
Dept. of Civil and Environmental Engineering, Colorado State Univ.
Lee, J. H., and P. Y. Julien. 2016a. “ENSO impacts on temperature over
South Korea.” Int. J. Climatol. 36 (11): 3651. https://doi.org/10.1002
/joc.4581.
Lee, J. H., and P. Y. Julien. 2016b. “Teleconnections of the ENSO and
South Korean precipitation patterns.” J. Hydrol. 534: 237–250.
https://doi.org/10.1016/j.jhydrol.2016.01.011.
Lee, J. H., and P. Y. Julien. 2017. “Influence of the El Nino/southern ˜
oscillation on South Korean streamflow variability.” Hydrol. Processes
31 (12): 2162–2178. https://doi.org/10.1002/hyp.11168.
Li, S., S. Cain, N. Wosnik, C. Miller, H. Kocahan, and R. Wyckoff. 2011.
“Numerical modeling of probable maximum flood flowing through a
system of spillways.” J. Hydraul. Eng. 137 (1): 66–74. https://doi.org
/10.1061/(ASCE)HY.1943-7900.0000279.
MOCT (Ministry of Construction and Transportation). 2003. Hydraulic
model study of Soyanggang multipurpose dam auxiliary spillway.
[In Korean.] Governing City, South Korea: MOCT.
Olsen, N. R., and H. M. Kjellesvig. 1998. “Three-dimensional numerical
flow modeling for estimation of spillway capacity.” J. Hydraul. Res.
36 (5): 775–784. https://doi.org/10.1080/00221689809498602.
Savage, B. M., and M. C. Johnson. 2001. “Flow over ogee spillway:
Physical and numerical model case study.” J. Hydraul. Eng. 127 (8):
640–649. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:8(640).
USACE (US Army Corps of Engineers). 2008. Hydrologic modeling
system HEC-HMS, user’s manual version 3.2. Davis, CA: USACE.
USBR (US Bureau of Reclamation). 1980. Hydraulic laboratory techniques: A water resources technical publication. Denver: US Dept.
of the Interior, Bureau of Reclamation.
Yakhot, V., and S. A. Orszag. 1986. “Renormalization group analysis of
turbulence. I: Basic theory.” J. Sci. Comput. 1 (1): 3–51. https://doi
.org/10.1007/BF01061452.
Yakhot, V., and L. M. Smith. 1992. “The renormalization group, the
e-expansion and derivation of turbulence models.” J. Sci. Comput.
7 (1): 35–61. https://doi.org/10.1007/BF01060210.
Zeng, J., L. Zhang, M. Ansar, E. Damisse, and J. A. Gonzalez-Castro. 2017.
“Applications of computational fluid dynamics to flow ratings at prototype spillways and weirs. I: Data generation and validation.” J. Irrig.
Drain. Eng. 143 (1): 04016072. https://doi.org/10.1061/(ASCE)IR
.1943-4774.0001112.

Fig. 2 Schematic diagram of the experimental Rijke tube

RIJKE 튜브 내부의 열음향 장에 대한 새로운 조사

A novel investigation of the thermoacoustic field inside a Rijke tube

B. EntezamW. Van Moorhem and J. MajdalaniPublished Online:22 Aug 2012 https://doi.org/10.2514/6.1998-2582

Abstract

이 논문에서는 Rijke 튜브 내부의 시간 종속 유동장의 실험 연구 및 계산 시뮬레이션에서 진행한 결과를 제시하고 해석합니다. 기존의 추측과 스케일링 분석을 기반으로 한 이론적 논의가 진행됩니다. 주요 결과에는 열 구동 진동에서 중요한 역할을 하는 것으로 보이는 유사성 매개변수가 포함됩니다. 이 매개변수는 열 섭동을 속도, 압력 및 특성 길이의 제곱과 관련시킵니다. 열 진동을 압력 및 속도 진동의 결합된 효과에 기인하는 간단한 이론은 계산, 실험 및 스케일링 고려 사항을 통해 논의됩니다. 이전의 분석 이론은 열 진동을 속도 또는 압력 진동에 연결했기 때문에 현재 분석 모델은 기존 추측에 동의하고 조정합니다. Rayleigh 기준에 따라 열원은 Rijke-tube 하단에서 1/4의 임계 거리에 위치해야 공명이 발생합니다. 이 관찰은 결합이 최대화되는 임계점이 음향 속도와 압력의 곱인 음향 강도가 가장 큰 공간 위치에 해당하기 때문에 제안된 해석을 확인합니다. 수치 시뮬레이션은 Rijke 튜브 내부의 압력 진동이 열 입력이 증가함에 따라 기하급수적으로 증가한다는 것을 보여줍니다. 충분히 작은 열 입력으로 음향 싱크가 소스를 초과하고 음향 감쇠가 발생합니다. 열 입력이 임계 임계값 이상으로 증가하면 음향 싱크가 불충분해져서 ​​내부 에너지 축적으로 인해 빠른 음향 증폭이 발생합니다.

In this paper, results proceeding from experimental studies and computational simulations of the time-dependent flowfield inside a Rijke tube are presented and interpreted. A theoretical discussion based on existing speculations and scaling analyses is carried out. The main results include a similarity parameter that appears to play an important role in the heat driven oscillations. This parameter relates heat perturbations to velocity, pressure, and the square of a characteristic length. A simple theory that attributes heat oscillations to the combined effects of pressure and velocity oscillations is discussed via computational, experimental, and scaling considerations. Since previous analytical theories link heat oscillations to either velocity or pressure oscillations, the current analytical model agrees with and reconciles between existing speculations. In compliance with the Rayleigh criterion, it is found that the heat source must be positioned at a critical distance of 1/4 from the Rijke-tube lower end for resonance to occur. This observation confirms our proposed interpretation since the critical point where coupling is maximized corresponds to a spatial location where the acoustic intensity, product of both acoustic velocities and pressures, is largest. Numerical simulations show that pressure oscillations inside the Rijke tube grow exponentially with increasing heat input With a sufficiently small heat input, the acoustic sinks exceed the sources and acoustic damping takes place. When the heat input is augmented beyond a critical threshold, acoustic sinks become insufficient causing rapid acoustic amplification by virtue of internal energy accumulation.

Fig. 2 Schematic diagram of the experimental Rijke tube
Fig. 2 Schematic diagram of the experimental Rijke tube
A novel investigation of the thermoacoustic field inside a Rijke tube
A novel investigation of the thermoacoustic field inside a Rijke tube

References

‘Entezam, B., Majdalani, J., and Van Moorhem, W. K.,
“Modeling of a Rijke-Tube Pulse Combustor Using
Computational Fluid Dynamics,” AIAA Paper 97-2718,
Seattle, WA, July 1997.

2George, W., and Reethof, G., “On the Fragility of
Acoustically Agglomerated Submicron Fly Ash
Particles,” Journal of Vibration, Acoustics, Stress, and
Reliability in Design, Vol. 108, July 1986, pp. 322-329.
3Tiwary R., and Reethof, G., “Hydrodynamic
Interaction of Spherical Aerosol Particles in a High
Intensity Acoustic Field,” Journal of Sound and
Vibration, Vol. 108, 1986, pp. 33-49.
4Reethof, G., “Acoustic Agglomeration of Power Plant
Fly Ash for Environmental and Hot Gas Clean-up,”
Transaction of the ASME, Vol. 110, Oct., 1988, pp.
552-557.
5
Song, L., Reethof, G., and Koopmann, G. H., “An
Improved Simulation Model of Acoustic
Agglomeration,” NCA Vol. 5, 89-WA, American
Society of Mechanical Engineers, Winter Annual
Meeting, San Francisco, CA, Dec., 10-15, 1989.
6Reethof, G., Koopmann, G. H., and Dorchak, T.,
“Acoustic Agglomeration for Paniculate Control at
High Temperature and high Pressure – Some Recent
results,” NCA Vol. 4, 89-WA, American Society of
Mechanical Engineers, Winter Annual Meeting, San
Francisco, CA, Dec., 10-15, 1989.
7Richards , G. A., and Bedick, R. C, “Application of
Acoustics in Advanced Energy Systems,” NCA Vol. 3,
89-WA, American Society of Mechanical Engineers,
Winter Annual Meeting, San Francisco, CA, Dec., 10-
15, 1989.
8Yavuzkurt, S., Ha, M. Y., Reethof, G., and Koopmann,
G., “Effect of Acoustic Field on the Combustion of
Coal Particles in a Rat Flame Burner,” Proceedings of
the Ist
Annual Pittsburgh Coal Conference, Pittsburgh,
PA, Sep., 1984, pp. 53-58.
^rice, E. W., “Review of Combustion Instability
Characteristics of Solid Propellants,” Advances in
Tactical Rocket Propulsion, AGARD Conference
Proceedings, No. 1, Part 2, Chap. 5, Technivision
Services, Maidenhead, England, 1968, pp. 141-194.
10Zinn, B.T., “State of the Art and Research Needs of
Pulsating Combustion,” NCA Vol. 19, 84-WA,
American Society of Mechanical Engineers, 1984.
“Rayleigh, J.W.S., The Theory of Sound, Vol. 1 and 2,
Dover Publications, New York, 1945, pp. 231-235.
12Zinn, B.T., Miller, N., Carvalho, J.A. Jr., and Daniel.
B. R., “Pulsating Combustion of Coal in a Rijke Type
Combustor,” Proceedings of the 19th International
Symposium on Combustion, 1982, pp. 1197-1203.
13Evans, R.E., and Putnam, A.A., “Rijke Tube
Apparatus,” Journal of Applied Physics, Vol. 360,
1966.
14Feldman, K. T., “Review of the Literature on Rijke
Thermoacoustic Phenomena, ” Journal of Sound and
Vibration, Vol. 7, 1968, pp. 83-89.
15Carvalho, J.R., Ferreira, C., Bressan, C., and Ferreira,
G., “Definition of Heater Location to Drive Maximum
Amplitude Acoustic Oscillations hi a Rijke Tube,”
Combustion and Flame, Vol. 76, 1989, pp. 17-27.
16Raun, R.L., Beckstead, M. W., Finlinson, J. C. , and
Brooks, K. P., “A Review of Rijke Tubes, Rijke
Burners and Related Devices,” Progress in Energy and
Combustion Science, Vol. 19, 1993, pp. 313-364.
17Chu, B. T., “Stability of Systems Containing a HeatSource-The Rayleigh Criterion, “NACA Research
Memorandum 56D27, 1956.
18Zinn, B. T., Daniel, B. R., and Shesdari, T.S.,
“Application of Pulsating Combustion in the Burning of
Solid Fuels,” Proceedings of the Symposium on Pulse
Combustion Technology for Heating Applications,
Argonne National Laboratory, 1979, pp. 239-248.
19Feldman, K.T., “Review of the Literature on
Soundhauss Thermoacoustic Phenomena ” Journal of
Sound and Vibration, Vol. 7, 1968, pp. 71-82.
20Flow Science Incorporated, Los Alamos, New
Mexico.

CFD Simulations of Conical Central Baffle Flumes | Journal of Irrigation and Drainage Engineering | Vol 148, No 2

원추형 중앙 배플 수로의 CFD 시뮬레이션

CFD Simulations of Conical Central Baffle Flumes

Abstract

Ankur KapoorAniruddha D. Ghare; and Avinash M. Badar

원추형 중앙 배플 수로는 개방 채널에서 임시 유량 측정을 위한 효과적인 솔루션을 제공합니다. 

원추형 중앙 배플 수로는 원뿔 모양의 장애물 또는 열린 수로의 중심에서 수직으로 향하는 중앙 배플로 구성됩니다. 본 연구에서, 원추형 중앙 배플 수로를 사용하여 개방 채널에서 유량 측정을 위해 이전에 개발된 배출 예측 모델은 더 넓은 적용 범위를 커버하기 위해 직사각형 및 사다리꼴 채널에서 사용하기 위해 실험적으로 재 보정되었습니다. 

제안된 보정 방정식은 FLOW-3D를 사용한 전산유체역학(CFD) 시뮬레이션 결과를 사용하여 확장된 범위의 흐름 및 기하학적 매개변수에 대해 검증되었습니다. 

시뮬레이션 연구는 두 단계로 수행됩니다. 첫 번째 단계는 시뮬레이션의 수면 프로파일과 동일한 배출 및 흐름 조건에 대한 실험 흐름을 비교하여 설정한 정의된 시뮬레이션 문제의 검증입니다. 

두 번째 단계는 무차원 방전 및 측면 경사(중1= 0중1=0, 0.50, 1.00 및 1.50). 80% 미만의 수중에서 방전 예측의 오류는 평균값이 거의 3%로 항상 10% 미만인 것으로 나타났습니다. 

CFD 분석 결과에 따르면 보정된 배출 예측 모델의 사용은 수중 한계 80%까지 권장되었으며, 그 이상에서는 오차가 10% 이상인 것으로 나타났습니다.

Conical central baffle flumes present an effective solution for temporary flow measurements in open channels. A conical central baffle flume consists of a cone-shaped obstruction, or a central baffle, oriented vertically at the center of an open channel. In the present study, a previously developed discharge prediction model for flow measurements in open channels using the conical central baffle flumes has been experimentally recalibrated for use in rectangular and trapezoidal channels to cover a wider application range. The proposed calibration equation has been validated for an extended range of flow and geometrical parameters using the results of computational fluid dynamics (CFD) simulations using Flow-3D. The simulation studies are carried out in two steps. The first step is the validation of the defined simulation problem set up by comparing the water surface profiles of the simulation and experiment flows for the same discharge and flow conditions. The second step is the validation of the proposed discharge prediction model for the extended range (0–0.50) of the dimensionless discharge and side slopes (m1=0m1=0, 0.50, 1.00, and 1.50). It is found that for submergence less than 80%, the error in discharge prediction is always less than 10% with a mean value of nearly 3%. Based on the results of the CFD analysis, the use of the calibrated discharge prediction model has been recommended up to a submergence limit of 80%, beyond which the errors are found to be greater than 10%.

ASCE Library CFD Simulations of Conical Central Baffle Flumes | Journal of Irrigation and Drainage Engineering | Vol 148, No 2
ASCE Library CFD Simulations of Conical Central Baffle Flumes | Journal of Irrigation and Drainage Engineering | Vol 148, No 2
CFD Simulations of Conical Central Baffle Flumes | Journal of Irrigation and Drainage Engineering | Vol 148, No 2
CFD Simulations of Conical Central Baffle Flumes | Journal of Irrigation and Drainage Engineering | Vol 148, No 2
CFD Simulations of Conical Central Baffle Flumes | Journal of Irrigation and Drainage Engineering | Vol 148, No 2
CFD Simulations of Conical Central Baffle Flumes | Journal of Irrigation and Drainage Engineering | Vol 148, No 2
Channel Flow Measurement Using Portable Conical Central Baffle | Journal of Irrigation and Drainage Engineering | Vol 145, No 11
Channel Flow Measurement Using Portable Conical Central Baffle | Journal of Irrigation and Drainage Engineering | Vol 145, No 11
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling

Laser Powder Bed에서 Laser Drilling에 의한 Keyhole 형성 Ti6Al4V 생체 의학 합금의 융합: 메조스코픽 전산유체역학 시뮬레이션 대 경험적 검증을 사용한 수학적 모델링

Keyhole Formation by Laser Drilling in Laser Powder Bed Fusion of Ti6Al4V Biomedical Alloy: Mesoscopic Computational Fluid Dynamics Simulation versus Mathematical Modelling Using Empirical Validation

Asif Ur Rehman 1,2,3,*
,† , Muhammad Arif Mahmood 4,*
,† , Fatih Pitir 1
, Metin Uymaz Salamci 2,3
,
Andrei C. Popescu 4 and Ion N. Mihailescu 4

Abstract

LPBF(Laser Powder Bed fusion) 공정에서 작동 조건은 열 분포를 기반으로 레이저 유도 키홀 영역을 결정하는 데 필수적입니다. 얕은 구멍과 깊은 구멍으로 분류되는 이러한 영역은 LPBF 프로세스에서 확률과 결함 형성 강도를 제어합니다.

LPBF 프로세스의 핵심 구멍을 연구하고 제어하기 위해 수학적 및 CFD(전산 유체 역학) 모델이 제공됩니다. CFD의 경우 이산 요소 모델링 기법을 사용한 유체 체적 방법이 사용되었으며, 분말 베드 보이드 및 표면에 의한 레이저 빔 흡수를 포함하여 수학적 모델이 개발되었습니다.

동적 용융 풀 거동을 자세히 살펴봅니다. 실험적, CFD 시뮬레이션 및 분석적 컴퓨팅 결과 간에 정량적 비교가 수행되어 좋은 일치를 얻습니다.

LPBF에서 레이저 조사 영역 주변의 온도는 높은 내열성과 분말 입자 사이의 공기로 인해 분말층 주변에 비해 급격히 상승하여 레이저 횡방향 열파의 이동이 느려집니다. LPBF에서 키홀은 에너지 밀도에 의해 제어되는 얕고 깊은 키홀 모드로 분류될 수 있습니다. 에너지 밀도를 높이면 얕은 키홀 구멍 모드가 깊은 키홀 구멍 모드로 바뀝니다.

깊은 키홀 구멍의 에너지 밀도는 다중 반사와 키홀 구멍 내의 2차 반사 빔의 집중으로 인해 더 높아져 재료가 빠르게 기화됩니다.

깊은 키홀 구멍 모드에서는 온도 분포가 높기 때문에 액체 재료가 기화 온도에 가까우므로 얕은 키홀 구멍보다 구멍이 형성될 확률이 훨씬 높습니다. 온도가 급격히 상승하면 재료 밀도가 급격히 떨어지므로 비열과 융해 잠열로 인해 유체 부피가 증가합니다.

그 대가로 표면 장력을 낮추고 용융 풀 균일성에 영향을 미칩니다.

In the laser powder bed fusion (LPBF) process, the operating conditions are essential in determining laser-induced keyhole regimes based on the thermal distribution. These regimes, classified into shallow and deep keyholes, control the probability and defects formation intensity in the LPBF process. To study and control the keyhole in the LPBF process, mathematical and computational fluid dynamics (CFD) models are presented. For CFD, the volume of fluid method with the discrete element modeling technique was used, while a mathematical model was developed by including the laser beam absorption by the powder bed voids and surface. The dynamic melt pool behavior is explored in detail. Quantitative comparisons are made among experimental, CFD simulation and analytical computing results leading to a good correspondence. In LPBF, the temperature around the laser irradiation zone rises rapidly compared to the surroundings in the powder layer due to the high thermal resistance and the air between the powder particles, resulting in a slow travel of laser transverse heat waves. In LPBF, the keyhole can be classified into shallow and deep keyhole mode, controlled by the energy density. Increasing the energy density, the shallow keyhole mode transforms into the deep keyhole mode. The energy density in a deep keyhole is higher due to the multiple reflections and concentrations of secondary reflected beams within the keyhole, causing the material to vaporize quickly. Due to an elevated temperature distribution in deep keyhole mode, the probability of pores forming is much higher than in a shallow keyhole as the liquid material is close to the vaporization temperature. When the temperature increases rapidly, the material density drops quickly, thus, raising the fluid volume due to the specific heat and fusion latent heat. In return, this lowers the surface tension and affects the melt pool uniformity.

Keywords: laser powder bed fusion; computational fluid dynamics; analytical modelling; shallow
and deep keyhole modes; experimental correlation

Figure 1. Powder bed schematic with voids.
Figure 1. Powder bed schematic with voids.
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling
Figure 3. Temperature field contour formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 3. Temperature field contour formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 4. Detailed view of shallow depth melt mode with temperature field at 0.695 ms
Figure 4. Detailed view of shallow depth melt mode with temperature field at 0.695 ms
Figure 5. Melt flow stream traces formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 5. Melt flow stream traces formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 6. Density evolution of the melt pool at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 6. Density evolution of the melt pool at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 7. Un-melted and melted regions at different time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 7. Un-melted and melted regions at different time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 8. Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from (a) 170 W to (b) 200 W
Figure 8. Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from (a) 170 W to (b) 200 W
Figure 9. Stream traces and laser beam multiple reflections in deep keyhole melt flow mode
Figure 9. Stream traces and laser beam multiple reflections in deep keyhole melt flow mode
Figure 10. A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep keyhole formation
Figure 10. A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep keyhole formation
Figure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width
Figure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width

References

  1. Kok, Y.; Tan, X.P.; Wang, P.; Nai, M.L.S.; Loh, N.H.; Liu, E.; Tor, S.B. Anisotropy and heterogeneity of microstructure and
    mechanical properties in metal additive manufacturing: A critical review. Mater. Des. 2018, 139, 565–586. [CrossRef]
  2. Ansari, P.; Salamci, M.U. On the selective laser melting based additive manufacturing of AlSi10Mg: The process parameter
    investigation through multiphysics simulation and experimental validation. J. Alloys Compd. 2022, 890, 161873. [CrossRef]
  3. Guo, N.; Leu, M.C. Additive manufacturing: Technology, applications and research needs. Front. Mech. Eng. 2013, 8, 215–243.
    [CrossRef]
  4. Mohsin Raza, M.; Lo, Y.L. Experimental investigation into microstructure, mechanical properties, and cracking mechanism of
    IN713LC processed by laser powder bed fusion. Mater. Sci. Eng. A 2021, 819, 141527. [CrossRef]
  5. Dezfoli, A.R.A.; Lo, Y.L.; Raza, M.M. Prediction of Epitaxial Grain Growth in Single-Track Laser Melting of IN718 Using Integrated
    Finite Element and Cellular Automaton Approach. Materials 2021, 14, 5202. [CrossRef]
  6. Tiwari, S.K.; Pande, S.; Agrawal, S.; Bobade, S.M. Selection of selective laser sintering materials for different applications. Rapid
    Prototyp. J. 2015, 21, 630–648. [CrossRef]
  7. Liu, F.H. Synthesis of bioceramic scaffolds for bone tissue engineering by rapid prototyping technique. J. Sol-Gel Sci. Technol.
    2012, 64, 704–710. [CrossRef]
  8. Ur Rehman, A.; Sglavo, V.M. 3D printing of geopolymer-based concrete for building applications. Rapid Prototyp. J. 2020, 26,
    1783–1788. [CrossRef]
  9. Ur Rehman, A.; Sglavo, V.M. 3D printing of Portland cement-containing bodies. Rapid Prototyp. J. 2021. ahead of print. [CrossRef]
  10. Popovich, A.; Sufiiarov, V. Metal Powder Additive Manufacturing. In New Trends in 3D Printing; InTech: Rijeka, Croatia, 2016.
  11. Jia, T.; Zhang, Y.; Chen, J.K.; He, Y.L. Dynamic simulation of granular packing of fine cohesive particles with different size
    distributions. Powder Technol. 2012, 218, 76–85. [CrossRef]
  12. Ansari, P.; Ur Rehman, A.; Pitir, F.; Veziroglu, S.; Mishra, Y.K.; Aktas, O.C.; Salamci, M.U. Selective Laser Melting of 316L
    Austenitic Stainless Steel: Detailed Process Understanding Using Multiphysics Simulation and Experimentation. Metals 2021,
    11, 1076. [CrossRef]
  13. Ur Rehman, A.; Tingting, L.; Liao, W. 4D Printing; Printing Ceramics from Metals with Selective Oxidation. Patent No.
    W0/2019/052128, 21 March 2019.
  14. Ullah, A.; Wu, H.; Ur Rehman, A.; Zhu, Y.; Liu, T.; Zhang, K. Influence of laser parameters and Ti content on the surface
    morphology of L-PBF fabricated Titania. Rapid Prototyp. J. 2021, 27, 71–80. [CrossRef]
  15. Ur Rehman, A. Additive Manufacturing of Ceramic Materials and Combinations with New Laser Strategies. Master’s Thesis,
    Nanjing University of Science and Technology, Nanjing, China, 2017.
  16. Wong, K.V.; Hernandez, A. A Review of Additive Manufacturing. ISRN Mech. Eng. 2012, 2012, 1–10. [CrossRef]
  17. Körner, C. Additive manufacturing of metallic components by selective electron beam melting—A review. Int. Mater. Rev. 2016,
    61, 361–377. [CrossRef]
  18. Fayazfar, H.; Salarian, M.; Rogalsky, A.; Sarker, D.; Russo, P.; Paserin, V.; Toyserkani, E. A critical review of powder-based additive
    manufacturing of ferrous alloys: Process parameters, microstructure and mechanical properties. Mater. Des. 2018, 144, 98–128.
    [CrossRef]
  19. Everton, S.K.; Hirsch, M.; Stavroulakis, P.I.; Leach, R.K.; Clare, A.T. Review of in-situ process monitoring and in-situ metrology
    for metal additive manufacturing. Mater. Des. 2016, 95, 431–445. [CrossRef]
  20. Sing, S.L.; An, J.; Yeong, W.Y.; Wiria, F.E. Laser and electron-beam powder-bed additive manufacturing of metallic implants: A
    review on processes, materials and designs. J. Orthop. Res. 2016, 34, 369–385. [CrossRef] [PubMed]
  21. Olakanmi, E.O.; Cochrane, R.F.; Dalgarno, K.W. A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy
    powders: Processing, microstructure, and properties. Prog. Mater. Sci. 2015, 74, 401–477. [CrossRef]
  22. Mahmood, M.A.; Popescu, A.C.; Hapenciuc, C.L.; Ristoscu, C.; Visan, A.I.; Oane, M.; Mihailescu, I.N. Estimation of clad geometry
    and corresponding residual stress distribution in laser melting deposition: Analytical modeling and experimental correlations.
    Int. J. Adv. Manuf. Technol. 2020, 111, 77–91. [CrossRef]
  23. Mahmood, M.A.; Popescu, A.C.; Oane, M.; Ristoscu, C.; Chioibasu, D.; Mihai, S.; Mihailescu, I.N. Three-jet powder flow
    and laser–powder interaction in laser melting deposition: Modelling versus experimental correlations. Metals 2020, 10, 1113.
    [CrossRef]
  24. King, W.; Anderson, A.T.; Ferencz, R.M.; Hodge, N.E.; Kamath, C.; Khairallah, S.A. Overview of modelling and simulation of
    metal powder bed fusion process at Lawrence Livermore National Laboratory. Mater. Sci. Technol. 2015, 31, 957–968. [CrossRef]
  1. Gong, H.; Rafi, K.; Gu, H.; Starr, T.; Stucker, B. Analysis of defect generation in Ti-6Al-4V parts made using powder bed fusion
    additive manufacturing processes. Addit. Manuf. 2014, 1, 87–98. [CrossRef]
  2. Frazier, W.E. Metal additive manufacturing: A review. J. Mater. Eng. Perform. 2014, 23, 1917–1928. [CrossRef]
  3. Panwisawas, C.; Qiu, C.L.; Sovani, Y.; Brooks, J.W.; Attallah, M.M.; Basoalto, H.C. On the role of thermal fluid dynamics into the
    evolution of porosity during selective laser melting. Scr. Mater. 2015, 105, 14–17. [CrossRef]
  4. Yan, W.; Ge, W.; Qian, Y.; Lin, S.; Zhou, B.; Liu, W.K.; Lin, F.; Wagner, G.J. Multi-physics modeling of single/multiple-track defect
    mechanisms in electron beam selective melting. Acta Mater. 2017, 134, 324–333. [CrossRef]
  5. Qian, Y.; Yan, W.; Lin, F. Parametric study and surface morphology analysis of electron beam selective melting. Rapid Prototyp. J.
    2018, 24, 1586–1598. [CrossRef]
  6. Panwisawas, C.; Perumal, B.; Ward, R.M.; Turner, N.; Turner, R.P.; Brooks, J.W.; Basoalto, H.C. Keyhole formation and thermal
    fluid flow-induced porosity during laser fusion welding in titanium alloys: Experimental and modelling. Acta Mater. 2017, 126,
    251–263. [CrossRef]
  7. King, W.E.; Barth, H.D.; Castillo, V.M.; Gallegos, G.F.; Gibbs, J.W.; Hahn, D.E.; Kamath, C.; Rubenchik, A.M. Observation of
    keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J. Mater. Process. Technol. 2014, 214, 2915–2925.
    [CrossRef]
  8. Panwisawas, C.; Sovani, Y.; Turner, R.P.; Brooks, J.W.; Basoalto, H.C.; Choquet, I. Modelling of thermal fluid dynamics for fusion
    welding. J. Mater. Process. Technol. 2018, 252, 176–182. [CrossRef]
  9. Martin, A.A.; Calta, N.P.; Hammons, J.A.; Khairallah, S.A.; Nielsen, M.H.; Shuttlesworth, R.M.; Sinclair, N.; Matthews, M.J.;
    Jeffries, J.R.; Willey, T.M.; et al. Ultrafast dynamics of laser-metal interactions in additive manufacturing alloys captured by in situ
    X-ray imaging. Mater. Today Adv. 2019, 1, 100002. [CrossRef]
  10. Cunningham, R.; Zhao, C.; Parab, N.; Kantzos, C.; Pauza, J.; Fezzaa, K.; Sun, T.; Rollett, A.D. Keyhole threshold and morphology
    in laser melting revealed by ultrahigh-speed x-ray imaging. Science 2019, 363, 849–852. [CrossRef] [PubMed]
  11. Tang, C.; Tan, J.L.; Wong, C.H. A numerical investigation on the physical mechanisms of single track defects in selective laser
    melting. Int. J. Heat Mass Transf. 2018, 126, 957–968. [CrossRef]
  12. Mirkoohi, E.; Ning, J.; Bocchini, P.; Fergani, O.; Chiang, K.-N.; Liang, S. Thermal Modeling of Temperature Distribution in Metal
    Additive Manufacturing Considering Effects of Build Layers, Latent Heat, and Temperature-Sensitivity of Material Properties. J.
    Manuf. Mater. Process. 2018, 2, 63. [CrossRef]
  13. Oane, M.; Sporea, D. Temperature profiles modeling in IR optical components during high power laser irradiation. Infrared Phys.
    Technol. 2001, 42, 31–40. [CrossRef]
  14. Cleary, P.W.; Sawley, M.L. DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper
    discharge. Appl. Math. Model. 2002, 26, 89–111. [CrossRef]
  15. Parteli, E.J.R.; Pöschel, T. Particle-based simulation of powder application in additive manufacturing. Powder Technol. 2016, 288,
    96–102. [CrossRef]
  16. Cao, L. Numerical simulation of the impact of laying powder on selective laser melting single-pass formation. Int. J. Heat Mass
    Transf. 2019, 141, 1036–1048. [CrossRef]
  17. Tian, Y.; Yang, L.; Zhao, D.; Huang, Y.; Pan, J. Numerical analysis of powder bed generation and single track forming for selective
    laser melting of SS316L stainless steel. J. Manuf. Process. 2020, 58, 964–974. [CrossRef]
  18. Lee, Y.S.; Zhang, W. Modeling of heat transfer, fluid flow and solidification microstructure of nickel-base superalloy fabricated by
    laser powder bed fusion. Addit. Manuf. 2016, 12, 178–188. [CrossRef]
  19. Tang, M.; Pistorius, P.C.; Beuth, J.L. Prediction of lack-of-fusion porosity for powder bed fusion. Addit. Manuf. 2017, 14, 39–48.
    [CrossRef]
  20. Promoppatum, P.; Yao, S.C.; Pistorius, P.C.; Rollett, A.D. A Comprehensive Comparison of the Analytical and Numerical
    Prediction of the Thermal History and Solidification Microstructure of Inconel 718 Products Made by Laser Powder-Bed Fusion.
    Engineering 2017, 3, 685–694. [CrossRef]
  21. Rosenthal, D. Mathematical Theory of Heat Distribution During Welding and Cutting. Weld. J. 1941, 20, 220–234.
  22. Chen, Q.; Zhao, Y.Y.; Strayer, S.; Zhao, Y.Y.; Aoyagi, K.; Koizumi, Y.; Chiba, A.; Xiong, W.; To, A.C. Elucidating the Effect
    of Preheating Temperature on Melt Pool Morphology Variation in Inconel 718 Laser Powder Bed Fusion via Simulation and
    Experiment. Available online: https://www.sciencedirect.com/science/article/pii/S2214860420310149#bb8 (accessed on 30
    April 2021).
  23. Ur Rehman, A.; Pitir, F.; Salamci, M.U. Laser Powder Bed Fusion (LPBF) of In718 and the Impact of Pre-Heating at 500 and
    1000 ◦C: Operando Study. Materials 2021, 14, 6683. [CrossRef] [PubMed]
  24. Ur Rehman, A.; Pitir, F.; Salamci, M.U. Full-Field Mapping and Flow Quantification of Melt Pool Dynamics in Laser Powder Bed
    Fusion of SS316L. Materials 2021, 14, 6264. [CrossRef] [PubMed]
  25. Gong, H.; Gu, H.; Zeng, K.; Dilip, J.J.S.; Pal, D.; Stucker, B.; Christiansen, D.; Beuth, J.; Lewandowski, J.J. Melt Pool Characterization
    for Selective Laser Melting of Ti-6Al-4V Pre-alloyed Powder. In Proceedings of the International Solid Freeform Fabrication
    Symposium, Austin, TX, USA, 10–12 August 2014; 2014; pp. 256–267.
  26. Song, B.; Dong, S.; Liao, H.; Coddet, C. Process parameter selection for selective laser melting of Ti6Al4V based on temperature
    distribution simulation and experimental sintering. Int. J. Adv. Manuf. Technol. 2012, 61, 967–974. [CrossRef]
  27. Guo, Q.; Zhao, C.; Qu, M.; Xiong, L.; Hojjatzadeh, S.M.H.; Escano, L.I.; Parab, N.D.; Fezzaa, K.; Sun, T.; Chen, L. In-situ full-field
  28. mapping of melt flow dynamics in laser metal additive manufacturing. Addit. Manuf. 2020, 31, 100939. [CrossRef]
  29. Messler, J.R.W. Principles of Welding: Processes, Physics, Chemistry, and Metallurgy; John Wiley & Sons: New York, NY, USA, 2008;
  30. ISBN 9783527617494.
  31. Khairallah, S.A.; Anderson, A.T.; Rubenchik, A.M.; King, W.E. Laser powder-bed fusion additive manufacturing: Physics of
  32. complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater. 2016, 108, 36–45. [CrossRef]
  33. Ur Rehman, A.; Mahmood, M.A.; Pitir, F.; Salamci, M.U.; Popescu, A.C.; Mihailescu, I.N. Mesoscopic Computational Fluid
  34. Dynamics Modelling for the Laser-Melting Deposition of AISI 304 Stainless Steel Single Tracks with Experimental Correlation: A
  35. Novel Study. Metals 2021, 11, 1569. [CrossRef]
  36. Paul, A.; Debroy, T. Free surface flow and heat transfer in conduction mode laser welding. Metall. Trans. B 1988, 19, 851–858.
  37. [CrossRef]
  38. Aucott, L.; Dong, H.; Mirihanage, W.; Atwood, R.; Kidess, A.; Gao, S.; Wen, S.; Marsden, J.; Feng, S.; Tong, M.; et al. Revealing
  39. internal flow behaviour in arc welding and additive manufacturing of metals. Nat. Commun. 2018, 9, 5414. [CrossRef]
  40. Abderrazak, K.; Bannour, S.; Mhiri, H.; Lepalec, G.; Autric, M. Numerical and experimental study of molten pool formation
  41. during continuous laser welding of AZ91 magnesium alloy. Comput. Mater. Sci. 2009, 44, 858–866. [CrossRef]
  42. Bayat, M.; Thanki, A.; Mohanty, S.; Witvrouw, A.; Yang, S.; Thorborg, J.; Tiedje, N.S.; Hattel, J.H. Keyhole-induced porosities in
  43. Laser-based Powder Bed Fusion (L-PBF) of Ti6Al4V: High-fidelity modelling and experimental validation. Addit. Manuf. 2019,
  44. 30, 100835. [CrossRef]
Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).

복합 광대보의 방류계수 예측을 위한 실험적 해석과 CFD 해석의 비교연구

Comparative study of experimental and CFD analysis for predicting discharge coefficient of compound broad crested weir

ABSTRACT

Present study highlights the behavior of weir crest head and width parameter on the discharge coefficient of compound broad crested (CBC) weir. Computational fluid dynamics model (CFD) is validated with laboratory experimental investigations.

In the discharge analysis through broad crested weirs, the upstream head over the weir crest (h) is crucial, where the result is mainly dependent upon the weir crest length (L) in transverse direction to flow, water depth from channel bed. Currently, minimal investigations are known for CFD validations on compound broad crested weirs.

The hydraulic research for measuring discharge numerically is carried out using FLOW 3D software. The model applies renormalized group (RNG) using volume of fluid (VOF) method for improved accuracy in free surface simulations. Structured hexagonal meshes of cubic elements define discretized meshing.

The comparative analysis of the numerical simulations and experimental observations confirm the performance of CBC weir for precise measurement of a wide range of discharges. Series of CFD model studies and experimental validation have led to constant range of discharg coefficients for various head over weir crest. The correlation coefficient of discharge predictions is 0.999 with mean error of 0.28%.

현재 연구에서는 CBC(compound broad crested) 위어의 배출 계수에 대한 위어 볏 머리 및 너비 매개변수의 거동을 강조합니다. 전산 유체 역학 모델(CFD)은 실험실 실험 조사를 통해 검증되었습니다.

넓은 볏이 있는 둑을 통한 유출 분석에서 둑 마루의 상류 수두(h)가 중요합니다. 여기서 결과는 주로 흐름에 대한 횡 방향의 둑 마루 길이(L), 수로 바닥에서 수심에 따라 달라집니다. . 현재 복합 넓은 볏 둑에 대한 CFD 검증에 대해 최소한의 조사가 알려져 있습니다.

수압 연구는 FLOW 3D 소프트웨어를 사용하여 수치적으로 측정합니다. 이 모델은 자유 표면 시뮬레이션의 정확도 향상을 위해 VOF(유체 체적) 방법을 사용하여 RNG(재정규화 그룹)를 적용합니다. 정육면체 요소의 구조화된 육각형 메쉬는 이산화된 메쉬를 정의합니다.

수치 시뮬레이션과 실험적 관찰의 비교 분석을 통해 광범위한 배출의 정확한 측정을 위한 CBC 둑의 성능을 확인했습니다. 일련의 CFD 모델 연구와 실험적 검증을 통해 다양한 head over weir crest에 대한 일정한 범위의 방전 계수가 나타났습니다. 방전 예측의 상관 계수는 0.999이고 평균 오차는 0.28%입니다.

Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).
Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).
Figure 4 | CFD Simulation for max discharge (y2 ¼ 13.557 cm, Qmax ¼ 10 lps) and min discharge (y2 ¼ 6.56 cm, Qmin ¼ 2 lps).
Figure 4 | CFD Simulation for max discharge (y2 ¼ 13.557 cm, Qmax ¼ 10 lps) and min discharge (y2 ¼ 6.56 cm, Qmin ¼ 2 lps).
Figure 5 | (a, b) Velocity profiles corresponding to max discharge (10 lps) and min discharge (2 lps).
Figure 5 | (a, b) Velocity profiles corresponding to max discharge (10 lps) and min discharge (2 lps).
Table 8 | Range of Froude number, Reynold number and Weber number
Table 8 | Range of Froude number, Reynold number and Weber number

Key words

compound weir, flow 3D, flow measurement, numerical technique, open channel

HIGHLIGHTS

• The Head-Discharge relation is established for discharge measurement using compound broad crested weir, experimentally and numerically.
• Assessment of head over weir crest for different step widths of proposed weir on discharge coefficient is executed.
• Experimental and CFD results of weir performance demonstrate good agreement between the theoretical discharges by traditional rectangular weir formulae keeping Cd constant.

CONCLUSION

  1. The head discharge relationship established for compound rectangular broad crested weir for various discharge ranges was validated by CFD technique. A three dimensional simulation software FLOW 3D was used for this purpose.
  2. Original theoretical compound weir model depicts the relative average error between discharge predictions with Flow 3D simulation as 4.96% which is found less than the predictions made by graphical interpolation technique which is 5.33%.
  3. The standard deviation in Cd parameter for CFD simulation model is less i.e. 0.0146 as compared to experimental output of 0.0502.
  4. The correlation coefficient for physical and CFD studies for modified compound weir model is high, around 0.999 with
    error in discharge predictions being 0.28% as compared to the accuracy limits of about +3–5% stated in literature so far.
  5. Discharge coefficient by experimental and CFD approach is maintained constant and equal to design input value of 0.6.
    Thus, the proposed CBC weir can be operated for various discharge ranges by maintaining constant discharge coefficients.
    Good agreement between the theoretical, experimental and CFD simulation results for obtaining discharge through compound broad crested weir ascertains the fact that CFD model can be used as an effective tool towards modeling flow through compound broad crested weir.

REFERENCES

Abd El-Hady Rady, R. M. 2011 2D 3D modeling of flow over sharp crested weirs. Journal of Applied Sciences Research 7 (12), 2495–2505.
ISSN 1819-544X.
Ackers, P., White, W. R. & Harrison, A. J. M. 1978 Weirs and Flumes for Flow Measurement. Wiley, New York.
Aydin, M. C. 2016 Investigation of a sill effect on rectangular side-weir flow by using CFD. Journal of Irrigation and Drainage Engineering
142 (2), 04015043.
Azimi, A. H. & Rajaratnam, N. 2009 Discharge characteristics of weirs of finite crest length. Journal of Hydraulic Engineering 135 (12),
1081–1085.
Bijankhan, M., Di Stefano, C., Ferro, V. & Kouchakzadeh, S. 2014 New stage discharge relationship for weirs of finite crest length. Journal of
Irrigation and Drainage Engineering 140 (3), 06013006.
Boiten, W. & Pitlo, H. R. 1982 The V- shaped broad-crested weir. Journal of Irrigation and Drainage Engineering 108 (2), 142–160.
Bos, M. G. 1989 Discharge Measurement Structures, 3rd edn. International Institute for Land Reclamation and Improvement, Publication 20,
Wageningen, The Netherlands.
Gogus, M., Defne, Z. & Ozkandemir, V. 2006 Broad-crested weirs with rectangular compound cross sections. Journal of Irrigation and
Drainage Engineering 132 (3), 272–280.

Gogus, M., Al-Khatib, I. A., Atalay, A. E. & Khatib, J. I. 2016 Discharge prediction in flow measurement flumes with different downstream
transition slopes. Flow Measurement and Instrumentation 47, 28–34.
Hager, W. H. & Schwalt, M. 1994 Broad – crested weir. Journal of Irrigation and Drainage Engineering 120 (1), 13–25.
Harrison, A. J. M. 1967 The streamlined broad-crested weir. Proceedings of the Institution of Civil Engineers 38, 657–678.
Hinge, G. A., Balkrishna, S. & Khare, K. C. 2010 Improved design of stilling basin for deficient tail water. Journal of Basic and Applied
Scientific Research 1 (1), 31–40.
Hinge, G. A., Balkrishna, S. & Khare, K. C. 2011 Experimental and numerical study of compound broad crested weir. International Journal of
Fluids Engineering 3 (2), 197–202.
Horton, R. E. 1907 Weir Experiments, Coefficients, and Formulas. Dept. of the Interior, U.S. Geological Survey, Water-Supply and Irrigation
Paper 200. Government Printing Office, Washington, DC.
Khan, L. A., Wicklein, E. A. & Teixeira, E. C. 2006 Validation of a three-dimensional computational fluid dynamics model of a contact tank.
Journal of Hydraulic Engineering 132 (7), 741–746.
Kindsvater, C. E. & Carter, R. W. 1959 Discharge characteristics of rectangular thin-plate weirs. Paper No. 3001, Transactions, American
Society of Civil Engineers 124.
Kulin, G. & Compton, P. R. 1975 A Guide to Methods and Standards for the Measurement of Water Flow. Special Publication 421, National
Bureau of Standards.
Kulkarni, K. H. & Hinge, G. A. 2017 Compound broad crested weir for measurement of discharge – a novel approach. In: Proceedings
International Conference Organized by Indian Society of Hydraulics – ISH HYDRO, 21–23 Dec 2017, India, pp. 678–687.
Kulkarni, K. H. & Hinge, G. A. 2020 Experimental study for measuring discharge through compound broad crested weir. Flow Measurement
Instrumentation 75, 101803. ISSN 0955-5986.
Man, C., Zhang, G., Hong, V., Zhou, S. & Feng, Y. 2019 Assessment of turbulence models on bridge-pier scour using flow-3D. World Journal
of Engineering and Technology 7, 241–255. ISSN Online: 2331-4249.
Omer, B., Cihan, A. M., Emin, E. M. & Miller, C. J. 2018 Experimental and CFD analysis of circular labyrinth weirs. Journal of Irrigation and
Drainage Engineering 144 (6), 04018007.
RangaRaju, K. G. 1981 Flow Through Open Channels. McGraw-Hill, New York.
Roushangar, K., Nouri, A., Shahnazi, S. & Azamathulla, H. M. 2021 Towards design of compound channels with minimum overall cost
through grey wolf optimization algorithm. IWA – Journal of Hydroinformatics (In – press).
Safarzadeh, A. & Mohajeri, S. H. 2018 Hydrodynamics of rectangular broad-crested porous weir. Journal of Irrigation and Drainage
Engineering 144 (10), 04018028.
Salmasi, F., Poorescandar, S., Dalir, A. H. & Zadeh, D. F. 2012 Discharge relations for rectangular broad crested weirs. Journal of
Agricultural Sciences 17, 324–336.
Samadi, A. & Arvanaghi, H. 2014 CFD simulation of flow over contracted compound arched rectangular sharp crested weirs. International
Journal of Optimization in Civil Engineering 4 (4), 549–560.
Savage, B. M. & Johnson, M. C. 2001 Flow over ogee spillway: physical and numerical model case study. Journal of Hydraulic Engineering
127 (8), 640–649.
Swamee, P. K. 1988 Generalized rectangular weir equations. Journal of Hydraulic Engineering 945–952. doi:10.1061/(ASCE),0733-9429
114:8(945).
The United States Bureau of Reclamation (USBR) 2001 Water Measurement Manual, Chapter 7 – Weirs. U.S. Government Printing Office,
Washington, DC, p. 20402. Available from: http://www/usbr.gov/pmts/hydraulics_lab/pubs/wmm.
Zahiri, A. & Azamathulla, H. M. 2014 Comparison between linear genetic programming and M5 tree models to predict flow discharge in
compound channels. Neural Computing and Application 24, 413–420.

Figure 1- The experimental model [17]

와류형 우수 저류지의 수치 모델링에 대한 난류 슈미트 수의 영향 조사

Investigation of the Turbulent Schmidt Number Effects On Numerical Modelling Of Vortex-Type Stormwater Retention Ponds

S. M. Yamini1; H. Shamloo2; S. H. Ghafari3
1M.Eng., Dep. of Civil Engineering K.N. Toosi University of Technology, Valiasr St., Tehran, Iran.
smyamini@alumni.kntu.ac.ir
2Associate Professor, Dep. of Civil Engineering K.N. Toosi University of Technology, Valiasr St., Tehran, Iran.
hshamloo@kntu.ac.ir
3Ph.D., Dep. of Civil Engineering Univ. of Tehran, Enqelab St., Tehran, Iran. sarvenazghafari@ut.ac.ir

Abstract

정확하고 신뢰할 수 있는 CFD 모델링 결과를 얻는 것은 이러한 시뮬레이션에서 입력의 중요성 때문에 종종 정밀 조사의 대상입니다.

난류 모델링이 RANS(Reynolds-Averaged Navier-Stokes) 방정식을 기반으로 하는 경우 난류 스칼라 전송을 추정하려면 난류 흐름에서 질량 1에 대한 운동량 확산의 비율로 정의되는 난류 슈미트 수(Sct)의 정의가 필요합니다.

그러나 이 매개변수는 난류 흐름의 속성이므로 보편적인 값이 허용되지 않았습니다. 우수 저류지의 수치 연구에서 적절한 Sct를 설정하는 실제 역할은 수력 효율의 평가가 추적자 테스트의 출력 질량 농도를 기반으로 하기 때문에 가장 중요합니다.

본 연구에서는 FLOW-3D를 사용하여 와류형 우수 저류지의 여러 수치 시뮬레이션을 체계적으로 수행했습니다. 다양한 난류 슈미트 수의 범위는 메쉬 감도를 조사하기 위해 다른 수의 계산 셀에 의해 수행된 수치 시뮬레이션에 도입되었습니다.

또한 사용자 정의 또는 자동 계산 값으로 최대 난류 혼합 길이의 영향을 평가했습니다. 이 연구의 결과는 실험 결과와 밀접한 일치를 제공하는 Sct= 0.625와 함께 수리학적 직경의 7%와 동일한 최대 난류 혼합 길이의 일정한 값을 갖는 확립된 수치 모델입니다.

특히 수치적 무차원 RDT 곡선의 피크 값은 극적으로 감소하여 실험 결과와 거의 일치했습니다. 이것은 FLOW-3D가 난류 유동의 와류형 물리학에서 질량 확산도를 적절하게 예측하는 상당한 능력을 가지고 있다는 결론을 내립니다.

– Achieving accurate and reliable CFD modelling results often is the subject of scrutiny because of the importance of the inputs in those simulations. If turbulence modelling is based on Reynolds-Averaged Navier-Stokes (RANS) equations, estimating the turbulent scalar transport requires the definition of the turbulent Schmidt number (Sct), defined as the ratio of momentum diffusivity to mass one in a turbulent flow. However, no universal value has been accepted for this parameter as it is a property of turbulent flows.

The practical role of establishing a suitable Sct in numerical studies of stormwater retention ponds is of the utmost importance because the assessment of the hydraulic efficiency of them is based on output mass concentration of tracer tests. In this study, several numerical simulations of a vortex-type stormwater retention pond were systematically carried out using FLOW-3D. A range of various turbulent Schmidt numbers were introduced in numerical simulations performed by different number of computational cells to investigate mesh sensitivity.

Moreover, the effects of maximum turbulent mixing length as a user-defined or automatically computed value were assessed. The outcome of this study is an established numerical model with a constant value of maximum turbulent mixing length equal to 7% of the hydraulic diameter along with Sct= 0.625 which provides a close agreement with experimental results.

Noticeably, the peak values of numerical dimensionless RDT curves are dramatically decreased, resulted in a close match with experimental results. This concludes that FLOW-3D has a considerable ability to appropriately predict mass diffusivity in vortex-type physics of turbulent flows.

Keywords:

turbulent Schmidt number – maximum turbulent mixing length – CFD – mesh sensitivity – vortex-type
stormwater retention pond – environmental fluid mechanics

Figure 1- The experimental model [17]
Figure 1- The experimental model [17]
Figure 2- Schematic of boundary conditions in the numerical model
Figure 2- Schematic of boundary conditions in the numerical model
Figure 3- Positioning of mesh blocks
Figure 3- Positioning of mesh blocks

References

[1] C. Gualtieri, A. Angeloudis, F. Bombardelli, S. Jha, and T. Stoesser, “On the Values for the Turbulent Schmidt Number
in Environmental Flows,” Fluids, vol. 2, p. 17, 2017.
[2] Å. Adamsson, L. Bergdahl, and S. Lyngfelt, “Measurement and three-dimensional simulation of flow in a rectangular
detention tank,” Urban Water Journal, vol. 2, no. 4, pp. 277-287, 2005/12/01 2005, doi: 10.1080/15730620500386545.
[3] C. Gualtieri, “Numerical simulation of flow and tracer transport in a disinfection contact tank,” 2006.
[4] S. Khan, B. Melville, and A. Shamseldin, Modeling the Layouts of Stormwater Retention Ponds using Residence Time.
2009, pp. 77-83.
[5] F. Martínez-Solano, P. L. I. Rey, C. Gualtieri, and P. López-Jiménez, “Modelling flow and concentration field in
rectangular water tanks,” 2010.
[6] W. B. Rauen, A. Angeloudis, and R. A. Falconer, “Appraisal of chlorine contact tank modelling practices,” Water
Research, vol. 46, no. 18, pp. 5834-5847, 2012/11/15/ 2012, doi: https://doi.org/10.1016/j.watres.2012.08.013.

[7] J. Zhang, A. Tejada-Martínez, and Q. Zhang, “Evaluation of LES and RANS for Determining Hydraulic Performance
of Disinfection Systems for Water Treatment,” Journal of Fluids Engineering, vol. 136, 05/15 2014, doi:
10.1115/1.4027652.
[8] J. Zhang, A. E. Tejada-Martínez, and Q. Zhang, “Developments in computational fluid dynamics-based modeling for
disinfection technologies over the last two decades: A review,” Environmental Modelling & Software, vol. 58, pp. 71-
85, 2014/08/01/ 2014, doi: https://doi.org/10.1016/j.envsoft.2014.04.003.
[9] C. Gualtieri and F. Salzano, “DIscussion on “The effect of baffle spacing on hydrodynamics and solute transport in
serpentine contact tanks”,” Journal of Hydraulic Research, vol. 52, pp. 152-154, 02/28 2014, doi:
10.1080/00221686.2013.877528.
[10] A. Angeloudis, T. Stoesser, R. A. Falconer, and D. Kim, “Flow, transport and disinfection performance in small- and
full-scale contact tanks,” Journal of Hydro-environment Research, vol. 9, no. 1, pp. 15-27, 2015/03/01/ 2015, doi:
https://doi.org/10.1016/j.jher.2014.07.001.
[11] A. Angeloudis, T. Stoesser, C. Gualtieri, and R. A. Falconer, “Contact Tank Design Impact on Process Performance,”
Environmental Modeling & Assessment, vol. 21, no. 5, pp. 563-576, 2016/10/01 2016, doi: 10.1007/s10666-016-9502-
x.
[12] D. Valero and D. B. Bung, “Sensitivity of turbulent Schmidt number and turbulence model to simulations of jets in
crossflow,” Environmental Modelling & Software, vol. 82, pp. 218-228, 2016/08/01/ 2016, doi:
https://doi.org/10.1016/j.envsoft.2016.04.030.
[13] F. Sonnenwald, I. Guymer, and V. Stovin, “Computational fluid dynamics modelling of residence times in vegetated
stormwater ponds,” Proceedings of the Institution of Civil Engineers – Water Management, vol. 171, pp. 1-11, 11/07
2017, doi: 10.1680/jwama.16.00117.
[14] F. Sonnenwald, I. Guymer, and V. Stovin, “A CFD-Based Mixing Model for Vegetated Flows,” Water Resources
Research, vol. 55, no. 3, pp. 2322-2347, 2019, doi: https://doi.org/10.1029/2018WR023628.
[15] S. B. Pope, Turbulent Flows. Cambridge, UK: Cambridge University Press, 2000.
[16] R. Rossi and G. Iaccarino, “Numerical simulation of scalar dispersion downstream of a square obstacle using gradienttransport type models,” Atmospheric Environment, vol. 43, no. 16, pp. 2518-2531, 2009/05/01/ 2009, doi:
https://doi.org/10.1016/j.atmosenv.2009.02.044.
[17] R. Chowdhury, M. Ahadi, K. A. Mazurek, G. Putz, D. Bergstrom, and C. Albers, “Physical Scale and Computational
Modeling in the Development of a Vortex-Type Stormwater Retention Pond,” in World Environmental and Water
Resources Congress 2016, 2016, pp. 388-397.
[18] V. Yakhot and L. M. Smith, “The renormalization group, the ɛ-expansion and derivation of turbulence models,” Journal
of Scientific Computing, vol. 7, no. 1, pp. 35-61, 1992/03/01 1992, doi: 10.1007/BF01060210.
[19] Flow Science, Inc., FLOW-3D User manual. Santa Fe, NM, USA. (2015).
[20] M. M. Bishop, J. M. Morgan, B. Cornwell, and D. K. Jamison, “Improving the Disinfection Detention Time of a Water
Plant Clearwell,” Journal AWWA, vol. 85, no. 3, pp. 68-75, 1993, doi: https://doi.org/10.1002/j.1551-
8833.1993.tb05958.x.
[21] F. L. Hart, “Improved Hydraulic Performance of Chlorine Contact Chambers.,” Jounal of Water Pollution Control
Federation, vol. 51(12), pp. 2868–2875, 1979.

Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

CFD 모델링을 이용한 침수 배수로 흐름의 수리학적 해석 및 슈트 폭기장치 성능 평가: Mangla Dam 배수로 사례 연구

Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

Muhammad Kaleem SarwarZohaib NisarGhulam NabiFaraz ul HaqIjaz AhmadMuhammad Masood & Noor Muhammad Khan 

Abstract

대용량 배출구가 있는 수중 여수로는 일반적으로 홍수 처리 및 침전물 세척의 이중 기능을 수행하기 위해 댐 정상 아래에 제공됩니다. 이 방수로를 통과하는 홍수 물은 난류 거동을 나타냅니다. 

게다가 이러한 난류의 수력학적 분석은 어려운 작업입니다. 

따라서 본 연구는 파키스탄 Mangla Dam에 건설된 수중 여수로의 수리학적 거동을 수치해석을 통해 조사하는 것을 목적으로 한다. 또한 다양한 작동 조건에서 화기의 유압 성능을 평가했습니다. 

Mangla Spillway의 흐름을 수치적으로 모델링하는 데 전산 유체 역학 코드 FLOW 3D가 사용되었습니다. 레이놀즈 평균 Navier-Stokes 방정식은 난류 흐름을 수치적으로 모델링하기 위해 FLOW 3D에서 사용됩니다. 

연구 결과에 따르면 개발된 모델은 최대 6%의 허용 오차로 흐름 매개변수를 계산하므로 수중 여수로 흐름을 시뮬레이션할 수 있습니다. 

또한, 여수로 슈트 베드 주변 모델에 의해 계산된 공기 농도는 폭기 장치에 램프를 설치한 후 6% 이상으로 상승한 3%로 개발된 모델도 침수형 폭기 장치의 성능을 평가할 수 있음을 보여주었습니다.

Submerged spillways with large capacity outlets are generally provided below the dam crest to perform the dual functions of flood disposal and sediment flushing. Flood water passing through these spillways exhibits turbulent behavior. Moreover; hydraulic analysis of such turbulent flows is a challenging task. Therefore, the present study aims to use numerical simulations to examine the hydraulic behavior of submerged spillways constructed at Mangla Dam, Pakistan. Besides, the hydraulic performance of aerator was also evaluated at different operating conditions. Computational fluid dynamics code FLOW 3D was used to numerically model the flows of Mangla Spillway. Reynolds-averaged Navier–Stokes equations are used in FLOW 3D to numerically model the turbulent flows. The study results indicated that the developed model can simulate the submerged spillway flows as it computed the flow parameters with an acceptable error of up to 6%. Moreover, air concentration computed by model near spillway chute bed was 3% which raised to more than 6% after the installation of ramp on aerator which showed that developed model is also capable of evaluating the performance of submerged spillway aerator.

Keywords

  • Aerator
  • CFD
  • FLOW 3D
  • Froude number
  • Submerged spillway
  • Fig. 1extended data figure 1Fig. 2extended data figure 2Fig. 3extended data figure 3Fig. 4extended data figure 4Fig. 5extended data figure 5Fig. 6extended data figure 6Fig. 7extended data figure 7Fig. 8

References

  1. Aydin MC (2018) Aeration efficiency of bottom-inlet aerators for spillways. ISH J Hydraul Eng 24(3):330–336. https://doi.org/10.1080/09715010.2017.1381576Article Google Scholar 
  2. Bennett P, Chesterton J, Neeve D, Ucuncu M, Wearing M, Jones SEL (2018) Use of CFD for modelling spillway performance. Dams Reserv 28(2):62–72. https://doi.org/10.1680/jdare.18.00001Article Google Scholar 
  3. Bhosekar VV, Jothiprakash V, Deolalikar PB (2012) Orifice Spillway Aerator: Hydraulic Design. J Hydraul Eng 138(6):563–572. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000548Article Google Scholar 
  4. Chanel PG, Doering JC (2008) Assessment of spillway modeling using computational fluid dynamics. Can J Civ Eng 35(12):1481–1485. https://doi.org/10.1139/L08-094Article Google Scholar 
  5. Flow Sciences, Inc. (2013) FLOW 3D user manual version 10.1.
  6. Gadge PP, Jothiprakash V, Bhosekar VV (2018) Hydraulic investigation and design of roof profile of an orifice spillway using experimental and numerical models. J Appl Water Eng Res 6(2):85–94. https://doi.org/10.1080/23249676.2016.1214627Article Google Scholar 
  7. Gadge PP, Jothiprakash V, Bhosekar VV (2019) Hydraulic design considerations for orifice spillways. ISH J Hydraul Eng 25(1):12–18. https://doi.org/10.1080/09715010.2018.1423579Article Google Scholar 
  8. Gu S, Ren L, Wang X, Xie H, Huang Y, Wei J, Shao S (2017) SPHysics simulation of experimental spillway hydraulics. Water 9(12):973. https://doi.org/10.3390/w9120973Article Google Scholar 
  9. Gurav NV (2015) Physical and Numerical Modeling of an Orifice Spillway. Int J Mech Prod Eng 3(10):71–75Google Scholar 
  10. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225. https://doi.org/10.1016/0021-9991(81)90145-5Article MATH Google Scholar 
  11. 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 
  12. Jothiprakash V, Bhosekar VV, Deolalikar PB (2015) Flow characteristics of orifice spillway aerator: numerical model studies. ISH J Hydraul Eng 21(2):216–230. https://doi.org/10.1080/09715010.2015.1007093Article Google Scholar 
  13. 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 
  14. Lian J, Qi C, Liu F, Gou W, Pan S, Ouyang Q (2017) Air entrainment and air demand in the spillway tunnel at the Jinping-I Dam. Appl Sci 7(9):930. https://doi.org/10.3390/app7090930Article Google Scholar 
  15. Luo M, Khayyer A, Lin P (2021) Particle methods in ocean and coastal engineering. Appl Ocean Res 114:102734Article Google Scholar 
  16. Moreira A, Leroy A, Violeau D, Taveira-Pinto F (2019) Dam spillways and the SPH method: two case studies in Portugal. J Appl Water Eng Res 7(3):228–245. https://doi.org/10.1080/23249676.2019.1611496Article Google Scholar 
  17. Moreira AB, Leroy A, Violeau D, Taveira-Pinto FA (2020) Overview of large-scale smoothed particle hydrodynamics modeling of dam hydraulics. J Hydraul Eng 146(2):03119001. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001658Article Google Scholar 
  18. O’Connor J, Rogers BD (2021) A fluid–structure interaction model for free-surface flows and flexible structures using smoothed particle hydrodynamics on a GPU. J Fluids Struct. https://doi.org/10.1016/j.jfluidstructs.2021.103312Article Google Scholar 
  19. Sarwar MK, Bhatti MT, Khan NM (2016) Evaluation of air vents and ramp angles on the performance of orifice spillway aerators. J Eng Appl Sci 35(1):85–93Google Scholar 
  20. Sarwar MK, Ahmad I, Chaudary ZA, Mughal H-U-R (2020) Experimental and numerical studies on orifice spillway aerator of Bunji Dam. J Chin Inst Eng 43(1):27–36. https://doi.org/10.1080/02533839.2019.1676652Article Google Scholar 
  21. Saunders K, Prakash M, Cleary PW, Cordell M (2014) Application of smoothed particle hydrodynamics for modelling gated spillway flows. Appl Math Model 38(17–18):4308–4322. https://doi.org/10.1016/j.apm.2014.05.008Article MATH Google Scholar 
  22. Savage BM, Johnson MC (2001) Flow over ogee spillway: physical and numerical model case study. J Hydraul Eng 127(8):640–649. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:8(640)Article Google Scholar 
  23. Shadloo MS, Oger G, le Touzé D (2016) Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: Motivations, current state, and challenges. Comput Fluids. https://doi.org/10.1016/j.compfluid.2016.05.029MathSciNet Article MATH Google Scholar 
  24. Shao Z, Jahangir Z, MuhammadYasir Q, Atta-ur-Rahman, Mahmood S (2020) Identification of potential sites for a multi-purpose dam using a dam suitability stream model. Water 12(11):3249. https://doi.org/10.3390/w12113249Article Google Scholar 
  25. Shimizu Y, Khayyer A, Gotoh H, Nagashima K (2020) An enhanced multiphase ISPH-based method for accurate modeling of oil spill. Coast Eng J 62(4):625–646. https://doi.org/10.1080/21664250.2020.1815362Article Google Scholar 
  26. Teng P, Yang J (2016) CFD modeling of two-phase flow of a spillway chute aerator of large width. J Appl Water Eng Res 4(2):163–177. https://doi.org/10.1080/23249676.2015.1124030Article Google Scholar 
  27. Teng P, Yang J, Pfister M (2016) Studies of two-phase flow at a chute aerator with experiments and CFD modelling. Model Simul Eng 2016:1–11. https://doi.org/10.1155/2016/4729128Article Google Scholar 
  28. Wapda (2004) Mangla dam raising project-sectional physical model study report of main spillway: Wapda model study cell, Gujrawala, Pakistan
  29. Yang J, Andreasson P, Teng P, Xie Q (2019) The past and present of discharge capacity modeling for spillways—a Swedish perspective. Fluids 4(1):10. https://doi.org/10.3390/fluids4010010Article Google Scholar 
  30. Yang J, Teng P, Xie Q, Li S (2020) Understanding water flows and air venting features of spillway—a case study. Water 12(8):2106. https://doi.org/10.3390/w12082106Article Google Scholar 
  31. Ye T, Pan D, Huang C, Liu M (2019) Smoothed particle hydrodynamics (SPH) for complex fluid flows: recent developments in methodology and applications. Phys Fluids 31(1):011301Article Google Scholar 
  32. Zhan X, Qin H, Liu Y, Yao L, Xie W, Liu G, Zhou J (2020) Variational Bayesian neural network for ensemble flood forecasting. Water 12(10):2740. https://doi.org/10.3390/w12102740Article Google Scholar 

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Solved Aging Dam Dilemma

노후 댐 대책

How Computational Fluid Dynamics Modeling Solved Aging Dam Dilemma

By AyresApril 6, 2021No Comments

Solved Aging Dam Dilemma
Solved Aging Dam Dilemma

Keyword : 3D Hydraulic Modeling,CFD, CFD Model, Computational Fluid Dynamics, Dam Hydraulics, Hydrology structure damage

급격한 변화나 예기치 못한 노후화로 인해 댐에서 복잡한 문제가 발생하는 경우 20세기에 개발된 산업 표준 설계 방정식과 방법론이 많은 경우 올바른 솔루션을 제공할 수는 없습니다. 다행스럽게도 엔지니어들은 적절한 조치나 수리를 적용할 수 있도록 유압 상황을 확인하기 위해 전산유체역학(CFD) 모델을 사용할 수 있게 되었습니다.

About the Expert:

Matthew Hickox, PE, brings civil engineering expertise in stormwater and river design, planning, and construction phase services. His experience is founded on a solid understanding of hydrologic modeling, 1- and 2-dimensional hydraulic modeling, in-stream hydraulic structures, scour protection measures, culvert and bridge hydraulics, and the regulatory environment for stormwater projects.

How Does CFD Work in Practice?

최근의 한 사례에서 하천 수문학 및 지형학은 낮은 수두 전환 댐 주변에서 변경되었습니다. 지난 수십 년 동안 빠르게 발전해 온 도시 지역의 하류에 있는 모래 바닥 하천 시스템에 위치한 댐의 문제는 주변 하천 시스템에서 일어나는 여러 가지 일들로 인해 복잡해졌습니다. 증가하는 도시화는 배출 빈도를 증가시켰을 뿐만 아니라 기본 흐름을 증가시켰습니다. 수리학적으로 가파른 시스템은 일시적인 지류에서 연간 베이스 흐름으로의 변화가 상류가 침식됨에 따라 퇴적물 부하도 증가했음을 의미했습니다.

이 조합은 전환 댐의 하류 수로가 지난 15년 동안 3-4피트 감소했고, 배수가 감소된 정수장 apron에서 속도가 증가했으며 구조물 표면에 마모를 유발하는 퇴적물 하중이 감소했음을 의미합니다. 이러한 문제 중 어느 것도 전환 댐의 원래 설계의 잘못이 아니었지만 변화하는 하천 수문 및 지형학으로 인해 원래 설계자가 예상하지 못한 조건이 발생했습니다.

기존 구조물의 단위 너비 CFD 모델은 기존 현장 조건으로 인해 정수기 계류장에 수압 점프가 형성되지 않았다는 현장 관찰을 확인했습니다. 1).

Figure 1. Existing conditions unit width CFD model results showing velocity, cross section view of structure.
Figure 1. Existing conditions unit width CFD model results showing velocity, cross section view of structure.

설계 표고(열화 전)에서 하류 하류 바닥 표고와 함께 개발된 유사한 단위 너비 CFD 모델은 원래 설계가 정수 유역 계류장과 배수로 전면 근처에서 수압 점프를 생성한다는 것을 보여주었습니다. 이 단위 너비 CFD 모델은 구조에 영향을 미치는 수력학의 가치 있는 검증을 제공하지만 구조 손상이 구조 중간에서 매우 뚜렷하고 다른 영역에서는 거의 손대지 않았기 때문에 이것만으로는 충분하지 않습니다. (그림 2)

Figure 2. Original design conditions unit width CFD model results showing velocity, cross section view of structure. The only difference with Figure 1 is the downstream bed elevation.
Figure 2. Original design conditions unit width CFD model results showing velocity, cross section view of structure. The only difference with Figure 1 is the downstream bed elevation.

전체 기존 조건 CFD 모델은 정수조 앞치마 마모의 범위와 그에 따른 손상을 확인했습니다. (그림 3 및 4)

Figure 3. Existing conditions CFD model results showing velocity streamlines at 2-year event discharge. High velocities are areas of significant abrasion damage, low velocity areas have little or no abrasion damage.
Figure 3. Existing conditions CFD model results showing velocity streamlines at 2-year event discharge. High velocities are areas of significant abrasion damage, low velocity areas have little or no abrasion damage.
Figure 4. Existing conditions shows rebar exposed from significant abrasion damage to stilling basin apron in high velocity areas
Figure 4. Existing conditions shows rebar exposed from significant abrasion damage to stilling basin apron in high velocity areas

이 구조물에 대한 수리를 위한 예비 설계 동안 간단한 분석에 따르면 구조물의 미수를 높이는 것이 방수로 토우 근처의 구조물에 수력학적 점프를 만드는 데 도움이 될 것이며, 이는 정수 유역 계류장과 계류장을 가로지르는 극한 속도를 감소시킬 것입니다. 따라서 구조의 마모를 크게 줄입니다(그림 5 참조). 이 예비 제안 조건 CFD 모델은 엔드 실 높이만 높였습니다. 구조물 하류의 하천 시스템의 상태와 지형은 나머지 설계 수명 동안 구조물의 안정성을 보장하기 위해 모든 최종 설계 조건에 대해 평가되어야 합니다.

Figure 5. Preliminary design check to verify velocities under a raised tailwater condition at a 2-year event discharge. Velocity cross section slices shown.
Figure 5. Preliminary design check to verify velocities under a raised tailwater condition at a 2-year event discharge. Velocity cross section slices shown.

CFD 모델은 설계 상황이 확립된 설계 방정식 및 절차의 한계 내에 깔끔하게 속하지 않을 때 유압을 확인하는 또 다른 도구를 제공합니다. 구조와 유역의 개요에 대해 자세히 설명하는 전체적인 관점은 프로젝트 현장의 현재와 미래의 상태를 평가하는 데 필요합니다. 이 예에서 구조의 설계 및 작동은 원래 설계와 매우 유사하게 유지됩니다. 구조 주변에서 변경된 것은 하천 시스템입니다. CFD는 현장 조건 변경으로 인해 예기치 않은 수리력 및 구조 손상이 발생할 때 복잡한 수리력을 분석할 수 있는 도구 상자의 또 다른 도구를 제공합니다.

CFD 또는 여기 Ayres에서 제공하는 유압 엔지니어링 서비스에 대한 자세한 내용은 Matthew Hickox, PE에게 문의하십시오.

Figure 3.4 Upstream View of the Radial Gated-Spillway

방사형 게이트 아래의 흐름에 대한 실험 및 수치 조사

EXPERIMENTAL AND NUMERICAL INVESTIGATION OF FLOW UNDER RADIAL GATES

submitted by MAHMUT TANYERİ in partial fulfillment of the requirements for
the degree of Master of Science in Civil Engineering, Middle East Technical
University by,
Prof. Dr. Halil Kalıpçılar
Dean, Graduate School of Natural and Applied Sciences
Prof. Dr. Ahmet Türer
Head of the Department, Civil Engineering
Prof. Dr. Mete Köken
Supervisor, Civil Engineering, METU
Prof. Dr. İsmail Aydın
Co-Supervisor, Civil Engineering, METU

Abstract

방사형 게이트는 여수로에서 일반적으로 사용됩니다. 부분 게이트 개구부에서 60년대에 수행된 실험 작업에서 얻은 경험 방정식을 사용하여 통과하는 방전을 계산합니다.

그러나 이러한 방정식에서 얻은 배출 값과 유한 체적 방법 및 수리적 모델을 기반으로 한 수치 계산에서 얻은 값 사이에는 약간의 불일치가 있습니다. 이러한 차이의 원인을 밝히는 것이 목적입니다.

이를 위해 다양한 게이트 구성에 대한 실험과 수치 계산이 수행되었습니다. 수많은 수치 시뮬레이션에서 나온 경향을 활용하여 연구 말미에 새로운 방전 방정식을 도출했습니다.

하나의 수리학적 매개변수와 두 개의 기하학적 매개변수가 있는 제안된 방정식을 사용하면 설계자가 지루한 정격 곡선 없이도 쉽게 배출을 계산할 수 있습니다.

Keywords

Radial Gate, Spillway, Empirical Equations, Discharge Coefficient, Discharge Rating Curve

Introduction

방사형 수문(또는 테인터 수문)은 특히 수두가 높은 댐에서 홍수 방출을 제어하기 위해 광범위하게 사용되는 오버플로 수문 유형 중 하나입니다. 그것은 강철 곡선 리프, 지지 암 및 슈트 채널의 측벽에 장착된 고정 조인트로 구성됩니다.

게이트는 하류의 물 수요를 충족시키거나 상류 수두를 조절하기 위해 원하는 각도로 피벗 지점을 중심으로 쉽게 회전할 수 있습니다. 방사형 게이트는 다른 유형에 비해 많은 장점이 있습니다. 그들의 가장 놀라운 특성은 게이트를 움직이는 데 필요한 호이스트 힘이 적다는 것입니다.

이는 상류의 물이 게이트에 양력을 가할 수 있는 아치형 덕분에 에너지 소비도 감소합니다. 더욱이, 방사형 게이트는 슬롯이 필요하지 않으며, 시간이 지남에 따라 떠다니는 파편이 그 안에 쌓일 수 있기 때문에 때때로 작동 문제를 일으킬 수 있습니다. 그 활용 분야는 여러 가지가 있지만, 본 연구의 범위는 오지형 여수로에만 수반되는 방사형 게이트로 제한됩니다.

부분적으로 열리면 래디얼 게이트 아래를 통과하는 흐름은 다양한 수리적 및 기하학적 요인의 영향을 받습니다. 따라서 정확한 배출 추정은 어려운 문제입니다. 이 문제는 주로 게이트 근처에서 유선형 ​​동작의 복잡성으로 인해 발생합니다.

유동 영역은 고도의 곡선 유선을 포함하기 때문에 유속에 대한 해석적 솔루션이 불가능합니다. 이러한 이유로 방전은 대부분 실험적 모델에서 조사되었으며 이에 따라 실증적 관계가 도출되었습니다.

방전 방정식은 유선의 총 에너지 변환과 관련된 베르누이 방정식을 기반으로 개발되었습니다. 게이트 바로 아래의 평균 속도는 에너지 방정식에서 추론할 수 있으며, 게이트 개방의 순 면적을 곱하면 체적 유량의 이론적인 값을 얻을 수 있습니다.

그러나 실제로는 바닥 게이트 립과 같은 날카로운 모서리를 유선이 완벽하게 따라갈 수 없고 마찰로 인해 이론 속도가 약간 감소하기 때문에 실제로 분사되는 워터젯의 단면적이 수축합니다.

이러한 효과 때문에 실제 배출량을 추정하기 위해 배출 계수라고 하는 경험적 보정 계수가 방정식에 도입됩니다(Tokyay, 2019). 사례 연구로 터키의 민간 엔지니어링 회사인 TEMELSU(2018)에서 수행한 Lower Kaleköy 댐에 속한 방사형 여수로의 수리학적 계산을 조사했습니다.

그들은 세계적으로 인기 있는 수력 설계 책인 ‘Design of Small Dams’에 제공된 배출 계수 등급 곡선을 사용하여 이러한 계산을 수행했습니다. 이러한 곡선을 기반으로 산출된 토출량 값을 CFD(Computational Fluid Dynamics) 프로그램에서 생성한 수치모델 결과와 비교하였다.

게이트가 부분적으로 열린 경우 이러한 결과 사이에 명백한 불일치가 있는 것으로 관찰되었습니다. 일반적으로 제안된 경험식은 시뮬레이션에 비해 최대 20%까지 유량을 과소평가한다.

본 연구의 목적은 크게 두 가지이다. 첫 번째 목표는 언급된 실험식과 수치해석 간의 불일치 이유를 조사하는 것이고, 두 번째 목표는 어떤 수리적 및 기하학적 매개변수가 방사형 게이트 아래의 배출에 실제로 영향을 미치는지 탐구하는 것입니다.

먼저 METU 수력학 연구소에서 건설한 Lower Kaleköy 댐의 물리적 모델에서 미리 결정된 수문 개구부의 배출 값을 측정했습니다. 이러한 실험에서 얻은 데이터 세트를 수치 모델의 결과와 비교하여 일치 여부를 확인했습니다.

이러한 방식으로 수치적 결과를 검증한 후 원래 수력 조건이 동일하게 유지되는 경우 수치 모델의 게이트 위치, 배수로 형상과 같은 다양한 구성을 시뮬레이션했습니다.

분석은 연구 전반에 걸쳐 모델 규모로 수행되었습니다. 상술한 효과와 관련된 연구 결과, 수치해를 기반으로 새로운 방전방정식을 공식화하였다. 마지막으로 기존 실험식과 새로운 공식에서 얻은 결과를 수치해와 비교하여 정확도를 관찰하였다.

Figure 3.3 General View of the Experimental Setup
Figure 3.3 General View of the Experimental Setup
Figure 3.4 Upstream View of the Radial Gated-Spillway
Figure 3.4 Upstream View of the Radial Gated-Spillway
Figure 3.5 Side View of the Radial Gate During Operation
Figure 3.5 Side View of the Radial Gate During Operation
Figure 4.2 Mesh Detail of the 3D Models
Figure 4.2 Mesh Detail of the 3D Models
Figure 4.7 Mesh Details of the 2D Numerical Model
Figure 4.7 Mesh Details of the 2D Numerical Model
Figure 4.12 Velocity Magnitude Contours of T1, T2, T3 and T4 at the Design Head (d=10cm)
Figure 4.12 Velocity Magnitude Contours of T1, T2, T3 and T4 at the Design Head (d=10cm)
e) 표시 탭에서 결과를 볼 수 있으며 필요한 경우 슬라이스 옵션을 사용하여 특정 영역을 분석할 수 있습니다.

유체 역학 및 응용 유압 분야에서 사용하기 위한 수치 모델링(CFD)을 적용한 가상 실험실 실습 매뉴얼

This manual was developed with the purpose of presenting and executing basic numerical models in the software known as Flow 3D within the virtual laboratories of Fluid Mechanics and Applied Hydraulics, to complement and reinforce what was learned in class, the development of the manual covers a theoretical content and an exemplified práctical part for the handling of the software, besides including some feedback for the students, in order to mark the characteristics that the software has. With the handling of the Flow 3D program, the student will be introduced to the concept of Computational Fluid Dynamics or CFD, and a simple procedure to represent numerically and graphically the behavior of hydraulic structures. The hydraulic structures presented in the laboratory manual are: thin and thick wall orifices, gates with free and submerged discharge, thin and thick wall spillways with free and submerged discharge, WES type spillway, submerged intake with pressure conduction and as a complement, hydrostatic pressures on vertical, curved and inclined walls were added. Each of the mentioned hydraulic structures obtained a práctical verification as a verification within the Flow 3D software, presenting a consistency in the results obtained in both ways.

이 매뉴얼은 Fluid Mechanics 및 Applied Hydraulics의 가상 연구실 내에서 Flow 3D로 알려진 소프트웨어에서 기본 수치 모델을 제시하고 실행하기 위해 개발되었으며, 수업에서 배운 내용을 보완하고 강화하기 위해 개발되었으며, 매뉴얼 개발은 이론적인 내용을 다룹니다. 소프트웨어의 특성을 표시하기 위해 학생들을 위한 일부 피드백을 포함하는 것 외에도 소프트웨어 처리에 대한 내용 및 예시된 실제적인 부분. Flow 3D 프로그램을 다루면서 학생은 전산유체역학(Computational Fluid Dynamics) 또는 CFD의 개념과 수력학적 구조의 거동을 수치 및 그래픽으로 표현하는 간단한 절차를 소개합니다. 실험실 매뉴얼에 제시된 유압 구조는 얇고 두꺼운 벽 오리피스, 자유 및 수중 배출이 있는 수문, 자유 및 수중 배출이 있는 얇고 두꺼운 벽 여수로, WES 유형 방수로, 압력 전도 및 보완으로 수중 유입이 있는 수중 흡입구입니다. 수직, 곡선 및 경사 벽에 추가되었습니다. 언급된 각 수력학적 구조는 Flow 3D 소프트웨어 내에서 검증으로 실제 검증을 획득하여 두 가지 방식에서 얻은 결과의 일관성을 나타냅니다.

Keywords: Flow 3D, numerical modeling, manual, practice, Fluid Mechanics.

e) 표시 탭에서 결과를 볼 수 있으며 필요한 경우 슬라이스 옵션을 사용하여 특정 영역을 분석할 수 있습니다.
e) 표시 탭에서 결과를 볼 수 있으며 필요한 경우 슬라이스 옵션을 사용하여 특정 영역을 분석할 수 있습니다.

REFERENCIAS

Anguisa, M., & Maza, X.(2012). Estudio de los procesos de flujo en una obra de
camptación mediante experimentación de un modelo físico de escala reducida.
[Tesis de grado,Universidad de Cuenca]. Archivo Digital
http://dspace.ucuenca.edu.ec/bitstream/123456789/775/1/ti901.pdf
Arreaga, W., & Mantilla, D. (2016). Determinación de coeficientes de descarga en
orificios circulares, de pared delgada en descarga libre para diferentes
diámetros en modelos físicos. [Tesis de grado,Universidad de Guayaquil].
Archivo Digital
http://repositorio.ug.edu.ec/bitstream/redug/15855/1/ARREAGA_WILLIAM_
MANTILLA_DIEGO_TRABAJO_TITULACIÓN_HIDRÁULICA_DICIEMB
RE_2016.pdf
Arrecis, J., (2018). Evaluación de las carácterísticas del prefil tipo Creager. [Tesis de
grado,Universidad de San Carlos de Guatemala]. Archivo Digital
http://www.repositorio.usac.edu.gt/11372/1/Jared%20Alexander%20V%C3%A
9liz%20Arrecis.pdf
Barba, C. A. B. (2020). Modelación numérica (CDF) del flujo combinado superior e
inferior en una compuerta plana con el program Flow 3D. [Tesis de
Maestria,Escuela Politénica Nacional]. Archivo Digital
Bureau of Reclamation, (2007). Traducida por: Martínez, M., Batanero, A., Martínez,
G., Martínez, O., Gonzáles, O.: Diseño de Presas Peuqeñas(3ra ed). España:
Editorial Bellisco.
Calderon, F. V., Cazares, L. G., & Camacho, F. F. (2017). Dificultades conceptuales
para la comprensión de la Ecuación de Bernoulli. Revista Eureka Sobre
Enseñanza y Divulgación de Las Ciencias, 14(12), 339–352.
Fernández, J.(2012).Técnicas numéricas en ingeniería de fluido: Introducción a la
dinámica de fluidos computacional (CFD) por el método de volúmenes
finitos.Barcelona , España.:Editorial Reverté, S.A.
Flow Science. (2008). Manual de Flow 3D.
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=r
ja&uact=8&ved=2ahUKEwie6p3mpfTsAhWJpFkKHRWpAHcQFjADegQIBh
AC&url=https%3A%2F%2Fwww.researchgate.net%2Fprofile%2FAli_Agha7%
2Fpost%2FSomebody_can_recommend_me_the_tutorials_pdf_video_of_Flow_
3d_v101_software%2Fattachment%2F59d6285e79197b8077986bf3%2FAS%2
53A330000659173377%25401455689696420%2Fdownload%2F%255BFlow_
Science%255D_FLOW3D_V9.3_User_Manual%252C_Volume_1%2528BookZZ.org%2529.pdf&usg
=AOvVaw3ALDHf9jsqn-wDYnhAXNB1
Intituto Internacional de la Investigación de Tecnología Educativa INITE. (2006).
Ecuaciones fundamentales de la hidráulica.
https://gc.scalahed.com/recursos/files/r144r/w226w/Problema_2/Problema2_Hi
draulica_Ecuaciones.pdf
Inciso, C. (2016). Análisis comparativo de las descargas en orificios y boquillas en
laboratorio de Hidráulica de un UPN, Cajamarca. [Tesis de grado,Universidad
Privada del Norte, Cajamarca. Perú]. Archivo Digital
https://repositorio.upn.edu.pe/bitstream/handle/11537/9980/Inciso%20Pajares%
20%20Carlos%20Jonathan.pdf?sequence=1&isAllowed=y

Gutiérrez, Y. (2016). Modelación numérica computacional del diseño de un vertedor
de pared delgada de sección compuesta. [Tesis de grado,Universidad Central
Marta Abreu de las Villas]. Archivo Digital
https://dspace.uclv.edu.cu/bitstream/handle/123456789/6671/Tesis%20Yunior%
20Gutierrez.pdf?sequence=1&isAllowed=y
Guncay, K. (2017). Estudio del desempeño hidráulico del canal multipropósito del
laboratorio de hidráulica y dinámica de fluidos LH&DF del campus Balzay.
[Tesis de grado,Universidad de Cuenca]. Archivo Digital
Jiménez, J., Jiménez J. (2018). Elaboración del modelo físico y la guia metodológica
para la práctica: vertederos de pared delgada, de la asignatura Mecánica de
Fluidos de la Universidad de Azuay. [Tesis de grado,Universidad de Cuenca].
Archivo Digital
http://dspace.uazuay.edu.ec/bitstream/datos/8371/1/14091.pdf
Monroy, M. (2010). Medidores De Flujo En Canales Abiertos. [Tesis de
grado,Universidad de San Carlos de Guatemala]. Archivo Digital
http://biblioteca.usac.edu.gt/tesis/08/08_3165_C.pdf
Penagos, D. F. R. (2012). Diseño y modelación de las uniones soldadas de las
compuertas planas para presas. [Tesis de posgrado,Universidad Libre de
Colombia]. Archivo Digital
https://core.ac.uk/download/pdf/198447125.pdf
Sotelo, A. (1997). Hidráulica General, Volumen 1(18va ed). Balderas 95, México,
D.F.: Editorial Limusa, S.A.
Vega, D. (2004). Vertederos de pared delgada.Centro Andino para la gestión y uso
del agua. Cochabamba.
https://www.academia.edu/6129654/Serie_T%C3%A9cnica_Agua_y_Suelo_N_
1_VERTEDEROS_DE_PARED_DELGADA_Rectangular_y_Triangular
Ven Te Chow. (1994). Hidráulica de canales abiertos. Santafé de Bogotá, Colombia.:
Editorial Martha Edna Suárez R.

Figure 1. Photorealistic view of an inclined axis TAST (photo A. Stergiopoulou).

그리스 수로의 작은 수력 전위를 활용하는 관형 아르키메데스 스크류 터빈의 CFD 시뮬레이션

CFD Simulations of Tubular Archimedean Screw Turbines Harnessing the Small Hydropotential of Greek Watercourses

Alkistis Stergiopoulou1
, Vassilios Stergiopoulos2
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 “그리스 아르키메데스의 부활: 아르키메데스 달팽이관 물레방아의 수리역학 및 유체역학적 거동 연구, 그리스 자연 및 기술 수로의 수력 잠재력 회복에 대한 기여”. 라는  제목의 최근 연구에서 수행한 최초의 아르키메데스 나사 터빈 CFD 모델링 결과에 대한 간략한 견해를 제시합니다.

FLOW-3D 코드를 기반으로 하는 이 CFD 분석은 일반적인 TAST(Tubular Archimedean Screw Turbines)에 관한 것으로, 그리스의 자연 및 기술 수로의 중요한 미개척 수력 잠재력을 활용하는 소규모 수력 발전 시스템에 대한 TWh/년 및 수천 MW 범위의 총 설치 용량등 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 4. Creation of the 3bladed Archimedean Screw with Solidworks.
Figure 4. Creation of the 3bladed Archimedean Screw with Solidworks.
Figure 8. Comparison of Archimedean Screw Turbine power performances P(W) for angle of orientation θ = 22ο and 32ο and for various water discharge values Q = 0.15, 0.30, 0.45 m3 /s.
Figure 8. Comparison of Archimedean Screw Turbine power performances P(W) for angle of orientation θ = 22ο and 32ο and for various water discharge values Q = 0.15, 0.30, 0.45 m3 /s.
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.

Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s.

Optimization Algorithms and Engineering: Recent Advances and Applications

Mahdi Feizbahr,1 Navid Tonekaboni,2Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4Show moreAcademic Editor: Mohammad YazdiReceived08 Apr 2021Revised18 Jun 2021Accepted17 Jul 2021Published11 Aug 2021

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.


강의 식생은 거칠기를 증가시키고 평균 유속을 감소시키며, 유속 에너지를 감소시키고 강의 단면에서 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받으므로 홍수시 유동저항에 큰 영향을 미칩니다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건 및 식물에 따라 다르므로 모델은 유속, 흐름 깊이 및 운하를 따라 식생 유형의 영향을 고려하여 현재 속도를 시뮬레이션해야 합니다. 근관의 거칠기의 영향을 조사하기 위해 총 48개의 모델이 시뮬레이션되었습니다. 결과는 유속을 높임으로써 유속을 감소시키는 식생의 영향은 무시할 수 있는 반면, 해류가 더 낮은 유속일 때 유속을 감소시키는 식생의 영향은 분명히 상당함을 나타냈다.

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.(a)
(a)(b)
(b)(c)
(c)(d)
(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.(a)
(a)(b)
(b)(c)
(c)(d)
(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.(a)
(a)(b)
(b)(c)
(c)(d)
(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.(a)
(a)(b)
(b)(c)
(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.(a)
(a)(b)
(b)(c)
(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].(a)
(a)(b)
(b)(c)
(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
Probabilistic investigation of cavitation occurrence in chute spillway based on the results of Flow-3D numerical modeling

Flow-3D 수치 모델링 결과를 기반으로 하는 슈트 여수로의 캐비테이션 발생 확률적 조사

Probabilistic investigation of cavitation occurrence in chute spillway based on the results of Flow-3D numerical modeling

Amin Hasanalipour Shahrabadi1*, Mehdi Azhdary Moghaddam2

1-University of Sistan and Baluchestan،amin.h.shahrabadi@gmail.com

2-University of Sistan and Baluchestan،Mazhdary@eng.usb.ac.ir

Abstract

Probabilistic designation is a powerful tool in hydraulic engineering. The uncertainty caused by random phenomenon in hydraulic design may be important. Uncertainty can be expressed in terms of probability density function, confidence interval, or statistical torques such as standard deviation or coefficient of variation of random parameters. Controlling cavitation occurrence is one of the most important factors in chute spillways designing due to the flow’s high velocity and the negative pressure (Azhdary Moghaddam & Hasanalipour Shahrabadi, ۲۰۲۰). By increasing dam’s height, overflow velocity increases on the weir and threats the structure and it may cause structural failure due to cavitation (Chanson, ۲۰۱۳). Cavitation occurs when the fluid pressure reaches its vapor pressure. Since high velocity and low pressure can cause cavitation, aeration has been recognized as one of the best ways to deal with cavitation (Pettersson, ۲۰۱۲). This study, considering the extracted results from the Flow-۳D numerical model of the chute spillway of Darian dam, investigates the probability of cavitation occurrence and examines its reliability. Hydraulic uncertainty in the design of this hydraulic structure can be attributed to the uncertainty of the hydraulic performance analysis. Therefore, knowing about the uncertainty characteristics of hydraulic engineering systems for assessing their reliability seems necessary (Yen et al., ۱۹۹۳). Hence, designation and operation of hydraulic engineering systems are always subject to uncertainties and probable failures. The reliability, ps, of a hydraulic engineering system is defined as the probability of safety in which the resistance, R, of the system exceeds the load, L, as follows (Chen, ۲۰۱۵): p_s=P(L≤R) (۱) Where P(۰) is probability. The failure probability, p_f, is a reliability complement and is expressed as follows: p_f=P[(L>R)]=۱- p_s (۲) Reliability development based on analytical methods of engineering applications has come in many references (Tung & Mays, ۱۹۸۰ and Yen & Tung, ۱۹۹۳). Therefore, based on reliability, in a control method, the probability of cavitation occurrence in the chute spillway can be investigated. In reliability analysis, the probabilistic calculations must be expressed in terms of a limited conditional function, W(X)=W(X_L ,X_R)as follows: p_s=P[W(X_L ,X_R)≥۰]= P[W(X)≥۰] (۳) Where X is the vector of basic random variables in load and resistance functions. In the reliability analysis, if W(X)> ۰, the system will be secure and in the W(X) <۰ system will fail. Accordingly, the eliability index, β, is used, which is defined as the ratio of the mean value, μ_W, to standard deviation, σ_W, the limited conditional function W(X) is defined as follows (Cornell, ۱۹۶۹): β=μ_W/σ_W (۴) The present study was carried out using the obtained results from the model developed by ۱:۵۰ scale plexiglass at the Water Research Institute of Iran. In this laboratory model, which consists of an inlet channel and a convergent thrower chute spillway, two aerators in the form of deflector were used at the intervals of ۲۱۱ and ۲۷۰ at the beginning of chute, in order to cope with cavitation phenomenon during the chute. An air duct was also used for air inlet on the left and right walls of the spillway. To measure the effective parameters in cavitation, seven discharges have been passed through spillway. As the pressure and average velocity are determined, the values of the cavitation index are calculated and compared with the values of the critical cavitation index, σ_cr. At any point when σ≤σ_cr, there is a danger of corrosion in that range (Chanson, ۱۹۹۳). In order to obtain uncertainty and calculate the reliability index of cavitation occurrence during a chute, it is needed to extract the limited conditional function. Therefore, for a constant flow between two points of flow, there would be the Bernoulli (energy) relation as follows (Falvey, ۱۹۹۰): σ= ( P_atm/γ- P_V/γ+h cos⁡θ )/(〖V_۰〗^۲/۲g) (۵) Where P_atm is the atmospheric pressure, γ is the unit weight of the water volume, θ is the angle of the ramp to the horizon, r is the curvature radius of the vertical arc, and h cos⁡θ is the flow depth perpendicular to the floor. Therefore, the limited conditional function can be written as follows: W(X)=(P_atm/γ- P_V/γ+h cos⁡θ )/(〖V_۰〗^۲/۲g) -σ_cr (۶) Flow-۳D is a powerful software in fluid dynamics. One of the major capabilities of this software is to model free-surface flows using finite volume method for hydraulic analysis. The spillway was modeled in three modes, without using aerator, ramp aerator, and ramp combination with aeration duct as detailed in Flow-۳D software. For each of the mentioned modes, seven discharges were tested. According to Equation (۶), velocity and pressure play a decisive and important role in the cavitation occurrence phenomenon. Therefore, the reliability should be evaluated with FORM (First Order Reliable Method) based on the probability distribution functions For this purpose, the most suitable probability distribution function of random variables of velocity and pressure on a laboratory model was extracted in different sections using Easy fit software. Probability distribution function is also considered normal for the other variables in the limited conditional function. These values are estimated for the constant gravity at altitudes of ۵۰۰ to ۷۰۰۰ m above the sea level for the unit weight, and vapor pressure at ۵ to ۳۵° C. For the critical cavitation index variable, the standard deviation is considered as ۰.۰۱. According to the conducted tests, for the velocity random variable, GEV (Generalized Extreme Value) distribution function, and for the pressure random variable, Burr (۴P) distribution function were presented as the best distribution function. The important point is to not follow the normal distribution above the random variables. Therefore, in order to evaluate the reliability with the FORM method, according to the above distributions, they should be converted into normal variables based on the existing methods. To this end, the non-normal distributions are transformed into the normal distribution by the method of Rackwitz and Fiiessler so that the value of the cumulative distribution function is equivalent to the original abnormal distribution at the design point of x_(i*). This point has the least distance from the origin in the standardized space of the boundary plane or the same limited conditional function. The reliability index will be equal to ۰.۴۲۰۴ before installing the aerator. As a result, reliability, p_s, and failure probability, p_f, are ۰.۶۶۲۹ and ۰.۳۳۷۱, respectively. This number indicates a high percentage for cavitation occurrence. Therefore, the use of aerator is inevitable to prevent imminent damage from cavitation. To deal with cavitation as planned in the laboratory, two aerators with listed specifications are embedded in a location where the cavitation index is critical. In order to analyze the reliability of cavitation occurrence after the aerator installation, the steps of the Hasofer-Lind algorithm are repeated. The modeling of ramps was performed separately in Flow-۳D software in order to compare the performance of aeration ducts as well as the probability of failure between aeration by ramp and the combination of ramps and aeration ducts. Installing an aerator in combination with a ramp and aerator duct greatly reduces the probability of cavitation occurrence. By installing aerator, the probability of cavitation occurrence will decrease in to about ۴ %. However, in the case of aeration only through the ramp, the risk of failure is equal to ۱۰%.

확률적 지정은 수력 공학에서 강력한 도구입니다. 유압 설계에서 임의 현상으로 인한 불확실성이 중요할 수 있습니다. 불확실성은 확률 밀도 함수, 신뢰 구간 또는 표준 편차 또는 무작위 매개변수의 변동 계수와 같은 통계적 토크로 표현될 수 있습니다. 캐비테이션 발생을 제어하는 ​​것은 흐름의 높은 속도와 음압으로 인해 슈트 여수로 설계에서 가장 중요한 요소 중 하나입니다(Azhdary Moghaddam & Hasanalipour Shahrabadi, ۲۰۲۰). 댐의 높이를 높이면 둑의 범람속도가 증가하여 구조물을 위협하고 캐비테이션으로 인한 구조물의 파손을 유발할 수 있다(Chanson, ۲۰۱۳). 캐비테이션은 유체 압력이 증기압에 도달할 때 발생합니다. 높은 속도와 낮은 압력은 캐비테이션을 유발할 수 있으므로, 통기는 캐비테이션을 처리하는 가장 좋은 방법 중 하나로 인식되어 왔습니다(Pettersson, ۲۰۱۲). 본 연구에서는 Darian 댐의 슈트 여수로의 Flow-۳D 수치모델에서 추출된 결과를 고려하여 캐비테이션 발생 확률을 조사하고 그 신뢰성을 조사하였다. 이 수력구조의 설계에서 수력학적 불확실성은 수력성능 해석의 불확실성에 기인할 수 있다. 따라서 신뢰성을 평가하기 위해서는 수력공학 시스템의 불확도 특성에 대한 지식이 필요해 보인다(Yen et al., ۱۹۹۳). 따라서 수력 공학 시스템의 지정 및 작동은 항상 불확실성과 가능한 고장의 영향을 받습니다. 유압 공학 시스템의 신뢰성 ps는 저항 R, 시스템의 부하 L은 다음과 같이 초과됩니다(Chen, ۲۰۱۵): p_s=P(L≤R)(۱) 여기서 P(۰)은 확률입니다. 고장 확률 p_f는 신뢰도 보완이며 다음과 같이 표현됩니다. Mays, ۱۹۸۰ 및 Yen & Tung, ۱۹۹۳). 따라서 신뢰성을 기반으로 제어 방법에서 슈트 여수로의 캐비테이션 발생 확률을 조사할 수 있습니다. 신뢰도 분석에서 확률적 계산은 제한된 조건부 함수 W(X)=W(X_L , X_R)은 다음과 같습니다. p_s=P[W(X_L,X_R)≥۰]= P[W(X)≥۰] (۳) 여기서 X는 부하 및 저항 함수의 기본 랜덤 변수 벡터입니다. 신뢰도 분석에서 W(X)> ۰이면 시스템은 안전하고 W(X) <۰에서는 시스템이 실패합니다. 따라서 표준편차 σ_W에 대한 평균값 μ_W의 비율로 정의되는 신뢰도 지수 β가 사용되며, 제한된 조건부 함수 W(X)는 다음과 같이 정의됩니다(Cornell, ۱۹۶۹). β= μ_W/σ_W (۴) 본 연구는 이란 물연구소의 ۱:۵۰ scale plexiglass로 개발된 모델로부터 얻은 결과를 이용하여 수행하였다. 이 실험 모델에서, 입구 수로와 수렴형 투수 슈트 여수로로 구성되며 슈트 중 캐비테이션 현상에 대처하기 위해 슈트 초기에 ۲۱۱과 ۲۷۰ 간격으로 편향기 형태의 2개의 에어레이터를 사용하였다. 여수로 좌우 벽의 공기 유입구에도 공기 덕트가 사용되었습니다. 캐비테이션의 효과적인 매개변수를 측정하기 위해 7번의 배출이 방수로를 통과했습니다. 압력과 평균 속도가 결정되면 캐비테이션 지수 값이 계산되고 임계 캐비테이션 지수 σ_cr 값과 비교됩니다. σ≤σ_cr일 때 그 범위에서 부식의 위험이 있다(Chanson, ۱۹۹۳). 슈트 중 캐비테이션 발생의 불확실성을 구하고 신뢰도 지수를 계산하기 위해서는 제한된 조건부 함수를 추출할 필요가 있다. 따라서 두 지점 사이의 일정한 흐름에 대해 다음과 같은 Bernoulli(에너지) 관계가 있습니다(Falvey, ۱۹۹۰). σ= ( P_atm/γ- P_V/γ+h cos⁡θ )/(〖V_۰〗 ^۲/۲g) (۵) 여기서 P_atm은 대기압, γ는 물의 단위 중량, θ는 수평선에 대한 경사로의 각도, r은 수직 호의 곡률 반경, h cos⁡ θ는 바닥에 수직인 흐름 깊이입니다. 따라서 제한된 조건부 함수는 다음과 같이 쓸 수 있습니다. W(X)=(P_atm/γ- P_V/γ+h cos⁡θ )/(〖V_۰〗^۲/۲g) -σ_cr (۶) Flow-۳D는 유체 역학의 강력한 소프트웨어. 이 소프트웨어의 주요 기능 중 하나는 수리학적 해석을 위해 유한 체적 방법을 사용하여 자유 표면 흐름을 모델링하는 것입니다. 방수로는 Flow-۳D 소프트웨어에 자세히 설명된 바와 같이 폭기 장치, 램프 폭기 장치 및 폭기 덕트가 있는 램프 조합을 사용하지 않고 세 가지 모드로 모델링되었습니다. 언급된 각 모드에 대해 7개의 방전이 테스트되었습니다. 식 (۶)에 따르면 속도와 압력은 캐비테이션 발생 현상에 결정적이고 중요한 역할을 합니다. 따라서 확률분포함수에 기반한 FORM(First Order Reliable Method)으로 신뢰도를 평가해야 한다 이를 위해 실험실 모델에 대한 속도와 압력의 확률변수 중 가장 적합한 확률분포함수를 Easy fit을 이용하여 구간별로 추출하였다. 소프트웨어. 확률 분포 함수는 제한된 조건부 함수의 다른 변수에 대해서도 정상으로 간주됩니다. 이 값은 단위 중량의 경우 해발 ۵۰۰ ~ ۷۰۰۰ m 고도에서의 일정한 중력과 ۵ ~ ۳۵ ° C에서의 증기압으로 추정됩니다. 임계 캐비테이션 지수 변수의 표준 편차는 ۰.۰۱으로 간주됩니다. . 수행된 시험에 따르면 속도 확률변수는 GEV(Generalized Extreme Value) 분포함수로, 압력변수는 Burr(۴P) 분포함수가 가장 좋은 분포함수로 제시되었다. 중요한 점은 확률 변수 위의 정규 분포를 따르지 않는 것입니다. 따라서 FORM 방법으로 신뢰도를 평가하기 위해서는 위의 분포에 따라 기존 방법을 기반으로 정규 변수로 변환해야 합니다. 이를 위해, 비정규분포를 Rackwitz와 Fiiessler의 방법에 의해 정규분포로 변환하여 누적분포함수의 값이 x_(i*)의 설계점에서 원래의 비정상분포와 같도록 한다. 이 점은 경계면의 표준화된 공간 또는 동일한 제한된 조건부 함수에서 원점으로부터 최소 거리를 갖습니다. 신뢰성 지수는 폭기 장치를 설치하기 전의 ۰.۴۲۰۴과 같습니다. 그 결과 신뢰도 p_s와 고장확률 p_f는 각각 ۰.۶۶۲۹과 ۰.۳۳۷۱이다. 이 숫자는 캐비테이션 발생의 높은 비율을 나타냅니다. 따라서 캐비테이션으로 인한 즉각적인 손상을 방지하기 위해 폭기 장치의 사용이 불가피합니다. 실험실에서 계획한 대로 캐비테이션을 처리하기 위해, 나열된 사양을 가진 두 개의 폭기 장치는 캐비테이션 지수가 중요한 위치에 내장되어 있습니다. 폭기장치 설치 후 캐비테이션 발생의 신뢰성을 분석하기 위해 Hasofer-Lind 알고리즘의 단계를 반복합니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 ​​폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 폭기 설치 후 캐비테이션 발생의 신뢰성을 분석하기 위해 Hasofer-Lind 알고리즘의 단계를 반복합니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 ​​폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 폭기장치 설치 후 캐비테이션 발생의 신뢰성을 분석하기 위해 Hasofer-Lind 알고리즘의 단계를 반복합니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 ​​폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 ​​폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 ​​폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다.

Keywords

Aerator Probable Failure Reliability Method FORM Flow ۳D. 

Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively

추가 생산용 전자빔 조사에 의한 316L 스테인리스 용융 · 응고 거동

Melting and Solidification Behavior of 316L Steel Induced by Electron-Beam Irradiation for Additive Manufacturing

付加製造用電子ビーム照射による 316L ステンレス鋼の溶融・凝固挙動

奥 川 将 行*・宮 田 雄一朗*・王     雷*・能 勢 和 史*
小 泉 雄一郎*・中 野 貴 由*
Masayuki OKUGAWA, Yuichiro MIYATA, Lei WANG, Kazufumi NOSE,
Yuichiro KOIZUMI and Takayoshi NAKANO

Abstract

적층 제조(AM) 기술은 복잡한 형상의 3D 부품을 쉽게 만들고 미세 구조 제어를 통해 재료 특성을 크게 제어할 수 있기 때문에 많은 관심을 받았습니다. PBF(Powderbed fusion) 방식의 AM 공정에서는 금속 분말을 레이저나 전자빔으로 녹이고 응고시키는 과정을 반복하여 3D 부품을 제작합니다.

일반적으로 응고 미세구조는 Hunt[Mater. 과학. 영어 65, 75(1984)]. 그러나 CET 이론이 일반 316L 스테인리스강에서도 높은 G와 R로 인해 PBF형 AM 공정에 적용될 수 있을지는 불확실하다.

본 연구에서는 미세구조와 응고 조건 간의 관계를 밝히기 위해 전자빔 조사에 의해 유도된 316L 강의 응고 미세구조를 분석하고 CtFD(Computational Thermal-Fluid Dynamics) 방법을 사용하여 고체/액체 계면에서의 응고 조건을 평가했습니다.

CET 이론과 반대로 높은 G 조건에서 등축 결정립이 종종 형성되는 것으로 밝혀졌다. CtFD 시뮬레이션은 약 400 mm s-1의 속도까지 유체 흐름이 있음을 보여 주며 수상 돌기의 파편 및 이동의 영향으로 등축 결정립이 형성됨을 시사했습니다.

Additive manufacturing(AM)technologies have attracted much attention because it enables us to build 3D parts with complicated geometry easily and control material properties significantly via the control of microstructures. In the powderbed fusion(PBF)type AM process, 3D parts are fabricated by repeating a process of melting and solidifying metal powders by laser or electron beams. In general, the solidification microstructures can be predicted from solidification conditions defined by the combination of temperature gradient G and solidification rate R on the basis of columnar-equiaxed transition(CET)theory proposed by Hunt [Mater. Sci. Eng. 65, 75(1984)]. However, it is unclear whether the CET theory can be applied to the PBF type AM process because of the high G and R, even for general 316L stainless steel. In this study, to reveal relationships between microstructures and solidification conditions, we have analyzed solidification microstructures of 316L steel induced by electronbeam irradiation and evaluated solidification conditions at the solid/liquid interface using a computational thermal-fluid dynamics (CtFD)method. It was found that equiaxed grains were often formed under high G conditions contrary to the CET theory. CtFD simulation revealed that there is a fluid flow up to a velocity of about 400 mm s-1, and suggested that equiaxed grains are formed owing to the effect of fragmentations and migrations of dendrites.

Keywords

Additive Manufacturing, 316L Stainless Steel, Powder Bed Fusion, Electron Beam Melting, Computational Thermal
Fluid Dynamics Simulation

Fig. 1 Width, height, and height differences calculated from laser microscope analysis of melt tracks formed by scanning electron beam. Fig. 2(a)Scanning electron microscope(SEM)image and(b) corresponding electron back-scattering diffraction(EBSD) IPF-map taken from the electron-beam irradiated region in P900-V100 sample. Fig. 3 Average grain size and their aspect ratio calculated from EBSD IPF-map taken from the electron-beam irradiated region.
Fig. 1 Width, height, and height differences calculated from laser microscope analysis of melt tracks formed by scanning electron beam. Fig. 2(a)Scanning electron microscope(SEM)image and(b) corresponding electron back-scattering diffraction(EBSD) IPF-map taken from the electron-beam irradiated region in P900-V100 sample. Fig. 3 Average grain size and their aspect ratio calculated from EBSD IPF-map taken from the electron-beam irradiated region.
Fig. 4 Comparison of experimental SEM image and computational thermal fluid dynamics(CtFD)simulated melt pool with a beam diameter of 700 μm and absorption rates of(a)0.3,(b)0.5, and (c)0.7. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively.
Fig. 4 Comparison of experimental SEM image and computational thermal fluid dynamics(CtFD)simulated melt pool with a beam diameter of 700 μm and absorption rates of(a)0.3,(b)0.5, and (c)0.7. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively.
Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively
Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively
Fig. 6 Depth of melt tracks calculated from experimental SEM image and CtFD simulation results.
Fig. 6 Depth of melt tracks calculated from experimental SEM image and CtFD simulation results.
Fig. 7 G-R plots of 316L steel colored by(a)aspect ratio of crystalline grains and(b)fluid velocity.
Fig. 7 G-R plots of 316L steel colored by(a)aspect ratio of crystalline grains and(b)fluid velocity.
Fig. 8 Comparison of solidification microstructure(EBSD IPF-map)of melt region formed by scanning electron beam and corresponding snap shot of CtFD simulation colored by fluid velocity
Fig. 8 Comparison of solidification microstructure(EBSD IPF-map)of melt region formed by scanning electron beam and corresponding snap shot of CtFD simulation colored by fluid velocity

References

1) M.C. Sow, T. De Terris, O. Castelnau, Z. Hamouche, F. Coste, R.
Fabbro and P. Peyre: “Influence of beam diameter on Laser Powder

Bed Fusion(L-PBF)process”, Addit. Manuf. 36(2020), 101532.
2) J.C. Simmons, X. Chen, A. Azizi, M.A. Daeumer, P.Y. Zavalij, G.
Zhou and S.N. Schiffres: “Influence of processing and microstructure
on the local and bulk thermal conductivity of selective laser melted
316L stainless steel”, Addit. Manuf. 32(2020), 100996.
3) S. Dryepondt, P. Nandwana, P. Fernandez-Zelaia and F. List:
“Microstructure and High Temperature Tensile properties of 316L
Fabricated by Laser Powder-Bed Fusion”, Addit. Manuf. 37(2020),
101723.
4) S.H. Sun, T. Ishimoto, K. Hagihara, Y. Tsutsumi, T. Hanawa and T.
Nakano: “Excellent mechanical and corrosion properties of austenitic
stainless steel with a unique crystallographic lamellar microstructure
via selective laser melting”, Scr. Mater. 159(2019), 89-93.
5) T. Ishimoto, S. Wu, Y. Ito, S.H. Sun, H. Amano and T. Nakano:
“Crystallographic orientation control of 316L austenitic stainless
steel via selective laser melting”, ISIJ Int. 60(2020), 1758-1764.
6) T. Ishimoto, K. Hagihara, K. Hisamoto, S.H. Sun and T. Nakano:
“Crystallographic texture control of beta-type Ti-15Mo-5Zr3Al alloy by selective laser melting for the development of novel
implants with a biocompatible low Young’s modulus”, Scr. Mater.
132(2017), 34-38.
7) X. Ding, Y. Koizumi, D. Wei and A. Chiba: “Effect of process
parameters on melt pool geometry and microstructure development
for electron beam melting of IN718: A systematic single bead
analysis study”, Addit. Manuf. 26(2019), 215-226.
8) K. Karayagiz, L. Johnson, R. Seede, V. Attari, B. Zhang, X. Huang,
S. Ghosh, T. Duong, I. Karaman, A. Elwany and R. Arróyave: “Finite
interface dissipation phase field modeling of Ni-Nb under additive
manufacturing conditions”, Acta Mater. 185(2020), 320-339.
9) M.M. Kirka, Y. Lee, D.A. Greeley, A. Okello, M.J. Goin, M.T.
Pearce and R.R. Dehoff: “Strategy for Texture Management in
Metals Additive Manufacturing”, JOM, 69(2017), 523-531.
10) S.S. Babu, N. Raghavan, J. Raplee, S.J. Foster, C. Frederick, M.
Haines, R. Dinwiddie, M.K. Kirka, A. Plotkowski, Y. Lee and
R.R. Dehoff: “Additive Manufacturing of Nickel Superalloys:
Opportunities for Innovation and Challenges Related to
Qualification”, Metall. Mater. Trans. A. 49(2018), 3764-3780.
11) M.R. Gotterbarm, A.M. Rausch and C. Körner: “Fabrication of
Single Crystals through a μ-Helix Grain Selection Process during
Electron Beam Metal Additive Manufacturing”, Metals, 10(2020),
313.
12) J.D.D. Hunt: “Steady state columnar and equiaxed growth of
dendrites and eutectic”, Mater. Sci. Eng. 65(1984), 75-83.
13) S. Bontha, N.W. Klingbeil, P.A. Kobryn and H.L. Fraser: “Effects of
process variables and size-scale on solidification microstructure in
beam-based fabrication of bulky 3D structures”, Mater. Sci. Eng. A.
513-514(2009), 311-318.
14) J. Gockel and J. Beuth: “Understanding Ti-6Al-4V microstructure
control in additive manufacturing via process maps”, 24th Int. SFF
Symp. – An Addit. Manuf. Conf. SFF 2013.(2013), 666-674.
15) B. Schoinochoritis, D. Chantzis and K. Salonitis: “Simulation of
metallic powder bed additive manufacturing processes with the finite
element method: A critical review”, Proc. of Instit. Mech. Eng., Part
B: J. Eng. Manuf. 231(2017), 96-117.
16)小泉雄一郎: “計算機シミュレーションを用いたAdditive
Manufacturing プロセス最適化予測”, スマートプロセス学会誌,
8-4(2019), 132-138.
17) Y. Zhao, Y. Koizumi, K. Aoyagi, D. Wei, K. Yamanaka and A. Chiba:
“Molten pool behavior and effect of fluid flow on solidification
conditions in selective electron beam melting(SEBM)of a
biomedical Co-Cr-Mo alloy”, Addit. Manuf. 26(2019), 202-214.
18) C. Tang, J.L. Tan and C.H. Wong: “A numerical investigation on
the physical mechanisms of single track defects in selective laser
melting”, Int. J. Heat Mass Transf. 126(2018), 957-968.
19) Technical data for Iron, [Online]. Available: http://periodictable.com/
Elements/026/data.html. [Accessed: 8-Feb-2021].
20) N. Raghavan, R. Dehoff, S. Pannala, S. Simunovic, M. Kirka, J.
Turner, N. Carl-son and S.S. Babu: “Numerical modeling of heattransfer and the influence of process parameters on tailoring the grain
morphology of IN718 in electron beam additive manufacturing”,
Acta Mater. 112(2016), 303-314.
21) S. Morita, Y. Miki and K. Toishi: “Introduction of Dendrite
Fragmentation to Microstructure Calculation by Cellular Automaton
Method”, Tetsu-to-Hagane. 104(2018), 559-566.
22) H. Esaka and M. Tamura: “Model Experiment Using Succinonitrile
on the Formation of Equiaxed Grains caused by Forced Convection”,
Tetsu-to-Hagane. 86(2000), 252-258.

Fig. 1. Hydraulic jump flow structure.

Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump

낮은 레이놀즈 수 유압 점프의 수치 모델링에서 OpenFOAM 및 FLOW-3D의 성능 평가

ArnauBayona DanielValerob RafaelGarcía-Bartuala Francisco ​JoséVallés-Morána P. AmparoLópez-Jiméneza

Abstract

A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-ε. A Volume Of Fluid (VOF) method is used to track the air–water interface, consequently aeration is modeled using an Eulerian–Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers.

CFD 플랫폼 OpenFOAM 및 FLOW-3D의 비교 성능 분석이 3D 소용돌이치는 난류인 낮은 레이놀즈 수에서 안정적인 유압 점프에 초점을 맞춰 제시됩니다. 난류는 RANS 접근법 RNG k-ε을 사용하여 처리됩니다.

VOF(Volume Of Fluid) 방법은 공기-물 계면을 추적하는 데 사용되며 결과적으로 Eulerian-Eulerian 접근 방식을 사용하여 폭기가 모델링됩니다. 입방체 요소의 구조화된 메쉬는 채널 형상을 이산화하는 데 사용됩니다. 수치 모델 정확도는 대표적인 유압 점프 변수(연속 깊이 비율, 롤러 길이, 평균 속도 프로파일, 속도 감쇠 또는 자유 표면 프로파일)를 실험 데이터와 비교하여 평가됩니다.

모델 결과는 또한 결과 검증을 확장하기 위해 이전 연구와 비교됩니다. 소용돌이 흐름이 발생할 때 특별한 주의가 필요하지만 두 코드 모두 실험 데이터와 일치하는 연구 중인 현상을 재현했습니다. 두 모델 모두 낮은 레이놀즈 수에서 에너지 소산 구조의 수리 성능을 재현하는 데 사용할 수 있습니다.

Keywords

CFDRANS, OpenFOAM, FLOW-3D ,Hydraulic jump, Air–water flow, Low Reynolds number

References

Ahmed, F., Rajaratnam, N., 1997. Three-dimensional turbulent boundary layers: a
review. J. Hydraulic Res. 35 (1), 81e98.
Ashgriz, N., Poo, J., 1991. FLAIR: Flux line-segment model for advection and interface
reconstruction. Elsevier J. Comput. Phys. 93 (2), 449e468.
Bakhmeteff, B.A., Matzke, A.E., 1936. .The hydraulic jump in terms dynamic similarity. ASCE Trans. Am. Soc. Civ. Eng. 101 (1), 630e647.
Balachandar, S., Eaton, J.K., 2010. Turbulent dispersed multiphase flow. Annu. Rev.
Fluid Mech. 42 (2010), 111e133.
Bayon, A., Lopez-Jimenez, P.A., 2015. Numerical analysis of hydraulic jumps using

OpenFOAM. J. Hydroinformatics 17 (4), 662e678.
Belanger, J., 1841. Notes surl’Hydraulique, Ecole Royale des Ponts et Chaussees
(Paris, France).
Bennett, N.D., Crok, B.F.W., Guariso, G., Guillaume, J.H.A., Hamilton, S.H.,
Jakeman, A.J., Marsili-Libelli, S., Newhama, L.T.H., Norton, J.P., Perrin, C.,
Pierce, S.A., Robson, B., Seppelt, R., Voinov, A.A., Fath, B.D., Andreassian, V., 2013.
Characterising performance of environmental models. Environ. Model. Softw.
40, 1e20.
Berberovic, E., 2010. Investigation of Free-surface Flow Associated with Drop
Impact: Numerical Simulations and Theoretical Modeling. Imperial College of
Science, Technology and Medicine, UK.
Bidone, G., 1819. Report to Academie Royale des Sciences de Turin, s  eance. Le 
Remou et sur la Propagation des Ondes, 12, pp. 21e112.
Biswas, R., Strawn, R.C., 1998. Tetrahedral and hexahedral mesh adaptation for CFD
problems. Elsevier Appl. Numer. Math. 26 (1), 135e151.
Blocken, B., Gualtieri, C., 2012. Ten iterative steps for model development and
evaluation applied to computational fluid dynamics for environmental fluid
mechanics. Environ. Model. Softw. 33, 1e22.
Bombardelli, F.A., Meireles, I., Matos, J., 2011. Laboratory measurements and multiblock numerical simulations of the mean flow and turbulence in the nonaerated skimming flow region of steep stepped spillways. Springer Environ.
Fluid Mech. 11 (3), 263e288.
Bombardelli, F.A., 2012. Computational multi-phase fluid dynamics to address flows
past hydraulic structures. In: 4th IAHR International Symposium on Hydraulic
Structures, 9e11 February 2012, Porto, Portugal, 978-989-8509-01-7.
Borges, J.E., Pereira, N.H., Matos, J., Frizell, K.H., 2010. Performance of a combined
three-hole conductivity probe for void fraction and velocity measurement in
airewater flows. Exp. fluids 48 (1), 17e31.
Borue, V., Orszag, S., Staroslesky, I., 1995. Interaction of surface waves with turbulence: direct numerical simulations of turbulent open channel flow. J. Fluid
Mech. 286, 1e23.
Boussinesq, J., 1871. Theorie de l’intumescence liquide, applelee onde solitaire ou de
translation, se propageantdans un canal rectangulaire. Comptes Rendus l’Academie Sci. 72, 755e759.
Bradley, J.N., Peterka, A.J., 1957. The hydraulic design of stilling Basins : hydraulic
jumps on a horizontal Apron (Basin I). In: Proceedings ASCE, J. Hydraulics
Division.
Bradshaw, P., 1996. Understanding and prediction of turbulent flow. Elsevier Int. J.
heat fluid flow 18 (1), 45e54.
Bung, D.B., 2013. Non-intrusive detection of airewater surface roughness in selfaerated chute flows. J. Hydraulic Res. 51 (3), 322e329.
Bung, D., Schlenkhoff, A., 2010. Self-aerated Skimming Flow on Embankment
Stepped Spillways-the Effect of Additional Micro-roughness on Energy Dissipation and Oxygen Transfer. IAHR European Congress.
Caisley, M.E., Bombardelli, F.A., Garcia, M.H., 1999. Hydraulic Model Study of a Canoe
Chute for Low-head Dams in Illinois. Civil Engineering Studies, Hydraulic Engineering Series No-63. University of Illinois at Urbana-Champaign.
Carvalho, R., Lemos, C., Ramos, C., 2008. Numerical computation of the flow in
hydraulic jump stilling basins. J. Hydraulic Res. 46 (6), 739e752.
Celik, I.B., Ghia, U., Roache, P.J., 2008. Procedure for estimation and reporting of
uncertainty due to discretization in CFD applications. ASME J. Fluids Eng. 130
(7), 1e4.
Chachereau, Y., Chanson, H., 2011. .Free-surface fluctuations and turbulence in hydraulic jumps. Exp. Therm. Fluid Sci. 35 (6), 896e909.
Chanson, H. (Ed.), 2015. Energy Dissipation in Hydraulic Structures. CRC Press.
Chanson, H., 2007. Bubbly flow structure in hydraulic jump. Eur. J. Mechanics-B/
Fluids 26.3(2007) 367e384.
Chanson, H., Carvalho, R., 2015. Hydraulic jumps and stilling basins. Chapter 4. In:
Chanson, H. (Ed.), Energy Dissipation in Hydraulic Structures. CRC Press, Taylor
& Francis Group, ABalkema Book.
Chanson, H., Gualtieri, C., 2008. Similitude and scale effects of air entrainment in
hydraulic jumps. J. Hydraulic Res. 46 (1), 35e44.
Chanson, H., Lubin, P., 2010. Discussion of “Verification and validation of a
computational fluid dynamics (CFD) model for air entrainment at spillway
aerators” Appears in the Canadian Journal of Civil Engineering 36(5): 826-838.
Can. J. Civ. Eng. 37 (1), 135e138.
Chanson, H., 1994. Drag reduction in open channel flow by aeration and suspended
load. Taylor & Francis J. Hydraulic Res. 32, 87e101.
Chanson, H., Montes, J.S., 1995. Characteristics of undular hydraulic jumps: experimental apparatus and flow patterns. J. hydraulic Eng. 121 (2), 129e144.
Chanson, H., Brattberg, T., 2000. Experimental study of the airewater shear flow in
a hydraulic jump. Int. J. Multiph. Flow 26 (4), 583e607.
Chanson, H., 2013. Hydraulics of aerated flows: qui pro quo? Taylor & Francis
J. Hydraulic Res. 51 (3), 223e243.
Chaudhry, M.H., 2007. Open-channel Flow, Springer Science & Business Media.
Chen, L., Li, Y., 1998. .A numerical method for two-phase flows with an interface.
Environ. Model. Softw. 13 (3), 247e255.
Chow, V.T., 1959. Open Channel Hydraulics. McGraw-Hill Book Company, Inc, New
York.
Daly, B.J., 1969. A technique for including surface tension effects in hydrodynamic
calculations. Elsevier J. Comput. Phys. 4 (1), 97e117.
De Padova, D., Mossa, M., Sibilla, S., Torti, E., 2013. 3D SPH modeling of hydraulic
jump in a very large channel. Taylor & Francis J. Hydraulic Res. 51 (2), 158e173.
Dewals, B., Andre, S., Schleiss, A., Pirotton, M., 2004. Validation of a quasi-2D model 
for aerated flows over stepped spillways for mild and steep slopes. Proc. 6th Int.
Conf. Hydroinformatics 1, 63e70.
Falvey, H.T., 1980. Air-water flow in hydraulic structures. NASA STI Recon Tech. Rep.
N. 81, 26429.
Fawer, C., 1937. Etude de quelquesecoulements permanents 
a filets courbes (‘Study
of some Steady Flows with Curved Streamlines’). Thesis. Imprimerie La Concorde, Lausanne, Switzerland, 127 pages (in French).
Gualtieri, C., Chanson, H., 2007. .Experimental analysis of Froude number effect on
air entrainment in the hydraulic jump. Springer Environ. Fluid Mech. 7 (3),
217e238.
Gualtieri, C., Chanson, H., 2010. Effect of Froude number on bubble clustering in a
hydraulic jump. J. Hydraulic Res. 48 (4), 504e508.
Hager, W., Sinniger, R., 1985. Flow characteristics of the hydraulic jump in a stilling
basin with an abrupt bottom rise. Taylor & Francis J. Hydraulic Res. 23 (2),
101e113.
Hager, W.H., 1992. Energy Dissipators and Hydraulic Jump, Springer.
Hager, W.H., Bremen, R., 1989. Classical hydraulic jump: sequent depths. J. Hydraulic
Res. 27 (5), 565e583.
Hartanto, I.M., Beevers, L., Popescu, I., Wright, N.G., 2011. Application of a coastal
modelling code in fluvial environments. Environ. Model. Softw. 26 (12),
1685e1695.
Hirsch, C., 2007. Numerical Computation of Internal and External Flows: the Fundamentals of Computational Fluid Dynamics. Butterworth-Heinemann, 1.
Hirt, C., Nichols, B., 1981. .Volume of fluid (VOF) method for the dynamics of free
boundaries. J. Comput. Phys. 39 (1), 201e225.
Hyman, J.M., 1984. Numerical methods for tracking interfaces. Elsevier Phys. D.
Nonlinear Phenom. 12 (1), 396e407.
Juez, C., Murillo, J., Garcia-Navarro, P., 2013. Numerical assessment of bed-load
discharge formulations for transient flow in 1D and 2D situations.
J. Hydroinformatics 15 (4).
Keyes, D., Ecer, A., Satofuka, N., Fox, P., Periaux, J., 2000. Parallel Computational Fluid
Dynamics’ 99: towards Teraflops, Optimization and Novel Formulations.
Elsevier.
Kim, J.J., Baik, J.J., 2004. A numerical study of the effects of ambient wind direction
on flow and dispersion in urban street canyons using the RNG keε turbulence
model. Atmos. Environ. 38 (19), 3039e3048.
Kim, S.-E., Boysan, F., 1999. Application of CFD to environmental flows. Elsevier
J. Wind Eng. Industrial Aerodynamics 81 (1), 145e158.
Liu, M., Rajaratnam, N., Zhu, D.Z., 2004. Turbulence structure of hydraulic jumps of
low Froude numbers. J. Hydraulic Eng. 130 (6), 511e520.
Lobosco, R., Schulz, H., Simoes, A., 2011. Analysis of Two Phase Flows on Stepped
Spillways, Hydrodynamics – Optimizing Methods and Tools. Available from. :
http://www.intechopen.com/books/hyd rodynamics-optimizing-methods-andtools/analysis-of-two-phase-flows-on-stepped-spillways. Accessed February
27th 2014.
Long, D., Rajaratnam, N., Steffler, P.M., Smy, P.R., 1991. Structure of flow in hydraulic
jumps. Taylor & Francis J. Hydraulic Res. 29 (2), 207e218.
Ma, J., Oberai, A.A., Lahey Jr., R.T., Drew, D.A., 2011. Modeling air entrainment and
transport in a hydraulic jump using two-fluid RANS and DES turbulence
models. Heat Mass Transf. 47 (8), 911e919.
Matos, J., Frizell, K., Andre, S., Frizell, K., 2002. On the performance of velocity 
measurement techniques in air-water flows. Hydraulic Meas. Exp. Methods
2002, 1e11. http://dx.doi.org/10.1061/40655(2002)58.
Meireles, I.C., Bombardelli, F.A., Matos, J., 2014. .Air entrainment onset in skimming
flows on steep stepped spillways: an analysis. J. Hydraulic Res. 52 (3), 375e385.
McDonald, P., 1971. The Computation of Transonic Flow through Two-dimensional
Gas Turbine Cascades.
Mossa, M., 1999. On the oscillating characteristics of hydraulic jumps, Journal of
Hydraulic Research. Taylor &Francis 37 (4), 541e558.
Murzyn, F., Chanson, H., 2009a. Two-phase Gas-liquid Flow Properties in the Hydraulic Jump: Review and Perspectives. Nova Science Publishers.
Murzyn, F., Chanson, H., 2009b. Experimental investigation of bubbly flow and
turbulence in hydraulic jumps. Environ. Fluid Mech. 2, 143e159.
Murzyn, F., Mouaze, D., Chaplin, J.R., 2007. Airewater interface dynamic and free
surface features in hydraulic jumps. J. Hydraulic Res. 45 (5), 679e685.
Murzyn, F., Mouaze, D., Chaplin, J., 2005. Optical fiber probe measurements of
bubbly flow in hydraulic jumps. Elsevier Int. J. Multiph. Flow 31 (1), 141e154.
Nagosa, R., 1999. Direct numerical simulation of vortex structures and turbulence
scalar transfer across a free surface in a fully developed turbulence. Phys. Fluids
11, 1581e1595.
Noh, W.F., Woodward, P., 1976. SLIC (Simple Line Interface Calculation), Proceedings
of the Fifth International Conference on Numerical Methods in Fluid Dynamics
June 28-July 2. 1976 Twente University, Enschede, pp. 330e340.
Oertel, M., Bung, D.B., 2012. Initial stage of two-dimensional dam-break waves:
laboratory versus VOF. J. Hydraulic Res. 50 (1), 89e97.
Olivari, D., Benocci, C., 2010. Introduction to Mechanics of Turbulence. Von Karman
Institute for Fluid Dynamics.
Omid, M.H., Omid, M., Varaki, M.E., 2005. Modelling hydraulic jumps with artificial
neural networks. Thomas Telford Proc. ICE-Water Manag. 158 (2), 65e70.
OpenFOAM, 2011. OpenFOAM: the Open Source CFD Toolbox User Guide. The Free
Software Foundation Inc.
Peterka, A.J., 1984. Hydraulic design of spillways and energy dissipators. A water
resources technical publication. Eng. Monogr. 25.
Pope, S.B., 2000. Turbulent Flows. Cambridge university press.
Pfister, M., 2011. Chute aerators: steep deflectors and cavity subpressure, Journal of
hydraulic engineering. Am. Soc. Civ. Eng. 137 (10), 1208e1215.
Prosperetti, A., Tryggvason, G., 2007. Computational Methods for Multiphase Flow.
Cambridge University Press.
Rajaratnam, N., 1965. The hydraulic jump as a Wall Jet. Proc. ASCE, J. Hydraul. Div. 91
(HY5), 107e132.
Resch, F., Leutheusser, H., 1972. Reynolds stress measurements in hydraulic jumps.
Taylor & Francis J. Hydraulic Res. 10 (4), 409e430.
Romagnoli, M., Portapila, M., Morvan, H., 2009. Computational simulation of a
hydraulic jump (original title, in Spanish: “Simulacioncomputacional del
resaltohidraulico”), MecanicaComputacional, XXVIII, pp. 1661e1672.
Rouse, H., Siao, T.T., Nagaratnam, S., 1959. Turbulence characteristics of the hydraulic jump. Trans. ASCE 124, 926e966.
Rusche, H., 2002. Computational Fluid Dynamics of Dispersed Two-phase Flows at
High Phase Fractions. Imperial College of Science, Technology and Medicine, UK.
Saint-Venant, A., 1871. Theorie du movement non permanent des eaux, avec
application aux crues des riviereset a l’introduction de mareesdansleurslits.
Comptesrendus des seances de l’Academie des Sciences.
Schlichting, H., Gersten, K., 2000. Boundary-layer Theory. Springer.
Spalart, P.R., 2000. Strategies for turbulence modelling and simulations. Int. J. Heat
Fluid Flow 21 (3), 252e263.
Speziale, C.G., Thangam, S., 1992. Analysis of an RNG based turbulence model for
separated flows. Int. J. Eng. Sci. 30 (10), 1379eIN4.
Toge, G.E., 2012. The Significance of Froude Number in Vertical Pipes: a CFD Study.
University of Stavanger, Norway.
Ubbink, O., 1997. Numerical Prediction of Two Fluid Systems with Sharp Interfaces.
Imperial College of Science, Technology and Medicine, UK.
Valero, D., García-Bartual, R., 2016. Calibration of an air entrainment model for CFD
spillway applications. Adv. Hydroinformatics 571e582. http://dx.doi.org/
10.1007/978-981-287-615-7_38. P. Gourbesville et al. Springer Water.
Valero, D., Bung, D.B., 2015. Hybrid investigations of air transport processes in
moderately sloped stepped spillway flows. In: E-Proceedings of the 36th IAHR
World Congress, 28 June e 3 July, 2015 (The Hague, the Netherlands).
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), 263e275.
Von Karman, T., 1930. MechanischeAhnlichkeit und Turbulenz, Nachrichten von der
Gesellschaft der WissenschaftenzuGottingen. Fachgr. 1 Math. 5, 58 € e76.
Wang, H., Murzyn, F., Chanson, H., 2014a. Total pressure fluctuations and two-phase
flow turbulence in hydraulic jumps. Exp. Fluids 55.11(2014) Pap. 1847, 1e16
(DOI: 10.1007/s00348-014-1847-9).
Wang, H., Felder, S., Chanson, H., 2014b. An experimental study of turbulent twophase flow in hydraulic jumps and application of a triple decomposition
technique. Exp. Fluids 55.7(2014) Pap. 1775, 1e18. http://dx.doi.org/10.1007/
s00348-014-1775-8.
Wang, H., Chanson, H., 2015a. .Experimental study of turbulent fluctuations in
hydraulic jumps. J. Hydraul. Eng. 141 (7) http://dx.doi.org/10.1061/(ASCE)
HY.1943-7900.0001010. Paper 04015010, 10 pages.
Wang, H., Chanson, H., 2015b. Integral turbulent length and time scales in hydraulic
jumps: an experimental investigation at large Reynolds numbers. In: E-Proceedings of the 36th IAHR World Congress 28 June e 3 July, 2015, The
Netherlands.
Weller, H., Tabor, G., Jasak, H., Fureby, C., 1998. A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys.
12, 620e631.
Wilcox, D., 1998. Turbulence Modeling for CFD, DCW Industries. La Canada, California (USA).
Witt, A., Gulliver, J., Shen, L., June 2015. Simulating air entrainment and vortex
dynamics in a hydraulic jump. Int. J. Multiph. Flow 72, 165e180. ISSN 0301-

  1. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2015.02.012. http://www.
    sciencedirect.com/science/article/pii/S0301932215000336.
    Wood, I.R., 1991. Air Entrainment in Free-surface Flows, IAHR Hydraulic Design
    Manual No.4, Hydraulic Design Considerations. Balkema Publications, Rotterdam, The Netherlands.
    Yakhot, V., Orszag, S., Thangam, S., Gatski, T., Speziale, C., 1992. Development of
    turbulence models for shear flows by a double expansion technique, Physics of
    Fluids A: fluid Dynamics (1989-1993). AIP Publ. 4 (7), 1510e1520.
    Youngs, D.L., 1984. An interface tracking method for a 3D Eulerian hydrodynamics
    code. Tech. Rep. 44 (92), 35e35.
    Zhang, G., Wang, H., Chanson, H., 2013. Turbulence and aeration in hydraulic jumps:
    free-surface fluctuation and integral turbulent scale measurements. Environ.
    fluid Mech. 13 (2), 189e204.
    Zhang, W., Liu, M., Zhu, D.Z., Rajaratnam, N., 2014. Mean and turbulent bubble
    velocities in free hydraulic jumps for small to intermediate froude numbers.
    J. Hydraulic Eng.
Stability and deformations of deposited layers in material extrusion additive manufacturing

Conflict resolution in the multi-stakeholder stepped spillway design under uncertainty by machine learning techniques

Md TusherMollah, Raphaël Comminal, Marcin P.Serdeczny, David B.Pedersen, Jon Spangenberg
Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark

Abstract

This paper presents computational fluid dynamics simulations of the deposition flow during printing of multiple layers in material extrusion additive manufacturing. The developed model predicts the morphology of the deposited layers and captures the layer deformations during the printing of viscoplastic materials. The physics is governed by the continuity and momentum equations with the Bingham constitutive model, formulated as a generalized Newtonian fluid. The cross-sectional shapes of the deposited layers are predicted, and the deformation of layers is studied for different constitutive parameters of the material. It is shown that the deformation of layers is due to the hydrostatic pressure of the printed material, as well as the extrusion pressure during the extrusion. The simulations show that a higher yield stress results in prints with less deformations, while a higher plastic viscosity leads to larger deformations in the deposited layers. Moreover, the influence of the printing speed, extrusion speed, layer height, and nozzle diameter on the deformation of the printed layers is investigated. Finally, the model provides a conservative estimate of the required increase in yield stress that a viscoplastic material demands after deposition in order to support the hydrostatic and extrusion pressure of the subsequently printed layers.

이 논문은 재료 압출 적층 제조에서 여러 레이어를 인쇄하는 동안 증착 흐름의 전산 유체 역학 시뮬레이션을 제공합니다. 개발된 모델은 증착된 레이어의 형태를 예측하고 점소성 재료를 인쇄하는 동안 레이어 변형을 캡처합니다.

물리학은 일반화된 뉴턴 유체로 공식화된 Bingham 구성 모델의 연속성 및 운동량 방정식에 의해 제어됩니다. 증착된 층의 단면 모양이 예측되고 재료의 다양한 구성 매개변수에 대해 층의 변형이 연구됩니다. 층의 변형은 인쇄물의 정수압과 압출시 압출압력으로 인한 것임을 알 수 있다.

시뮬레이션에 따르면 항복 응력이 높을수록 변형이 적은 인쇄물이 생성되는 반면 플라스틱 점도가 높을수록 증착된 레이어에서 변형이 커집니다. 또한 인쇄 속도, 압출 속도, 층 높이 및 노즐 직경이 인쇄된 층의 변형에 미치는 영향을 조사했습니다.

마지막으로, 이 모델은 후속 인쇄된 레이어의 정수압 및 압출 압력을 지원하기 위해 증착 후 점소성 재료가 요구하는 항복 응력의 필요한 증가에 대한 보수적인 추정치를 제공합니다.

Stability and deformations of deposited layers in material extrusion additive manufacturing
Stability and deformations of deposited layers in material extrusion additive manufacturing

Keywords

Viscoplastic MaterialsMaterial Extrusion Additive Manufacturing (MEX-AM)Multiple-Layers DepositionComputational Fluid Dynamics (CFD)Deformation Control

The Optimal Operation on Auxiliary Spillway to Minimize the Flood Damage in Downstream River with Various Outflow Conditions

류하천의 영향 최소화를 위한 보조 여수로 최적 활용방안 검토

Hyung Ju Yoo1 Sung Sik Joo2 Beom Jae Kwon3 Seung Oh Lee4*
유 형주1 주 성식2 권 범재3 이 승오4*
1Ph.D Student, Dept. of Civil & Environmental Engineering, Hongik University2Director, Water Resources & Environment Department, HECOREA3Director, Water Resources Department, ISAN4Professor, Dept. of Civil & Environmental Engineering, Hongik University
1홍익대학교 건설환경공학과 박사과정
2㈜헥코리아 수자원환경사업부 이사
3㈜이산 수자원부 이사
4홍익대학교 건설환경공학과 교수*Corresponding Author

ABSTRACT

최근 기후변화로 인해 강우강도 및 빈도의 증가에 따른 집중호우의 영향 및 기존 여수로의 노후화에 대비하여 홍수 시 하류 하천의 영향을 최소화할 수 있는 보조 여수로 활용방안 구축이 필요한 실정이다. 이를 위해, 수리모형 실험 및 수치모형 실험을 통하여 보조 여수로 운영에 따른 흐름특성 변화 검토에 관한 연구가 많이 진행되어 왔다.

그러나 대부분의 연구는 여수로에서의 흐름특성 및 기능성에 대한 검토를 수행하였을 뿐 보조 여수로의 활용방안에 따른 하류하천 영향 검토 및 호안 안정성 검토에 관한 연구는 미비한 실정이다.

이에 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류영향 분석 및 호안 안정성 측면에서 최적 방류 시나리오 검토를 3차원 수치모형인 FLOW-3D를 사용하여 검토하였다. 또한 FLOW-3D 수치모의 수행을 통한 유속, 수위 결과와 소류력 산정 결과를 호안 설계허용 기준과 비교하였다.

수문 완전 개도 조건으로 가정하고 계획홍수량 유입 시 다양한 보조 여수로 활용방안에 대하여 수치모의를 수행한 결과, 보조 여수로 단독 운영 시 기존 여수로 단독운영에 비하여 최대유속 및 최대 수위의 감소효과를 확인하였다. 다만 계획홍수량의 45% 이하 방류 조건에서 대안부의 호안 안정성을 확보하였고 해당 방류량 초과 경우에는 처오름 현상이 발생하여 월류에 대한 위험성 증가를 확인하였다.

따라서 기존 여수로와의 동시 운영 방안 도출이 중요하다고 판단하였다. 여수로의 배분 비율 및 총 허용 방류량에 대하여 검토한 결과 보조 여수로의 방류량이 기존 여수로의 방류량보다 큰 경우 하류하천의 흐름이 중심으로 집중되어 대안부의 유속 저감 및 수위 감소를 확인하였고, 계획 홍수량의 77% 이하의 조건에서 호안의 허용 유속 및 허용 소류력 조건을 만족하였다.

이를 통하여 본 연구에서 제안한 보조 여수로 활용방안으로는 기존 여수로와 동시 운영 시 총 방류량에 대하여 보조 여수로의 배분량이 기존 여수로의 배분량보다 크게 설정하는 것이 하류하천의 영향을 최소화 할 수 있는 것으로 나타났다.

그러나 본 연구는 여수로 방류에 따른 대안부에서의 영향에 대해서만 검토하였고 수문 전면 개도 조건에서 검토하였다는 한계점은 분명히 있다. 이에 향후에는 다양한 수문 개도 조건 및 방류 시나리오를 적용 및 검토한다면 보다 효율적이고, 효과적인 보조 여수로 활용방안을 도출이 가능할 것으로 기대 된다.

키워드

보조 여수로, FLOW-3D, 수치모의, 호안 안정성, 소류력

Recently, as the occurrence frequency of sudden floods due to climate change increased and the aging of the existing spillway, it is necessary to establish a plan to utilize an auxiliary spillway to minimize the flood damage of downstream rivers. Most studies have been conducted on the review of flow characteristics according to the operation of auxiliary spillway through the hydraulic experiments and numerical modeling. However, the studies on examination of flood damage in the downstream rivers and the stability of the revetment according to the operation of the auxiliary spillway were relatively insufficient in the literature. In this study, the stability of the revetment on the downstream river according to the outflow conditions of the existing and auxiliary spillway was examined by using 3D numerical model, FLOW-3D. The velocity, water surface elevation and shear stress results of FLOW-3D were compared with the permissible velocity and shear stress of design criteria. It was assumed the sluice gate was fully opened. As a result of numerical simulations of various auxiliary spillway operations during flood season, the single operation of the auxiliary spillway showed the reduction effect of maximum velocity and the water surface elevation compared with the single operation of the existing spillway. The stability of the revetment on downstream was satisfied under the condition of outflow less than 45% of the design flood discharge. However, the potential overtopping damage was confirmed in the case of exceeding the 45% of the design flood discharge. Therefore, the simultaneous operation with the existing spillway was important to ensure the stability on design flood discharge condition. As a result of examining the allocation ratio and the total allowable outflow, the reduction effect of maximum velocity was confirmed on the condition, where the amount of outflow on auxiliary spillway was more than that on existing spillway. It is because the flow of downstream rivers was concentrated in the center due to the outflow of existing spillway. The permissible velocity and shear stress were satisfied under the condition of less than 77% of the design flood discharge with simultaneous operation. It was found that the flood damage of downstream rivers can be minimized by setting the amount allocated to the auxiliary spillway to be larger than the amount allocated to the existing spillway for the total outflow with simultaneous operation condition. However, this study only reviewed the flow characteristics around the revetment according to the outflow of spillway under the full opening of the sluice gate condition. Therefore, the various sluice opening conditions and outflow scenarios will be asked to derive more efficient utilization of the auxiliary spillway in th future.KeywordsAuxiliary spillway FLOW-3D Numerical simulation Revetment stability Shear stress

1. 서 론

최근 기후변화로 인한 집중호우의 영향으로 홍수 시 댐으로 유입되는 홍수량이 설계 홍수량보다 증가하여 댐 안정성 확보가 필요한 실정이다(Office for Government Policy Coordination, 2003). MOLIT & K-water(2004)에서는 기존댐의 수문학적 안정성 검토를 수행하였으며 이상홍수 발생 시 24개 댐에서 월류 등으로 인한 붕괴위험으로 댐 하류지역의 극심한 피해를 예상하여 보조여수로 신설 및 기존여수로 확장 등 치수능력 증대 기본계획을 수립하였고 이를 통하여 극한홍수 발생 시 홍수량 배제능력을 증대하여 기존댐의 안전성 확보 및 하류지역의 피해를 방지하고자 하였다. 여기서 보조 여수로는 기존 여수로와 동시 또는 별도 운영하는 여수로로써 비상상황 시 방류 기능을 포함하고 있고(K-water, 2021), 최근에는 기존 여수로의 노후화에 따라 보조여수로의 활용방안에 대한 관심이 증가하고 있다. 따라서 본 연구에서는 3차원 수치해석을 수행하여 기존 및 보조 여수로의 방류량 조합에 따른 하류 영향을 분석하고 하류 호안 안정성 측면에서 최적 방류 시나리오를 검토하고자 한다.

기존의 댐 여수로 검토에 관한 연구는 주로 수리실험을 통하여 방류조건 별 흐름특성을 검토하였으나 최근에는 수치모형 실험결과가 수리모형실험과 비교하여 근사한 것을 확인하는 등 점차 수치모형실험을 수리모형실험의 대안으로 활용하고 있다(Jeon et al., 2006Kim, 2007Kim et al., 2008). 국내의 경우, Jeon et al.(2006)은 수리모형 실험과 수치모의를 이용하여 임하댐 바상여수로의 기본설계안을 도출하였고, Kim et al.(2008)은 가능최대홍수량 유입 시 비상여수로 방류에 따른 수리학적 안정성과 기능성을 3차원 수치모형인 FLOW-3D를 활용하여 검토하였다. 또한 Kim and Kim(2013)은 충주댐의 홍수조절 효과 검토 및 방류량 변화에 따른 상·하류의 수위 변화를 수치모형을 통하여 검토하였다. 국외의 경우 Zeng et al.(2017)은 3차원 수치모형인 Fluent를 활용한 여수로 방류에 따른 흐름특성 결과와 측정결과를 비교하여 수치모형 결과의 신뢰성을 검토하였다. Li et al.(2011)은 가능 최대 홍수량(Probable Maximum Flood, PMF)조건에서 기존 여수로와 신규 보조 여수로 유입부 주변의 흐름특성에 대하여 3차원 수치모형 Fluent를 활용하여 검토하였고, Lee et al.(2019)는 서로 근접해있는 기존 여수로와 보조여수로 동시 운영 시 방류능 검토를 수리모형 실험 및 수치모형 실험(FLOW-3D)을 통하여 수행하였으며 기존 여수로와 보조 여수로를 동시운영하게 되면 배수로 간섭으로 인하여 총 방류량이 7.6%까지 감소되어 댐의 방류능력이 감소하였음을 확인하였다.

그러나 대부분의 여수로 검토에 대한 연구는 여수로 내에서의 흐름특성 및 기능성에 대한 검토를 수행하였고. 이에 기존 여수로와 보조 여수로 방류운영에 따른 하류하천의 흐름특성 변화 및 호안 안정성 평가에 관한 추가적인 검토가 필요한 실정이다. 따라서 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류하천의 흐름특성 및 호안 안정성분석을 3차원 수치모형인 FLOW-3D를 이용하여 검토하였다. 또한 다양한 방류 배분 비율 및 허용 방류량 조건 변화에 따른 하류하천의 흐름특성 및 소류력 분석결과를 호안 설계 허용유속 및 허용 소류력 기준과 비교하여 하류하천의 영향을 최소화 할 수 있는 최적의 보조 여수로 활용방안을 도출하고자 한다.

2. 본 론

2.1 이론적 배경

2.1.1 3차원 수치모형의 기본이론

FLOW-3D는 미국 Flow Science, Inc에서 개발한 범용 유체역학 프로그램(CFD, Computational Fluid Dynamics)으로 자유 수면을 갖는 흐름모의에 사용되는 3차원 수치해석 모형이다. 난류모형을 통해 난류 해석이 가능하고, 댐 방류에 따른 하류 하천의 흐름 해석에도 많이 사용되어 왔다(Flow Science, 2011). 본 연구에서는 FLOW-3D(version 12.0)을 이용하여 홍수 시 기존 여수로의 노후화에 대비하여 보조 여수로의 활용방안에 대한 검토를 하류하천의 호안 안정성 측면에서 검토하였다.

2.1.2 유동해석의 지배방정식

1) 연속 방정식(Continuity Equation)

FLOW-3D는 비압축성 유체에 대하여 연속방정식을 사용하며, 밀도는 상수항으로 적용된다. 연속 방정식은 Eqs. (1)(2)와 같다.

(1)

∇·v=0

(2)

∂∂x(uAx)+∂∂y(vAy)+∂∂z(wAz)=RSORρ

여기서, ρ는 유체 밀도(kg/m3), u, v, w는 x, y, z방향의 유속(m/s), Ax, Ay, Az는 각 방향의 요소면적(m2), RSOR는 질량 생성/소멸(mass source/sink)항을 의미한다.

2) 운동량 방정식(Momentum Equation)

각 방향 속도성분 u, v, w에 대한 운동방정식은 Navier-Stokes 방정식으로 다음 Eqs. (3)(4)(5)와 같다.

(3)

∂u∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂x+Gx+fx-bx-RSORρVFu

(4)

∂v∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂y+Gy+fy-by-RSORρVFv

(5)

∂w∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂z+Gz+fz-bz-RSORρVFw

여기서, Gx, Gy, Gz는 체적력에 의한 가속항, fx, fy, fz는 점성에 의한 가속항, bx, by, bz는 다공성 매체에서의 흐름손실을 의미한다.

2.1.3 소류력 산정

호안설계 시 제방사면 호안의 안정성 확보를 위해서는 하천의 흐름에 의하여 호안에 작용하는 소류력에 저항할 수 있는 재료 및 공법 선택이 필요하다. 국내의 경우 하천공사설계실무요령(MOLIT, 2016)에서 계획홍수량 유하 시 소류력 산정 방법을 제시하고 있다. 소류력은 하천의 평균유속을 이용하여 산정할 수 있으며, 소류력 산정식은 Eqs. (6)(7)과 같다.

1) Schoklitsch 공식

Schoklitsch(1934)는 Chezy 유속계수를 적용하여 소류력을 산정하였다.

(6)

τ=γRI=γC2V2

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), I는 에너지경사, C는 Chezy 유속계수, V는 평균유속(m/s)을 의미한다.

2) Manning 조도계수를 고려한 공식

Chezy 유속계수를 대신하여 Manning의 조도계수를 고려하여 소류력을 산정할 수 있다.

(7)

τ=γn2V2R1/3

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), n은 Manning의 조도계수, V는 평균유속(m/s)을 의미한다.

FLOW-3D 수치모의 수행을 통하여 하천의 바닥 유속을 도출할 수 있으며, 본 연구에서는 Maning 조도계수롤 고려하여 소류력을 산정하고자 한다. 소류력을 산정하기 위해서 여수로 방류에 따른 대안부의 바닥유속 변화를 검토하여 최대 유속 값을 이용하였다. 최종적으로 산정한 소류력과 호안의 재료 및 공법에 따른 허용 소류력과 비교하여 제방사면 호안의 안정성 검토를 수행하게 된다.

2.2 하천호안 설계기준

하천 호안은 계획홍수위 이하의 유수작용에 대하여 안정성이 확보되도록 계획하여야 하며, 호안의 설계 시에는 사용재료의 확보용이성, 시공상의 용이성, 세굴에 대한 굴요성(flexibility) 등을 고려하여 호안의 형태, 시공방법 등을 결정한다(MOLIT, 2019). 국내의 경우, 하천공사설계실무요령(MOLIT, 2016)에서는 다양한 호안공법에 대하여 비탈경사에 따라 설계 유속을 비교하거나, 허용 소류력을 비교함으로써 호안의 안정성을 평가한다. 호안에 대한 국외의 설계기준으로 미국의 경우, ASTM(미국재료시험학회)에서 호안블록 및 식생매트 시험방법을 제시하였고 제품별로 ASTM 시험에 의한 허용유속 및 허용 소류력을 제시하였다. 일본의 경우, 호안 블록에 대한 축소실험을 통하여 항력을 측정하고 이를 통해서 호안 블록에 대한 항력계수를 제시하고 있다. 설계 시에는 항력계수에 의한 블록의 안정성을 평가하고 있으나, 최근에는 세굴의 영향을 고려할 수 있는 호안 안정성 평가의 필요성을 제기하고 있다(MOLIT, 2019). 관련된 국내·외의 하천호안 설계기준은 Table 1에 정리하여 제시하였고, 본 연구에서 하천 호안 안정성 평가 시 하천공사설계실무요령(MOLIT, 2016)과 ASTM 시험에서 제시한 허용소류력 및 허용유속 기준을 비교하여 각각 0.28 kN/m2, 5.0 m/s 미만일 경우 호안 안정성을 확보하였다고 판단하였다.

Table 1.

Standard of Permissible Velocity and Shear on Revetment

Country (Reference)MaterialPermissible velocity (Vp, m/s)Permissible Shear (τp, kN/m2)
KoreaRiver Construction Design Practice Guidelines
(MOLIT, 2016)
Vegetated5.00.50
Stone5.00.80
USAASTM D’6460Vegetated6.10.81
Unvegetated5.00.28
JAPANDynamic Design Method of Revetment5.0

2.3. 보조여수로 운영에 따른 하류하천 영향 분석

2.3.1 모형의 구축 및 경계조건

본 연구에서는 기존 여수로의 노후화에 대비하여 홍수 시 보조여수로의 활용방안에 따른 하류하천의 흐름특성 및 호안안정성 평가를 수행하기 위해 FLOW-3D 모형을 이용하였다. 기존 여수로 및 보조 여수로는 치수능력 증대사업(MOLIT & K-water, 2004)을 통하여 완공된 ○○댐의 제원을 이용하여 구축하였다. ○○댐은 설계빈도(100년) 및 200년빈도 까지는 계획홍수위 이내로 기존 여수로를 통하여 운영이 가능하나 그 이상 홍수조절은 보조여수로를 통하여 조절해야 하며, 또한 2011년 기존 여수로 정밀안전진단 결과 사면의 표층 유실 및 옹벽 밀림현상 등이 확인되어 노후화에 따른 보수·보강이 필요한 상태이다. 이에 보조여수로의 활용방안 검토가 필요한 것으로 판단하여 본 연구의 대상댐으로 선정하였다. 하류 하천의 흐름특성을 예측하기 위하여 격자간격을 0.99 ~ 8.16 m의 크기로 하여 총 격자수는 49,102,500개로 구성하였으며, 여수로 방류에 따른 하류하천의 흐름해석을 위한 경계조건으로 상류는 유입유량(inflow), 바닥은 벽면(wall), 하류는 수위(water surface elevation)조건으로 적용하도록 하였다(Table 2Fig. 1 참조). FLOW-3D 난류모형에는 혼합길이 모형, 난류에너지 모형, k-ϵ모형, RNG(Renormalized Group Theory) k-ϵ모형, LES 모형 등이 있으며, 본 연구에서는 여수로 방류에 따른 복잡한 난류 흐름 및 높은 전단흐름을 정확하게 모의(Flow Science, 2011)할 수 있는 RNG k-ϵ모형을 사용하였고, 하류하천 호안의 안정성 측면에서 보조여수로의 활용방안을 검토하기 위하여 방류시나리오는 Table 3에 제시된 것 같이 설정하였다. Case 1 및 Case 2를 통하여 계획홍수량에 대하여 기존 여수로와 보조 여수로의 단독 운영이 하류하천에 미치는 영향을 확인하였고 보조 여수로의 방류량 조절을 통하여 호안 안정성 측면에서 보조 여수로 방류능 검토를 수행하였다(Case 3 ~ Case 6). 또한 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천의 영향 검토(Case 7 ~ Case 10) 및 방류 배분에 따른 허용 방류량을 호안 안정성 측면에서 검토를 수행하였다(Case 11 ~ Case 14).

수문은 완전개도 조건으로 가정하였으며 하류하천의 계획홍수량에 대한 기존 여수로와 보조여수로의 배분량을 조절하여 모의를 수행하였다. 여수로는 콘크리트의 조도계수 값(Chow, 1959)을 채택하였고, 댐 하류하천의 조도계수는 하천기본계획(Busan Construction and Management Administration, 2009) 제시된 조도계수 값을 채택하였으며 FLOW-3D의 적용을 위하여 Manning-Strickler 공식(Vanoni, 2006)을 이용하여 조도계수를 조고값으로 변환하여 사용하였다. Manning-Strickler 공식은 Eq. (8)과 같으며, FLOW-3D에 적용한 조도계수 및 조고는 Table 4와 같다.

(8)

n=ks1/68.1g1/2

여기서, kS는 조고 (m), n은 Manning의 조도계수, g는 중력가속도(m/s2)를 의미한다.

시간에 따라 동일한 유량이 일정하게 유입되도록 모의를 수행하였으며, 시간간격(Time Step)은 0.0001초로 설정(CFL number < 1.0) 하였다. 또한 여수로 수문을 통한 유량의 변동 값이 1.0%이내일 경우는 연속방정식을 만족하고 있다고 가정하였다. 이는, 유량의 변동 값이 1.0%이내일 경우 유속의 변동 값 역시 1.0%이내이며, 수치모의 결과 1.0%의 유속변동은 호안의 유속설계기준에 크게 영향을 미치지 않는다고 판단하였다. 그 결과 모든 수치모의 Case에서 2400초 이내에 결과 값이 수렴하는 것을 확인하였다.

Table 2.

Mesh sizes and numerical conditions

MeshNumbers49,102,500 EA
Increment (m)DirectionExisting SpillwayAuxiliary Spillway
∆X0.99 ~ 4.301.00 ~ 4.30
∆Y0.99 ~ 8.161.00 ~ 5.90
∆Z0.50 ~ 1.220.50 ~ 2.00
Boundary ConditionsXmin / YmaxInflow / Water Surface Elevation
Xmax, Ymin, Zmin / ZmaxWall / Symmetry
Turbulence ModelRNG model
Table 3.

Case of numerical simulation (Qp : Design flood discharge)

CaseExisting Spillway (Qe, m3/s)Auxiliary Spillway (Qa, m3/s)Remarks
1Qp0Reference case
20Qp
300.58QpReview of discharge capacity on
auxiliary spillway
400.48Qp
500.45Qp
600.32Qp
70.50Qp0.50QpDetermination of optimal division
ratio on Spillways
80.61Qp0.39Qp
90.39Qp0.61Qp
100.42Qp0.58Qp
110.32Qp0.45QpDetermination of permissible
division on Spillways
120.35Qp0.48Qp
130.38Qp0.53Qp
140.41Qp0.56Qp
Table 4.

Roughness coefficient and roughness height

CriteriaRoughness coefficient (n)Roughness height (ks, m)
Structure (Concrete)0.0140.00061
River0.0330.10496
/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F1.jpg
Fig. 1

Layout of spillway and river in this study

2.3.2 보조 여수로의 방류능 검토

본 연구에서는 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천 대안부의 유속분포 및 수위분포를 검토하기 위해 수치모의 Case 별 다음과 같이 관심구역을 설정하였다(Fig. 2 참조). 관심구역(대안부)의 길이(L)는 총 1.3 km로 10 m 등 간격으로 나누어 검토하였으며, Section 1(0 < X/L < 0.27)은 기존 여수로 방류에 따른 영향이 지배적인 구간, Section 2(0.27 < X/L < 1.00)는 보조 여수로 방류에 따른 영향이 지배적인 구간으로 각 구간에서의 수위, 유속, 수심결과를 확인하였다. 기존 여수로의 노후화에 따른 보조 여수로의 방류능 검토를 위하여 Case 1 – Case 6까지의 결과를 비교하였다.

보조 여수로의 단독 운영 시 기존 여수로 운영 시 보다 하류하천의 대안부의 최대 유속(Vmax)은 약 3% 감소하였으며, 이는 보조 여수로의 하천 유입각이 기존 여수로 보다 7°작으며 유입하천의 폭이 증가하여 유속이 감소한 것으로 판단된다. 대안부의 최대 유속 발생위치는 하류 쪽으로 이동하였으며 교량으로 인한 단면의 축소로 최대유속이 발생하는 것으로 판단된다. 또한 보조 여수로의 배분량(Qa)이 증가함에 따라 하류하천 대안부의 최대 유속이 증가하였다. 하천호안 설계기준에서 제시하고 있는 허용유속(Vp)과 비교한 결과, 계획홍수량(Qp)의 45% 이하(Case 5 & 6)를 보조 여수로에서 방류하게 되면 허용 유속(5.0 m/s)조건을 만족하여 호안안정성을 확보하였다(Fig. 3 참조). 허용유속 외에도 대안부에서의 소류력을 산정하여 하천호안 설계기준에서 제시한 허용 소류력(τp)과 비교한 결과, 유속과 동일하게 보조 여수로의 방류량이 계획홍수량의 45% 이하일 경우 허용소류력(0.28 kN/m2) 조건을 만족하였다(Fig. 4 참조). 각 Case 별 호안설계조건과 비교한 결과는 Table 5에 제시하였다.

하류하천의 수위도 기존 여수로 운영 시 보다 보조 여수로 단독 운영 시 최대 수위(ηmax)가 약 2% 감소하는 효과를 보였으며 최대 수위 발생위치는 수충부로 여수로 방류시 처오름에 의한 수위 상승으로 판단된다. 기존 여수로의 단독운영(Case 1)의 수위(ηref)를 기준으로 보조 여수로의 방류량이 증가함에 따라 수위는 증가하였으나 계획홍수량의 58%까지 방류할 경우 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보되었다(Fig. 5 참조). 그러나 계획홍수량 조건에서는 월류에 대한 위험성이 존재하기 때문에 기존여수로와 보조여수로의 적절한 방류량 배분 조합을 도출하는 것이 중요하다고 판단되어 진다.

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F2.jpg
Fig. 2

Region of interest in this study

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F3.jpg
Fig. 3

Maximum velocity and location of Vmax according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F4.jpg
Fig. 4

Maximum shear according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F5.jpg
Fig. 5

Maximum water surface elevation and location of ηmax according to Qa

Table 5.

Numerical results for each cases (Case 1 ~ Case 6)

CaseMaximum Velocity
(Vmax, m/s)
Maximum Shear
(τmax, kN/m2)
Evaluation
in terms of Vp
Evaluation
in terms of τp
1
(Qa = 0)
9.150.54No GoodNo Good
2
(Qa = Qp)
8.870.56No GoodNo Good
3
(Qa = 0.58Qp)
6.530.40No GoodNo Good
4
(Qa = 0.48Qp)
6.220.36No GoodNo Good
5
(Qa = 0.45Qp)
4.220.12AccpetAccpet
6
(Qa = 0.32Qp)
4.040.14AccpetAccpet

2.3.3 기존 여수로와 보조 여수로 방류량 배분 검토

기존 여수로 및 보조 여수로 단독운영에 따른 하류하천 및 호안의 안정성 평가를 수행한 결과 계획홍수량 방류 시 하류하천 대안부에서 호안 설계 조건(허용유속 및 허용 소류력)을 초과하였으며, 처오름에 의한 수위 상승으로 월류에 대한 위험성 증가를 확인하였다. 따라서 계획 홍수량 조건에서 기존 여수로와 보조 여수로의 방류량 배분을 통하여 호안 안정성을 확보하고 하류하천에 방류로 인한 피해를 최소화할 수 있는 배분조합(Case 7 ~ Case 10)을 검토하였다. Case 7은 기존 여수로와 보조여수로의 배분 비율을 균등하게 적용한 경우이고, Case 8은 기존 여수로의 배분량이 보조 여수로에 비하여 많은 경우, Case 9는 보조 여수로의 배분량이 기존 여수로에 비하여 많은 경우를 의미한다. 최대유속을 비교한 결과 보조 여수로의 배분 비율이 큰 경우 기존 여수로의 배분량에 의하여 흐름이 하천 중심에 집중되어 대안부의 유속을 저감하는 효과를 확인하였다. 보조여수로의 방류량 배분 비율이 증가할수록 기존 여수로 대안부 측(0.00<X/L<0.27, Section 1) 유속 분포는 감소하였으나, 신규여수로 대안부 측(0.27<X/L<1.00, Section 2) 유속은 증가하는 것을 확인하였다(Fig. 6 참조). 그러나 유속 저감 효과에도 대안부 전구간에서 설계 허용유속 조건을 초과하여 제방의 안정성을 확보하지는 못하였다. 소류력 산정 결과 유속과 동일하게 보조 여수로의 방류량이 기존 여수로의 방류량 보다 크면 감소하는 것을 확인하였고 일부 구간에서는 허용 소류력 조건을 만족하는 것을 확인하였다(Fig. 7 참조).

따라서 유속 저감효과가 있는 배분 비율 조건(Qa>Qe)에서 Section 2에 유속 저감에 영향을 미치는 기존 여수로 방류량 배분 비율을 증가시켜 추가 검토(Case 10)를 수행하였다. 단독운영과 비교 시 하류하천에 유입되는 유량은 증가하였음에도 불구하고 기존 여수로 방류량에 의해 흐름이 하천 중심으로 집중되는 현상에 따라 대안부의 유속은 단독 운영에 비하여 감소하는 것을 확인하였고(Fig. 8 참조), 호안 설계 허용유속 및 허용 소류력 조건을 만족하는 구간이 발생하여 호안 안정성도 확보한 것으로 판단되었다. 최종적으로 각 Case 별 수위 결과의 경우 여수로 동시 운영을 수행하게 되면 대안부 전 구간에서 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보하였다(Fig. 9 참조). 각 Case 별 대안부에서 최대 유속결과 및 산정한 소류력은 Table 6에 제시하였다.

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F6.jpg
Fig. 6

Maximum velocity on section 1 & 2 according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F7.jpg
Fig. 7

Maximum shear on section 1 & 2 according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F8.jpg
Fig. 8

Velocity results of FLOW-3D (a: auxiliary spillway operation only , b : simultaneous operation of spillways)

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F9.jpg
Fig. 9

Maximum water surface elevation on section 1 & 2 according to Qa

Table 6.

Numerical results for each cases (Case 7 ~ Case 10)

Case (Qe &amp; Qa)Maximum Velocity (Vmax, m/s)Maximum Shear
(τmax, kN/m2)
Evaluation in terms of VpEvaluation in terms of τp
Section 1Section 2Section 1Section 2Section 1Section 2Section 1Section 2
7
Qe : 0.50QpQa : 0.50Qp
8.106.230.640.30No GoodNo GoodNo GoodNo Good
8
Qe : 0.61QpQa : 0.39Qp
8.886.410.610.34No GoodNo GoodNo GoodNo Good
9
Qe : 0.39QpQa : 0.61Qp
6.227.330.240.35No GoodNo GoodAcceptNo Good
10
Qe : 0.42QpQa : 0.58Qp
6.394.790.300.19No GoodAcceptNo GoodAccept

2.3.4 방류량 배분 비율의 허용 방류량 검토

계획 홍수량 방류 시 기존 여수로와 보조 여수로의 배분 비율 검토 결과 Case 10(Qe = 0.42Qp, Qa = 0.58Qp)에서 방류에 따른 하류 하천의 피해를 최소화시킬 수 있는 것을 확인하였다. 그러나 대안부 전 구간에 대하여 호안 설계조건을 만족하지 못하였다. 따라서 기존 여수로와 보조 여수로의 방류 배분 비율을 고정시킨 후 총 방류량을 조절하여 허용 방류량을 검토하였다(Case 11 ~ Case 14).

호안 안정성 측면에서 검토한 결과 계획홍수량 대비 총 방류량이 감소하면 최대 유속 및 최대 소류력이 감소하고 최종적으로 계획 홍수량의 77%를 방류할 경우 하류하천의 대안부에서 호안 설계조건을 모두 만족하는 것을 확인하였다(Fig. 10Fig. 11 참조). 각 Case 별 대안부에서 최대 유속결과 및 산정한 소류력은 Table 7에 제시하였다. 또한 Case 별 수위 검토 결과 처오름으로 인한 대안부 전 구간에서 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보하였다(Fig. 12 참조).

Table 7.

Numerical results for each cases (Case 11 ~ Case 14)

Case (Qe &amp; Qa)Maximum Velocity
(Vmax, m/s)
Maximum Shear
(τmax, kN/m2)
Evaluation in terms of VpEvaluation in terms of τp
Section 1Section 2Section 1Section 2Section 1Section 2Section 1Section 2
11
Qe : 0.32QpQa : 0.45Qp
3.634.530.090.26AcceptAcceptAcceptAccept
12
Qe : 0.35QpQa : 0.48Qp
5.745.180.230.22No GoodNo GoodAcceptAccept
13
Qe : 0.38QpQa : 0.53Qp
6.704.210.280.11No GoodAcceptAcceptAccept
14
Qe : 0.41QpQa : 0.56Qp
6.545.240.280.24No GoodNo GoodAcceptAccept
/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F10.jpg
Fig. 10

Maximum velocity on section 1 & 2 according to total outflow

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F11.jpg
Fig. 11

Maximum shear on section 1 & 2 according to total outflow

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F12.jpg
Fig. 12

Maximum water surface elevation on section 1 & 2 according to total outflow

3. 결 론

본 연구에서는 홍수 시 기존 여수로의 노후화로 인한 보조 여수로의 활용방안에 대하여 하류하천의 호안 안정성 측면에서 검토하였다. 여수로 방류로 인한 하류하천의 흐름특성을 검토하기 위하여 3차원 수치모형인 FLOW-3D를 활용하였고, 여수로 지형은 치수능력 증대사업을 통하여 완공된 ○○댐의 제원을 이용하였다. 하류하천 조도 계수 및 여수로 방류량은 하천기본계획을 참고하여 적용하였다. 최종적으로 여수로 방류로 인한 하류하천의 피해를 최소화 시킬 수 있는 적절한 보조 여수로의 활용방안을 도출하기 위하여 보조 여수로 단독 운영과 기존 여수로와의 동시 운영에 따른 하류 하천의 흐름특성 및 소류력의 변화를 검토하였다.

수문은 완전 개도 상태에서 방류한다는 가정으로 계획 홍수량 조건에서 보조 여수로 단독 운영 시 하류하천 대안부의 유속 및 수위를 검토한 결과 기존 여수로 단독운영에 비하여 최대 유속 및 최대 수위가 감소하는 것을 확인할 수 있었으며, 이는 보조 여수로 단독 운영 시 하류하천으로 유입각도가 작아지고, 유입되는 하천의 폭이 증가되기 때문이다. 그러나 계획 홍수량 조건에서 하천호안 설계기준에서 제시한 허용 유속(5.0 m/s)과 허용 소류력(0.28 kN/m2)과 비교하였을 때 호안 안정성을 확보하지 못하였으며, 계획홍수량의 45% 이하 방류 시에 대안부의 호안 안정성을 확보하였다. 수위의 경우 여수로 방류에 따른 대안부에서 처오름 현상이 발생하여 월류에 대한 위험성을 확인하였고 이를 통하여 기존 여수로와의 동시 운영 방안을 도출하는 것이 중요하다고 판단된다. 따라서 기존 여수로와의 동시 운영 측면에서 기존 여수로와 보조 여수로의 배분 비율 및 총 방류량을 변화시켜가며 하류 하천의 흐름특성 및 소류력의 변화를 검토하였다. 배분 비율의 경우 기존 여수로와 보조 여수로의 균등 배분(Case 7) 및 편중 배분(Case 8 & Case 9)을 검토하여 보조 여수로의 방류량이 기존 여수로의 방류량보다 큰 경우 하류하천의 중심부로 집중되어 대안부의 최대유속, 최대소류력 및 최대수위가 감소하는 것을 확인하였다. 이를 근거로 기존 여수로의 방류 비율을 증가(Qe=0.42Qp, Qa=0.58Qp)시켜 검토한 결과 대안부 일부 구간에서 허용 유속 및 허용소류력 조건을 만족하는 것을 확인하였다. 이를 통하여 기존 여수로와 보조 여수로의 동시 운영을 통하여 적절한 방류량 배분 비율을 도출하는 것이 방류로 인한 하류하천의 피해를 저감하는데 효과적인 것으로 판단된다. 그러나 설계홍수량 방류 시 전 구간에서 허용 유속 및 소류력 조건을 만족하지 못하였다. 최종적으로 전체 방류량에서 기존 여수로의 방류 비율을 42%, 보조 여수로의 방류 비율을 58%로 설정하여 허용방류량을 검토한 결과, 계획홍수량의 77%이하로 방류 시 대안부의 최대유속은 기존여수로 방류의 지배영향구간(section 1)에서 3.63 m/s, 기존 여수로와 보조 여수로 방류의 영향구간(section 2)에서 4.53 m/s로 허용유속 조건을 만족하였고, 산정한 소류력도 각각 0.09 kN/m2 및 0.26 kN/m2로 허용 소류력 조건을 만족하여 대안부 호안의 안정성을 확보하였다고 판단된다.

본 연구 결과는 기후변화 및 기존여수로의 노후화로 인하여 홍수 시 기존여수로의 단독운영으로 하류하천의 피해가 발생할 수 있는 현시점에서 치수증대 사업으로 완공된 보조 여수로의 활용방안에 대한 기초자료로 활용될 수 있고, 향후 계획 홍수량 유입 시 최적의 배분 비율 및 허용 방류량 도출에 이용할 수 있다. 다만 본 연구는 여수로 방류에 따른 제방에 작용하는 수충력은 검토하지 못하고, 허용 유속 및 허용소류력은 제방과 유수의 방향이 일정한 구간에 대하여 검토하였다. 또한 여수로 방류에 따른 대안부에서의 영향에 대해서만 검토하였고 수문 전면 개도 조건에서 검토하였다는 한계점은 분명히 있다. 이에 향후에는 다양한 수문 개도 조건 및 방류 시나리오를 적용 및 검토하여 보다 효율적이고, 효과적인 보조 여수로 활용방안을 도출하고자 한다.

Acknowledgements

본 결과물은 K-water에서 수행한 기존 및 신규 여수로 효율적 연계운영 방안 마련(2021-WR-GP-76-149)의 지원을 받아 연구되었습니다.

References

1 Busan Construction and Management Administration (2009). Nakdonggang River Master Plan. Busan: BCMA.
2 Chow, V. T. (1959). Open-channel Hydraulics. McGraw-Hill. New York.
3 Flow Science (2011). Flow3D User Manual. Santa Fe: NM.
4 Jeon, T. M., Kim, H. I., Park, H. S., and Baek, U. I. (2006). Design of Emergency Spillway Using Hydraulic and Numerical Model-ImHa Multipurpose Dam. Proceedings of the Korea Water Resources Association Conference. 1726-1731.
5 Kim, D. G., Park, S. J., Lee, Y. S., and Hwang, J. H. (2008). Spillway Design by Using Numerical Model Experiment – Case Study of AnDong Multipurpose Dam. Proceedings of the Korea Water Resources Association Conference. 1604-1608.
6 Kim, J. S. (2007). Comparison of Hydraulic Experiment and Numerical Model on Spillway. Water for Future. 40(4): 74-81.
7 Kim, S. H. and Kim, J. S. (2013). Effect of Chungju Dam Operation for Flood Control in the Upper Han River. Journal of the Korean Society of Civil Engineers. 33(2): 537-548. 10.12652/Ksce.2013.33.2.537
8 K-water (2021). Regulations of Dam Management. Daejeon: K-water.
9 K-water and MOLIT (2004). Report on the Establishment of Basic Plan for the Increasing Flood Capacity and Review of Hydrological Stability of Dams. Sejong: K-water and MOLIT.
10 Lee, J. H., Julien, P. Y., and Thornton, C. I. (2019). Interference of Dual Spillways Operations. Journal of Hydraulic Engineering. 145(5): 1-13. 10.1061/(ASCE)HY.1943-7900.0001593
11 Li, S., Cain, S., Wosnik, M., Miller, C., Kocahan, H., and Wyckoff, R. (2011). Numerical Modeling of Probable Maximum Flood Flowing through a System of Spillways. Journal of Hydraulic Engineering. 137(1): 66-74. 10.1061/(ASCE)HY.1943-7900.0000279
12 MOLIT (2016). Practice Guidelines of River Construction Design. Sejong: MOLIT.
13 MOLIT (2019). Standards of River Design. Sejong: MOLIT.
14 Prime Minister’s Secretariat (2003). White Book on Flood Damage Prevention Measures. Sejong: PMS.
15 Schoklitsch, A. (1934). Der Geschiebetrieb und Die Geschiebefracht. Wasserkraft Wasserwirtschaft. 4: 1-7.
16 Vanoni, V. A. (Ed.). (2006). Sedimentation Engineering. American Society of Civil Engineers. Virginia: ASCE. 10.1061/9780784408230
17 Zeng, J., Zhang, L., Ansar, M., Damisse, E., and González-Castro, J. A. (2017). Applications of Computational Fluid Dynamics to Flow Ratings at Prototype Spillways and Weirs. I: Data Generation and Validation. Journal of Irrigation and Drainage Engineering. 143(1): 1-13. 10.1061/(ASCE)IR.1943-4774.0001112

Korean References Translated from the English

1 건설교통부·한국수자원공사 (2004). 댐의 수문학적 안정성 검토 및 치수능력증대방안 기본계획 수립 보고서. 세종: 국토교통부.
2 국무총리실 수해방지대책단 (2003). 수해방지대책 백서. 세종: 국무총리실.
3 국토교통부 (2016). 하천공사 설계실무요령. 세종: 국토교통부.
4 국토교통부 (2019). 하천설계기준해설. 세종: 국토교통부.
5 김대근, 박선중, 이영식, 황종훈 (2008). 수치모형실험을 이용한 여수로 설계 – 안동다목적댐. 한국수자원학회 학술발표회. 1604-1608.
6 김상호, 김지성 (2013). 충주댐 방류에 따른 댐 상하류 홍수위 영향 분석. 대한토목학회논문집. 33(2): 537-548. 10.12652/Ksce.2013.33.2.537
7 김주성 (2007). 댐 여수로부 수리 및 수치모형실험 비교 고찰. Water for Future. 40(4): 74-81.
8 부산국토관리청 (2009). 낙동강수계 하천기본계획(변경). 부산: 부산국토관리청.
9 전태명, 김형일, 박형섭, 백운일 (2006). 수리모형실험과 수치모의를 이용한 비상여수로 설계-임하댐. 한국수자원학회 학술발표회. 1726-1731.
10 한국수자원공사 (2021). 댐관리 규정. 대전: 한국수자원공사.

Figure 17. Longitudinal turbulent kinetic energy distribution on the smooth and triangular macroroughnesses: (A) Y/2; (B) Y/6.

Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses

Triangular Macroroughnesses 대한 잠긴 수압 점프의 유동장 수치 시뮬레이션

by Amir Ghaderi 1,2,Mehdi Dasineh 3,Francesco Aristodemo 2 andCostanza Aricò 4,*1Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan 537138791, Iran2Department of Civil Engineering, University of Calabria, Arcavacata, 87036 Rende, Italy3Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh 8311155181, Iran4Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy*Author to whom correspondence should be addressed.Academic Editor: Anis YounesWater202113(5), 674; https://doi.org/10.3390/w13050674

Abstract

The submerged hydraulic jump is a sudden change from the supercritical to subcritical flow, specified by strong turbulence, air entrainment and energy loss. Despite recent studies, hydraulic jump characteristics in smooth and rough beds, the turbulence, the mean velocity and the flow patterns in the cavity region of a submerged hydraulic jump in the rough beds, especially in the case of triangular macroroughnesses, are not completely understood. The objective of this paper was to numerically investigate via the FLOW-3D model the effects of triangular macroroughnesses on the characteristics of submerged jump, including the longitudinal profile of streamlines, flow patterns in the cavity region, horizontal velocity profiles, streamwise velocity distribution, thickness of the inner layer, bed shear stress coefficient, Turbulent Kinetic Energy (TKE) and energy loss, in different macroroughness arrangements and various inlet Froude numbers (1.7 < Fr1 < 9.3). To verify the accuracy and reliability of the present numerical simulations, literature experimental data were considered.

Keywords: submerged hydraulic jumptriangular macroroughnessesTKEbed shear stress coefficientvelocityFLOW-3D model

수중 유압 점프는 강한 난류, 공기 동반 및 에너지 손실로 지정된 초임계에서 아임계 흐름으로의 급격한 변화입니다. 최근 연구에도 불구하고, 특히 삼각형 거시적 거칠기의 경우, 평활 및 거친 베드에서의 수압 점프 특성, 거친 베드에서 잠긴 수압 점프의 공동 영역에서 난류, 평균 속도 및 유동 패턴이 완전히 이해되지 않았습니다.

이 논문의 목적은 유선의 종방향 프로파일, 캐비티 영역의 유동 패턴, 수평 속도 프로파일, 스트림 방향 속도 분포, 두께를 포함하여 서브머지드 점프의 특성에 대한 삼각형 거시 거칠기의 영향을 FLOW-3D 모델을 통해 수치적으로 조사하는 것이었습니다.

내부 층의 층 전단 응력 계수, 난류 운동 에너지(TKE) 및 에너지 손실, 다양한 거시 거칠기 배열 및 다양한 입구 Froude 수(1.7 < Fr1 < 9.3). 현재 수치 시뮬레이션의 정확성과 신뢰성을 검증하기 위해 문헌 실험 데이터를 고려했습니다.

 Introduction

격렬한 난류 혼합과 기포 동반이 있는 수압 점프는 초임계에서 아임계 흐름으로의 변화 과정으로 간주됩니다[1]. 자유 및 수중 유압 점프는 일반적으로 게이트, 배수로 및 둑과 같은 수력 구조 아래의 에너지 손실에 적합합니다. 매끄러운 베드에서 유압 점프의 특성은 널리 연구되었습니다[2,3,4,5,6,7,8,9].

베드의 거칠기 요소가 매끄러운 베드와 비교하여 수압 점프의 특성에 어떻게 영향을 미치는지 예측하기 위해 거시적 거칠기에 대한 자유 및 수중 수력 점프에 대해 여러 실험 및 수치 연구가 수행되었습니다. Ead와 Rajaratnam[10]은 사인파 거대 거칠기에 대한 수리학적 점프의 특성을 조사하고 무차원 분석을 통해 수면 프로파일과 배출을 정규화했습니다.

Tokyayet al. [11]은 두 사인 곡선 거대 거칠기에 대한 점프 길이 비율과 에너지 손실이 매끄러운 베드보다 각각 35% 더 작고 6% 더 높다는 것을 관찰했습니다. Abbaspur et al. [12]는 6개의 사인파형 거대 거칠기에 대한 수력학적 점프의 특성을 연구했습니다. 그 결과, 꼬리수심과 점프길이는 평상보다 낮았고 Froude 수는 점프길이에 큰 영향을 미쳤습니다.

Shafai-Bejestan과 Neisi[13]는 수압 점프에 대한 마름모꼴 거대 거칠기의 영향을 조사했습니다. 결과는 마름모꼴 거시 거칠기를 사용하면 매끄러운 침대와 비교하여 꼬리 수심과 점프 길이를 감소시키는 것으로 나타났습니다. Izadjoo와 Shafai-Bejestan[14]은 다양한 사다리꼴 거시 거칠기에 대한 수압 점프를 연구했습니다.

그들은 전단응력계수가 평활층보다 10배 이상 크고 점프길이가 50% 감소하는 것을 관찰하였습니다. Nikmehr과 Aminpour[15]는 Flow-3D 모델 버전 11.2[16]를 사용하여 사다리꼴 블록이 있는 거시적 거칠기에 대한 수력학적 점프의 특성을 조사했습니다. 결과는 거시 거칠기의 높이와 거리가 증가할수록 전단 응력 계수뿐만 아니라 베드 근처에서 속도가 감소하는 것으로 나타났습니다.

Ghaderi et al. [17]은 다양한 형태의 거시 거칠기(삼각형, 정사각형 및 반 타원형)에 대한 자유 및 수중 수력 점프 특성을 연구했습니다. 결과는 Froude 수의 증가에 따라 자유 및 수중 점프에서 전단 응력 계수, 에너지 손실, 수중 깊이, 미수 깊이 및 상대 점프 길이가 증가함을 나타냅니다.

자유 및 수중 점프에서 가장 높은 전단 응력과 에너지 손실은 삼각형의 거시 거칠기가 존재할 때 발생했습니다. Elsebaie와 Shabayek[18]은 5가지 형태의 거시적 거칠기(삼각형, 사다리꼴, 2개의 측면 경사 및 직사각형이 있는 정현파)에 대한 수력학적 점프의 특성을 연구했습니다. 결과는 모든 거시적 거칠기에 대한 에너지 손실이 매끄러운 베드에서보다 15배 이상이라는 것을 보여주었습니다.

Samadi-Boroujeni et al. [19]는 다양한 각도의 6개의 삼각형 거시 거칠기에 대한 수력 점프를 조사한 결과 삼각형 거시 거칠기가 평활 베드에 비해 점프 길이를 줄이고 에너지 손실과 베드 전단 응력 계수를 증가시키는 것으로 나타났습니다.

Ahmed et al. [20]은 매끄러운 베드와 삼각형 거시 거칠기에서 수중 수력 점프 특성을 조사했습니다. 결과는 부드러운 침대와 비교할 때 잠긴 깊이와 점프 길이가 감소했다고 밝혔습니다. 표 1은 다른 연구자들이 제시한 과거의 유압 점프에 대한 실험 및 수치 연구의 세부 사항을 나열합니다.

Table 1. Main characteristics of some past experimental and numerical studies on hydraulic jumps.

ReferenceShape Bed-Channel Type-
Jump Type
Channel Dimension (m)Roughness (mm)Fr1Investigated Flow
Properties
Ead and Rajaratnam [10]-Smooth and rough beds-Rectangular channel-Free jumpCL1 = 7.60
CW2 = 0.44
CH3 = 0.60
-Corrugated sheets (RH4 = 13 and 22)4–10-Upstream and tailwater depths-Jump length-Roller length-Velocity-Water surface profile
Tokyay et al. [11]-Smooth and rough beds-Rectangular channel-Free jumpCL = 10.50
CW = 0.253
CH = 0.432
-Two sinusoidal corrugated (RH = 10 and 13)5–12-Depth ratio-Jump length-Energy loss
Izadjoo and Shafai-Bejestan [14]-Smooth and rough beds-Two rectangular-channel-Free jumpCL = 1.2, 9
CW = 0.25, 0.50
CH = 0.40
Baffle with trapezoidal cross section
(RH: 13 and 26)
6–12-Upstream and tailwater depths-Jump length-Velocity-Bed shear stress coefficient
Abbaspour et al. [12]-Horizontal bed with slope 0.002-Rectangular channel—smooth and rough beds-Free jumpCL = 10
CW = 0.25
CH = 0.50
-Sinusoidal bed (RH = 15,20, 25 and 35)3.80–8.60-Water surface profile-Depth ratio-Jump length-Energy loss-Velocity profiles-Bed shear stress coefficient
Shafai-Bejestan and Neisi [13]-Smooth and rough beds-Rectangular channel-Free jumpCL = 7.50
CW = 0.35
CH = 0.50
Lozenge bed4.50–12-Sequent depth-Jump length
Elsebaie and Shabayek [18]-Smooth and rough beds-Rectangular channel-With side slopes of 45 degrees for two trapezoidal and triangular macroroughnesses and of 60 degrees for other trapezoidal macroroughnesses-Free jumpCL = 9
CW = 0.295
CH = 0.32
-Sinusoidal-Triangular-Trapezoidal with two side-Rectangular-(RH = 18 and corrugation wavelength = 65)50-Water surface profile-Sequent depth-Jump length-Bed shear stress coefficient
Samadi-Boroujeni et al. [19]-Rectangular channel-Smooth and rough beds-Free jumpCL = 12
CW = 0.40
CH = 0.40
-Six triangular corrugated (RH = 2.5)6.10–13.10-Water surface profile-Sequent depth-Jump length-Energy loss-Velocity profiles-Bed shear stress coefficient
Ahmed et al. [20]-Smooth and rough beds-Rectangular channel-Submerged jumpCL = 24.50
CW = 0.75
CH = 0.70
-Triangular corrugated sheet (RH = 40)1.68–9.29-Conjugated and tailwater depths-Submerged ratio-Deficit depth-Relative jump length-Jump length-Relative roller jump length-Jump efficiency-Bed shear stress coefficient
Nikmehr and Aminpour [15]-Horizontal bed with slope 0.002-Rectangular channel-Rough bed-Free jumpCL = 12
CW = 0.25
CH = 0.50
-Trapezoidal blocks (RH = 2, 3 and 4)5.01–13.70-Water surface profile-Sequent depth-Jump length-Roller length-Velocity
Ghaderi et al. [17]-Smooth and rough beds-Rectangular channel-Free and submerged jumpCL = 4.50
CW = 0.75
CH = 0.70
-Triangular, square and semi-oval macroroughnesses (RH = 40 and distance of roughness of I = 40, 80, 120, 160 and 200)1.70–9.30-Horizontal velocity distributions-Bed shear stress coefficient-Sequent depth ratio and submerged depth ratio-Jump length-Energy loss
Present studyRectangular channel
Smooth and rough beds
Submerged jump
CL = 4.50
CW = 0.75
CH = 0.70
-Triangular macroroughnesses (RH = 40 and distance of roughness of I = 40, 80, 120, 160 and 200)1.70–9.30-Longitudinal profile of streamlines-Flow patterns in the cavity region-Horizontal velocity profiles-Streamwise velocity distribution-Bed shear stress coefficient-TKE-Thickness of the inner layer-Energy loss

CL1: channel length, CW2: channel width, CH3: channel height, RH4: roughness height.

이전에 논의된 조사의 주요 부분은 실험실 접근 방식을 기반으로 하며 사인파, 마름모꼴, 사다리꼴, 정사각형, 직사각형 및 삼각형 매크로 거칠기가 공액 깊이, 잠긴 깊이, 점프 길이, 에너지 손실과 같은 일부 자유 및 수중 유압 점프 특성에 어떻게 영향을 미치는지 조사합니다.

베드 및 전단 응력 계수. 더욱이, 저자[17]에 의해 다양한 형태의 거시적 거칠기에 대한 수력학적 점프에 대한 이전 발표된 논문을 참조하면, 삼각형의 거대조도는 가장 높은 층 전단 응력 계수 및 에너지 손실을 가지며 또한 가장 낮은 잠긴 깊이, tailwater를 갖는 것으로 관찰되었습니다.

다른 거친 모양, 즉 정사각형 및 반 타원형과 부드러운 침대에 비해 깊이와 점프 길이. 따라서 본 논문에서는 삼각형 매크로 거칠기를 사용하여(일정한 거칠기 높이가 T = 4cm이고 삼각형 거칠기의 거리가 I = 4, 8, 12, 16 및 20cm인 다른 T/I 비율에 대해), 특정 캐비티 영역의 유동 패턴, 난류 운동 에너지(TKE) 및 흐름 방향 속도 분포와 같은 연구가 필요합니다.

CFD(Computational Fluid Dynamics) 방법은 자유 및 수중 유압 점프[21]와 같은 복잡한 흐름의 모델링 프로세스를 수행하는 중요한 도구로 등장하며 수중 유압 점프의 특성은 CFD 시뮬레이션을 사용하여 정확하게 예측할 수 있습니다 [22,23 ].

본 논문은 초기에 수중 유압 점프의 주요 특성, 수치 모델에 대한 입력 매개변수 및 Ahmed et al.의 참조 실험 조사를 제시합니다. [20], 검증 목적으로 보고되었습니다. 또한, 본 연구에서는 유선의 종방향 프로파일, 캐비티 영역의 유동 패턴, 수평 속도 프로파일, 내부 층의 두께, 베드 전단 응력 계수, TKE 및 에너지 손실과 같은 특성을 조사할 것입니다.

Figure 1. Definition sketch of a submerged hydraulic jump at triangular macroroughnesses.
Figure 1. Definition sketch of a submerged hydraulic jump at triangular macroroughnesses.

Table 2. Effective parameters in the numerical model.

Bed TypeQ
(l/s)
I
(cm)
T (cm)d (cm)y1
(cm)
y4
(cm)
Fr1= u1/(gy1)0.5SRe1= (u1y1)/υ
Smooth30, 4551.62–3.839.64–32.101.7–9.30.26–0.5039,884–59,825
Triangular macroroughnesses30, 454, 8, 12, 16, 20451.62–3.846.82–30.081.7–9.30.21–0.4439,884–59,825
Figure 2. Longitudinal profile of the experimental flume (Ahmed et al. [20]).
Figure 2. Longitudinal profile of the experimental flume (Ahmed et al. [20]).

Table 3. Main flow variables for the numerical and physical models (Ahmed et al. [20]).

ModelsBed TypeQ (l/s)d (cm)y1 (cm)u1 (m/s)Fr1
Numerical and PhysicalSmooth4551.62–3.831.04–3.701.7–9.3
T/I = 0.54551.61–3.831.05–3.711.7–9.3
T/I = 0.254551.60–3.841.04–3.711.7–9.3
Figure 3. The boundary conditions governing the simulations.
Figure 3. The boundary conditions governing the simulations.
Figure 4. Sketch of mesh setup.
Figure 4. Sketch of mesh setup.

Table 4. Characteristics of the computational grids.

MeshNested Block Cell Size (cm)Containing Block Cell Size (cm)
10.551.10
20.651.30
30.851.70

Table 5. The numerical results of mesh convergence analysis.

ParametersAmounts
fs1 (-)7.15
fs2 (-)6.88
fs3 (-)6.19
K (-)5.61
E32 (%)10.02
E21 (%)3.77
GCI21 (%)3.03
GCI32 (%)3.57
GCI32/rp GCI210.98
Figure 5. Time changes of the flow discharge in the inlet and outlet boundaries conditions (A): Q = 0.03 m3/s (B): Q = 0.045 m3/s.
Figure 5. Time changes of the flow discharge in the inlet and outlet boundaries conditions (A): Q = 0.03 m3/s (B): Q = 0.045 m3/s.
Figure 6. The evolutionary process of a submerged hydraulic jump on the smooth bed—Q = 0.03 m3/s.
Figure 6. The evolutionary process of a submerged hydraulic jump on the smooth bed—Q = 0.03 m3/s.
Figure 7. Numerical versus experimental basic parameters of the submerged hydraulic jump. (A): y3/y1; and (B): y4/y1.
Figure 7. Numerical versus experimental basic parameters of the submerged hydraulic jump. (A): y3/y1; and (B): y4/y1.
Figure 8. Velocity vector field and flow pattern through the gate in a submerged hydraulic jump condition: (A) smooth bed; (B) triangular macroroughnesses.
Figure 8. Velocity vector field and flow pattern through the gate in a submerged hydraulic jump condition: (A) smooth bed; (B) triangular macroroughnesses.
Figure 9. Velocity vector distributions in the x–z plane (y = 0) within the cavity region.
Figure 9. Velocity vector distributions in the x–z plane (y = 0) within the cavity region.
Figure 10. Typical vertical distribution of the mean horizontal velocity in a submerged hydraulic jump [46].
Figure 10. Typical vertical distribution of the mean horizontal velocity in a submerged hydraulic jump [46].
Figure 11. Typical horizontal velocity profiles in a submerged hydraulic jump on smooth bed and triangular macroroughnesses.
Figure 11. Typical horizontal velocity profiles in a submerged hydraulic jump on smooth bed and triangular macroroughnesses.
Figure 12. Horizontal velocity distribution at different distances from the sluice gate for the different T/I for Fr1 = 6.1
Figure 12. Horizontal velocity distribution at different distances from the sluice gate for the different T/I for Fr1 = 6.1
Figure 13. Stream-wise velocity distribution for the triangular macroroughnesses with T/I = 0.5 and 0.25.
Figure 13. Stream-wise velocity distribution for the triangular macroroughnesses with T/I = 0.5 and 0.25.
Figure 14. Dimensionless horizontal velocity distribution in the submerged hydraulic jump for different Froude numbers in triangular macroroughnesses.
Figure 14. Dimensionless horizontal velocity distribution in the submerged hydraulic jump for different Froude numbers in triangular macroroughnesses.
Figure 15. Spatial variations of (umax/u1) and (δ⁄y1).
Figure 15. Spatial variations of (umax/u1) and (δ⁄y1).
Figure 16. The shear stress coefficient (ε) versus the inlet Froude number (Fr1).
Figure 16. The shear stress coefficient (ε) versus the inlet Froude number (Fr1).
Figure 17. Longitudinal turbulent kinetic energy distribution on the smooth and triangular macroroughnesses: (A) Y/2; (B) Y/6.
Figure 17. Longitudinal turbulent kinetic energy distribution on the smooth and triangular macroroughnesses: (A) Y/2; (B) Y/6.
Figure 18. The energy loss (EL/E3) of the submerged jump versus inlet Froude number (Fr1).
Figure 18. The energy loss (EL/E3) of the submerged jump versus inlet Froude number (Fr1).

Conclusions

  • 본 논문에서는 유선의 종방향 프로파일, 공동 영역의 유동 패턴, 수평 속도 프로파일, 스트림 방향 속도 분포, 내부 층의 두께, 베드 전단 응력 계수, 난류 운동 에너지(TKE)를 포함하는 수중 유압 점프의 특성을 제시하고 논의했습니다. ) 및 삼각형 거시적 거칠기에 대한 에너지 손실. 이러한 특성은 FLOW-3D® 모델을 사용하여 수치적으로 조사되었습니다. 자유 표면을 시뮬레이션하기 위한 VOF(Volume of Fluid) 방법과 난류 RNG k-ε 모델이 구현됩니다. 본 모델을 검증하기 위해 평활층과 삼각형 거시 거칠기에 대해 수치 시뮬레이션과 실험 결과를 비교했습니다. 본 연구의 다음과 같은 결과를 도출할 수 있다.
  • 개발 및 개발 지역의 삼각형 거시 거칠기의 흐름 패턴은 수중 유압 점프 조건의 매끄러운 바닥과 비교하여 더 작은 영역에서 동일합니다. 삼각형의 거대 거칠기는 거대 거칠기 사이의 공동 영역에서 또 다른 시계 방향 와류의 형성으로 이어집니다.
  • T/I = 1, 0.5 및 0.33과 같은 거리에 대해 속도 벡터 분포는 캐비티 영역에서 시계 방향 소용돌이를 표시하며, 여기서 속도의 크기는 평균 유속보다 훨씬 작습니다. 삼각형 거대 거칠기(T/I = 0.25 및 0.2) 사이의 거리를 늘리면 캐비티 영역에 크기가 다른 두 개의 소용돌이가 형성됩니다.
  • 삼각형 거시조도 사이의 거리가 충분히 길면 흐름이 다음 조도에 도달할 때까지 속도 분포가 회복됩니다. 그러나 짧은 거리에서 흐름은 속도 분포의 적절한 회복 없이 다음 거칠기에 도달합니다. 따라서 거시 거칠기 사이의 거리가 감소함에 따라 마찰 계수의 증가율이 감소합니다.
  • 삼각형의 거시적 거칠기에서, 잠수 점프의 지정된 섹션에서 최대 속도는 자유 점프보다 높은 값으로 이어집니다. 또한, 수중 점프에서 두 가지 유형의 베드(부드러움 및 거친 베드)에 대해 깊이 및 와류 증가로 인해 베드로부터의 최대 속도 거리는 감소합니다. 잠수 점프에서 경계층 두께는 자유 점프보다 얇습니다.
  • 매끄러운 베드의 난류 영역은 게이트로부터의 거리에 따라 생성되고 자유 표면 롤러 영역 근처에서 발생하는 반면, 거시적 거칠기에서는 난류가 게이트 근처에서 시작되어 더 큰 강도와 제한된 스위프 영역으로 시작됩니다. 이는 반시계 방향 순환의 결과입니다. 거시 거칠기 사이의 공간에서 자유 표면 롤러 및 시계 방향 와류.
  • 삼각 거시 거칠기에서 침지 점프의 베드 전단 응력 계수와 에너지 손실은 유입구 Froude 수의 증가에 따라 증가하는 매끄러운 베드에서 발견된 것보다 더 큽니다. T/I = 0.50 및 0.20에서 최고 및 최저 베드 전단 응력 계수 및 에너지 손실이 평활 베드에 비해 거칠기 요소의 거리가 증가함에 따라 발생합니다.
  • 거의 거칠기 요소가 있는 삼각형 매크로 거칠기의 존재에 의해 주어지는 점프 길이와 잠긴 수심 및 꼬리 수심의 감소는 결과적으로 크기, 즉 길이 및 높이가 감소하는 정수조 설계에 사용될 수 있습니다.
  • 일반적으로 CFD 모델은 다양한 수력 조건 및 기하학적 배열을 고려하여 잠수 점프의 특성 예측을 시뮬레이션할 수 있습니다. 캐비티 영역의 흐름 패턴, 흐름 방향 및 수평 속도 분포, 베드 전단 응력 계수, TKE 및 유압 점프의 에너지 손실은 수치적 방법으로 시뮬레이션할 수 있습니다. 그러나 거시적 차원과 유동장 및 공동 유동의 변화에 ​​대한 다양한 배열에 대한 연구는 향후 과제로 남아 있다.

References

  1. White, F.M. Viscous Fluid Flow, 2nd ed.; McGraw-Hill University of Rhode Island: Montreal, QC, Canada, 1991. [Google Scholar]
  2. Launder, B.E.; Rodi, W. The turbulent wall jet. Prog. Aerosp. Sci. 197919, 81–128. [Google Scholar] [CrossRef]
  3. McCorquodale, J.A. Hydraulic jumps and internal flows. In Encyclopedia of Fluid Mechanics; Cheremisinoff, N.P., Ed.; Golf Publishing: Houston, TX, USA, 1986; pp. 120–173. [Google Scholar]
  4. Federico, I.; Marrone, S.; Colagrossi, A.; Aristodemo, F.; Antuono, M. Simulating 2D open-channel flows through an SPH model. Eur. J. Mech. B Fluids 201234, 35–46. [Google Scholar] [CrossRef]
  5. Khan, S.A. An analytical analysis of hydraulic jump in triangular channel: A proposed model. J. Inst. Eng. India Ser. A 201394, 83–87. [Google Scholar] [CrossRef]
  6. Mortazavi, M.; Le Chenadec, V.; Moin, P.; Mani, A. Direct numerical simulation of a turbulent hydraulic jump: Turbulence statistics and air entrainment. J. Fluid Mech. 2016797, 60–94. [Google Scholar] [CrossRef]
  7. Daneshfaraz, R.; Ghahramanzadeh, A.; Ghaderi, A.; Joudi, A.R.; Abraham, J. Investigation of the effect of edge shape on characteristics of flow under vertical gates. J. Am. Water Works Assoc. 2016108, 425–432. [Google Scholar] [CrossRef]
  8. Azimi, H.; Shabanlou, S.; Kardar, S. Characteristics of hydraulic jump in U-shaped channels. Arab. J. Sci. Eng. 201742, 3751–3760. [Google Scholar] [CrossRef]
  9. De Padova, D.; Mossa, M.; Sibilla, S. SPH numerical investigation of characteristics of hydraulic jumps. Environ. Fluid Mech. 201818, 849–870. [Google Scholar] [CrossRef]
  10. Ead, S.A.; Rajaratnam, N. Hydraulic jumps on corrugated beds. J. Hydraul. Eng. 2002128, 656–663. [Google Scholar] [CrossRef]
  11. Tokyay, N.D. Effect of channel bed corrugations on hydraulic jumps. In Proceedings of the World Water and Environmental Resources Congress 2005, Anchorage, AK, USA, 15–19 May 2005; pp. 1–9. [Google Scholar]
  12. Abbaspour, A.; Dalir, A.H.; Farsadizadeh, D.; Sadraddini, A.A. Effect of sinusoidal corrugated bed on hydraulic jump characteristics. J. Hydro-Environ. Res. 20093, 109–117. [Google Scholar] [CrossRef]
  13. Shafai-Bejestan, M.S.; Neisi, K. A new roughened bed hydraulic jump stilling basin. Asian J. Appl. Sci. 20092, 436–445. [Google Scholar] [CrossRef]
  14. Izadjoo, F.; Shafai-Bejestan, M. Corrugated bed hydraulic jump stilling basin. J. Appl. Sci. 20077, 1164–1169. [Google Scholar] [CrossRef]
  15. Nikmehr, S.; Aminpour, Y. Numerical Simulation of Hydraulic Jump over Rough Beds. Period. Polytech. Civil Eng. 201764, 396–407. [Google Scholar] [CrossRef]
  16. Flow Science Inc. FLOW-3D V 11.2 User’s Manual; Flow Science Inc.: Santa Fe, NM, USA, 2016. [Google Scholar]
  17. Ghaderi, A.; Dasineh, M.; Aristodemo, F.; Ghahramanzadeh, A. Characteristics of free and submerged hydraulic jumps over different macroroughnesses. J. Hydroinform. 202022, 1554–1572. [Google Scholar] [CrossRef]
  18. Elsebaie, I.H.; Shabayek, S. Formation of hydraulic jumps on corrugated beds. Int. J. Civil Environ. Eng. IJCEE–IJENS 201010, 37–47. [Google Scholar]
  19. Samadi-Boroujeni, H.; Ghazali, M.; Gorbani, B.; Nafchi, R.F. Effect of triangular corrugated beds on the hydraulic jump characteristics. Can. J. Civil Eng. 201340, 841–847. [Google Scholar] [CrossRef]
  20. Ahmed, H.M.A.; El Gendy, M.; Mirdan, A.M.H.; Ali, A.A.M.; Haleem, F.S.F.A. Effect of corrugated beds on characteristics of submerged hydraulic jump. Ain Shams Eng. J. 20145, 1033–1042. [Google Scholar] [CrossRef]
  21. Viti, N.; Valero, D.; Gualtieri, C. Numerical simulation of hydraulic jumps. Part 2: Recent results and future outlook. Water 201911, 28. [Google Scholar] [CrossRef]
  22. Gumus, V.; Simsek, O.; Soydan, N.G.; Akoz, M.S.; Kirkgoz, M.S. Numerical modeling of submerged hydraulic jump from a sluice gate. J. Irrig. Drain. Eng. 2016142, 04015037. [Google Scholar] [CrossRef]
  23. Jesudhas, V.; Roussinova, V.; Balachandar, R.; Barron, R. Submerged hydraulic jump study using DES. J. Hydraul. Eng. 2017143, 04016091. [Google Scholar] [CrossRef]
  24. Rajaratnam, N. The hydraulic jump as a wall jet. J. Hydraul. Div. 196591, 107–132. [Google Scholar] [CrossRef]
  25. Hager, W.H. Energy Dissipaters and Hydraulic Jump; Kluwer Academic Publisher: Dordrecht, The Netherlands, 1992; pp. 185–224. [Google Scholar]
  26. Long, D.; Steffler, P.M.; Rajaratnam, N. LDA study of flow structure in submerged Hydraulic jumps. J. Hydraul. Res. 199028, 437–460. [Google Scholar] [CrossRef]
  27. Chow, V.T. Open Channel Hydraulics; McGraw-Hill: New York, NY, USA, 1959. [Google Scholar]
  28. Wilcox, D.C. Turbulence Modeling for CFD, 3rd ed.; DCW Industries, Inc.: La Canada, CA, USA, 2006. [Google Scholar]
  29. Hirt, C.W.; Nichols, B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 198139, 201–225. [Google Scholar] [CrossRef]
  30. Pourshahbaz, H.; Abbasi, S.; Pandey, M.; Pu, J.H.; Taghvaei, P.; Tofangdar, N. Morphology and hydrodynamics numerical simulation around groynes. ISH J. Hydraul. Eng. 2020, 1–9. [Google Scholar] [CrossRef]
  31. Choufu, L.; Abbasi, S.; Pourshahbaz, H.; Taghvaei, P.; Tfwala, S. Investigation of flow, erosion, and sedimentation pattern around varied groynes under different hydraulic and geometric conditions: A numerical study. Water 201911, 235. [Google Scholar] [CrossRef]
  32. Zhenwei, Z.; Haixia, L. Experimental investigation on the anisotropic tensorial eddy viscosity model for turbulence flow. Int. J. Heat Technol. 201634, 186–190. [Google Scholar]
  33. Carvalho, R.; Lemos Ramo, C. Numerical computation of the flow in hydraulic jump stilling basins. J. Hydraul. Res. 200846, 739–752. [Google Scholar] [CrossRef]
  34. Bayon, A.; Valero, D.; García-Bartual, R.; López-Jiménez, P.A. Performance assessment of Open FOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environ. Model. Softw. 201680, 322–335. [Google Scholar] [CrossRef]
  35. Daneshfaraz, R.; Ghaderi, A.; Akhtari, A.; Di Francesco, S. On the Effect of Block Roughness in Ogee Spillways with Flip Buckets. Fluids 20205, 182. [Google Scholar] [CrossRef]
  36. Ghaderi, A.; Abbasi, S. CFD simulation of local scouring around airfoil-shaped bridge piers with and without collar. Sādhanā 201944, 216. [Google Scholar] [CrossRef]
  37. Ghaderi, A.; Daneshfaraz, R.; Dasineh, M.; Di Francesco, S. Energy Dissipation and Hydraulics of Flow over Trapezoidal–Triangular Labyrinth Weirs. Water 202012, 1992. [Google Scholar] [CrossRef]
  38. Ghaderi, A.; Abbasi, S.; Abraham, J.; Azamathulla, H.M. Efficiency of trapezoidal labyrinth shaped stepped spillways. Flow Meas. Instrum. 202072, 101711. [Google Scholar] [CrossRef]
  39. Yakhot, V.; Orszag, S.A. Renormalization group analysis of turbulence. I. basic theory. J. Sci. Comput. 19861, 3–51. [Google Scholar] [CrossRef] [PubMed]
  40. Biscarini, C.; Di Francesco, S.; Ridolfi, E.; Manciola, P. On the simulation of floods in a narrow bending valley: The malpasset dam break case study. Water 20168, 545. [Google Scholar] [CrossRef]
  41. Ghaderi, A.; Daneshfaraz, R.; Abbasi, S.; Abraham, J. Numerical analysis of the hydraulic characteristics of modified labyrinth weirs. Int. J. Energy Water Resour. 20204, 425–436. [Google Scholar] [CrossRef]
  42. Alfonsi, G. Reynolds-averaged Navier–Stokes equations for turbulence modeling. Appl. Mech. Rev. 200962. [Google Scholar] [CrossRef]
  43. Abbasi, S.; Fatemi, S.; Ghaderi, A.; Di Francesco, S. The Effect of Geometric Parameters of the Antivortex on a Triangular Labyrinth Side Weir. Water 202113, 14. [Google Scholar] [CrossRef]
  44. Celik, I.B.; Ghia, U.; Roache, P.J. Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J. Fluids Eng. 2008130, 0780011–0780013. [Google Scholar]
  45. Khan, M.I.; Simons, R.R.; Grass, A.J. Influence of cavity flow regimes on turbulence diffusion coefficient. J. Vis. 20069, 57–68. [Google Scholar] [CrossRef]
  46. Javanappa, S.K.; Narasimhamurthy, V.D. DNS of plane Couette flow with surface roughness. Int. J. Adv. Eng. Sci. Appl. Math. 2020, 1–13. [Google Scholar] [CrossRef]
  47. Nasrabadi, M.; Omid, M.H.; Farhoudi, J. Submerged hydraulic jump with sediment-laden flow. Int. J. Sediment Res. 201227, 100–111. [Google Scholar] [CrossRef]
  48. Pourabdollah, N.; Heidarpour, M.; Abedi Koupai, J. Characteristics of free and submerged hydraulic jumps in different stilling basins. In Water Management; Thomas Telford Ltd.: London, UK, 2019; pp. 1–11. [Google Scholar]
  49. Rajaratnam, N. Turbulent Jets; Elsevier Science: Amsterdam, The Netherlands, 1976. [Google Scholar]
  50. Aristodemo, F.; Marrone, S.; Federico, I. SPH modeling of plane jets into water bodies through an inflow/outflow algorithm. Ocean Eng. 2015105, 160–175. [Google Scholar] [CrossRef]
  51. Shekari, Y.; Javan, M.; Eghbalzadeh, A. Three-dimensional numerical study of submerged hydraulic jumps. Arab. J. Sci. Eng. 201439, 6969–6981. [Google Scholar] [CrossRef]
  52. Khan, A.A.; Steffler, P.M. Physically based hydraulic jump model for depth-averaged computations. J. Hydraul. Eng. 1996122, 540–548. [Google Scholar] [CrossRef]
  53. De Dios, M.; Bombardelli, F.A.; García, C.M.; Liscia, S.O.; Lopardo, R.A.; Parravicini, J.A. Experimental characterization of three-dimensional flow vortical structures in submerged hydraulic jumps. J. Hydro-Environ. Res. 201715, 1–12. [Google Scholar] [CrossRef]
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Flow on the inclined drop with bat-shaped elements: (a) Non-submerged flow

Numerical Methods in Civil Engineering

Rasoul Daneshfaraz*, Ehsan Aminvash**, Silvia Di Francesco***, Amir Najibi**, John Abraham****

토목공학의 수치해석법

Abstract

The main purpose of this study is to provide a method to increase energy dissipation on an inclined drop. Therefore, three types of rough elements with cylindrical, triangular and batshaped geometries are used on the inclined slope in the relative critical depth range of 0.128 to 0.36 and the effect of the geometry of these elements is examined using Flow 3D software. The results showed demonstrate that the downstream relative depth obtained from the numerical analysis is in good agreement with the laboratory results. The application of rough elements on the inclined drop increased the downstream relative depth and also the relative energy dissipation. The application of rough elements on the sloping surface of the drop significantly reduced the downstream Froude number, so that the Froude number in all models ranging from 4.7~7.5 to 1.45~3.36 also decreased compared to the plain drop. Bat-shaped elements are structurally smaller in size, so the use of these elements, in addition to dissipating more energy, is also economically viable.

이 연구의 주요 목적은 경사진 낙하에서 에너지 소산을 증가시키는 방법을 제공하는 것입니다. 따라서 0.128 ~ 0.36의 상대 임계 깊이 범위에서 경사면에 원통형, 삼각형 및 박쥐 모양의 형상을 가진 세 가지 유형의 거친 요소가 사용되며 이러한 요소의 형상의 영향은 Flow 3D 소프트웨어를 사용하여 조사됩니다. 결과는 수치 분석에서 얻은 하류 상대 깊이가 실험실 결과와 잘 일치함을 보여줍니다. 경 사진 낙하에 거친 요소를 적용하면 하류 상대 깊이와 상대 에너지 소산이 증가했습니다. 낙차 경사면에 거친 요소를 적용하면 하류의 Froude 수를 크게 감소시켜 4.7~7.5에서 1.45~3.36 범위의 모든 모델에서 Froude 수도 일반 낙차에 비해 감소했습니다. 박쥐 모양의 요소는 구조적으로 크기가 더 작기 때문에 더 많은 에너지를 분산시키는 것 외에도 이러한 요소를 사용하는 것이 경제적으로도 가능합니다.

Keywords: Downstream depth, Energy dissipation, Froude number, Inclined drop, Roughness elements

Introduction

급수 네트워크 시스템, 침식 수로, 수처리 시스템 및 경사가 큰 경우 흐름 에너지를 더 잘 제어하기 위해 경사 방울을 사용할 수 있습니다. 낙하 구조는 지반의 자연 경사를 설계 경사로 변환하여 에너지 소산, 유속 감소 및 수심 증가를 유발합니다. 따라서 흐름의 하류 에너지를 분산 시키기 위해 에너지 분산 구조를 사용할 수 있습니다. 난기류와 혼합된 물과 공기의 형성은 에너지 소비를 증가 시키는 효과적인 방법입니다. 흐름 경로에서 거칠기 요소를 사용하는 것은 에너지 소산을 위한 알려진 방법입니다. 이러한 요소는 흐름 경로에 배치됩니다. 그들은 종종 에너지 소산을 증가시키기 위해 다른 기하학적 구조와 배열을 가지고 있습니다. 이 연구의 목적은 직사각형 경사 방울에 대한 거칠기 요소의 영향을 조사하는 것입니다.

Fig. 1: Model made in Ardabil, Iran
Fig. 1: Model made in Ardabil, Iran
Fig. 2: Geometric and hydraulic parameters of an inclined drop equipped with roughness elements
Fig. 2: Geometric and hydraulic parameters of an inclined drop equipped with roughness elements
Fig. 3: Views of the incline with (a) Bat-shaped, (b) Cylindrical, (c) Triangular roughness elements
Fig. 3: Views of the incline with (a) Bat-shaped, (b) Cylindrical, (c) Triangular roughness elements
Fig. 4: Geometric profile of inclined drop and boundary conditions with the bat-shape roughness element
Fig. 4: Geometric profile of inclined drop and boundary conditions with the bat-shape roughness element
Fig. 5: Variation of the RMSE varying cell size
Fig. 5: Variation of the RMSE varying cell size
Fig. 6: Numerical and laboratory comparison of the downstream relative depth
Fig. 6: Numerical and laboratory comparison of the downstream relative depth
Fig. 7: Flow profile on inclined drop in discharge of 5 L/s: (a) Without roughness elements; (b) Bat-shaped roughness element; (c) Cylindrical roughness element; (d) Triangular roughness element
Fig. 7: Flow profile on inclined drop in discharge of 5 L/s: (a) Without roughness elements; (b) Bat-shaped roughness element; (c) Cylindrical roughness element; (d) Triangular roughness element
Fig. 8: Relative edge depth versus the relative critical depth
Fig. 8: Relative edge depth versus the relative critical depth
Flow on the inclined drop with bat-shaped elements: (a) Non-submerged flow
Flow on the inclined drop with bat-shaped elements: (a) Non-submerged flow
Fig. 9: Flow on the inclined drop with bat-shaped elements: (b) Submerged flow
Fig. 9: Flow on the inclined drop with bat-shaped elements: (b) Submerged flow
Fig. 10: Relative downstream depth versus the relative critical depth
Fig. 10: Relative downstream depth versus the relative critical depth
Fig. 11: Relative downstream depth versus the relative critical depth
Fig. 11: Relative downstream depth versus the relative critical depth

Conclusions

현재 연구에서 FLOW-3D 소프트웨어를 사용하여 한 높이, 한 각도, 밀도 15% 및 지그재그 배열에서 삼각형, 원통형 및 박쥐 모양의 형상을 가진 세 가지 유형의 거칠기 요소를 사용하여 경사 낙하 수리학적 매개변수에 대한 거칠기 요소 형상의 영향 평가되었다. VOF 방법을 사용하여 자유 표면 흐름을 시뮬레이션하고 초기에 3개의 난류 모델 RNG, k-ɛ 및 kω를 검증에 사용하고 이를 검토한 후 RNG 방법을 사용하여 다른 모델을 시뮬레이션했습니다. 1- 수치 결과에서 얻은 부드러운 경사 방울의 하류 상대 깊이는 실험실 데이터와 매우 좋은 상관 관계가 있으며 원통형 요소가 장착 된 경사 방울의 상대 에지 깊이 값이 가장 높았습니다. 2- 하류 상대깊이는 임계상대깊이가 증가함에 따라 상승하는 경향을 나타내어 박쥐형 요소를 구비한 경사낙하와 완만한 경사낙하가 각각 하류상대깊이가 가장 높고 가장 낮았다. 3- 하류 깊이의 증가로 인해 상대적 임계 깊이가 증가함에 따라 상대적 에너지 소산이 감소합니다. 한편, 가장 높은 에너지 소산은 박쥐 모양의 요소가 장착된 경사 낙하와 관련이 있으며 가장 낮은 에너지 소산은 부드러운 낙하와 관련이 있습니다. 삼각형, 원통형 및 박쥐 모양의 거친 요소가 장착된 드롭은 부드러운 드롭보다 각각 65%, 76% 및 85% 더 많은 흐름 에너지를 소산합니다. 4- 낙차의 경사면에 거친 요소를 적용하여 다운 스트림 Froude 수를 크게 줄여 4.7 ~ 7.5에서 1.45 ~ 3.36까지의 모든 모델에서 Froude 수가 부드러운 낙하에 비해 감소했습니다. 또한, 다른 원소보다 부피가 작은 박쥐 모양의 거칠기의 부피로 인해 이러한 유형의 거칠기를 사용하는 것이 경제적입니다.

References

References:
[1] Abbaspour, A., Shiravani, P., and Hosseinzadeh dalir, A.,
“Experimental study of the energy dissipation on the rough ramps”,
ISH journal of hydraulic engineering, 2019, p. 1-9.
[2] Abraham, J.P., Sparrow, E.M., Gorman, J.M., Zhao, Y., and
Minkowycz, W.J., “Application of an Intermittency model for
laminar, transitional, and turbulent internal flows”, Journal of
Fluids Engineering, vol. 141, 2019, paper no. 071204.
[3] Ahmad, Z., Petappa, N.M., and Westrich, B., “Energy
dissipation on block ramps with staggered boulders”, Journal of
hydraulic engineering, vol. 135(6), 2009, p. 522-526.
[4] Babaali, H.R., Shamsai, A., and Vosoughifar, H.R.,
“Computational modeling of the hydraulic jump in the stilling
basin with convergence walls using CFD codes”, Arabian Journal
for Science and Engineering, vol. 40(2), 2014, p. 381-395.
[5] Castillo, L.G., Carrillo, J.M., and Cacía, J.T., “Numerical
simulations and laboratory measurements in hydraulic jumps”,
International conference on hydroinformatics. (2014, August) New
York city.
[6] Daneshfaraz, R., Aminvash, E., Esmaeli, R., Sadeghfam, S.,
and Abraham, J., “Experimental and numerical investigation for
energy dissipation of supercritical flow in sudden contractions”,
Journal of groundwater science and engineering, vol. 8(4), 2020a,
p. 396-406.
[7] Daneshfaraz, R., Aminvash, E., Ghaderi, A., Kuriqi, A., and
Abraham, J., “Three-dimensional investigation of hydraulic
properties of vertical drop in the presence of step and grid
dissipators”, Symmetry, vol. 13 (5), 2021a, p. 895.
[8] Daneshfaraz, R., Aminvash, E., Ghaderi, A., Abraham, J., and
Bagherzadeh, M., “SVM performance for predicting the effect of
horizontal screen diameters on the hydraulic parameters of a
vertical drop”, Applied sciences, vol. 11 (9), 2021b, p. 4238.
[9] Daneshfaraz, R., Bagherzadeh, M., Esmaeeli, R., Norouzi, R.,
and Abraham, J. “Study of the performance of support vector
machine for predicting vertical drop hydraulic parameters in the
presence of dual horizontal screens”, Water supply, vol 21(1),
2021c, p. 217-231.
[10] Daneshfaraz, R., and Ghaderi, A., “Numerical investigation of
inverse curvature ogee spillways”, Civil engineering journal, vol.
3(11), 2017, p. 1146-1156.
[11] Daneshfaraz, R., Majedi Asl, M., and Bagherzadeh, M.,
“Experimental Investigation of the Energy Dissipation and the
Downstream Relative Depth of Pool in the Sloped Gabion Drop
and the Sloped simple Drop”, AUT Journal of Civil Engineering,
2020b (In persian).
[12] Daneshfaraz, R., Majedi Asl, M., Bazyar, A., Abraham, J.,
Norouzi, R., “The laboratory study of energy dissipation in inclined
drops equipped with a screen”, Journal of Applied Water
Engineering and Research, 2020c, p. 1-10.
[13] Daneshfaraz, R., Minaei, O., Abraham, J., Dadashi, S., and
Ghaderi, A., “3-D Numerical simulation of water flow over a
broad-crested weir with openings”, ISH Journal of Hydraulic
Engineering, 2019, p.1-9.
[14] Daneshfaraz, R., Sadeghfam, S., and Kashani, M., “Numerical
simulation of flow over stepped spillways”, Research in civil
engineering and environmental engineering, vol. 2(4), 2014, p.
190-198.
[15] Ghaderi, A., Abbasi, S., Abraham, J., and Azamathulla, H.M.,
“Efficiency of trapezoidal labyrinth shaped stepped spillways”,
Flow measurement and instrumentation, vol. 72, 2020a.
[16] Ghaderi, A., Daneshfaraz, R., Dasineh, M., and Di Francesco,
S., “Energy dissipation and hydraulics of flow over trapezoidaltriangular labyrinth weirs”, Water, vol. 12(7), 2020b, p. 1-18.
[17] Ghaderi, A., Daneshfaraz, R., Torabi, M., Abraham, and
Azamathulla, H.M. “Experimental investigation on effective
scouring parameters downstream from stepped spillways”, Water
supply, vol. 20(4), 2020c, p. 1-11.
[18] Ghare, A.D., Ingle, R.N., Porey, P.D., and Gokhale, S.S.
“Block ramp design for efficient energy dissipation”, Journal of
energy dissipation, vol. 136(1), 2010, p. 1-5.
[19] Gorman, J.M., Sparrow, E.M., Smith, C.J., Ghoash, A.,
Abraham, J.P., Daneshfaraz, R., Rezezadeh, J., “In-bend pressure
drop and post-bend heat transfer for a bend with partial blockage at
its inlet”, Numerical Heat Transfer A, vol, 73, 2018, p. 743-767.
[20] Jamil, M., and Khan, S.A., “Theorical study of hydraulic jump
in circular channel section”, ISH journal of hydraulic engineering,
vol. 16(1), 2010, p. 1-10.
[21] Katourani, S., and Kashefipour, S.M., “Effect of the geometric
characteristics of baffle on hydraulic flow condition in baffled
apron drop”, Irrigation sciences and engineering, vol. 37(2), 2012,
p. 51-59.
[22] Lai, Y.G., and Wu, K.A., “Three-dimensional flow and
sediment transport model for free surface open channel flow on
unstructured flexible meshes”, Fluids, vol. 4(1), 2019, p. 1-19.

[23] Nayebzadeh, B., Lotfollahi yaghin, M.A., and Daneshfaraz,
R., “Numerical investigation of hydraulic characteristics of vertical
drops with screens and gradually wall expanding”, Amirkabir
journal of civil engineering, 2020 (In Persian).
[24] Nurouzi, R., Daneshfaraz, R., and Bazyar, A., “The study of
energy dissipation due to the use of vertical screen in the
downstream of inclined drop by adaptive Neuro-Fuzzy inference
system (ANFIS)”, AUT journal of civil engineering, 2019, (In
Persian).
[25] Ohtsu, I., and Yasuda, Y., “Hydraulic jump in sloping
channel”, Journal of hydraulic engineering, vol. 117(7), 1991, p.
905-921.
[26] Olsen, L., Abraham, J.P., Cheng, L.K., Gorman, J.M., and
Sparrow, E.M., “Summary of forced-convection fluid flow and
heat transfer for square cylinders of different aspect ratios ranging
from the cube to a two-dimensional cylinder”, Advances in Heat
Transfer, Vol. 51, 2019, p. 351-457.
[27] Pagliara, S., Das, R., and Palermo, M., “Energy dissipation on
submerged block ramps”, Journal of irrigation and drainage
engineering, vol. 134(4), 2008, p.527-532.
[28] Pagliara, S., and Palermo, M., “Effect of stilling basin
geometry on the dissipative process in the presence of block
ramps”, Journal of irrigation and drainage engineering, vol.
138(11), 2012, p. 1027-1031.
[29] Simsek, O., Akoz, M.S, and Soydan, N.G., “Numerical
validation of open channel flow over a curvilinear broad-creasted
weir”, Progress in computational fluid dynamics an international
journal, vol. 16(6), 2016, p. 364-378.
[30] Sharif, N., and Rostami, A., “Experimental and numerical
study of the effect of flow sepration on dissipating energy in
compound bucket”, APCBEE procedia, vol. 9, 2014, p. 334-338.
[31] Sparrow, E.M., Tong, J.C.K., and Abraham, J.P., “Fluid flow
in a system with separate laminar and turbulent zones”, Numerical
Heat Transfer A, vol. 53(4), 2008, p. 341-353.
[32] Sparrow, E.M., Gorman, J.M., Abraham, J.P., and
Minkowycz, W.J., “Validation of turbulence models for numerical
simulation of fluid flow and convective heat transfers”, Advances
in Heat Transfer, vol. 49, 2017, p. 397-421.
[33] Wagner, W.E., “Hydraulic model studies of the check intake
structure-potholes East canal”, Bureau of reclamation hydraulic
laboratory report hyd, 1956, 411.

Fig. 1. A) Computational domain showing the cylinder, the profiles PF1, PF2 and the mining pit as set-up in the laboratory (B).

Numerical analysis of water flow around a bridge pier in a sand mined channel

모래 채굴 수로에서 교각 주변의 물 흐름에 대한 수치 해석

Oscar HERRERA-GRANADOS1,, Abhijit LADE2, , Bimlesh KUMAR3
1 Faculty of Civil Engineering, Wroclaw University of Science and Technology, Poland
email: Oscar.Herrera-Granados@pwr.edu.pl
2 3Department of Civil Engineering, Indian Institute of Technology, Guwahati, India
email: lade176104013@iitg.ac.in
email: bimk@iitg.ac.in

ABSTRACT

Extraction of sand from river beds has a variety of effects on the hydraulic and morphological characteristicsof the fluvial systems. Recent studies on mining pit have revealed that downstream reaches of the mining pitare more prone to erosion due to increased bed shear stresses. Bridge piers in the vicinity of such mining pitsare also prone to streambed instabilities due to turbulence alterations as suggested by a few recent studies.Thus, a numerical study was carried out to study the effects of a mining pit on the hydrodynamics around acircular pier. The numerical experiments were conducted with the Computational Fluid Dynamics (CFD) codeFlow-3D, which can run several turbulence model closures. In this contribution, the authors applied theclassical RANS equations with the volume of fluid (VOF) method (Savage and Johnson, 2001).

강바닥에서 모래를 추출하는 것은 하강 시스템의 수력 학적 및 형태 학적 특성에 다양한 영향을 미칩니다. 광산 구덩이에 대한 최근 연구에 따르면 광산 구덩이의 하류 도달은 베드 전단 응력 증가로 인해 침식되기 쉽습니다. 이러한 광산 구덩이 근처의 교각은 최근 몇 가지 연구에서 제안한 바와 같이 난류 변화로 인해 유동 불안정성이 발생하기 쉽습니다. 따라서 원형 부두 주변의 유체 역학에 대한 광산 구덩이의 영향을 연구하기 위해 수치 연구가 수행되었습니다. 수치 실험은 CFD (Computational Fluid Dynamics) 코드 Flow-3D로 수행되었으며, 여러 난류 모델 폐쇄를 실행할 수 있습니다. 이 공헌에서 저자는 VOF (volume of fluid) 방법 (Savage and Johnson, 2001)과 함께 고전적인 RANS 방정식을 적용했습니다.

1. Set-up and boundary conditions

두 번의 수치 실행 결과가 이 기여도에서 비교됩니다. 첫 번째 실험에서 0.044 [m3-s-1]의 정상 유량이 원통 부두가 있는 1.0 [m] 폭의 채널을 따라 흐르는 상류 경계 조건으로 설정되었습니다. 계산 영역은 IIT Guwahati 수력학 실험실 (Lade et al., 2019b)의 틸팅 유체 크기를 기반으로 정의됩니다. 두 번째 실행에서는 동일한 배출물이 실린더의 상류에 있는 준설 사다리꼴 구덩이와 함께 실린더 주위로 통과되었습니다. 구덩이의 깊이는 0.1 [m]이고 수로 전체에 걸쳐 확장되었습니다. 수로의 길이 방향을 따라 피트의 상단 너비는 0.67 [m], 하단 너비는 0.33 [m]였습니다.

이 연구의 주요 초점은 채굴 구덩이 (그림 1의 PF2)가있을 때 구덩이 하류 (그림 1의 PF1)와 실린더 하류의 흐름 특성의 변화를 조사하는 것이 었습니다. 따라서 채널 베드는 고정 베드 모델을 사용하여 시뮬레이션 되었습니다. 두 실험의 수압 조건은 CFD 경계 조건으로 설정된 표 1에 나와 있습니다. 배출구 (하류 경계 조건)는 실험실 기록 중에 측정된 수심을 사용하여 설정되었습니다 (Lade et al., 2019a).

Fig. 1. A) Computational domain showing the cylinder, the profiles PF1, PF2 and the mining pit as set-up in the laboratory (B).
Fig. 1. A) Computational domain showing the cylinder, the profiles PF1, PF2 and the mining pit as set-up in the laboratory (B).
Fig. 2. Output of the CFD model (velocity magnitude) without the sand pit (left side) and with the trapezoidal sand pit (right side).
Fig. 2. Output of the CFD model (velocity magnitude) without the sand pit (left side) and with the trapezoidal sand pit (right side).
Fig. 3. Output of the CFD model. Streamwise velocity ux, TKE as well as Lt profiles along the locations PF1 and PF2
Fig. 3. Output of the CFD model. Streamwise velocity ux, TKE as well as Lt profiles along the locations PF1 and PF2

References

Herrera-Granados O (2018) Turbulence flow modeling of one-sharp-groyne field. In Free surface flows and transport processes :
36th International School of Hydraulics. Geoplanet: Earth and Planetary Series. Springer IP AG, 207-218.
Lade AD, Deshpande V, Kumar B (2019a) Study of flow turbulence around a circular bridge pier in sand-mined stream channel.
Proceedings of the Institution of Civil Engineers – Water Management,https://doi.org/10.1680/jwama.19.00041
Lade AD, A, DT, Kumar B (2019b) Randomness in flow turbulence around a bridge pier in a sand
mined channel..Physica A 535 122426
Savage, BM, Johnson, M.C (2001). Flow over ogee spillway: Physical and numerical model case study. J. Hydraulic Eng.,
127(8), 640–649.

Figure 6. Evolution of melt pool in the overhang region (θ = 45°, P = 100 W, v = 1000 mm/s, the streamlines are shown by arrows).

Experimental and numerical investigation of the origin of surface roughness in laser powder bed fused overhang regions

레이저 파우더 베드 융합 오버행 영역에서 표면 거칠기의 원인에 대한 실험 및 수치 조사

Shaochuan Feng,Amar M. Kamat,Soheil Sabooni &Yutao PeiPages S66-S84 | Received 18 Jan 2021, Accepted 25 Feb 2021, Published online: 10 Mar 2021

ABSTRACT

Surface roughness of laser powder bed fusion (L-PBF) printed overhang regions is a major contributor to deteriorated shape accuracy/surface quality. This study investigates the mechanisms behind the evolution of surface roughness (Ra) in overhang regions. The evolution of surface morphology is the result of a combination of border track contour, powder adhesion, warp deformation, and dross formation, which is strongly related to the overhang angle (θ). When 0° ≤ θ ≤ 15°, the overhang angle does not affect Ra significantly since only a small area of the melt pool boundaries contacts the powder bed resulting in slight powder adhesion. When 15° < θ ≤ 50°, powder adhesion is enhanced by the melt pool sinking and the increased contact area between the melt pool boundary and powder bed. When θ > 50°, large waviness of the overhang contour, adhesion of powder clusters, severe warp deformation and dross formation increase Ra sharply.

레이저 파우더 베드 퓨전 (L-PBF) 프린팅 오버행 영역의 표면 거칠기는 형상 정확도 / 표면 품질 저하의 주요 원인입니다. 이 연구 는 오버행 영역에서 표면 거칠기 (Ra ) 의 진화 뒤에 있는 메커니즘을 조사합니다 . 표면 형태의 진화는 오버행 각도 ( θ ) 와 밀접한 관련이있는 경계 트랙 윤곽, 분말 접착, 뒤틀림 변형 및 드로스 형성의 조합의 결과입니다 . 0° ≤  θ  ≤ 15° 인 경우 , 용융풀 경계의 작은 영역 만 분말 베드와 접촉하여 약간의 분말 접착이 발생하기 때문에 오버행 각도가 R a에 큰 영향을 주지 않습니다 . 15° < θ 일 때  ≤ 50°, 용융 풀 싱킹 및 용융 풀 경계와 분말 베드 사이의 증가된 접촉 면적으로 분말 접착력이 향상됩니다. θ  > 50° 일 때 오버행 윤곽의 큰 파형, 분말 클러스터의 접착, 심한 휨 변형 및 드 로스 형성이 Ra 급격히 증가 합니다.

KEYWORDS: Laser powder bed fusion (L-PBF), melt pool dynamics, overhang region, shape deviation, surface roughness

1. Introduction

레이저 분말 베드 융합 (L-PBF)은 첨단 적층 제조 (AM) 기술로, 집중된 레이저 빔을 사용하여 금속 분말을 선택적으로 융합하여 슬라이스 된 3D 컴퓨터 지원에 따라 층별로 3 차원 (3D) 금속 부품을 구축합니다. 설계 (CAD) 모델 (Chatham, Long 및 Williams 2019 ; Tan, Zhu 및 Zhou 2020 ). 재료가 인쇄 층 아래에 ​​존재하는지 여부에 따라 인쇄 영역은 각각 솔리드 영역 또는 돌출 영역으로 분류 될 수 있습니다. 따라서 오버행 영역은 고체 기판이 아니라 분말 베드 바로 위에 건설되는 특수 구조입니다 (Patterson, Messimer 및 Farrington 2017). 오버행 영역은지지 구조를 포함하거나 포함하지 않고 구축 할 수 있으며, 지지대가있는 돌출 영역의 L-PBF는 지지체가 더 낮은 밀도로 구축된다는 점을 제외 하고 (Wang and Chou 2018 ) 고체 기판의 공정과 유사합니다 (따라서 기계적 강도가 낮기 때문에 L-PBF 공정 후 기계적으로 쉽게 제거 할 수 있습니다. 따라서지지 구조로 인쇄 된 오버행 영역은 L-PBF 공정 후 지지물 제거, 연삭 및 연마와 같은 추가 후 처리 단계가 필요합니다.

수평 내부 채널의 제작과 같은 일부 특정 경우에는 공정 후 지지대를 제거하기가 어려우므로 채널 상단 절반의 돌출부 영역을 지지대없이 건설해야합니다 (Hopkinson and Dickens 2000 ). 수평 내부 채널에 사용할 수없는지지 구조 외에도 내부 표면, 특히 등각 냉각 채널 (Feng, Kamat 및 Pei 2021 ) 에서 발생하는 복잡한 3D 채널 네트워크의 경우 표면 마감 프로세스를 구현하는 것도 어렵습니다 . 결과적으로 오버행 영역은 (i) 잔류 응력에 의한 변형, (ii) 계단 효과 (Kuo et al. 2020 ; Li et al. 2020 )로 인해 설계된 모양에서 벗어날 수 있습니다 .) 및 (iii) 원하지 않는 분말 소결로 인한 향상된 표면 거칠기; 여기서, 앞의 두 요소는 일반적으로 mm 길이 스케일에서 ‘매크로’편차로 분류되고 후자는 일반적으로 µm 길이 스케일에서 ‘마이크로’편차로 인식됩니다.

열 응력에 의한 변형은 오버행 영역에서 발생하는 중요한 문제입니다 (Patterson, Messimer 및 Farrington 2017 ). 국부적 인 용융 / 냉각은 용융 풀 내부 및 주변에서 큰 온도 구배를 유도하여 응고 된 층에 집중적 인 열 응력을 유발합니다. 열 응력에 의한 뒤틀림은 고체 영역을 현저하게 변형하지 않습니다. 이러한 영역은 아래의 여러 레이어에 의해 제한되기 때문입니다. 반면에 오버행 영역은 구속되지 않고 공정 중 응력 완화로 인해 상당한 변형이 발생합니다 (Kamat 및 Pei 2019 ). 더욱이 용융 깊이는 레이어 두께보다 큽니다 (이전 레이어도 재용 해되어 빌드 된 레이어간에 충분한 결합을 보장하기 때문입니다 [Yadroitsev et al. 2013 ; Kamath et al.2014 ]),응고 된 두께가 설계된 두께보다 크기 때문에형태 편차 (예 : 드 로스 [Charles et al. 2020 ; Feng et al. 2020 ])가 발생합니다. 마이크로 스케일에서 인쇄 된 표면 (R a 및 S a ∼ 10 μm)은 기계적으로 가공 된 표면보다 거칠다 (Duval-Chaneac et al. 2018 ; Wen et al. 2018 ). 이 문제는고형화 된 용융 풀의 가장자리에 부착 된 용융되지 않은 분말의 결과로 표면 거칠기 (R a )가 일반적으로 약 20 μm인 오버행 영역에서 특히 심각합니다 (Mazur et al. 2016 ; Pakkanen et al. 2016 ).

오버행 각도 ( θ , 빌드 방향과 관련하여 측정)는 오버행 영역의 뒤틀림 편향과 표면 거칠기에 영향을 미치는 중요한 매개 변수입니다 (Kamat and Pei 2019 ; Mingear et al. 2019 ). θ ∼ 45 ° 의 오버행 각도 는 일반적으로지지 구조없이 오버행 영역을 인쇄 할 수있는 임계 값으로 합의됩니다 (Pakkanen et al. 2016 ; Kadirgama et al. 2018 ). θ 일 때이 임계 값보다 크면 오버행 영역을 허용 가능한 표면 품질로 인쇄 할 수 없습니다. 오버행 각도 외에도 레이저 매개 변수 (레이저 에너지 밀도와 관련된)는 용융 풀의 모양 / 크기 및 용융 풀 역학에 영향을줌으로써 오버행 영역의 표면 거칠기에 영향을줍니다 (Wang et al. 2013 ; Mingear et al . 2019 ).

용융 풀 역학은 고체 (Shrestha 및 Chou 2018 ) 및 오버행 (Le et al. 2020 ) 영역 모두에서 수행되는 L-PBF 공정을 포함한 레이저 재료 가공의 일반적인 물리적 현상입니다 . 용융 풀 모양, 크기 및 냉각 속도는 잔류 응력으로 인한 변형과 ​​표면 거칠기에 모두 영향을 미치므로 처리 매개 변수와 표면 형태 / 품질 사이의 다리 역할을하며 용융 풀을 이해하기 위해 수치 시뮬레이션을 사용하여 추가 조사를 수행 할 수 있습니다. 거동과 표면 거칠기에 미치는 영향. 현재까지 고체 영역의 L-PBF 동안 용융 풀 동작을 시뮬레이션하기 위해 여러 연구가 수행되었습니다. 유한 요소 방법 (FEM)과 같은 시뮬레이션 기술 (Roberts et al. 2009 ; Du et al.2019 ), 유한 차분 법 (FDM) (Wu et al. 2018 ), 전산 유체 역학 (CFD) (Lee and Zhang 2016 ), 임의의 Lagrangian-Eulerian 방법 (ALE) (Khairallah and Anderson 2014 )을 사용하여 증발 반동 압력 (Hu et al. 2018 ) 및 Marangoni 대류 (Zhang et al. 2018 ) 현상을포함하는 열 전달 (온도 장) 및 물질 전달 (용융 흐름) 프로세스. 또한 이산 요소법 (DEM)을 사용하여 무작위 분산 분말 베드를 생성했습니다 (Lee and Zhang 2016 ; Wu et al. 2018 ). 이 모델은 분말 규모의 L-PBF 공정을 시뮬레이션했습니다 (Khairallah et al. 2016) 메조 스케일 (Khairallah 및 Anderson 2014 ), 단일 트랙 (Leitz et al. 2017 )에서 다중 트랙 (Foroozmehr et al. 2016 ) 및 다중 레이어 (Huang, Khamesee 및 Toyserkani 2019 )로.

그러나 결과적인 표면 거칠기를 결정하는 오버행 영역의 용융 풀 역학은 문헌에서 거의 관심을받지 못했습니다. 솔리드 영역의 L-PBF에 대한 기존 시뮬레이션 모델이 어느 정도 참조가 될 수 있지만 오버행 영역과 솔리드 영역 간의 용융 풀 역학에는 상당한 차이가 있습니다. 오버행 영역에서 용융 금속은 분말 입자 사이의 틈새로 아래로 흘러 용융 풀이 다공성 분말 베드가 제공하는 약한 지지체 아래로 가라 앉습니다. 이것은 중력과 표면 장력의 영향이 용융 풀의 결과적인 모양 / 크기를 결정하는 데 중요하며, 결과적으로 오버행 영역의 마이크로 스케일 형태의 진화에 중요합니다. 또한 분말 입자 사이의 공극, 열 조건 (예 : 에너지 흡수,2019 ; Karimi et al. 2020 ; 노래와 영 2020 ). 표면 거칠기는 (마이크로) 형상 편차를 증가시킬뿐만 아니라 주기적 하중 동안 미세 균열의 시작 지점 역할을함으로써 기계적 강도를 저하시킵니다 (Günther et al. 2018 ). 오버행 영역의 높은 표면 거칠기는 (마이크로) 정확도 / 품질에 대한 엄격한 요구 사항이있는 부품 제조에서 L-PBF의 적용을 제한합니다.

본 연구는 실험 및 시뮬레이션 연구를 사용하여 오버행 영역 (지지물없이 제작)의 미세 형상 편차 형성 메커니즘과 표면 거칠기의 기원을 체계적이고 포괄적으로 조사합니다. 결합 된 DEM-CFD 시뮬레이션 모델은 경계 트랙 윤곽, 분말 접착 및 뒤틀림 변형의 효과를 고려하여 오버행 영역의 용융 풀 역학과 표면 형태의 형성 메커니즘을 나타 내기 위해 개발되었습니다. 표면 거칠기 R의 시뮬레이션 및 단일 요인 L-PBF 인쇄 실험을 사용하여 오버행 각도의 함수로 연구됩니다. 용융 풀의 침몰과 관련된 오버행 영역에서 분말 접착의 세 가지 메커니즘이 식별되고 자세히 설명됩니다. 마지막으로, 인쇄 된 오버행 영역에서 높은 표면 거칠기 문제를 완화 할 수 있는 잠재적 솔루션에 대해 간략하게 설명합니다.

The shape and size of the L-PBF printed samples are illustrated in Figure 1
The shape and size of the L-PBF printed samples are illustrated in Figure 1
Figure 2. Borders in the overhang region depending on the overhang angle θ
Figure 2. Borders in the overhang region depending on the overhang angle θ
Figure 3. (a) Profile of the volumetric heat source, (b) the model geometry of single-track printing on a solid substrate (unit: µm), and (c) the comparison of melt pool dimensions obtained from the experiment (right half) and simulation (left half) for a calibrated optical penetration depth of 110 µm (laser power 200 W and scan speed 800 mm/s, solidified layer thickness 30 µm, powder size 10–45 µm).
Figure 3. (a) Profile of the volumetric heat source, (b) the model geometry of single-track printing on a solid substrate (unit: µm), and (c) the comparison of melt pool dimensions obtained from the experiment (right half) and simulation (left half) for a calibrated optical penetration depth of 110 µm (laser power 200 W and scan speed 800 mm/s, solidified layer thickness 30 µm, powder size 10–45 µm).
Figure 4. The model geometry of an overhang being L-PBF processed: (a) 3D view and (b) right view.
Figure 4. The model geometry of an overhang being L-PBF processed: (a) 3D view and (b) right view.
Figure 5. The cross-sectional contour of border tracks in a 45° overhang region.
Figure 5. The cross-sectional contour of border tracks in a 45° overhang region.
Figure 6. Evolution of melt pool in the overhang region (θ = 45°, P = 100 W, v = 1000 mm/s, the streamlines are shown by arrows).
Figure 6. Evolution of melt pool in the overhang region (θ = 45°, P = 100 W, v = 1000 mm/s, the streamlines are shown by arrows).
Figure 7. The overhang contour is contributed by (a) only outer borders when θ ≤ 60° (b) both inner borders and outer borders when θ > 60°.
Figure 7. The overhang contour is contributed by (a) only outer borders when θ ≤ 60° (b) both inner borders and outer borders when θ > 60°.
Figure 8. Schematic of powder adhesion on a 45° overhang region.
Figure 8. Schematic of powder adhesion on a 45° overhang region.
Figure 9. The L-PBF printed samples with various overhang angle (a) θ = 0° (cube), (b) θ = 30°, (c) θ = 45°, (d) θ = 55° and (e) θ = 60°.
Figure 9. The L-PBF printed samples with various overhang angle (a) θ = 0° (cube), (b) θ = 30°, (c) θ = 45°, (d) θ = 55° and (e) θ = 60°.
Figure 10. Two mechanisms of powder adhesion related to the overhang angle: (a) simulation-predicted, θ = 45°; (b) simulation-predicted, θ = 60°; (c, e) optical micrographs, θ = 45°; (d, f) optical micrographs, θ = 60°. (e) and (f) are partial enlargement of (c) and (d), respectively.
Figure 10. Two mechanisms of powder adhesion related to the overhang angle: (a) simulation-predicted, θ = 45°; (b) simulation-predicted, θ = 60°; (c, e) optical micrographs, θ = 45°; (d, f) optical micrographs, θ = 60°. (e) and (f) are partial enlargement of (c) and (d), respectively.
Figure 11. Simulation-predicted surface morphology in the overhang region at different overhang angle: (a) θ = 15°, (b) θ = 30°, (c) θ = 45°, (d) θ = 60° and (e) θ = 80° (Blue solid lines: simulation-predicted contour; red dashed lines: the planar profile of designed overhang region specified by the overhang angles).
Figure 11. Simulation-predicted surface morphology in the overhang region at different overhang angle: (a) θ = 15°, (b) θ = 30°, (c) θ = 45°, (d) θ = 60° and (e) θ = 80° (Blue solid lines: simulation-predicted contour; red dashed lines: the planar profile of designed overhang region specified by the overhang angles).
Figure 12. Effect of overhang angle on surface roughness Ra in overhang regions
Figure 12. Effect of overhang angle on surface roughness Ra in overhang regions
Figure 13. Surface morphology of L-PBF printed overhang regions with different overhang angle: (a) θ = 15°, (b) θ = 30°, (c) θ = 45° and (d) θ = 60° (overhang border parameters: P = 100 W, v = 1000 mm/s).
Figure 13. Surface morphology of L-PBF printed overhang regions with different overhang angle: (a) θ = 15°, (b) θ = 30°, (c) θ = 45° and (d) θ = 60° (overhang border parameters: P = 100 W, v = 1000 mm/s).
Figure 14. Effect of (a) laser power (scan speed = 1000 mm/s) and (b) scan speed (lase power = 100 W) on surface roughness Ra in overhang regions (θ = 45°, laser power and scan speed referred to overhang border parameters, and the other process parameters are listed in Table 2).
Figure 14. Effect of (a) laser power (scan speed = 1000 mm/s) and (b) scan speed (lase power = 100 W) on surface roughness Ra in overhang regions (θ = 45°, laser power and scan speed referred to overhang border parameters, and the other process parameters are listed in Table 2).

References

  • Cai, Chao, Chrupcala Radoslaw, Jinliang Zhang, Qian Yan, Shifeng Wen, Bo Song, and Yusheng Shi. 2019. “In-Situ Preparation and Formation of TiB/Ti-6Al-4V Nanocomposite via Laser Additive Manufacturing: Microstructure Evolution and Tribological Behavior.” Powder Technology 342: 73–84. doi:10.1016/j.powtec.2018.09.088. [Crossref], [Web of Science ®], [Google Scholar]
  • Cai, Chao, Wei Shian Tey, Jiayao Chen, Wei Zhu, Xingjian Liu, Tong Liu, Lihua Zhao, and Kun Zhou. 2021. “Comparative Study on 3D Printing of Polyamide 12 by Selective Laser Sintering and Multi Jet Fusion.” Journal of Materials Processing Technology 288 (August 2020): 116882. doi:10.1016/j.jmatprotec.2020.116882. [Crossref], [Web of Science ®], [Google Scholar]
  • Cai, Chao, Xu Wu, Wan Liu, Wei Zhu, Hui Chen, Jasper Dong Qiu Chua, Chen Nan Sun, Jie Liu, Qingsong Wei, and Yusheng Shi. 2020. “Selective Laser Melting of Near-α Titanium Alloy Ti-6Al-2Zr-1Mo-1V: Parameter Optimization, Heat Treatment and Mechanical Performance.” Journal of Materials Science and Technology 57: 51–64. doi:10.1016/j.jmst.2020.05.004. [Crossref], [Web of Science ®], [Google Scholar]
  • Charles, Amal, Ahmed Elkaseer, Lore Thijs, and Steffen G. Scholz. 2020. “Dimensional Errors Due to Overhanging Features in Laser Powder Bed Fusion Parts Made of Ti-6Al-4V.” Applied Sciences 10 (7): 2416. doi:10.3390/app10072416. [Crossref], [Google Scholar]
  • Chatham, Camden A., Timothy E. Long, and Christopher B. Williams. 2019. “A Review of the Process Physics and Material Screening Methods for Polymer Powder Bed Fusion Additive Manufacturing.” Progress in Polymer Science 93: 68–95. doi:10.1016/j.progpolymsci.2019.03.003. [Crossref], [Web of Science ®], [Google Scholar]
  • Du, Yang, Xinyu You, Fengbin Qiao, Lijie Guo, and Zhengwu Liu. 2019. “A Model for Predicting the Temperature Field during Selective Laser Melting.” Results in Physics 12 (November 2018): 52–60. doi:10.1016/j.rinp.2018.11.031. [Crossref], [Web of Science ®], [Google Scholar]
  • Duval-Chaneac, M. S., S. Han, C. Claudin, F. Salvatore, J. Bajolet, and J. Rech. 2018. “Experimental Study on Finishing of Internal Laser Melting (SLM) Surface with Abrasive Flow Machining (AFM).” Precision Engineering 54 (July 2017): 1–6. doi:10.1016/j.precisioneng.2018.03.006. [Crossref], [Web of Science ®], [Google Scholar]
  • Feng, Shaochuan, Shijie Chen, Amar M. Kamat, Ru Zhang, Mingji Huang, and Liangcai Hu. 2020. “Investigation on Shape Deviation of Horizontal Interior Circular Channels Fabricated by Laser Powder Bed Fusion.” Additive Manufacturing 36 (December): 101585. doi:10.1016/j.addma.2020.101585. [Crossref], [Web of Science ®], [Google Scholar]
  • Feng, Shaochuan, Chuanzhen Huang, Jun Wang, Hongtao Zhu, Peng Yao, and Zhanqiang Liu. 2017. “An Analytical Model for the Prediction of Temperature Distribution and Evolution in Hybrid Laser-Waterjet Micro-Machining.” Precision Engineering 47: 33–45. doi:10.1016/j.precisioneng.2016.07.002. [Crossref], [Web of Science ®], [Google Scholar]
  • Feng, Shaochuan, Amar M. Kamat, and Yutao Pei. 2021. “Design and Fabrication of Conformal Cooling Channels in Molds: Review and Progress Updates.” International Journal of Heat and Mass Transfer. doi:10.1016/j.ijheatmasstransfer.2021.121082. [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
  • Flow-3D V11.2 Documentation. 2016. Flow Science, Inc. [Crossref], [Google Scholar]
  • Foroozmehr, Ali, Mohsen Badrossamay, Ehsan Foroozmehr, and Sa’id Golabi. 2016. “Finite Element Simulation of Selective Laser Melting Process Considering Optical Penetration Depth of Laser in Powder Bed.” Materials and Design 89: 255–263. doi:10.1016/j.matdes.2015.10.002. [Crossref], [Web of Science ®], [Google Scholar]
  • “Geometrical Product Specifications (GPS) — Surface Texture: Profile Method — Rules and Procedures for the Assessment of Surface Texture (ISO 4288).” 1996. International Organization for Standardization. https://www.iso.org/standard/2096.html. [Google Scholar]
  • Günther, Johannes, Stefan Leuders, Peter Koppa, Thomas Tröster, Sebastian Henkel, Horst Biermann, and Thomas Niendorf. 2018. “On the Effect of Internal Channels and Surface Roughness on the High-Cycle Fatigue Performance of Ti-6Al-4V Processed by SLM.” Materials & Design 143: 1–11. doi:10.1016/j.matdes.2018.01.042. [Crossref], [Web of Science ®], [Google Scholar]
  • Hopkinson, Neil, and Phill Dickens. 2000. “Conformal Cooling and Heating Channels Using Laser Sintered Tools.” In Solid Freeform Fabrication Conference, 490–497. Texas. doi:10.26153/tsw/3075. [Crossref], [Google Scholar]
  • Hu, Zhiheng, Haihong Zhu, Changchun Zhang, Hu Zhang, Ting Qi, and Xiaoyan Zeng. 2018. “Contact Angle Evolution during Selective Laser Melting.” Materials and Design 139: 304–313. doi:10.1016/j.matdes.2017.11.002. [Crossref], [Web of Science ®], [Google Scholar]
  • Hu, Cheng, Kejia Zhuang, Jian Weng, and Donglin Pu. 2019. “Three-Dimensional Analytical Modeling of Cutting Temperature for Round Insert Considering Semi-Infinite Boundary and Non-Uniform Heat Partition.” International Journal of Mechanical Sciences 155 (October 2018): 536–553. doi:10.1016/j.ijmecsci.2019.03.019. [Crossref], [Web of Science ®], [Google Scholar]
  • Huang, Yuze, Mir Behrad Khamesee, and Ehsan Toyserkani. 2019. “A New Physics-Based Model for Laser Directed Energy Deposition (Powder-Fed Additive Manufacturing): From Single-Track to Multi-Track and Multi-Layer.” Optics & Laser Technology 109 (August 2018): 584–599. doi:10.1016/j.optlastec.2018.08.015. [Crossref], [Web of Science ®], [Google Scholar]
  • Kadirgama, K., W. S. W. Harun, F. Tarlochan, M. Samykano, D. Ramasamy, Mohd Zaidi Azir, and H. Mehboob. 2018. “Statistical and Optimize of Lattice Structures with Selective Laser Melting (SLM) of Ti6AL4V Material.” International Journal of Advanced Manufacturing Technology 97 (1–4): 495–510. doi:10.1007/s00170-018-1913-1. [Crossref], [Web of Science ®], [Google Scholar]
  • Kamat, Amar M, and Yutao Pei. 2019. “An Analytical Method to Predict and Compensate for Residual Stress-Induced Deformation in Overhanging Regions of Internal Channels Fabricated Using Powder Bed Fusion.” Additive Manufacturing 29 (March): 100796. doi:10.1016/j.addma.2019.100796. [Crossref], [Web of Science ®], [Google Scholar]
  • Kamath, Chandrika, Bassem El-Dasher, Gilbert F. Gallegos, Wayne E. King, and Aaron Sisto. 2014. “Density of Additively-Manufactured, 316L SS Parts Using Laser Powder-Bed Fusion at Powers up to 400 W.” International Journal of Advanced Manufacturing Technology 74 (1–4): 65–78. doi:10.1007/s00170-014-5954-9. [Crossref], [Web of Science ®], [Google Scholar]
  • Karimi, J., C. Suryanarayana, I. Okulov, and K. G. Prashanth. 2020. “Selective Laser Melting of Ti6Al4V: Effect of Laser Re-Melting.” Materials Science and Engineering A (July): 140558. doi:10.1016/j.msea.2020.140558. [Crossref], [Web of Science ®], [Google Scholar]
  • Khairallah, Saad A., and Andy Anderson. 2014. “Mesoscopic Simulation Model of Selective Laser Melting of Stainless Steel Powder.” Journal of Materials Processing Technology 214 (11): 2627–2636. doi:10.1016/j.jmatprotec.2014.06.001. [Crossref], [Web of Science ®], [Google Scholar]
  • Khairallah, Saad A., Andrew T. Anderson, Alexander Rubenchik, and Wayne E. King. 2016. “Laser Powder-Bed Fusion Additive Manufacturing: Physics of Complex Melt Flow and Formation Mechanisms of Pores, Spatter, and Denudation Zones.” Edited by Adedeji B. Badiru, Vhance V. Valencia, and David Liu. Acta Materialia 108 (April): 36–45. doi:10.1016/j.actamat.2016.02.014. [Crossref], [Web of Science ®], [Google Scholar]
  • Kuo, C. N., C. K. Chua, P. C. Peng, Y. W. Chen, S. L. Sing, S. Huang, and Y. L. Su. 2020. “Microstructure Evolution and Mechanical Property Response via 3D Printing Parameter Development of Al–Sc Alloy.” Virtual and Physical Prototyping 15 (1): 120–129. doi:10.1080/17452759.2019.1698967. [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
  • Le, K. Q., C. H. Wong, K. H. G. Chua, C. Tang, and H. Du. 2020. “Discontinuity of Overhanging Melt Track in Selective Laser Melting Process.” International Journal of Heat and Mass Transfer 162 (December): 120284. doi:10.1016/j.ijheatmasstransfer.2020.120284. [Crossref], [Web of Science ®], [Google Scholar]
  • Lee, Y. S., and W. Zhang. 2016. “Modeling of Heat Transfer, Fluid Flow and Solidification Microstructure of Nickel-Base Superalloy Fabricated by Laser Powder Bed Fusion.” Additive Manufacturing 12: 178–188. doi:10.1016/j.addma.2016.05.003. [Crossref], [Web of Science ®], [Google Scholar]
  • Leitz, K. H., P. Singer, A. Plankensteiner, B. Tabernig, H. Kestler, and L. S. Sigl. 2017. “Multi-Physical Simulation of Selective Laser Melting.” Metal Powder Report 72 (5): 331–338. doi:10.1016/j.mprp.2016.04.004. [Crossref], [Google Scholar]
  • Li, Jian, Jing Hu, Yi Zhu, Xiaowen Yu, Mengfei Yu, and Huayong Yang. 2020. “Surface Roughness Control of Root Analogue Dental Implants Fabricated Using Selective Laser Melting.” Additive Manufacturing 34 (September 2019): 101283. doi:10.1016/j.addma.2020.101283. [Crossref], [Web of Science ®], [Google Scholar]
  • Li, Yingli, Kun Zhou, Pengfei Tan, Shu Beng Tor, Chee Kai Chua, and Kah Fai Leong. 2018. “Modeling Temperature and Residual Stress Fields in Selective Laser Melting.” International Journal of Mechanical Sciences 136 (February): 24–35. doi:10.1016/j.ijmecsci.2017.12.001. [Crossref], [Web of Science ®], [Google Scholar]
  • Mazur, MacIej, Martin Leary, Matthew McMillan, Joe Elambasseril, and Milan Brandt. 2016. “SLM Additive Manufacture of H13 Tool Steel with Conformal Cooling and Structural Lattices.” Rapid Prototyping Journal 22 (3): 504–518. doi:10.1108/RPJ-06-2014-0075. [Crossref], [Web of Science ®], [Google Scholar]
  • Mingear, Jacob, Bing Zhang, Darren Hartl, and Alaa Elwany. 2019. “Effect of Process Parameters and Electropolishing on the Surface Roughness of Interior Channels in Additively Manufactured Nickel-Titanium Shape Memory Alloy Actuators.” Additive Manufacturing 27 (October 2018): 565–575. doi:10.1016/j.addma.2019.03.027. [Crossref], [Web of Science ®], [Google Scholar]
  • Pakkanen, Jukka, Flaviana Calignano, Francesco Trevisan, Massimo Lorusso, Elisa Paola Ambrosio, Diego Manfredi, and Paolo Fino. 2016. “Study of Internal Channel Surface Roughnesses Manufactured by Selective Laser Melting in Aluminum and Titanium Alloys.” Metallurgical and Materials Transactions A 47 (8): 3837–3844. doi:10.1007/s11661-016-3478-7. [Crossref], [Web of Science ®], [Google Scholar]
  • Patterson, Albert E., Sherri L. Messimer, and Phillip A. Farrington. 2017. “Overhanging Features and the SLM/DMLS Residual Stresses Problem: Review and Future Research Need.” Technologies 5 (4): 15. doi:10.3390/technologies5020015. [Crossref], [Web of Science ®], [Google Scholar]
  • Roberts, I. A., C. J. Wang, R. Esterlein, M. Stanford, and D. J. Mynors. 2009. “A Three-Dimensional Finite Element Analysis of the Temperature Field during Laser Melting of Metal Powders in Additive Layer Manufacturing.” International Journal of Machine Tools and Manufacture 49 (12–13): 916–923. doi:10.1016/j.ijmachtools.2009.07.004. [Crossref], [Web of Science ®], [Google Scholar]
  • Shrestha, Subin, and Kevin Chou. 2018. “Computational Analysis of Thermo-Fluid Dynamics with Metallic Powder in SLM.” In CFD Modeling and Simulation in Materials Processing 2018, edited by Laurentiu Nastac, Koulis Pericleous, Adrian S. Sabau, Lifeng Zhang, and Brian G. Thomas, 85–95. Cham, Switzerland: Springer Nature. doi:10.1007/978-3-319-72059-3_9. [Crossref], [Google Scholar]
  • Sing, S. L., and W. Y. Yeong. 2020. “Laser Powder Bed Fusion for Metal Additive Manufacturing: Perspectives on Recent Developments.” Virtual and Physical Prototyping 15 (3): 359–370. doi:10.1080/17452759.2020.1779999. [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
  • Šmilauer, Václav, Emanuele Catalano, Bruno Chareyre, Sergei Dorofeenko, Jérôme Duriez, Nolan Dyck, Jan Eliáš, et al. 2015. Yade Documentation. 2nd ed. The Yade Project. doi:10.5281/zenodo.34073. [Crossref], [Google Scholar]
  • Tan, Pengfei, Fei Shen, Biao Li, and Kun Zhou. 2019. “A Thermo-Metallurgical-Mechanical Model for Selective Laser Melting of Ti6Al4V.” Materials & Design 168 (April): 107642. doi:10.1016/j.matdes.2019.107642. [Crossref], [Web of Science ®], [Google Scholar]
  • Tan, Lisa Jiaying, Wei Zhu, and Kun Zhou. 2020. “Recent Progress on Polymer Materials for Additive Manufacturing.” Advanced Functional Materials 30 (43): 1–54. doi:10.1002/adfm.202003062. [Crossref], [Web of Science ®], [Google Scholar]
  • Wang, Xiaoqing, and Kevin Chou. 2018. “Effect of Support Structures on Ti-6Al-4V Overhang Parts Fabricated by Powder Bed Fusion Electron Beam Additive Manufacturing.” Journal of Materials Processing Technology 257 (February): 65–78. doi:10.1016/j.jmatprotec.2018.02.038. [Crossref], [Web of Science ®], [Google Scholar]
  • Wang, Di, Yongqiang Yang, Ziheng Yi, and Xubin Su. 2013. “Research on the Fabricating Quality Optimization of the Overhanging Surface in SLM Process.” International Journal of Advanced Manufacturing Technology 65 (9–12): 1471–1484. doi:10.1007/s00170-012-4271-4. [Crossref], [Web of Science ®], [Google Scholar]
  • Wen, Peng, Maximilian Voshage, Lucas Jauer, Yanzhe Chen, Yu Qin, Reinhart Poprawe, and Johannes Henrich Schleifenbaum. 2018. “Laser Additive Manufacturing of Zn Metal Parts for Biodegradable Applications: Processing, Formation Quality and Mechanical Properties.” Materials and Design 155: 36–45. doi:10.1016/j.matdes.2018.05.057. [Crossref], [Web of Science ®], [Google Scholar]
  • Wu, Yu-che, Cheng-hung San, Chih-hsiang Chang, Huey-jiuan Lin, Raed Marwan, Shuhei Baba, and Weng-Sing Hwang. 2018. “Numerical Modeling of Melt-Pool Behavior in Selective Laser Melting with Random Powder Distribution and Experimental Validation.” Journal of Materials Processing Technology 254 (November 2017): 72–78. doi:10.1016/j.jmatprotec.2017.11.032. [Crossref], [Web of Science ®], [Google Scholar]
  • Yadroitsev, I., P. Krakhmalev, I. Yadroitsava, S. Johansson, and I. Smurov. 2013. “Energy Input Effect on Morphology and Microstructure of Selective Laser Melting Single Track from Metallic Powder.” Journal of Materials Processing Technology 213 (4): 606–613. doi:10.1016/j.jmatprotec.2012.11.014. [Crossref], [Web of Science ®], [Google Scholar]
  • Yu, Wenhui, Swee Leong Sing, Chee Kai Chua, and Xuelei Tian. 2019. “Influence of Re-Melting on Surface Roughness and Porosity of AlSi10Mg Parts Fabricated by Selective Laser Melting.” Journal of Alloys and Compounds 792: 574–581. doi:10.1016/j.jallcom.2019.04.017. [Crossref], [Web of Science ®], [Google Scholar]
  • Zhang, Dongyun, Pudan Zhang, Zhen Liu, Zhe Feng, Chengjie Wang, and Yanwu Guo. 2018. “Thermofluid Field of Molten Pool and Its Effects during Selective Laser Melting (SLM) of Inconel 718 Alloy.” Additive Manufacturing 21 (100): 567–578. doi:10.1016/j.addma.2018.03.031. [Crossref], [Web of Science ®], [Google Scholar]
Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).

Continuous-Flow Separation of Magnetic Particles from Biofluids: How Does the Microdevice Geometry Determine the Separation Performance?

1Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
2William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 W. Woodruff Ave., Columbus, OH 43210, USA
*Author to whom correspondence should be addressed.
Sensors 202020(11), 3030; https://doi.org/10.3390/s20113030
Received: 16 April 2020 / Revised: 21 May 2020 / Accepted: 25 May 2020 / Published: 27 May 2020
(This article belongs to the Special Issue Lab-on-a-Chip and Microfluidic Sensors)

Abstract

The use of functionalized magnetic particles for the detection or separation of multiple chemicals and biomolecules from biofluids continues to attract significant attention. After their incubation with the targeted substances, the beads can be magnetically recovered to perform analysis or diagnostic tests. Particle recovery with permanent magnets in continuous-flow microdevices has gathered great attention in the last decade due to the multiple advantages of microfluidics. As such, great efforts have been made to determine the magnetic and fluidic conditions for achieving complete particle capture; however, less attention has been paid to the effect of the channel geometry on the system performance, although it is key for designing systems that simultaneously provide high particle recovery and flow rates. Herein, we address the optimization of Y-Y-shaped microchannels, where magnetic beads are separated from blood and collected into a buffer stream by applying an external magnetic field. The influence of several geometrical features (namely cross section shape, thickness, length, and volume) on both bead recovery and system throughput is studied. For that purpose, we employ an experimentally validated Computational Fluid Dynamics (CFD) numerical model that considers the dominant forces acting on the beads during separation. Our results indicate that rectangular, long devices display the best performance as they deliver high particle recovery and high throughput. Thus, this methodology could be applied to the rational design of lab-on-a-chip devices for any magnetically driven purification, enrichment or isolation.

Keywords: particle magnetophoresisCFDcross sectionchip fabrication

Korea Abstract

생체 유체에서 여러 화학 물질과 생체 분자의 검출 또는 분리를위한 기능화 된 자성 입자의 사용은 계속해서 상당한 관심을 받고 있습니다. 표적 물질과 함께 배양 한 후 비드를 자기 적으로 회수하여 분석 또는 진단 테스트를 수행 할 수 있습니다. 연속 흐름 마이크로 장치에서 영구 자석을 사용한 입자 회수는 마이크로 유체의 여러 장점으로 인해 지난 10 년 동안 큰 관심을 모았습니다. 

따라서 완전한 입자 포획을 달성하기 위한 자기 및 유체 조건을 결정하기 위해 많은 노력을 기울였습니다. 그러나 높은 입자 회수율과 유속을 동시에 제공하는 시스템을 설계하는 데있어 핵심이기는 하지만 시스템 성능에 대한 채널 형상의 영향에 대해서는 덜주의를 기울였습니다. 

여기에서 우리는 자기 비드가 혈액에서 분리되고 외부 자기장을 적용하여 버퍼 스트림으로 수집되는 YY 모양의 마이크로 채널의 최적화를 다룹니다. 비드 회수 및 시스템 처리량에 대한 여러 기하학적 특징 (즉, 단면 형상, 두께, 길이 및 부피)의 영향을 연구합니다. 

이를 위해 분리 중에 비드에 작용하는 지배적인 힘을 고려하는 실험적으로 검증 된 CFD (Computational Fluid Dynamics) 수치 모델을 사용합니다. 우리의 결과는 직사각형의 긴 장치가 높은 입자 회수율과 높은 처리량을 제공하기 때문에 최고의 성능을 보여줍니다. 

따라서 이 방법론은 자기 구동 정제, 농축 또는 분리를 위한 랩온어 칩 장치의 합리적인 설계에 적용될 수 있습니다.

Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.

References

  1. Gómez-Pastora, J.; Xue, X.; Karampelas, I.H.; Bringas, E.; Furlani, E.P.; Ortiz, I. Analysis of separators for magnetic beads recovery: From large systems to multifunctional microdevices. Sep. Purif. Technol. 2017172, 16–31. [Google Scholar] [CrossRef]
  2. Wise, N.; Grob, T.; Morten, K.; Thompson, I.; Sheard, S. Magnetophoretic velocities of superparamagnetic particles, agglomerates and complexes. J. Magn. Magn. Mater. 2015384, 328–334. [Google Scholar] [CrossRef]
  3. Khashan, S.A.; Elnajjar, E.; Haik, Y. CFD simulation of the magnetophoretic separation in a microchannel. J. Magn. Magn. Mater. 2011323, 2960–2967. [Google Scholar] [CrossRef]
  4. Khashan, S.A.; Furlani, E.P. Scalability analysis of magnetic bead separation in a microchannel with an array of soft magnetic elements in a uniform magnetic field. Sep. Purif. Technol. 2014125, 311–318. [Google Scholar] [CrossRef]
  5. Furlani, E.P. Magnetic biotransport: Analysis and applications. Materials 20103, 2412–2446. [Google Scholar] [CrossRef]
  6. Gómez-Pastora, J.; Bringas, E.; Ortiz, I. Design of novel adsorption processes for the removal of arsenic from polluted groundwater employing functionalized magnetic nanoparticles. Chem. Eng. Trans. 201647, 241–246. [Google Scholar]
  7. Gómez-Pastora, J.; Bringas, E.; Lázaro-Díez, M.; Ramos-Vivas, J.; Ortiz, I. The reverse of controlled release: Controlled sequestration of species and biotoxins into nanoparticles (NPs). In Drug Delivery Systems; Stroeve, P., Mahmoudi, M., Eds.; World Scientific: Hackensack, NJ, USA, 2017; pp. 207–244. ISBN 9789813201057. [Google Scholar]
  8. Ruffert, C. Magnetic bead-magic bullet. Micromachines 20167, 21. [Google Scholar] [CrossRef]
  9. Yáñez-Sedeño, P.; Campuzano, S.; Pingarrón, J.M. Magnetic particles coupled to disposable screen printed transducers for electrochemical biosensing. Sensors 201616, 1585. [Google Scholar] [CrossRef]
  10. Schrittwieser, S.; Pelaz, B.; Parak, W.J.; Lentijo-Mozo, S.; Soulantica, K.; Dieckhoff, J.; Ludwig, F.; Guenther, A.; Tschöpe, A.; Schotter, J. Homogeneous biosensing based on magnetic particle labels. Sensors 201616, 828. [Google Scholar] [CrossRef]
  11. He, J.; Huang, M.; Wang, D.; Zhang, Z.; Li, G. Magnetic separation techniques in sample preparation for biological analysis: A review. J. Pharm. Biomed. Anal. 2014101, 84–101. [Google Scholar] [CrossRef]
  12. Ha, Y.; Ko, S.; Kim, I.; Huang, Y.; Mohanty, K.; Huh, C.; Maynard, J.A. Recent advances incorporating superparamagnetic nanoparticles into immunoassays. ACS Appl. Nano Mater. 20181, 512–521. [Google Scholar] [CrossRef]
  13. Gómez-Pastora, J.; González-Fernández, C.; Fallanza, M.; Bringas, E.; Ortiz, I. Flow patterns and mass transfer performance of miscible liquid-liquid flows in various microchannels: Numerical and experimental studies. Chem. Eng. J. 2018344, 487–497. [Google Scholar] [CrossRef]
  14. Gale, B.K.; Jafek, A.R.; Lambert, C.J.; Goenner, B.L.; Moghimifam, H.; Nze, U.C.; Kamarapu, S.K. A review of current methods in microfluidic device fabrication and future commercialization prospects. Inventions 20183, 60. [Google Scholar] [CrossRef]
  15. Nanobiotechnology; Concepts, Applications and Perspectives; Niemeyer, C.M.; Mirkin, C.A. (Eds.) Wiley-VCH: Weinheim, Germany, 2004; ISBN 3527305068. [Google Scholar]
  16. Khashan, S.A.; Dagher, S.; Alazzam, A.; Mathew, B.; Hilal-Alnaqbi, A. Microdevice for continuous flow magnetic separation for bioengineering applications. J. Micromech. Microeng. 201727, 055016. [Google Scholar] [CrossRef]
  17. Basauri, A.; Gomez-Pastora, J.; Fallanza, M.; Bringas, E.; Ortiz, I. Predictive model for the design of reactive micro-separations. Sep. Purif. Technol. 2019209, 900–907. [Google Scholar] [CrossRef]
  18. Abdollahi, P.; Karimi-Sabet, J.; Moosavian, M.A.; Amini, Y. Microfluidic solvent extraction of calcium: Modeling and optimization of the process variables. Sep. Purif. Technol. 2020231, 115875. [Google Scholar] [CrossRef]
  19. Khashan, S.A.; Alazzam, A.; Furlani, E. A novel design for a microfluidic magnetophoresis system: Computational study. In Proceedings of the 12th International Symposium on Fluid Control, Measurement and Visualization (FLUCOME2013), Nara, Japan, 18–23 November 2013. [Google Scholar]
  20. Pamme, N. Magnetism and microfluidics. Lab Chip 20066, 24–38. [Google Scholar] [CrossRef]
  21. Gómez-Pastora, J.; Amiri Roodan, V.; Karampelas, I.H.; Alorabi, A.Q.; Tarn, M.D.; Iles, A.; Bringas, E.; Paunov, V.N.; Pamme, N.; Furlani, E.P.; et al. Two-step numerical approach to predict ferrofluid droplet generation and manipulation inside multilaminar flow chambers. J. Phys. Chem. C 2019123, 10065–10080. [Google Scholar] [CrossRef]
  22. Gómez-Pastora, J.; Karampelas, I.H.; Bringas, E.; Furlani, E.P.; Ortiz, I. Numerical analysis of bead magnetophoresis from flowing blood in a continuous-flow microchannel: Implications to the bead-fluid interactions. Sci. Rep. 20199, 7265. [Google Scholar] [CrossRef]
  23. Tarn, M.D.; Pamme, N. On-Chip Magnetic Particle-Based Immunoassays Using Multilaminar Flow for Clinical Diagnostics. In Microchip Diagnostics Methods and Protocols; Taly, V., Viovy, J.L., Descroix, S., Eds.; Humana Press: New York, NY, USA, 2017; pp. 69–83. [Google Scholar]
  24. Phurimsak, C.; Tarn, M.D.; Peyman, S.A.; Greenman, J.; Pamme, N. On-chip determination of c-reactive protein using magnetic particles in continuous flow. Anal. Chem. 201486, 10552–10559. [Google Scholar] [CrossRef]
  25. Wu, X.; Wu, H.; Hu, Y. Enhancement of separation efficiency on continuous magnetophoresis by utilizing L/T-shaped microchannels. Microfluid. Nanofluid. 201111, 11–24. [Google Scholar] [CrossRef]
  26. Vojtíšek, M.; Tarn, M.D.; Hirota, N.; Pamme, N. Microfluidic devices in superconducting magnets: On-chip free-flow diamagnetophoresis of polymer particles and bubbles. Microfluid. Nanofluid. 201213, 625–635. [Google Scholar] [CrossRef]
  27. Gómez-Pastora, J.; González-Fernández, C.; Real, E.; Iles, A.; Bringas, E.; Furlani, E.P.; Ortiz, I. Computational modeling and fluorescence microscopy characterization of a two-phase magnetophoretic microsystem for continuous-flow blood detoxification. Lab Chip 201818, 1593–1606. [Google Scholar] [CrossRef] [PubMed]
  28. Forbes, T.P.; Forry, S.P. Microfluidic magnetophoretic separations of immunomagnetically labeled rare mammalian cells. Lab Chip 201212, 1471–1479. [Google Scholar] [CrossRef]
  29. Nandy, K.; Chaudhuri, S.; Ganguly, R.; Puri, I.K. Analytical model for the magnetophoretic capture of magnetic microspheres in microfluidic devices. J. Magn. Magn. Mater. 2008320, 1398–1405. [Google Scholar] [CrossRef]
  30. Plouffe, B.D.; Lewis, L.H.; Murthy, S.K. Computational design optimization for microfluidic magnetophoresis. Biomicrofluidics 20115, 013413. [Google Scholar] [CrossRef] [PubMed]
  31. Hale, C.; Darabi, J. Magnetophoretic-based microfluidic device for DNA isolation. Biomicrofluidics 20148, 044118. [Google Scholar] [CrossRef] [PubMed]
  32. Becker, H.; Gärtner, C. Polymer microfabrication methods for microfluidic analytical applications. Electrophoresis 200021, 12–26. [Google Scholar] [CrossRef]
  33. Pekas, N.; Zhang, Q.; Nannini, M.; Juncker, D. Wet-etching of structures with straight facets and adjustable taper into glass substrates. Lab Chip 201010, 494–498. [Google Scholar] [CrossRef]
  34. Wang, T.; Chen, J.; Zhou, T.; Song, L. Fabricating microstructures on glass for microfluidic chips by glass molding process. Micromachines 20189, 269. [Google Scholar] [CrossRef]
  35. Castaño-Álvarez, M.; Pozo Ayuso, D.F.; García Granda, M.; Fernández-Abedul, M.T.; Rodríguez García, J.; Costa-García, A. Critical points in the fabrication of microfluidic devices on glass substrates. Sens. Actuators B Chem. 2008130, 436–448. [Google Scholar] [CrossRef]
  36. Prakash, S.; Kumar, S. Fabrication of microchannels: A review. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 2015229, 1273–1288. [Google Scholar] [CrossRef]
  37. Leester-Schädel, M.; Lorenz, T.; Jürgens, F.; Ritcher, C. Fabrication of Microfluidic Devices. In Microsystems for Pharmatechnology: Manipulation of Fluids, Particles, Droplets, and Cells; Dietzel, A., Ed.; Springer: Basel, Switzerland, 2016; pp. 23–57. ISBN 9783319269207. [Google Scholar]
  38. Bartlett, N.W.; Wood, R.J. Comparative analysis of fabrication methods for achieving rounded microchannels in PDMS. J. Micromech. Microeng. 201626, 115013. [Google Scholar] [CrossRef]
  39. Ng, P.F.; Lee, K.I.; Yang, M.; Fei, B. Fabrication of 3D PDMS microchannels of adjustable cross-sections via versatile gel templates. Polymers 201911, 64. [Google Scholar] [CrossRef] [PubMed]
  40. Furlani, E.P.; Sahoo, Y.; Ng, K.C.; Wortman, J.C.; Monk, T.E. A model for predicting magnetic particle capture in a microfluidic bioseparator. Biomed. Microdevices 20079, 451–463. [Google Scholar] [CrossRef]
  41. Tarn, M.D.; Peyman, S.A.; Robert, D.; Iles, A.; Wilhelm, C.; Pamme, N. The importance of particle type selection and temperature control for on-chip free-flow magnetophoresis. J. Magn. Magn. Mater. 2009321, 4115–4122. [Google Scholar] [CrossRef]
  42. Furlani, E.P. Permanent Magnet and Electromechanical Devices; Materials, Analysis and Applications; Academic Press: Waltham, MA, USA, 2001. [Google Scholar]
  43. White, F.M. Viscous Fluid Flow; McGraw-Hill: New York, NY, USA, 1974. [Google Scholar]
  44. Mathew, B.; Alazzam, A.; El-Khasawneh, B.; Maalouf, M.; Destgeer, G.; Sung, H.J. Model for tracing the path of microparticles in continuous flow microfluidic devices for 2D focusing via standing acoustic waves. Sep. Purif. Technol. 2015153, 99–107. [Google Scholar] [CrossRef]
  45. Furlani, E.J.; Furlani, E.P. A model for predicting magnetic targeting of multifunctional particles in the microvasculature. J. Magn. Magn. Mater. 2007312, 187–193. [Google Scholar] [CrossRef]
  46. Furlani, E.P.; Ng, K.C. Analytical model of magnetic nanoparticle transport and capture in the microvasculature. Phys. Rev. E 200673, 061919. [Google Scholar] [CrossRef]
  47. Eibl, R.; Eibl, D.; Pörtner, R.; Catapano, G.; Czermak, P. Cell and Tissue Reaction Engineering; Springer: Berlin/Heidelberg, Germany, 2009. [Google Scholar]
  48. Pamme, N.; Eijkel, J.C.T.; Manz, A. On-chip free-flow magnetophoresis: Separation and detection of mixtures of magnetic particles in continuous flow. J. Magn. Magn. Mater. 2006307, 237–244. [Google Scholar] [CrossRef]
  49. Alorabi, A.Q.; Tarn, M.D.; Gómez-Pastora, J.; Bringas, E.; Ortiz, I.; Paunov, V.N.; Pamme, N. On-chip polyelectrolyte co