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

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

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

Abstract

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

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

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

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

KEYWORDS: 

1. Introduction

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

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

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

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

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

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

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

(6)

1.2. Engineering Approach of Microfluidic Transport Phenomena in LOC Systems

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

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

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

1.3. Scope of the Review

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

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

2. Blood Flow Phenomena

ARTICLE SECTIONS

Jump To


2.1. Physiological Blood Flow Behavior

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

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

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

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

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

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

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

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

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

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

2.1.1. RBC Aggregation

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

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

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

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

2.1.2. Fåhræus-Lindqvist Effect

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

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

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

2.1.3. Cell-Free Layer Formation

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

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

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

2.1.4. Plasma Skimming in Bifurcation Networks

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

(20) thickness of the CFL, 

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

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

2.2. Modeling on Blood Flow Dynamics

2.2.1. Blood Properties and Mathematical Models of Blood Rheology

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

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

(1)where τ

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

0 = 0.0056 Pa and η = 0.0035 Pa·s. 

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

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

(24−26)

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

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

t) and the fibrinogen concentration (c

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

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

(27) The study from Apostolidis et al. 

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

(29) and the Oldroyd-B model 

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

(31) and thixotropy 

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

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

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

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

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

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

(36)

2.2.2. Numerical Methods (FDM, FEM, FVM)

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

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

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

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

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

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

(42)

2.2.3. Modeling Methods of Blood Flow Dynamics

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

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

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

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

(46) The study by Xu et al. 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(61,62) and capillaries, 

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

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

(64−70) Ye at al. 

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

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

(66) Literature by Li et al. 

(68) and Beris et al. 

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

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

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

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

3. Capillary Driven Blood Flow in LOC Systems

ARTICLE SECTIONS

Jump To


3.1. Capillary Driven Flow Phenomena

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

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

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

3.2. Theoretical and Numerical Modeling of Capillary Driven Blood Flow

3.2.1. Theoretical Basis and Assumptions of Microfluidic Flow

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

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

∇·𝐮⇀=0∇·�⇀=0

(7)

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

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

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

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

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

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

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

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

(74) is as follows:

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

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

bθ

tθ

l, and θ

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

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

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

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

(75) can be shown below:

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

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

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

𝜇=𝑘·(𝛾˙)𝑛−1�=�·(�˙)�−1

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

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

ij. The updated L–W equation by Cito 

(76) is expressed as

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

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

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

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

Berthier et al. 

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

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

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

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

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

(78) through Casson’s law, 

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

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

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

ARTICLE SECTIONS

Jump To


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

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

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

4.1. EOF Phenomena

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

D), expressed as

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

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

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

0 is the ionic density.

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

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

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

4.2. Modeling on Electro-osmotic Viscoelastic Fluid Flow

4.2.1. Theoretical Basis of EOF Mechanisms

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

𝐹⇀=𝑝𝐸𝐸⇀�⇀=���⇀, where ρ

E and 

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

∇2𝜙=0∇2�=0

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

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

(17)where D

in

i, and z

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

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

(18)where n

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

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

4.2.2. EOF Modeling for Viscoelastic Fluids

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

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

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

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

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

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

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

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

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

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

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

𝜏=𝜂p𝜆(𝐜−𝐈)�=�p�(�−�)

(19)where η

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

Θ=ln(𝐜)=𝐑ln(𝚲)𝐑Θ=ln(�)=�⁡ln(�)�

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

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

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

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

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

xx). 

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

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

(91)

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

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

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

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

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

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

4.3. EOF Applications in LOC Systems

4.3.1. Mixing in LOC Systems

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

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

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

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

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

(1) as described below:

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

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

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

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

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

(23)where c

i is the species concentration of species i and D

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

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

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

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

(24)where C*(y*) and C

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

𝐶∗=𝐶𝐶ref�*=��ref, where C

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

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

(97) can then be calculated as below:

𝜀𝑥=1−𝜎sd𝜎sd,0��=1−�sd�sd,0

(25)where σ

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

5. Summary

ARTICLE SECTIONS

Jump To


5.1. Conclusion

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

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

5.2. Future Directions

5.2.1. Electro-osmosis Mixing in LOC Systems

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

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

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

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

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

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

5.2.2. Electro-osmosis Separation in LOC Systems

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

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

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

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

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

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

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

5.2.3. Relationship between External Forces and Microfluidic Systems

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

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

+.

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

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

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

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

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

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

5.3. Challenges

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

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

Author Information

ARTICLE SECTIONS

Jump To


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

Acknowledgments

ARTICLE SECTIONS

Jump To


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

Vocabulary

ARTICLE SECTIONS

Jump To


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

References

ARTICLE SECTIONS

Jump To


This article references 108 other publications.

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

새로운 콘크리트의 유체 흐름 모델링

Sous la direction de :
Marc Jolin, directeur de recherche
Benoit Bissonnette, codirecteur de recherche

Modélisation de l’écoulement du béton frais

Abstract

현재의 기후 비상 사태와 기후 변화에 관한 다양한 과학적 보고서를 고려할 때 인간이 만든 오염을 대폭 줄이는 것은 필수적이며 심지어 중요합니다. 최신 IPCC(기후변화에 관한 정부 간 패널) 보고서(2022)는 2030년까지 배출량을 절반으로 줄여야 함을 나타내며, 지구 보존을 위해 즉각적인 조치를 취해야 한다고 강력히 강조합니다.

이러한 의미에서 콘크리트 생산 산업은 전체 인간 이산화탄소 배출량의 4~8%를 담당하고 있으므로 환경에 미치는 영향을 줄이기 위한 진화가 시급히 필요합니다.

본 연구의 주요 목적은 이미 사용 가능한 기술적 품질 관리 도구를 사용하여 생산을 최적화하고 혼합 시간을 단축하며 콘크리트 폐기물을 줄이기 위한 신뢰할 수 있고 활용 가능한 수치 모델을 개발함으로써 이러한 산업 전환에 참여하는 것입니다.

실제로, 혼합 트럭 내부의 신선한 콘크리트의 거동과 흐름 프로파일을 더 잘 이해할 수 있는 수치 시뮬레이션을 개발하면 혼합 시간과 비용을 더욱 최적화할 수 있으므로 매우 유망합니다. 이러한 복잡한 수치 도구를 활용할 수 있으려면 수치 시뮬레이션을 검증, 특성화 및 보정하기 위해 기본 신 콘크리트 흐름 모델의 구현이 필수적입니다.

이 논문에서는 세 가지 단순 유동 모델의 개발이 논의되고 얻은 결과는 신선한 콘크리트 유동의 수치적 거동을 검증하는 데 사용됩니다. 이러한 각 모델은 강점과 약점을 갖고 있으며, 신선한 콘크리트의 유변학과 유동 거동을 훨씬 더 잘 이해할 수 있는 수치 작업 환경을 만드는 데 기여합니다.

따라서 이 연구 프로젝트는 새로운 콘크리트 생산의 완전한 모델링을 위한 진정한 관문입니다.

In view of the current climate emergency and the various scientific reports on climate change, it is essential and even vital to drastically reduce man-made pollution. The latest IPCC (Intergovernmental Panel on Climate Change) report (2022) indicates that emissions must be halved by 2030 and strongly emphasizes the need to act immediately to preserve the planet. In this sense, the concrete production industry is responsible for 4-8% of total human carbon dioxide emissions and therefore urgently needs to evolve to reduce its environmental impact. The main objective of this study is to participate in this industrial transition by developing a reliable and exploitable numerical model to optimize the production, reduce mixing time and also reduce concrete waste by using technological quality control tools already available. Indeed, developing a numerical simulation allowing to better understand the behavior and flow profiles of fresh concrete inside a mixing-truck is extremely promising as it allows for further optimization of mixing times and costs. In order to be able to exploit such a complex numerical tool, the implementation of elementary fresh concrete flow models is essential to validate, characterize and calibrate the numerical simulations. In this thesis, the development of three simple flow models is discussed and the results obtained are used to validate the numerical behavior of fresh concrete flow. Each of these models has strengths and weaknesses and contributes to the creation of a numerical working environment that provides a much better understanding of the rheology and flow behavior of fresh concrete. This research project is therefore a real gateway to a full modelling of fresh concrete production.


Key words

fresh concrete, rheology, numerical simulation, mixer-truck, rheological probe.

Figure 2-15: Système expérimental du plan incliné
Figure 2-15: Système expérimental du plan incliné
Figure 2-19: Essai d'affaissement au cône d'Abrams
Figure 2-19: Essai d’affaissement au cône d’Abrams

Reference

Amziane, S., Ferraris, C. F., & Koehler, E. (2006). Feasibility of Using a Concrete
Mixing Truck as a Rheometer.
Anderson, J. D. (1991). Fundamentals of aerodynamics. McGraw-Hill.
Balmforth, N. J., Craster, R. V., & Sassi, R. (2002). Shallow viscoplastic flow on an
inclined plane. Journal of Fluid Mechanics, 470, 1-29.
https://doi.org/10.1017/S0022112002001660
Banfill, P., Beaupré, D., Chapdelaine, F., de Larrard, F., Domone, P., Nachbaur, L.,
Sedran, T., Wallevik, O., & Wallevik, J. E. (2000). Comparison of concrete
rheometers International tests at LCPC (Nantes, France) in October 2000. In
NIST.
Baracu T. (2012). Computational analysis of the flow around a cylinder and of the
drag force.
Barreto, D., & Leak, J. (2020). A guide to modeling the geotechnical behavior of soils
using the discrete element method. In Modeling in Geotechnical Engineering (p.
79-100). Elsevier. https://doi.org/10.1016/B978-0-12-821205-9.00016-2
Baudez, J. C., Chabot, F., & Coussot, P. (2002). Rheological interpretation of the
slump test. Applied Rheology, 12(3), 133-141. https://doi.org/10.1515/arh-2002-
0008
Beaupre, D. (2012). Mixer-mounted probe measures concrete workability.
Berger, X. (2023). Proposition de recherche et préparation orale de doctorat (GCI8084).
Bergeron, P. (1953). Considérations sur les facteurs influençant l’usure due au
transport hydraulique de matériaux solides. Application plus particulière aux
machines. https://www.persee.fr/doc/jhydr_0000-0001_1953_act_2_1_3256
Bingham, E. (1922). Fluidity and Plasticity (Digitized by the Internet Archive in 2007).
http://www.archive.org/details/fluidityplasticiOObinguoft
Bruschi, G., Nishioka, T., Tsang, K., & Wang, R. (2003). A comparison of analytical
methods drag coefficient of a cylinder.

Caceres, E. C. (2019). Impact de la rhéologie des matériaux cimentaires sur l’aspect
des parements et les procédés de mise en place. https://tel.archivesouvertes.fr/tel-01982159
Chanson, H., Jarny, ; S, & Coussot, P. (2006). Dam Break Wave of Thixotropic Fluid.
https://doi.org/10.1061/ASCE0733-94292006132:3280
Chi, Z. P., Yang, H., Li, R., & Sun, Q. C. (2021). Measurements of unconfined fresh
concrete flow on a slope using spatial filtering velocimetry. Powder Technology,
393, 349-356. https://doi.org/10.1016/j.powtec.2021.07.088
Cochard, S., & Ancey, C. (2009). Experimental investigation of the spreading of
viscoplastic fluids on inclined planes. Journal of Non-Newtonian Fluid
Mechanics, 158(1-3), 73-84. https://doi.org/10.1016/j.jnnfm.2008.08.007
Coussot, Philippe., & Ancey, C. (Christophe). (1999). Rhéophysique des pâtes et
des suspensions. EDP Sciences.
CSA Group. (2019). CSA A23.1:19 / CSA A23.2:19 : Concrete materials and
methods of concret construction / Test methods and standard practices for
concrete.
Daczko, J. A. (2000). A proposal for measuring rheology of production concrete.
De Larrard, F. (1999). Structures granulaires et formulation des bétons.
http://www.lcpc.fr/betonlabpro
De Larrard, F., Ferraris, C. F., & Sedran, T. (1998). Fresh concrete: A HerscheIBulkley material (Vol. 31).
Domone P.L.J., J. J. (1999). Properties of mortar for self-compacting concrete.
RILEM, 109-120.
El-Reedy, M. (2009). Advanced Materials and Techniques for Reinforced Concrete
Structures.
Emborg M. (1999). Rheology tests for self-compacting concrete – how useful are
they for the design of concrete mix for full-scale production.
Fall A. (2008). Rhéophysique des fluides complexes : Ecoulement et Blocage de
suspensions concentrées. https://www.researchgate.net/publication/30515545
Ferraris, C. F., Brower, L. E., Beaupré, D., Chapdelaine, F., Domone, P., Koehler,
E., Shen, L., Sonebi, M., Struble, L., Tepke, D., Wallevik, O., & Wallevik, J. E.

(2003). Comparison of concrete rheometers: International tests at MB.
https://doi.org/10.6028/NIST.IR.7154
Ferraris, C. F., & de Larrard, F. (1998a). Rhéologie du béton frais remanié III – L’essai
au cône d’Abrams modifié.
Ferraris, C. F., & de Larrard, F. (1998b, février). NISTIR 6094 Testing and modelling
of fresh concrete rheology. NISTIR 6094.
https://ciks.cbt.nist.gov/~garbocz/rheologyNISTIR/FR97html.htm
Fischedick, M., Roy, J., Abdel-Aziz, A., Acquaye Ghana, A., Allwood, J., Baiocchi,
G., Clift, R., Nenov, V., Yetano Roche Spain, M., Roy, J., Abdel-Aziz, A.,
Acquaye, A., Allwood, J. M., Ceron, J., Geng, Y., Kheshgi, H., Lanza, A.,
Perczyk, D., Price, L., … Minx, J. (2014). Climate Change 2014.
Fox R., & McDonald A. (2004). Introduction to fluid mechanics.
Franco Correa I.-D. (2019). Étude tribologique à hautes températures de matériaux
céramiques structurés à différentes échelles.
GIEC. (2022). Climate Change 2022 : Mitigation of Climate Change. www.ipcc.ch
Gouvernement du Canada. (2021, mai 31). Déclaration commune : L’industrie
canadienne du ciment et le gouvernement du Canada annoncent un partenariat.
https://www.ic.gc.ca/eic/site/icgc.nsf/fra/07730.html
Grenier, M. (1998). Microstructure et résistance à l’usure de revêtements crées par
fusion laser avec gaz réactifs sur du titane.
Herschel, W. H., & Bulkley, R. (1926). Konsistenzmessungen von GummiBenzollösungen. Kolloid-Zeitschrift, 39(4), 291-300.
https://doi.org/10.1007/BF01432034
Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics
of free boundaries. Journal of Computational Physics, 39(1), 201-225.
https://doi.org/https://doi.org/10.1016/0021-9991(81)90145-5
Hoornahad, H., & Koenders, E. A. B. (2012). Simulation of the slump test based on
the discrete element method (DEM). Advanced Materials Research, 446-449,
3766-3773. https://doi.org/10.4028/www.scientific.net/AMR.446-449.3766

Hu, C., de Larrard, F., Sedran, T., Boulay, C., Bosd, F., & Deflorenne, F. (1996).
Validation of BTRHEOM, the new rheometer for soft-to-fluid concrete. In
Materials and Structures/Mat~riaux et Constructions (Vol. 29).
Jeong, S. W., Locat, J., Leroueil, S., & Malet, J. P. (2007). Rheological properties of
fine-grained sediments in modeling submarine mass movements: The role of
texture. Submarine Mass Movements and Their Consequences, 3rd
International Symposium, 191-198. https://doi.org/10.1007/978-1-4020-6512-
5_20
Kabagire, K. D. (2018). Modélisation expérimentale et analytique des propriétés
rhéologiques des bétons autoplaçants.
Katopodes, N. D. (2019). Volume of Fluid Method. In Free-Surface Flow (p.
766-802). Elsevier. https://doi.org/10.1016/b978-0-12-815485-4.00018-8
Khayat. (2008). Personnal Communication.
Kosmatka, S. (2011). Dosage et contrôle des mélanges de béton (8ème édition).
Li, H., Wu, A., & Cheng, H. (2022). Generalized models of slump and spread in
combination for higher precision in yield stress determination. Cement and
Concrete Research, 159. https://doi.org/10.1016/j.cemconres.2022.106863
Massey, B., & Smith, J. (2012). Mechanics of fluids 9ème édition.
Mokéddem, S. (2014). Contrôle de la rhéologie d’un béton et de son évolution lors
du malaxage par des mesures en ligne à l’aide de la sonde Viscoprobe.
https://tel.archives-ouvertes.fr/tel-00993153
Munson, B. R., & Young, D. R. (2006). Fundamental of Fluid Mechanics (5th éd.).
Munson, M., Young, M. , & Okiishi, M. (2020). Mécanique des fluides (8ème édition).
Murata, J., & Kikukawa, H. (1992). Viscosity Equation for Fresh Concrete.
Nakayama, Y., & Boucher, R. F. (2000). Introduction to fluid mechanics. ButterworthHeinemann.
Němeček, J. (2021). Numerical simulation of slump flow test of cement paste
composites. Acta Polytechnica CTU Proceedings, 30, 58-62.
https://doi.org/10.14311/APP.2021.30.0058
Nikitin, K. D., Olshanskii, M. A., Terekhov, K. M., & Vassilevski, Y. V. (2011). A
numerical method for the simulation of free surface flows of viscoplastic fluid in

3D. Journal of Computational Mathematics, 29(6), 605-622.
https://doi.org/10.4208/jcm.1109-m11si01
Noh, W. F., & Woodward, P. (1976). SLIC (Simple Line Interface Calculation).
Odabas, D. (2018). Effects of Load and Speed on Wear Rate of Abrasive Wear for
2014 Al Alloy. IOP Conference Series: Materials Science and Engineering,
295(1). https://doi.org/10.1088/1757-899X/295/1/012008
Pintaude, G. (s. d.). Characteristics of Abrasive Particles and Their Implications on
Wear. www.intechopen.com
Poullain, P. (2003). Étude comparative de l’écoulement d’un fluide viscoplastique
dans une maquette de malaxeur pour béton.
R. J. Cattolica. (2003). Experiment F2: Water Tunnel. In MAE171A/175A Mechanical
Engineering Laboratory Manual (Winter Quarter).
Raper, R. M. (1966). Drag force and pressure distribution on cylindrical
protuberances immersed in a turbulent channel flow.
RMCAO. (2013). CSA A23.2-5C: Concrete Basics Slump Test.
Roques, A., & School, H. (2006). High resolution seismic imaging applied to the
geometrical characterization of very high voltage electric pylons.
https://www.researchgate.net/publication/281566156
Roussel, N. (2006). Correlation between yield stress and slump: Comparison
between numerical simulations and concrete rheometers results. Materials and
Structures/Materiaux et Constructions, 39(4), 501-509.
https://doi.org/10.1617/s11527-005-9035-2
Roussel, N., & Coussot, P. (2005). “Fifty-cent rheometer” for yield stress
measurements: From slump to spreading flow. Journal of Rheology, 49(3),
705-718. https://doi.org/10.1122/1.1879041
Roussel, N., Geiker, M. R., Dufour, F., Thrane, L. N., & Szabo, P. (2007).
Computational modeling of concrete flow: General overview. Cement and
Concrete Research, 37(9), 1298-1307.
https://doi.org/10.1016/j.cemconres.2007.06.007
Schaer, N. (2019). Modélisation des écoulements à surface libre de fluides nonnewtoniens. https://theses.hal.science/tel-02166968

Schowalter, W. R., & Christensen, G. (1998). Toward a rationalization of the slump
test for fresh concrete: Comparisons of calculations and experiments. Journal
of Rheology, 42(4), 865-870. https://doi.org/10.1122/1.550905
Sofiane Amziane, Chiara F. Ferraris, & Eric P. Koehler. (2005). Measurement of
Workability of Fresh Concrete Using a Mixing Truck. Journal of Research of the
National Institute of Standards Technology, 55-56.
Sooraj, P., Agrawal, A., & Sharma, A. (2018). Measurement of Drag Coefficient for
an Elliptical Cylinder. Journal of Energy and Environmental Sustainability, 5,
1-7. https://doi.org/10.47469/jees.2018.v05.100050
Stachowiak G. (2006). Wear – Materials, Mechanisms and Pratice.
Stachowiak G.W. (1993). Tribology Series (Vol. 24, p. 557-612). Elsevier.
Tattersall, G., & Banfill, P. F. G. (1983). The rheology of fresh concrete.
The European Guidelines for Self-Compacting Concrete Specification, Production
and Use « The European Guidelines for Self Compacting Concrete ». (2005).
www.efnarc.org
University College London. (2010). Pressure around a cylinder and cylinder drag.
Van Oudheusden, B. W., Scarano, F., Roosenboom, E. W. M., Casimiri, E. W. F., &
Souverein, L. J. (2007). Evaluation of integral forces and pressure fields from
planar velocimetry data for incompressible and compressible flows.
Experiments in Fluids, 43(2-3), 153-162. https://doi.org/10.1007/s00348-007-
0261-y
Vasilic, K., Gram, A., & Wallevik, J. E. (2019). Numerical simulation of fresh concrete
flow: Insight and challenges. RILEM Technical Letters, 4, 57-66.
https://doi.org/10.21809/rilemtechlett.2019.92
Viccione, G., Ferlisi, S., & Marra, E. (2010). A numerical investigation of the
interaction between debris flows and defense barriers.
http://www.unisa.it/docenti/giacomoviccione/en/index
Wallevik J. (2006). Relation between the Bingham parameters and slump.
Wallevik, J. E. (2006). Relationship between the Bingham parameters and slump.
Cement and Concrete Research, 36(7), 1214-1221.
https://doi.org/10.1016/j.cemconres.2006.03.001

Wallevik, J. E., & Wallevik, O. H. (2020). Concrete mixing truck as a rheometer.
Cement and Concrete Research, 127.
https://doi.org/10.1016/j.cemconres.2019.105930

Validity evaluation of popular liquid-vapor phase change models for cryogenic self-pressurization process

극저온 자체 가압 공정을 위한 인기 있는 액체-증기 상 변화 모델의 타당성 평가

액체-증기 상 변화 모델은 밀폐된 용기의 자체 가압 프로세스 시뮬레이션에 매우 큰 영향을 미칩니다. Hertz-Knudsen 관계, 에너지 점프 모델 및 그 파생물과 같은 널리 사용되는 액체-증기 상 변화 모델은 실온 유체를 기반으로 개발되었습니다. 액체-증기 전이를 통한 극저온 시뮬레이션에 널리 적용되었지만 각 모델의 성능은 극저온 조건에서 명시적으로 조사 및 비교되지 않았습니다. 본 연구에서는 171가지 일반적인 액체-증기 상 변화 모델을 통합한 통합 다상 솔버가 제안되었으며, 이를 통해 이러한 모델을 실험 데이터와 직접 비교할 수 있습니다. 증발 및 응축 모델의 예측 정확도와 계산 속도를 평가하기 위해 총 <>개의 자체 가압 시뮬레이션이 수행되었습니다. 압력 예측은 최적화 전략이 서로 다른 모델 계수에 크게 의존하는 것으로 나타났습니다. 에너지 점프 모델은 극저온 자체 가압 시뮬레이션에 적합하지 않은 것으로 나타났습니다. 평균 편차와 CPU 소비량에 따르면 Lee 모델과 Tanasawa 모델은 다른 모델보다 안정적이고 효율적인 것으로 입증되었습니다.

Elsevier

International Journal of Heat and Mass Transfer

Volume 181, December 2021, 121879

International Journal of Heat and Mass Transfer

Validity evaluation of popular liquid-vapor phase change models for cryogenic self-pressurization process

Author links open overlay panelZhongqi Zuo, Jingyi Wu, Yonghua HuangShow moreAdd to MendeleyShareCite

https://doi.org/10.1016/j.ijheatmasstransfer.2021.121879Get rights and content

Abstract

Liquid-vapor phase change models vitally influence the simulation of self-pressurization processes in closed containers. Popular liquid-vapor phase change models, such as the Hertz-Knudsen relation, energy jump model, and their derivations were developed based on room-temperature fluids. Although they had widely been applied in cryogenic simulations with liquid-vapor transitions, the performance of each model was not explicitly investigated and compared yet under cryogenic conditions. A unified multi-phase solver incorporating four typical liquid-vapor phase change models has been proposed in the present study, which enables direct comparison among those models against experimental data. A total number of 171 self-pressurization simulations were conducted to evaluate the evaporation and condensation models’ prediction accuracy and calculation speed. It was found that the pressure prediction highly depended on the model coefficients, whose optimization strategies differed from each other. The energy jump model was found inadequate for cryogenic self-pressurization simulations. According to the average deviation and CPU consumption, the Lee model and the Tanasawa model were proven to be more stable and more efficient than the others.

Introduction

The liquid-vapor phase change of cryogenic fluids is widely involved in industrial applications, such as the hydrogen transport vehicles [1], shipborne liquid natural gas (LNG) containers [2] and on-orbit cryogenic propellant tanks [3]. These applications require cryogenic fluids to be stored for weeks to months. Although high-performance insulation measures are adopted, heat inevitably enters the tank via radiation and conduction. The self-pressurization in the tank induced by the heat leakage eventually causes the venting loss of the cryogenic fluids and threatens the safety of the craft in long-term missions. To reduce the boil-off loss and extend the cryogenic storage duration, a more comprehensive understanding of the self-pressurization mechanism is needed.

Due to the difficulties and limitations in implementing cryogenic experiments, numerical modeling is a convenient and powerful way to study the self-pressurization process of cryogenic fluids. However, how the phase change models influence the mass and heat transfer under cryogenic conditions is still unsettled [4]. As concluded by Persad and Ward [5], a seemingly slight variation in the liquid-vapor phase change models can lead to erroneous predictions.

Among the liquid-vapor phase change models, the kinetic theory gas (KTG) based models and the energy jump model are the most popular ones used in recent self-pressurization simulations [6]. The KTG based models, also known as the Hertz-Knudsen relation models, were developed on the concept of the Maxwell-Boltzmann distribution of the gas molecular [7]. The Hertz-Knudsen relation has evolved to several models, including the Schrage model [8], the Tanasawa model [9], the Lee model [10] and the statistical rate theory (SRT) [11], which will be described in Section 2.2. Since the Schrage model and the Lee model are embedded and configured as the default ones in the commercial CFD solvers Flow-3D® and Ansys Fluent® respectively, they have been widely used in self-pressurization simulations for liquid nitrogen [12], [13] and liquid hydrogen [14], [15]. The major drawback of the KTG models lies in the difficulty of selecting model coefficients, which were reported in a considerably wide range spanning three magnitudes even for the same working fluid [16], [17], [18], [19], [20], [21]. Studies showed that the liquid level, pressure and mass transfer rate are directly influenced by the model coefficients [16], [22], [23], [24], [25]. Wrong coefficients will lead to deviation or even divergence of the results. The energy jump model is also known as the thermal limitation model. It assumes that the evaporation and condensation at the liquid-vapor interface are induced only by heat conduction. The model is widely adopted in lumped node simulations due to its simplicity [6], [26], [27]. To improve the accuracy of mass flux prediction, the energy jump model was modified by including the convection heat transfer [28], [29]. However, the convection correlations are empirical and developed mainly for room-temperature fluids. Whether the correlation itself can be precisely applied in cryogenic simulations still needs further investigation.

Fig. 1 summarizes the cryogenic simulations involving the modeling of evaporation and condensation processes in recent years. The publication has been increasing rapidly. However, the characteristics of each evaporation and condensation model are not explicitly revealed when simulating self-pressurization. A comparative study of the phase change models is highly needed for cryogenic fluids for a better simulation of the self-pressurization processes.

In the present paper, a unified multi-phase solver incorporating four typical liquid-vapor phase change models, namely the Tanasawa model, the Lee model, the energy jump model, and the modified energy jump model has been proposed, which enables direct comparison among different models. The models are used to simulate the pressure and temperature evolutions in an experimental liquid nitrogen tank in normal gravity, which helps to evaluate themselves in the aspects of accuracy, calculation speed and robustness.

Section snippets

Governing equations for the self-pressurization tank

In the present study, both the fluid domain and the solid wall of the tank are modeled and discretized. The heat transportation at the solid boundaries is considered to be irrelevant with the nearby fluid velocity. Consequently, two sets of the solid and the fluid governing equations can be decoupled and solved separately. The pressures in the cryogenic container are usually from 100 kPa to 300 kPa. Under these conditions, the Knudsen number is far smaller than 0.01, and the fluids are

Self-pressurization results and phase change model comparison

This section compares the simulation results by different phase change models. Section 3.1 compares the pressure and temperature outputs from two KTG based models, namely the Lee model and the Tanasawa model. Section 3.2 presents the pressure predictions from the energy transport models, namely the energy jump model and the modified energy jump model, and compares pressure prediction performances between the KTG based models and the energy transport models. Section 3.3 evaluates the four models 

Conclusion

A unified vapor-liquid-solid multi-phase numerical solver has been accomplished for the self pressurization simulation in cryogenic containers. Compared to the early fluid-only solver, the temperature prediction in the vicinity of the tank wall improves significantly. Four liquid-vapor phase change models were integrated into the solver, which enables fair and effective comparison for performances between each other. The pressure and temperature prediction accuracies, and the calculation speed

CRediT authorship contribution statement

Zhongqi Zuo: Data curation, Formal analysis, Writing – original draft, Validation. Jingyi Wu: Conceptualization, Writing – review & editing, Validation. Yonghua Huang: Conceptualization, Formal analysis, Writing – review & editing, Validation.

Declaration of Competing Interest

Authors declare that they have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Validity evaluation of popular liquid-vapor phase change models for cryogenic self-pressurization process”.

Acknowledgement

This project is supported by the National Natural Science Foundation of China (No. 51936006).

References (40)

There are more references available in the full text version of this article.

Cited by (7)

Design optimization of perforation on deflector for improved performance of vortex settling basin

와류 침전 수조의 성능 향상을 위한 디플렉터의 천공 설계 최적화*

Abstract

Zhuoyun MuYiyi MaLin Li

First published: 18 August 2021

https://doi.org/10.1002/ird.2640

*Optimisation de la conception de la perforation sur le déflecteur pour une meilleure performance du bassin de décantation par vortex.

Funding information: Graduate Research and Innovation Project of Xinjiang Autonomous Region, Grant/Award Number: XJ2020G171; Xinjiang Agricultural University, Grant/Award Number: SLXK-YJS-2019-04; National Natural Science Foundation of China, Grant/Award Number: 52069028; Tianshan Youth Project, Grant/Award Number: 2018Q017; Department of Education, Xinjiang Uygur Autonomous Region, Grant/Award Number: XJEDU2018I010

ENTHIS LINK GOES TO A ENGLISH SECTIONFRTHIS LINK GOES TO A FRENCH SECTION

For vortex settling basins (VSBs) installed with a deflector, perforation is an effective retrofit to reduce the self-weight of the deflector and sediment deposition on it. The current study investigated experimentally the performance of VSBs the deflector of which was perforated at different locations with various opening ratios. The results showed that perforating the outside overflow area of the deflector was the optimum for reducing sediment deposition. With an opening ratio of 8.67–13% in the outside overflow area of the deflector, the VSB exhibited similar sediment removal efficiency to the original design without any openings on the deflector. The current study provided the design optimization for deflector perforation in VSBs.

디플렉터와 함께 설치된 와류 침전 분지(VSB)의 경우 천공은 디플렉터의 자체 중량과 침전물 증착을 줄이기 위한 효과적인 개조입니다. 현재 연구는 다양한 개방 비율로 다른 위치에서 디플렉터가 천공된 VSB의 성능을 실험적으로 조사했습니다. 결과는 디플렉터의 외부 오버플로 영역을 천공하는 것이 침전물 퇴적을 줄이는 데 최적임을 보여주었습니다. 디플렉터의 외부 오버플로 영역에서 8.67-13%의 개구부로 VSB는 디플렉터에 개구부가 없는 원래 설계와 유사한 침전물 제거 효율을 나타냈습니다. 현재 연구는 VSB의 디플렉터 천공에 대한 설계 최적화를 제공했습니다.

Figure 4 Snapshots of the trimaran model during the tests. a Inboard side hulls in the Tri-1confguration, b Outboard side hulls in the Tri-4 confguration, c Symmetric side hulls in the Tri-4confguration

조파식 3동선의 선체측면대칭이 저항성능에 미치는 영향에 관한 실험적 연구

Abolfath Askarian KhoobAtabak FeiziAlireza MohamadiKarim Akbari VakilabadiAbbas Fazeliniai & Shahryar Moghaddampour

Abstract

이 논문은 비대칭 인보드, 비대칭 아웃보드 및 다양한 스태거/분리 위치에서의 대칭을 포함하는 세 가지 대안적인 측면 선체 형태를 가진 웨이브 피어싱 3동선의 저항 성능에 대한 실험적 조사 결과를 제시했습니다. 

모델 테스트는 0.225에서 0.60까지의 Froude 수에서 삼동선 축소 모형을 사용하여 National Iranian Marine Laboratory(NIMALA) 예인 탱크에서 수행되었습니다. 

결과는 측면 선체를 주 선체 트랜섬의 앞쪽으로 이동함으로써 삼동선의 총 저항 계수가 감소하는 것으로 나타났습니다. 

또한 조사 결과, 측면 선체의 대칭 형태가 3개의 측면 선체 형태 중 전체 저항에 대한 성능이 가장 우수한 것으로 나타났습니다. 본 연구의 결과는 저항 관점에서 측면 선체 구성을 선택하는 데 유용합니다.

Keywords

  • Resistance performance
  • Wave-piercing trimaran
  • Seakeeping characteristics
  • Side hull symmetry
  • Model test
  • Experimental study
Figure 4 Snapshots of the trimaran model during the tests. a Inboard side hulls in the Tri-1confguration, b Outboard side hulls in the Tri-4 confguration, c Symmetric side hulls in the Tri-4confguration
Figure 4 Snapshots of the trimaran model during the tests. a Inboard side hulls in the Tri-1confguration, b Outboard side hulls in the Tri-4 confguration, c Symmetric side hulls in the Tri-4confguration

References

  • Ackers BB, Thad JM, Tredennick OW, Landen CH, Miller EJ, Sodowsky JP, Hadler JB (1997) An investigation of the resistance characteristics of powered trimaran side-hull configurations. SNAME Transactions 105:349–373Google Scholar 
  • ASME (2005) Test uncertainty, The American society of mechanical engineers performance test code, American Society of Mechanical Engineers, No. PTC 19. 1–2005, New York
  • Chen Y, Yang L, Xie Y, Yu S (2016) The research on characteristic parameters and resistance chart of operation and maintenance trimaran in the sea. Polish Maritime Research 23(s1):20–24. https://doi.org/10.1515/pomr-2016-0041Article Google Scholar 
  • Claire M, Andrea M (2014) Resistance analysis for a trimaran. International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering 8(1):7–15Google Scholar 
  • Deng R, Li C, Huang D, Zhou G (2015) The effect of trimming and sinkage on the trimaran resistance calculation. Procedia Engineering 126:327–331. https://doi.org/10.1016/j.proeng.2015.11.199Article Google Scholar 
  • Doctors L, Scrace R (2003) The optimization of trimaran side hull position for minimum resistance. Seventh International Conference on Fast Transportation (FAST 2003), Ischia, Italy, 1–12
  • Du L, Hefazi H, Sahoo P (2019) Rapid resistance estimation method of non-Wigley trimarans. Ships and Offshore Structures 14(8):910–920. https://doi.org/10.1080/17445302.2019.1588499Article Google Scholar 
  • Ghadimi P, Nazemian A, Ghadimi A (2019) Numerical scrutiny of the influence of side hulls arrangement on the motion of a Trimaran vessel in regular waves through CFD analysis. Journal of the Brazilian Society of Mechanical Sciences and Engineering 41(1):1–10. https://doi.org/10.1007/s40430-018-1505-xArticle Google Scholar 
  • Hafez K, El-Kot A-R (2011) Comparative analysis of the separation variation influence on the hydrodynamic performance of a high speed trimaran. Journal of Marine Science and Application 10(4):377–393. https://doi.org/10.1007/s11804-011-1083-0Article Google Scholar 
  • Hafez KA, El-Kot AA (2012) Comparative investigation of the stagger variation influence on the hydrodynamic interference of high speed trimaran. Alexandria Engineering Journal 51(3):153–169. https://doi.org/10.1016/j.aej.2012.02.002Article Google Scholar 
  • Hashimoto H, Amano S, Umeda N, Matsuda A (2011) Influence of side-hull positions on dynamic behaviors of a trimaran running in following and stern quartering seas. Proceedings of the 21th International Conference on Offshore and Polar Engineering, 573–580
  • Insel M, Molland AF (1991) An investigation into the resistance components of high speed displacement catamarans. Transactions of the Royal Institution of Naval Architects 134:1–20. https://doi.org/10.1007/s11804-013-1193-yArticle Google Scholar 
  • ITTC (2014) Testing and extrapolation methods in resistance towing tank tests, Recommended Procedures, 7.5–02–02–01
  • Iqbal M, Utama IKAP (2014) An investigation into the effect of water depth on the resistance components of trimaran configuration. Proceedings of the 9th International Conference on Marine Technology, Surabaya
  • Lewis EV (1988) Principles of Naval Architecture. The Society of Naval Architects and Marine Engineers III: 323–324
  • Luhulima RB, Utama I, Sulisetyono A (2016) Experimental investigation into the resistance components of displacement trimaran at various lateral spacing. International Journal of Engineering Research & Science (IJOER) 2:21–29Google Scholar 
  • Luhulima RB (2017) An Investigation into the resistance of displacement trimaran: a comparative analysis between experimental and CFD approaches. International Journal of Mechanical Engineering (IJME) 6:9–18Google Scholar 
  • Molland AF, Turnock SR, Hudson DA (2011) Ship resistance and propulsion: practical estimation of ship propulsive power. Cambridge University Press, 544.
  • Verna S, Khan K, Praveen PC (2012) Trimaran hull form optimization, using ship flow. International Journal of Innovative Research and Development 1(10):5–15
  • Yanuar Y, Gunawan G, Talahatu MA, Indrawati RT, Jamaluddin A (2013) Resistance analysis of unsymmetrical trimaran model with outboard side hulls configuration. Journal of Marine Science and Application 12(3):293–297Article Google Scholar 
  • Yanuar Y, Gunawan G, Talahatu MA, Indrawati RT, Jamaluddin A (2015a) Resistance reduction on trimaran ship model by biopolymer of eel slime. Journal of Naval Architecture and Marine Engineering 12(2):95–102. https://doi.org/10.3329/jname.v12i2.19549Article Google Scholar 
  • Yanuar Y, Gunawan G, Waskito KT, Jamaluddin A (2015b) Experimental study resistances of asymmetrical Pentamaran model with separation and staggered hull variation of inner side-hulls. International Journal of Fluid Mechanics Research 42(1):82–94. https://doi.org/10.1615/interjfluidmechres.v42.i1.60Article Google Scholar 
  • Zhang WP, Zong Z, Wang WH (2012) Special problems and solutions for numerical prediction on longitudinal motion of trimaran. Applied Mechanics and Materials 152-154: 1262–75. https://doi.org/10.4028/www.scientific.net/amm.152-154.1262
  • Zhang L, Zhang JN, Shang YC (2019) A potential flow theory and boundary layer theory based hybrid method for waterjet propulsion. Journal of Marine Science and Engineering 7(4):113–132. https://doi.org/10.3390/jmse7040113Article Google Scholar 
Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

레이저 보조 분말 기반 직접 에너지 증착에서 용융 풀 거동에 대한 감쇠 레이저 빔 강도 프로파일의 영향에 대한 열유체 모델링

Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

Mohammad Sattari, Amin Ebrahimi, Martin Luckabauer, Gert-willem R.B.E. Römer

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Professional

5Downloads (Pure)

Abstract

A numerical framework based on computational fluid dynamics (CFD), using the finite volume method (FVM) and volume of fluid (VOF) technique is presented to investigate the effect of the laser beam intensity profile on melt pool behavior in laser-assisted powder-based directed energy deposition (L-DED). L-DED is an additive manufacturing (AM) process that utilizes a laser beam to fuse metal powder particles. To assure high-fidelity modeling, it was found that it is crucial to accurately model the interaction between the powder stream and the laser beam in the gas region above the substrate. The proposed model considers various phenomena including laser energy attenuation and absorption, multiple reflections of the laser rays, powder particle stream, particle-fluid interaction, temperature-dependent properties, buoyancy effects, thermal expansion, solidification shrinkage and drag, and Marangoni flow. The latter is induced by temperature and element-dependent surface tension. The model is validated using experimental results and highlights the importance of considering laser energy attenuation. Furthermore, the study investigates how the laser beam intensity profile affects melt pool size and shape, influencing the solidification microstructure and mechanical properties of the deposited material. The proposed model has the potential to optimize the L-DED process for a variety of materials and provides insights into the capability of numerical modeling for additive manufacturing optimization.

Original languageEnglish
Title of host publicationFlow-3D World Users Conference
Publication statusPublished – 2023
EventFlow-3D World User Conference – Strasbourg, France
Duration: 5 Jun 2023 → 7 Jun 2023

Conference

ConferenceFlow-3D World User Conference
Country/TerritoryFrance
CityStrasbourg
Period5/06/23 → 7/06/23
Figure 2 Modeling the plant with cylindrical tubes at the bottom of the canal.

Optimized Vegetation Density to Dissipate Energy of Flood Flow in Open Canals

열린 운하에서 홍수 흐름의 에너지를 분산시키기 위해 최적화된 식생 밀도

Mahdi Feizbahr,1Navid Tonekaboni,2Guang-Jun Jiang,3,4and Hong-Xia Chen3,4
Academic Editor: Mohammad Yazdi

Abstract

강을 따라 식생은 조도를 증가시키고 평균 유속을 감소시키며, 유동 에너지를 감소시키고 강 횡단면의 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받기 때문에 홍수시 유동저항에 큰 영향을 미친다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건과 식물에 따라 달라지므로 모델은 유속, 유속 깊이 및 수로를 따라 식생 유형의 영향을 고려하여 유속을 시뮬레이션해야 합니다. 총 48개의 모델을 시뮬레이션하여 근관의 거칠기 효과를 조사했습니다. 결과는 속도를 높임으로써 베드 속도를 감소시키는 식생의 영향이 무시할만하다는 것을 나타냅니다.

Abstract

Vegetation along the river increases the roughness and reduces the average flow velocity, reduces flow energy, and changes the flow velocity profile in the cross section of the river. Many canals and rivers in nature are covered with vegetation during the floods. Canal’s roughness is strongly affected by plants and therefore it has a great effect on flow resistance during flood. Roughness resistance against the flow due to the plants depends on the flow conditions and plant, so the model should simulate the current velocity by considering the effects of velocity, depth of flow, and type of vegetation along the canal. Total of 48 models have been simulated to investigate the effect of roughness in the canal. The results indicated that, by enhancing the velocity, the effect of vegetation in decreasing the bed velocity is negligible, while when the current has lower speed, the effect of vegetation on decreasing the bed velocity is obviously considerable.

1. Introduction

Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [114]. This can help research for better modeling considering the relation of variables or interaction of them toward reaching a better condition for the objective function in control and engineering [1527]. Consequently, it is necessary to study the effects of the passive factors on the active domain [2836]. Because of the effect of vegetation on reducing the discharge capacity of rivers [37], pruning plants was necessary to improve the condition of rivers. One of the important effects of vegetation in river protection is the action of roots, which cause soil consolidation and soil structure improvement and, by enhancing the shear strength of soil, increase the resistance of canal walls against the erosive force of water. The outer limbs of the plant increase the roughness of the canal walls and reduce the flow velocity and deplete the flow energy in vicinity of the walls. Vegetation by reducing the shear stress of the canal bed reduces flood discharge and sedimentation in the intervals between vegetation and increases the stability of the walls [3841].

One of the main factors influencing the speed, depth, and extent of flood in this method is Manning’s roughness coefficient. On the other hand, soil cover [42], especially vegetation, is one of the most determining factors in Manning’s roughness coefficient. Therefore, it is expected that those seasonal changes in the vegetation of the region will play an important role in the calculated value of Manning’s roughness coefficient and ultimately in predicting the flood wave behavior [4345]. The roughness caused by plants’ resistance to flood current depends on the flow and plant conditions. Flow conditions include depth and velocity of the plant, and plant conditions include plant type, hardness or flexibility, dimensions, density, and shape of the plant [46]. In general, the issue discussed in this research is the optimization of flood-induced flow in canals by considering the effect of vegetation-induced roughness. Therefore, the effect of plants on the roughness coefficient and canal transmission coefficient and in consequence the flow depth should be evaluated [4748].

Current resistance is generally known by its roughness coefficient. The equation that is mainly used in this field is Manning equation. The ratio of shear velocity to average current velocity  is another form of current resistance. The reason for using the  ratio is that it is dimensionless and has a strong theoretical basis. The reason for using Manning roughness coefficient is its pervasiveness. According to Freeman et al. [49], the Manning roughness coefficient for plants was calculated according to the Kouwen and Unny [50] method for incremental resistance. This method involves increasing the roughness for various surface and plant irregularities. Manning’s roughness coefficient has all the factors affecting the resistance of the canal. Therefore, the appropriate way to more accurately estimate this coefficient is to know the factors affecting this coefficient [51].

To calculate the flow rate, velocity, and depth of flow in canals as well as flood and sediment estimation, it is important to evaluate the flow resistance. To determine the flow resistance in open ducts, Manning, Chézy, and Darcy–Weisbach relations are used [52]. In these relations, there are parameters such as Manning’s roughness coefficient (n), Chézy roughness coefficient (C), and Darcy–Weisbach coefficient (f). All three of these coefficients are a kind of flow resistance coefficient that is widely used in the equations governing flow in rivers [53].

The three relations that express the relationship between the average flow velocity (V) and the resistance and geometric and hydraulic coefficients of the canal are as follows:where nf, and c are Manning, Darcy–Weisbach, and Chézy coefficients, respectively. V = average flow velocity, R = hydraulic radius, Sf = slope of energy line, which in uniform flow is equal to the slope of the canal bed,  = gravitational acceleration, and Kn is a coefficient whose value is equal to 1 in the SI system and 1.486 in the English system. The coefficients of resistance in equations (1) to (3) are related as follows:

Based on the boundary layer theory, the flow resistance for rough substrates is determined from the following general relation:where f = Darcy–Weisbach coefficient of friction, y = flow depth, Ks = bed roughness size, and A = constant coefficient.

On the other hand, the relationship between the Darcy–Weisbach coefficient of friction and the shear velocity of the flow is as follows:

By using equation (6), equation (5) is converted as follows:

Investigation on the effect of vegetation arrangement on shear velocity of flow in laboratory conditions showed that, with increasing the shear Reynolds number (), the numerical value of the  ratio also increases; in other words the amount of roughness coefficient increases with a slight difference in the cases without vegetation, checkered arrangement, and cross arrangement, respectively [54].

Roughness in river vegetation is simulated in mathematical models with a variable floor slope flume by different densities and discharges. The vegetation considered submerged in the bed of the flume. Results showed that, with increasing vegetation density, canal roughness and flow shear speed increase and with increasing flow rate and depth, Manning’s roughness coefficient decreases. Factors affecting the roughness caused by vegetation include the effect of plant density and arrangement on flow resistance, the effect of flow velocity on flow resistance, and the effect of depth [4555].

One of the works that has been done on the effect of vegetation on the roughness coefficient is Darby [56] study, which investigates a flood wave model that considers all the effects of vegetation on the roughness coefficient. There are currently two methods for estimating vegetation roughness. One method is to add the thrust force effect to Manning’s equation [475758] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [455961]. These two methods provide acceptable results in models designed to simulate floodplain flow. Wang et al. [62] simulate the floodplain with submerged vegetation using these two methods and to increase the accuracy of the results, they suggested using the effective height of the plant under running water instead of using the actual height of the plant. Freeman et al. [49] provided equations for determining the coefficient of vegetation roughness under different conditions. Lee et al. [63] proposed a method for calculating the Manning coefficient using the flow velocity ratio at different depths. Much research has been done on the Manning roughness coefficient in rivers, and researchers [496366] sought to obtain a specific number for n to use in river engineering. However, since the depth and geometric conditions of rivers are completely variable in different places, the values of Manning roughness coefficient have changed subsequently, and it has not been possible to choose a fixed number. In river engineering software, the Manning roughness coefficient is determined only for specific and constant conditions or normal flow. Lee et al. [63] stated that seasonal conditions, density, and type of vegetation should also be considered. Hydraulic roughness and Manning roughness coefficient n of the plant were obtained by estimating the total Manning roughness coefficient from the matching of the measured water surface curve and water surface height. The following equation is used for the flow surface curve:where  is the depth of water change, S0 is the slope of the canal floor, Sf is the slope of the energy line, and Fr is the Froude number which is obtained from the following equation:where D is the characteristic length of the canal. Flood flow velocity is one of the important parameters of flood waves, which is very important in calculating the water level profile and energy consumption. In the cases where there are many limitations for researchers due to the wide range of experimental dimensions and the variety of design parameters, the use of numerical methods that are able to estimate the rest of the unknown results with acceptable accuracy is economically justified.

FLOW-3D software uses Finite Difference Method (FDM) for numerical solution of two-dimensional and three-dimensional flow. This software is dedicated to computational fluid dynamics (CFD) and is provided by Flow Science [67]. The flow is divided into networks with tubular cells. For each cell there are values of dependent variables and all variables are calculated in the center of the cell, except for the velocity, which is calculated at the center of the cell. In this software, two numerical techniques have been used for geometric simulation, FAVOR™ (Fractional-Area-Volume-Obstacle-Representation) and the VOF (Volume-of-Fluid) method. The equations used at this model for this research include the principle of mass survival and the magnitude of motion as follows. The fluid motion equations in three dimensions, including the Navier–Stokes equations with some additional terms, are as follows:where  are mass accelerations in the directions xyz and  are viscosity accelerations in the directions xyz and are obtained from the following equations:

Shear stresses  in equation (11) are obtained from the following equations:

The standard model is used for high Reynolds currents, but in this model, RNG theory allows the analytical differential formula to be used for the effective viscosity that occurs at low Reynolds numbers. Therefore, the RNG model can be used for low and high Reynolds currents.

Weather changes are high and this affects many factors continuously. The presence of vegetation in any area reduces the velocity of surface flows and prevents soil erosion, so vegetation will have a significant impact on reducing destructive floods. One of the methods of erosion protection in floodplain watersheds is the use of biological methods. The presence of vegetation in watersheds reduces the flow rate during floods and prevents soil erosion. The external organs of plants increase the roughness and decrease the velocity of water flow and thus reduce its shear stress energy. One of the important factors with which the hydraulic resistance of plants is expressed is the roughness coefficient. Measuring the roughness coefficient of plants and investigating their effect on reducing velocity and shear stress of flow is of special importance.

Roughness coefficients in canals are affected by two main factors, namely, flow conditions and vegetation characteristics [68]. So far, much research has been done on the effect of the roughness factor created by vegetation, but the issue of plant density has received less attention. For this purpose, this study was conducted to investigate the effect of vegetation density on flow velocity changes.

In a study conducted using a software model on three density modes in the submerged state effect on flow velocity changes in 48 different modes was investigated (Table 1).

Table 1 

The studied models.

The number of cells used in this simulation is equal to 1955888 cells. The boundary conditions were introduced to the model as a constant speed and depth (Figure 1). At the output boundary, due to the presence of supercritical current, no parameter for the current is considered. Absolute roughness for floors and walls was introduced to the model (Figure 1). In this case, the flow was assumed to be nonviscous and air entry into the flow was not considered. After  seconds, this model reached a convergence accuracy of .

Figure 1 

The simulated model and its boundary conditions.

Due to the fact that it is not possible to model the vegetation in FLOW-3D software, in this research, the vegetation of small soft plants was studied so that Manning’s coefficients can be entered into the canal bed in the form of roughness coefficients obtained from the studies of Chow [69] in similar conditions. In practice, in such modeling, the effect of plant height is eliminated due to the small height of herbaceous plants, and modeling can provide relatively acceptable results in these conditions.

48 models with input velocities proportional to the height of the regular semihexagonal canal were considered to create supercritical conditions. Manning coefficients were applied based on Chow [69] studies in order to control the canal bed. Speed profiles were drawn and discussed.

Any control and simulation system has some inputs that we should determine to test any technology [7077]. Determination and true implementation of such parameters is one of the key steps of any simulation [237881] and computing procedure [8286]. The input current is created by applying the flow rate through the VFR (Volume Flow Rate) option and the output flow is considered Output and for other borders the Symmetry option is considered.

Simulation of the models and checking their action and responses and observing how a process behaves is one of the accepted methods in engineering and science [8788]. For verification of FLOW-3D software, the results of computer simulations are compared with laboratory measurements and according to the values of computational error, convergence error, and the time required for convergence, the most appropriate option for real-time simulation is selected (Figures 2 and 3 ).

Figure 2 

Modeling the plant with cylindrical tubes at the bottom of the canal.

Figure 3 

Velocity profiles in positions 2 and 5.

The canal is 7 meters long, 0.5 meters wide, and 0.8 meters deep. This test was used to validate the application of the software to predict the flow rate parameters. In this experiment, instead of using the plant, cylindrical pipes were used in the bottom of the canal.

The conditions of this modeling are similar to the laboratory conditions and the boundary conditions used in the laboratory were used for numerical modeling. The critical flow enters the simulation model from the upstream boundary, so in the upstream boundary conditions, critical velocity and depth are considered. The flow at the downstream boundary is supercritical, so no parameters are applied to the downstream boundary.

The software well predicts the process of changing the speed profile in the open canal along with the considered obstacles. The error in the calculated speed values can be due to the complexity of the flow and the interaction of the turbulence caused by the roughness of the floor with the turbulence caused by the three-dimensional cycles in the hydraulic jump. As a result, the software is able to predict the speed distribution in open canals.

2. Modeling Results

After analyzing the models, the results were shown in graphs (Figures 414 ). The total number of experiments in this study was 48 due to the limitations of modeling.


(d)


(a)


(b)


(c)


(d)


(a)


(b)


(c)


(d)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)
  • (d)
    (d)

Figure 4 

Flow velocity profiles for canals with a depth of 1 m and flow velocities of 3–3.3 m/s. Canal with a depth of 1 meter and a flow velocity of (a) 3 meters per second, (b) 3.1 meters per second, (c) 3.2 meters per second, and (d) 3.3 meters per second.

Figure 5 

Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.

Figure 6 

Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.

Figure 7 

Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.

Figure 8 

Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second.


(d)


(a)


(b)


(c)


(d)


(a)


(b)


(c)


(d)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)
  • (d)
    (d)

Figure 9 

Flow velocity profiles for canals with a depth of 2 m and flow velocities of 4–4.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

Figure 10 

Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.

Figure 11 

Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.

Figure 12 

Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.

Figure 13 

Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second.


(d)


(a)


(b)


(c)


(d)


(a)


(b)


(c)


(d)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)
  • (d)
    (d)

Figure 14 

Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

To investigate the effects of roughness with flow velocity, the trend of flow velocity changes at different depths and with supercritical flow to a Froude number proportional to the depth of the section has been obtained.

According to the velocity profiles of Figure 5, it can be seen that, with the increasing of Manning’s coefficient, the canal bed speed decreases.

According to Figures 5 to 8, it can be found that, with increasing the Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the models 1 to 12, which can be justified by increasing the speed and of course increasing the Froude number.

According to Figure 10, we see that, with increasing Manning’s coefficient, the canal bed speed decreases.

According to Figure 11, we see that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 510, which can be justified by increasing the speed and, of course, increasing the Froude number.

With increasing Manning’s coefficient, the canal bed speed decreases (Figure 12). But this deceleration is more noticeable than the deceleration of the higher models (Figures 58 and 1011), which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 13, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5 to 12, which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 15, with increasing Manning’s coefficient, the canal bed speed decreases.

Figure 15 

Canal diagram with a depth of 3 meters and a flow rate of 5 meters per second.

According to Figure 16, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher model, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 16 

Canal diagram with a depth of 3 meters and a flow rate of 5.1 meters per second.

According to Figure 17, it is clear that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 17 

Canal diagram with a depth of 3 meters and a flow rate of 5.2 meters per second.

According to Figure 18, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 18 

Canal diagram with a depth of 3 meters and a flow rate of 5.3 meters per second.

According to Figure 19, it can be seen that the vegetation placed in front of the flow input velocity has negligible effect on the reduction of velocity, which of course can be justified due to the flexibility of the vegetation. The only unusual thing is the unexpected decrease in floor speed of 3 m/s compared to higher speeds.


(c)


(a)


(b)


(c)


(a)


(b)


(c)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)

Figure 19 

Comparison of velocity profiles with the same plant densities (depth 1 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 1 m; (b) plant densities of 50%, depth 1 m; and (c) plant densities of 75%, depth 1 m.

According to Figure 20, by increasing the speed of vegetation, the effect of vegetation on reducing the flow rate becomes more noticeable. And the role of input current does not have much effect in reducing speed.


(c)


(a)


(b)


(c)


(a)


(b)


(c)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)

Figure 20 

Comparison of velocity profiles with the same plant densities (depth 2 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 2 m; (b) plant densities of 50%, depth 2 m; and (c) plant densities of 75%, depth 2 m.

According to Figure 21, it can be seen that, with increasing speed, the effect of vegetation on reducing the bed flow rate becomes more noticeable and the role of the input current does not have much effect. In general, it can be seen that, by increasing the speed of the input current, the slope of the profiles increases from the bed to the water surface and due to the fact that, in software, the roughness coefficient applies to the channel floor only in the boundary conditions, this can be perfectly justified. Of course, it can be noted that, due to the flexible conditions of the vegetation of the bed, this modeling can show acceptable results for such grasses in the canal floor. In the next directions, we may try application of swarm-based optimization methods for modeling and finding the most effective factors in this research [27815188994]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [9599].


(c)


(a)


(b)


(c)


(a)


(b)


(c)

  • (a)
    (a)
  • (b)
    (b)
  • (c)
    (c)

Figure 21 

Comparison of velocity profiles with the same plant densities (depth 3 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 3 m; (b) plant densities of 50%, depth 3 m; and (c) plant densities of 75%, depth 3 m.

3. Conclusion

The effects of vegetation on the flood canal were investigated by numerical modeling with FLOW-3D software. After analyzing the results, the following conclusions were reached:(i)Increasing the density of vegetation reduces the velocity of the canal floor but has no effect on the velocity of the canal surface.(ii)Increasing the Froude number is directly related to increasing the speed of the canal floor.(iii)In the canal with a depth of one meter, a sudden increase in speed can be observed from the lowest speed and higher speed, which is justified by the sudden increase in Froude number.(iv)As the inlet flow rate increases, the slope of the profiles from the bed to the water surface increases.(v)By reducing the Froude number, the effect of vegetation on reducing the flow bed rate becomes more noticeable. And the input velocity in reducing the velocity of the canal floor does not have much effect.(vi)At a flow rate between 3 and 3.3 meters per second due to the shallow depth of the canal and the higher landing number a more critical area is observed in which the flow bed velocity in this area is between 2.86 and 3.1 m/s.(vii)Due to the critical flow velocity and the slight effect of the roughness of the horseshoe vortex floor, it is not visible and is only partially observed in models 1-2-3 and 21.(viii)As the flow rate increases, the effect of vegetation on the rate of bed reduction decreases.(ix)In conditions where less current intensity is passing, vegetation has a greater effect on reducing current intensity and energy consumption increases.(x)In the case of using the flow rate of 0.8 cubic meters per second, the velocity distribution and flow regime show about 20% more energy consumption than in the case of using the flow rate of 1.3 cubic meters per second.

Nomenclature

n:Manning’s roughness coefficient
C:Chézy roughness coefficient
f:Darcy–Weisbach coefficient
V:Flow velocity
R:Hydraulic radius
g:Gravitational acceleration
y:Flow depth
Ks:Bed roughness
A:Constant coefficient
:Reynolds number
y/∂x:Depth of water change
S0:Slope of the canal floor
Sf:Slope of energy line
Fr:Froude number
D:Characteristic length of the canal
G:Mass acceleration
:Shear stresses.

Data Availability

All data are included within the paper.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.

References

  1. H. Yu, L. Jie, W. Gui et al., “Dynamic Gaussian bare-bones fruit fly optimizers with abandonment mechanism: method and analysis,” Engineering with Computers, vol. 20, pp. 1–29, 2020.View at: Publisher Site | Google Scholar
  2. X. Zhao, D. Li, B. Yang, C. Ma, Y. Zhu, and H. Chen, “Feature selection based on improved ant colony optimization for online detection of foreign fiber in cotton,” Applied Soft Computing, vol. 24, pp. 585–596, 2014.View at: Publisher Site | Google Scholar
  3. J. Hu, H. Chen, A. A. Heidari et al., “Orthogonal learning covariance matrix for defects of grey wolf optimizer: insights, balance, diversity, and feature selection,” Knowledge-Based Systems, vol. 213, Article ID 106684, 2021.View at: Publisher Site | Google Scholar
  4. C. Yu, M. Chen, K. Chen et al., “SGOA: annealing-behaved grasshopper optimizer for global tasks,” Engineering with Computers, vol. 4, pp. 1–28, 2021.View at: Publisher Site | Google Scholar
  5. W. Shan, Z. Qiao, A. A. Heidari, H. Chen, H. Turabieh, and Y. Teng, “Double adaptive weights for stabilization of moth flame optimizer: balance analysis, engineering cases, and medical diagnosis,” Knowledge-Based Systems, vol. 8, Article ID 106728, 2020.View at: Google Scholar
  6. J. Tu, H. Chen, J. Liu et al., “Evolutionary biogeography-based whale optimization methods with communication structure: towards measuring the balance,” Knowledge-Based Systems, vol. 212, Article ID 106642, 2021.View at: Publisher Site | Google Scholar
  7. Y. Zhang, R. Liu, X. Wang et al., “Towards augmented kernel extreme learning models for bankruptcy prediction: algorithmic behavior and comprehensive analysis,” Neurocomputing, vol. 430, 2020.View at: Google Scholar
  8. H.-L. Chen, G. Wang, C. Ma, Z.-N. Cai, W.-B. Liu, and S.-J. Wang, “An efficient hybrid kernel extreme learning machine approach for early diagnosis of Parkinson׳s disease,” Neurocomputing, vol. 184, pp. 131–144, 2016.View at: Publisher Site | Google Scholar
  9. J. Xia, H. Chen, Q. Li et al., “Ultrasound-based differentiation of malignant and benign thyroid Nodules: an extreme learning machine approach,” Computer Methods and Programs in Biomedicine, vol. 147, pp. 37–49, 2017.View at: Publisher Site | Google Scholar
  10. C. Li, L. Hou, B. Y. Sharma et al., “Developing a new intelligent system for the diagnosis of tuberculous pleural effusion,” Computer Methods and Programs in Biomedicine, vol. 153, pp. 211–225, 2018.View at: Publisher Site | Google Scholar
  11. X. Xu and H.-L. Chen, “Adaptive computational chemotaxis based on field in bacterial foraging optimization,” Soft Computing, vol. 18, no. 4, pp. 797–807, 2014.View at: Publisher Site | Google Scholar
  12. M. Wang, H. Chen, B. Yang et al., “Toward an optimal kernel extreme learning machine using a chaotic moth-flame optimization strategy with applications in medical diagnoses,” Neurocomputing, vol. 267, pp. 69–84, 2017.View at: Publisher Site | Google Scholar
  13. L. Chao, K. Zhang, Z. Li, Y. Zhu, J. Wang, and Z. Yu, “Geographically weighted regression based methods for merging satellite and gauge precipitation,” Journal of Hydrology, vol. 558, pp. 275–289, 2018.View at: Publisher Site | Google Scholar
  14. F. J. Golrokh, G. Azeem, and A. Hasan, “Eco-efficiency evaluation in cement industries: DEA malmquist productivity index using optimization models,” ENG Transactions, vol. 1, 2020.View at: Google Scholar
  15. D. Zhao, L. Lei, F. Yu et al., “Chaotic random spare ant colony optimization for multi-threshold image segmentation of 2D Kapur entropy,” Knowledge-Based Systems, vol. 8, Article ID 106510, 2020.View at: Google Scholar
  16. Y. Zhang, R. Liu, X. Wang, H. Chen, and C. Li, “Boosted binary Harris hawks optimizer and feature selection,” Engineering with Computers, vol. 517, pp. 1–30, 2020.View at: Publisher Site | Google Scholar
  17. L. Hu, G. Hong, J. Ma, X. Wang, and H. Chen, “An efficient machine learning approach for diagnosis of paraquat-poisoned patients,” Computers in Biology and Medicine, vol. 59, pp. 116–124, 2015.View at: Publisher Site | Google Scholar
  18. L. Shen, H. Chen, Z. Yu et al., “Evolving support vector machines using fruit fly optimization for medical data classification,” Knowledge-Based Systems, vol. 96, pp. 61–75, 2016.View at: Publisher Site | Google Scholar
  19. X. Zhao, X. Zhang, Z. Cai et al., “Chaos enhanced grey wolf optimization wrapped ELM for diagnosis of paraquat-poisoned patients,” Computational Biology and Chemistry, vol. 78, pp. 481–490, 2019.View at: Publisher Site | Google Scholar
  20. Y. Xu, H. Chen, J. Luo, Q. Zhang, S. Jiao, and X. Zhang, “Enhanced Moth-flame optimizer with mutation strategy for global optimization,” Information Sciences, vol. 492, pp. 181–203, 2019.View at: Publisher Site | Google Scholar
  21. M. Wang and H. Chen, “Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis,” Applied Soft Computing Journal, vol. 88, Article ID 105946, 2020.View at: Publisher Site | Google Scholar
  22. Y. Chen, J. Li, H. Lu, and P. Yan, “Coupling system dynamics analysis and risk aversion programming for optimizing the mixed noise-driven shale gas-water supply chains,” Journal of Cleaner Production, vol. 278, Article ID 123209, 2020.View at: Google Scholar
  23. H. Tang, Y. Xu, A. Lin et al., “Predicting green consumption behaviors of students using efficient firefly grey wolf-assisted K-nearest neighbor classifiers,” IEEE Access, vol. 8, pp. 35546–35562, 2020.View at: Publisher Site | Google Scholar
  24. H.-J. Ma and G.-H. Yang, “Adaptive fault tolerant control of cooperative heterogeneous systems with actuator faults and unreliable interconnections,” IEEE Transactions on Automatic Control, vol. 61, no. 11, pp. 3240–3255, 2015.View at: Google Scholar
  25. H.-J. Ma and L.-X. Xu, “Decentralized adaptive fault-tolerant control for a class of strong interconnected nonlinear systems via graph theory,” IEEE Transactions on Automatic Control, vol. 66, 2020.View at: Google Scholar
  26. H. J. Ma, L. X. Xu, and G. H. Yang, “Multiple environment integral reinforcement learning-based fault-tolerant control for affine nonlinear systems,” IEEE Transactions on Cybernetics, vol. 51, pp. 1–16, 2019.View at: Publisher Site | Google Scholar
  27. J. Hu, M. Wang, C. Zhao, Q. Pan, and C. Du, “Formation control and collision avoidance for multi-UAV systems based on Voronoi partition,” Science China Technological Sciences, vol. 63, no. 1, pp. 65–72, 2020.View at: Publisher Site | Google Scholar
  28. C. Zhang, H. Li, Y. Qian, C. Chen, and X. Zhou, “Locality-constrained discriminative matrix regression for robust face identification,” IEEE Transactions on Neural Networks and Learning Systems, vol. 99, pp. 1–15, 2020.View at: Publisher Site | Google Scholar
  29. X. Zhang, D. Wang, Z. Zhou, and Y. Ma, “Robust low-rank tensor recovery with rectification and alignment,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 43, no. 1, pp. 238–255, 2019.View at: Google Scholar
  30. X. Zhang, J. Wang, T. Wang, R. Jiang, J. Xu, and L. Zhao, “Robust feature learning for adversarial defense via hierarchical feature alignment,” Information Sciences, vol. 560, 2020.View at: Google Scholar
  31. X. Zhang, R. Jiang, T. Wang, and J. Wang, “Recursive neural network for video deblurring,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 03, p. 1, 2020.View at: Publisher Site | Google Scholar
  32. X. Zhang, T. Wang, J. Wang, G. Tang, and L. Zhao, “Pyramid channel-based feature attention network for image dehazing,” Computer Vision and Image Understanding, vol. 197-198, Article ID 103003, 2020.View at: Publisher Site | Google Scholar
  33. X. Zhang, T. Wang, W. Luo, and P. Huang, “Multi-level fusion and attention-guided CNN for image dehazing,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 3, p. 1, 2020.View at: Publisher Site | Google Scholar
  34. L. He, J. Shen, and Y. Zhang, “Ecological vulnerability assessment for ecological conservation and environmental management,” Journal of Environmental Management, vol. 206, pp. 1115–1125, 2018.View at: Publisher Site | Google Scholar
  35. Y. Chen, W. Zheng, W. Li, and Y. Huang, “Large group Activity security risk assessment and risk early warning based on random forest algorithm,” Pattern Recognition Letters, vol. 144, pp. 1–5, 2021.View at: Publisher Site | Google Scholar
  36. J. Hu, H. Zhang, Z. Li, C. Zhao, Z. Xu, and Q. Pan, “Object traversing by monocular UAV in outdoor environment,” Asian Journal of Control, vol. 25, 2020.View at: Google Scholar
  37. P. Tian, H. Lu, W. Feng, Y. Guan, and Y. Xue, “Large decrease in streamflow and sediment load of Qinghai-Tibetan Plateau driven by future climate change: a case study in Lhasa River Basin,” Catena, vol. 187, Article ID 104340, 2020.View at: Publisher Site | Google Scholar
  38. A. Stokes, C. Atger, A. G. Bengough, T. Fourcaud, and R. C. Sidle, “Desirable plant root traits for protecting natural and engineered slopes against landslides,” Plant and Soil, vol. 324, no. 1, pp. 1–30, 2009.View at: Publisher Site | Google Scholar
  39. T. B. Devi, A. Sharma, and B. Kumar, “Studies on emergent flow over vegetative channel bed with downward seepage,” Hydrological Sciences Journal, vol. 62, no. 3, pp. 408–420, 2017.View at: Google Scholar
  40. G. Ireland, M. Volpi, and G. Petropoulos, “Examining the capability of supervised machine learning classifiers in extracting flooded areas from Landsat TM imagery: a case study from a Mediterranean flood,” Remote Sensing, vol. 7, no. 3, pp. 3372–3399, 2015.View at: Publisher Site | Google Scholar
  41. L. Goodarzi and S. Javadi, “Assessment of aquifer vulnerability using the DRASTIC model; a case study of the Dezful-Andimeshk Aquifer,” Computational Research Progress in Applied Science & Engineering, vol. 2, no. 1, pp. 17–22, 2016.View at: Google Scholar
  42. K. Zhang, Q. Wang, L. Chao et al., “Ground observation-based analysis of soil moisture spatiotemporal variability across a humid to semi-humid transitional zone in China,” Journal of Hydrology, vol. 574, pp. 903–914, 2019.View at: Publisher Site | Google Scholar
  43. L. De Doncker, P. Troch, R. Verhoeven, K. Bal, P. Meire, and J. Quintelier, “Determination of the Manning roughness coefficient influenced by vegetation in the river Aa and Biebrza river,” Environmental Fluid Mechanics, vol. 9, no. 5, pp. 549–567, 2009.View at: Publisher Site | Google Scholar
  44. M. Fathi-Moghadam and K. Drikvandi, “Manning roughness coefficient for rivers and flood plains with non-submerged vegetation,” International Journal of Hydraulic Engineering, vol. 1, no. 1, pp. 1–4, 2012.View at: Google Scholar
  45. F.-C. Wu, H. W. Shen, and Y.-J. Chou, “Variation of roughness coefficients for unsubmerged and submerged vegetation,” Journal of Hydraulic Engineering, vol. 125, no. 9, pp. 934–942, 1999.View at: Publisher Site | Google Scholar
  46. M. K. Wood, “Rangeland vegetation-hydrologic interactions,” in Vegetation Science Applications for Rangeland Analysis and Management, vol. 3, pp. 469–491, Springer, 1988.View at: Publisher Site | Google Scholar
  47. C. Wilson, O. Yagci, H.-P. Rauch, and N. Olsen, “3D numerical modelling of a willow vegetated river/floodplain system,” Journal of Hydrology, vol. 327, no. 1-2, pp. 13–21, 2006.View at: Publisher Site | Google Scholar
  48. R. Yazarloo, M. Khamehchian, and M. R. Nikoodel, “Observational-computational 3d engineering geological model and geotechnical characteristics of young sediments of golestan province,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 03, 2017.View at: Google Scholar
  49. G. E. Freeman, W. H. Rahmeyer, and R. R. Copeland, “Determination of resistance due to shrubs and woody vegetation,” International Journal of River Basin Management, vol. 19, 2000.View at: Google Scholar
  50. N. Kouwen and T. E. Unny, “Flexible roughness in open channels,” Journal of the Hydraulics Division, vol. 99, no. 5, pp. 713–728, 1973.View at: Publisher Site | Google Scholar
  51. S. Hosseini and J. Abrishami, Open Channel Hydraulics, Elsevier, Amsterdam, Netherlands, 2007.
  52. C. S. James, A. L. Birkhead, A. A. Jordanova, and J. J. O’Sullivan, “Flow resistance of emergent vegetation,” Journal of Hydraulic Research, vol. 42, no. 4, pp. 390–398, 2004.View at: Publisher Site | Google Scholar
  53. F. Huthoff and D. Augustijn, “Channel roughness in 1D steady uniform flow: Manning or Chézy?,,” NCR-days, vol. 102, 2004.View at: Google Scholar
  54. M. S. Sabegh, M. Saneie, M. Habibi, A. A. Abbasi, and M. Ghadimkhani, “Experimental investigation on the effect of river bank tree planting array, on shear velocity,” Journal of Watershed Engineering and Management, vol. 2, no. 4, 2011.View at: Google Scholar
  55. A. Errico, V. Pasquino, M. Maxwald, G. B. Chirico, L. Solari, and F. Preti, “The effect of flexible vegetation on flow in drainage channels: estimation of roughness coefficients at the real scale,” Ecological Engineering, vol. 120, pp. 411–421, 2018.View at: Publisher Site | Google Scholar
  56. S. E. Darby, “Effect of riparian vegetation on flow resistance and flood potential,” Journal of Hydraulic Engineering, vol. 125, no. 5, pp. 443–454, 1999.View at: Publisher Site | Google Scholar
  57. V. Kutija and H. Thi Minh Hong, “A numerical model for assessing the additional resistance to flow introduced by flexible vegetation,” Journal of Hydraulic Research, vol. 34, no. 1, pp. 99–114, 1996.View at: Publisher Site | Google Scholar
  58. T. Fischer-Antze, T. Stoesser, P. Bates, and N. R. B. Olsen, “3D numerical modelling of open-channel flow with submerged vegetation,” Journal of Hydraulic Research, vol. 39, no. 3, pp. 303–310, 2001.View at: Publisher Site | Google Scholar
  59. U. Stephan and D. Gutknecht, “Hydraulic resistance of submerged flexible vegetation,” Journal of Hydrology, vol. 269, no. 1-2, pp. 27–43, 2002.View at: Publisher Site | Google Scholar
  60. F. G. Carollo, V. Ferro, and D. Termini, “Flow resistance law in channels with flexible submerged vegetation,” Journal of Hydraulic Engineering, vol. 131, no. 7, pp. 554–564, 2005.View at: Publisher Site | Google Scholar
  61. W. Fu-sheng, “Flow resistance of flexible vegetation in open channel,” Journal of Hydraulic Engineering, vol. S1, 2007.View at: Google Scholar
  62. P.-f. Wang, C. Wang, and D. Z. Zhu, “Hydraulic resistance of submerged vegetation related to effective height,” Journal of Hydrodynamics, vol. 22, no. 2, pp. 265–273, 2010.View at: Publisher Site | Google Scholar
  63. J. K. Lee, L. C. Roig, H. L. Jenter, and H. M. Visser, “Drag coefficients for modeling flow through emergent vegetation in the Florida Everglades,” Ecological Engineering, vol. 22, no. 4-5, pp. 237–248, 2004.View at: Publisher Site | Google Scholar
  64. G. J. Arcement and V. R. Schneider, Guide for Selecting Manning’s Roughness Coefficients for Natural Channels and Flood Plains, US Government Printing Office, Washington, DC, USA, 1989.
  65. Y. Ding and S. S. Y. Wang, “Identification of Manning’s roughness coefficients in channel network using adjoint analysis,” International Journal of Computational Fluid Dynamics, vol. 19, no. 1, pp. 3–13, 2005.View at: Publisher Site | Google Scholar
  66. E. T. Engman, “Roughness coefficients for routing surface runoff,” Journal of Irrigation and Drainage Engineering, vol. 112, no. 1, pp. 39–53, 1986.View at: Publisher Site | Google Scholar
  67. M. Feizbahr, C. Kok Keong, F. Rostami, and M. Shahrokhi, “Wave energy dissipation using perforated and non perforated piles,” International Journal of Engineering, vol. 31, no. 2, pp. 212–219, 2018.View at: Publisher Site | Google Scholar
  68. M. Farzadkhoo, A. Keshavarzi, H. Hamidifar, and M. Javan, “Sudden pollutant discharge in vegetated compound meandering rivers,” Catena, vol. 182, Article ID 104155, 2019.View at: Publisher Site | Google Scholar
  69. V. T. Chow, Open-channel Hydraulics, Mcgraw-Hill Civil Engineering Series, Chennai, TN, India, 1959.
  70. X. Zhang, R. Jing, Z. Li, Z. Li, X. Chen, and C.-Y. Su, “Adaptive pseudo inverse control for a class of nonlinear asymmetric and saturated nonlinear hysteretic systems,” IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 4, pp. 916–928, 2020.View at: Google Scholar
  71. C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: the phase space perspective,” Optics and Lasers in Engineering, vol. 71, pp. 20–32, 2015.View at: Publisher Site | Google Scholar
  72. C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Scientific Reports, vol. 7, no. 1, pp. 7654–7722, 2017.View at: Publisher Site | Google Scholar
  73. B.-H. Li, Y. Liu, A.-M. Zhang, W.-H. Wang, and S. Wan, “A survey on blocking technology of entity resolution,” Journal of Computer Science and Technology, vol. 35, no. 4, pp. 769–793, 2020.View at: Publisher Site | Google Scholar
  74. Y. Liu, B. Zhang, Y. Feng et al., “Development of 340-GHz transceiver front end based on GaAs monolithic integration technology for THz active imaging array,” Applied Sciences, vol. 10, no. 21, p. 7924, 2020.View at: Publisher Site | Google Scholar
  75. J. Hu, H. Zhang, L. Liu, X. Zhu, C. Zhao, and Q. Pan, “Convergent multiagent formation control with collision avoidance,” IEEE Transactions on Robotics, vol. 36, no. 6, pp. 1805–1818, 2020.View at: Publisher Site | Google Scholar
  76. M. B. Movahhed, J. Ayoubinejad, F. N. Asl, and M. Feizbahr, “The effect of rain on pedestrians crossing speed,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 6, no. 3, 2020.View at: Google Scholar
  77. A. Li, D. Spano, J. Krivochiza et al., “A tutorial on interference exploitation via symbol-level precoding: overview, state-of-the-art and future directions,” IEEE Communications Surveys & Tutorials, vol. 22, no. 2, pp. 796–839, 2020.View at: Publisher Site | Google Scholar
  78. W. Zhu, C. Ma, X. Zhao et al., “Evaluation of sino foreign cooperative education project using orthogonal sine cosine optimized kernel extreme learning machine,” IEEE Access, vol. 8, pp. 61107–61123, 2020.View at: Publisher Site | Google Scholar
  79. G. Liu, W. Jia, M. Wang et al., “Predicting cervical hyperextension injury: a covariance guided sine cosine support vector machine,” IEEE Access, vol. 8, pp. 46895–46908, 2020.View at: Publisher Site | Google Scholar
  80. Y. Wei, H. Lv, M. Chen et al., “Predicting entrepreneurial intention of students: an extreme learning machine with Gaussian barebone harris hawks optimizer,” IEEE Access, vol. 8, pp. 76841–76855, 2020.View at: Publisher Site | Google Scholar
  81. A. Lin, Q. Wu, A. A. Heidari et al., “Predicting intentions of students for master programs using a chaos-induced sine cosine-based fuzzy K-Nearest neighbor classifier,” Ieee Access, vol. 7, pp. 67235–67248, 2019.View at: Publisher Site | Google Scholar
  82. Y. Fan, P. Wang, A. A. Heidari et al., “Rationalized fruit fly optimization with sine cosine algorithm: a comprehensive analysis,” Expert Systems with Applications, vol. 157, Article ID 113486, 2020.View at: Publisher Site | Google Scholar
  83. E. Rodríguez-Esparza, L. A. Zanella-Calzada, D. Oliva et al., “An efficient Harris hawks-inspired image segmentation method,” Expert Systems with Applications, vol. 155, Article ID 113428, 2020.View at: Publisher Site | Google Scholar
  84. S. Jiao, G. Chong, C. Huang et al., “Orthogonally adapted Harris hawks optimization for parameter estimation of photovoltaic models,” Energy, vol. 203, Article ID 117804, 2020.View at: Publisher Site | Google Scholar
  85. Z. Xu, Z. Hu, A. A. Heidari et al., “Orthogonally-designed adapted grasshopper optimization: a comprehensive analysis,” Expert Systems with Applications, vol. 150, Article ID 113282, 2020.View at: Publisher Site | Google Scholar
  86. A. Abbassi, R. Abbassi, A. A. Heidari et al., “Parameters identification of photovoltaic cell models using enhanced exploratory salp chains-based approach,” Energy, vol. 198, Article ID 117333, 2020.View at: Publisher Site | Google Scholar
  87. M. Mahmoodi and K. K. Aminjan, “Numerical simulation of flow through sukhoi 24 air inlet,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 03, 2017.View at: Google Scholar
  88. F. J. Golrokh and A. Hasan, “A comparison of machine learning clustering algorithms based on the DEA optimization approach for pharmaceutical companies in developing countries,” ENG Transactions, vol. 1, 2020.View at: Google Scholar
  89. H. Chen, A. A. Heidari, H. Chen, M. Wang, Z. Pan, and A. H. Gandomi, “Multi-population differential evolution-assisted Harris hawks optimization: framework and case studies,” Future Generation Computer Systems, vol. 111, pp. 175–198, 2020.View at: Publisher Site | Google Scholar
  90. J. Guo, H. Zheng, B. Li, and G.-Z. Fu, “Bayesian hierarchical model-based information fusion for degradation analysis considering non-competing relationship,” IEEE Access, vol. 7, pp. 175222–175227, 2019.View at: Publisher Site | Google Scholar
  91. J. Guo, H. Zheng, B. Li, and G.-Z. Fu, “A Bayesian approach for degradation analysis with individual differences,” IEEE Access, vol. 7, pp. 175033–175040, 2019.View at: Publisher Site | Google Scholar
  92. M. M. A. Malakoutian, Y. Malakoutian, P. Mostafapour, and S. Z. D. Abed, “Prediction for monthly rainfall of six meteorological regions and TRNC (case study: north Cyprus),” ENG Transactions, vol. 2, no. 2, 2021.View at: Google Scholar
  93. H. Arslan, M. Ranjbar, and Z. Mutlum, “Maximum sound transmission loss in multi-chamber reactive silencers: are two chambers enough?,,” ENG Transactions, vol. 2, no. 1, 2021.View at: Google Scholar
  94. N. Tonekaboni, M. Feizbahr, N. Tonekaboni, G.-J. Jiang, and H.-X. Chen, “Optimization of solar CCHP systems with collector enhanced by porous media and nanofluid,” Mathematical Problems in Engineering, vol. 2021, Article ID 9984840, 12 pages, 2021.View at: Publisher Site | Google Scholar
  95. Z. Niu, B. Zhang, J. Wang et al., “The research on 220GHz multicarrier high-speed communication system,” China Communications, vol. 17, no. 3, pp. 131–139, 2020.View at: Publisher Site | Google Scholar
  96. B. Zhang, Z. Niu, J. Wang et al., “Four‐hundred gigahertz broadband multi‐branch waveguide coupler,” IET Microwaves, Antennas & Propagation, vol. 14, no. 11, pp. 1175–1179, 2020.View at: Publisher Site | Google Scholar
  97. Z.-Q. Niu, L. Yang, B. Zhang et al., “A mechanical reliability study of 3dB waveguide hybrid couplers in the submillimeter and terahertz band,” Journal of Zhejiang University Science, vol. 1, no. 1, 1998.View at: Google Scholar
  98. B. Zhang, D. Ji, D. Fang, S. Liang, Y. Fan, and X. Chen, “A novel 220-GHz GaN diode on-chip tripler with high driven power,” IEEE Electron Device Letters, vol. 40, no. 5, pp. 780–783, 2019.View at: Publisher Site | Google Scholar
  99. M. Taleghani and A. Taleghani, “Identification and ranking of factors affecting the implementation of knowledge management engineering based on TOPSIS technique,” ENG Transactions, vol. 1, no. 1, 2020.View at: Google Scholar
Strain rate magnitude at the free surface, illustrating Kelvin-Helmoltz (KH) shear instabilities.

On the reef scale hydrodynamics at Sodwana Bay, South Africa

Environmental Fluid Mechanics (2022)Cite this article

Abstract

The hydrodynamics of coral reefs strongly influences their biological functioning, impacting processes such as nutrient availability and uptake, recruitment success and bleaching. For example, coral reefs located in oligotrophic regions depend on upwelling for nutrient supply. Coral reefs at Sodwana Bay, located on the east coast of South Africa, are an example of high latitude marginal reefs. These reefs are subjected to complex hydrodynamic forcings due to the interaction between the strong Agulhas current and the highly variable topography of the region. In this study, we explore the reef scale hydrodynamics resulting from the bathymetry for two steady current scenarios at Two-Mile Reef (TMR) using a combination of field data and numerical simulations. The influence of tides or waves was not considered for this study as well as reef-scale roughness. Tilt current meters with onboard temperature sensors were deployed at selected locations within TMR. We used field observations to identify the dominant flow conditions on the reef for numerical simulations that focused on the hydrodynamics driven by mean currents. During the field campaign, southerly currents were the predominant flow feature with occasional flow reversals to the north. Northerly currents were associated with greater variability towards the southern end of TMR. Numerical simulations showed that Jesser Point was central to the development of flow features for both the northerly and southerly current scenarios. High current variability in the south of TMR during reverse currents is related to the formation of Kelvin-Helmholtz type shear instabilities along the outer edge of an eddy formed north of Jesser Point. Furthermore, downward vertical velocities were computed along the offshore shelf at TMR during southerly currents. Current reversals caused a change in vertical velocities to an upward direction due to the orientation of the bathymetry relative to flow directions.

Highlights

  • A predominant southerly current was measured at Two-Mile Reef with occasional reversals towards the north.
  • Field observations indicated that northerly currents are spatially varied along Two-Mile Reef.
  • Simulation of reverse currents show the formation of a separated flow due to interaction with Jesser Point with Kelvin–Helmholtz type shear instabilities along the seaward edge.

지금까지 Sodwana Bay에서 자세한 암초 규모 유체 역학을 모델링하려는 시도는 없었습니다. 이러한 모델의 결과는 규모가 있는 산호초 사이의 흐름이 산호초 건강에 어떤 영향을 미치는지 탐색하는 데 사용할 수 있습니다. 이 연구에서는 Sodwana Bay의 유체역학을 탐색하는 데 사용할 수 있는 LES 모델을 개발하기 위한 단계별 접근 방식을 구현합니다. 여기서 우리는 이 초기 단계에서 파도와 조수의 영향을 배제하면서 Agulhas 해류의 유체역학에 초점을 맞춥니다. 이 접근법은 흐름의 첫 번째 LES를 제시하고 Sodwana Bay의 산호초에서 혼합함으로써 향후 연구의 기초를 제공합니다.

This is a preview of subscription content, access via your institution.

References

  1. Anarde K, Myres H, Figlus J (2016) Tilt current meter field validation in the surf zone. In: AGU fall meeting abstracts, vol 2016, pp EP23A—-0950
  2. Blocken B (2018) LES over RANS in building simulation for outdoor and indoor applications: A foregone conclusion? Build Simul 11(5):821–870. https://doi.org/10.1007/s12273-018-0459-3Article Google Scholar 
  3. Booij N, Ris RC, Holthuijsen LH (1999) A third-generation wave model for coastal regions: 1. Model description and validation. J Geophys Res Ocean 104(C4):7649–7666. https://doi.org/10.1029/98JC02622Article Google Scholar 
  4. Bouffanais R (2010) Advances and challenges of applied large-eddy simulation. Comput Fluids 39:735–738. https://doi.org/10.1016/j.compfluid.2009.12.003Article Google Scholar 
  5. Celliers L, Schleyer MH (2002) Coral bleaching on high-latitude marginal reefs at Sodwana Bay, South Africa. Mar Pollut Bull 44:1380–1387Article Google Scholar 
  6. Celliers L, Schleyer MH (2008) Coral community structure and risk assessment of high-latitude reefs at Sodwana Bay, South Africa. Biodivers Conserv 17(13):3097–3117. https://doi.org/10.1007/s10531-007-9271-6Article Google Scholar 
  7. Chen SC (2018) Performance assessment of FLOW-3D and XFlow in the numerical modelling of fish-bone type fishway hydraulics https://doi.org/10.15142/T3HH1J
  8. Corbella S, Pringle J, Stretch DD (2015) Assimilation of ocean wave spectra and atmospheric circulation patterns to improve wave modelling. Coast Eng 100:1–10. https://doi.org/10.1016/j.coastaleng.2015.03.003Article Google Scholar 
  9. Davis KA, Pawlak G, Monismith SG (2021) Turbulence and coral reefs. Ann Rev Mar Sci. https://doi.org/10.1146/annurev-marine-042120-071823Article Google Scholar 
  10. Flow Science Inc (2018) FLOW-3D, Version 12.0 Users Manual. Santa Fe, NM, https://www.flow3d.com/
  11. Flow Science Inc (2019) FLOW-3D, Version 12.0 [Computer Software]. Santa Fe, NM, https://www.flow3d.com/
  12. Franco A, Moernaut J, Schneider-Muntau B, Strasser M, Gems B (2020) The 1958 Lituya Bay tsunami – pre-event bathymetry reconstruction and 3D numerical modelling utilising the computational fluid dynamics software Flow-3D. Nat Hazards Earth Syst Sci 20(8):2255–2279Article Google Scholar 
  13. Fringer OB, Gerritsen M, Street RL (2006) An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator. Ocean Model 14(3):139–173Article Google Scholar 
  14. Fringer OB, Dawson CN, He R, Ralston DK, Zhang YJ (2019) The future of coastal and estuarine modeling: findings from a workshop. Ocean Model 143(September):101458. https://doi.org/10.1016/j.ocemod.2019.101458Article Google Scholar 
  15. Glassom D, Celliers L, Schleyer MH (2006) Coral recruitment patterns at Sodwana Bay, South Africa. Coral Reefs 25(3):485–492. https://doi.org/10.1007/s00338-006-0117-6Article Google Scholar 
  16. Gomes A, Pinho JLS, Valente T, do Carmo JS, Hegde VA (2020) Performance assessment of a semi-circular breakwater through CFD modelling. J Mar Sci Eng. https://doi.org/10.3390/jmse8030226Article Google Scholar 
  17. Green RH, Lowe RJ, Buckley ML (2018) Hydrodynamics of a tidally forced coral reef atoll. J Geophys Res Oceans 123(10):7084–7101. https://doi.org/10.1029/2018JC013946Article Google Scholar 
  18. Hansen AB, Carstensen S, Christensen DF, Aagaard T (2017) Performance of a tilt current meter in the surf zone. Coastal dynamics
  19. Hench JL, Rosman JH (2013) Observations of spatial flow patterns at the coral colony scale on a shallow reef flat. J Geophys Res Ocean 118(3):1142–1156. https://doi.org/10.1002/jgrc.20105Article Google Scholar 
  20. Hirt CW (1993) Volume-fraction techniques: powerful tools for wind engineering. J Wind Eng Ind Aerodyn 46–47:327–338. https://doi.org/10.1016/0167-6105(93)90298-3Article Google Scholar 
  21. Hirt CW, Sicilian JM (1985) A porosity technique for the definition of obstacles in rectangular cell meshes. In: Proceedings of 4th International Conference on Ship Hydrodynamics https://ci.nii.ac.jp/naid/10009570543/en/
  22. Hocker LO, Hruska MA (2004) Interleaving synchronous data and asynchronous data in a single data storage file
  23. Hossain MM, Staples AE (2020) Effects of coral colony morphology on turbulent flow dynamics. PLoS ONE 15(10):e0225676. https://doi.org/10.1371/journal.pone.0225676Article Google Scholar 
  24. Jacob B, Stanev EV (2021) Understanding the impact of bathymetric changes in the german bight on coastal hydrodynamics: one step toward realistic morphodynamic modeling. Front Mar Sci. https://doi.org/10.3389/fmars.2021.640214Article Google Scholar 
  25. Koehl MAR, Hadfield MG (2010) Hydrodynamics of larval settlement from a larva’s point of view. Integr Comp Biol 50(4):539–551. https://doi.org/10.1093/icb/icq101Article Google Scholar 
  26. Lim A, Wheeler AJ, Price DM, O’Reilly L, Harris K, Conti L (2020) Influence of benthic currents on cold-water coral habitats: a combined benthic monitoring and 3D photogrammetric investigation. Sci Rep 10(1):19433. https://doi.org/10.1038/s41598-020-76446-yArticle Google Scholar 
  27. Limer BD, Bloomberg J, Holstein DM (2020) The influence of eddies on coral larval retention in the flower garden banks. Front Mar Sci 7:372. https://doi.org/10.3389/fmars.2020.00372Article Google Scholar 
  28. Monismith SG (2007) Hydrodynamics of coral reefs. Annu Rev Fluid Mech 39(1):37–55. https://doi.org/10.1146/annurev.fluid.38.050304.092125Article Google Scholar 
  29. Morris T (2009) Physical oceanography of Sodwana Bay and its effect on larval transport and coral bleaching. PhD thesis, Cape Peninsula University of Technology
  30. Morris T, Lamont T, Roberts MJ (2013) Effects of deep-sea eddies on the northern KwaZulu-Natal shelf, South Africa. Afr J Mar Sci 35(3):343–350. https://doi.org/10.2989/1814232X.2013.827991Article Google Scholar 
  31. Perry C, Larcombe P (2003) Marginal and non-reef-building coral environments. Coral Reefs 22:427–432. https://doi.org/10.1007/s00338-003-0330-5Article Google Scholar 
  32. Pope SB (2001) Turbulent flows. Cambridge University Press, CambridgeGoogle Scholar 
  33. Porter SN (2009) Biogeography and potential factors regulating shallow subtidal reef communities in the Western Indian Ocean. PhD thesis, University of Cape Town
  34. Porter SN, Schleyer MH (2017) Long-term dynamics of a high-latitude coral reef community at Sodwana Bay, South Africa. Coral Reefs 36(2):369–382. https://doi.org/10.1007/s00338-016-1531-zArticle Google Scholar 
  35. Porter SN, Schleyer MH (2019) Environmental variation and how its spatial structure influences the cross-shelf distribution of high-latitude coral communities in South Africa. Diversity. https://doi.org/10.3390/d11040057Article Google Scholar 
  36. Ramsay PJ (1994) Marine geology of the Sodwana Bay shelf, southeast Africa. Mar Geol 120(3–4):225–247. https://doi.org/10.1016/0025-3227(94)90060-4Article Google Scholar 
  37. Ramsay PJ, Mason TR (1990) Development of a type zoning model for Zululand coral reefs, Sodwana Bay, South Africa. J Coastal Res 6(4):829–852Google Scholar 
  38. Reguero BG, Beck MW, Agostini VN, Kramer P, Hancock B (2018) Coral reefs for coastal protection: a new methodological approach and engineering case study in Grenada. J Environ Manag 210:146–161. https://doi.org/10.1016/j.jenvman.2018.01.024Article Google Scholar 
  39. Reidenbach M, Stocking J, Szczyrba L, Wendelken C (2021) Hydrodynamic interactions with coral topography and its impact on larval settlement. Coral Reefs 40:1–15. https://doi.org/10.1007/s00338-021-02069-yArticle Google Scholar 
  40. Reidenbach MA, Koseff JR, Koehl MAR (2009) Hydrodynamic forces on larvae affect their settlement on coral reefs in turbulent, wave-driven flow. Limnol Oceanogr 54(1):318–330. https://doi.org/10.4319/lo.2009.54.1.0318Article Google Scholar 
  41. Roberts H, Richardson J, Lagumbay R, Meselhe E, Ma Y (2013) Hydrodynamic and sediment transport modeling using FLOW-3D for siting and optimization of the LCA medium diversion at white ditch hydrodynamic and sediment transport modeling using FLOW-3D for siting and optimization of the LCA medium diversion at white D (December)
  42. Roberts MJ, Ribbink AJ, Morris T, Berg MAVD, Engelbrecht DC, Harding RT (2006) Oceanographic environment of the Sodwana Bay coelacanths (Latimeria chalumnae), South Africa: coelacanth research. South Afr J Sci 102(9):435–443Google Scholar 
  43. Rogers JS, Monismith SG, Feddersen F, Storlazzi CD (2013) Hydrodynamics of spur and groove formations on a coral reef. J Geophys Res Ocean 118(6):3059–3073. https://doi.org/10.1002/jgrc.20225Article Google Scholar 
  44. Rogers JS, Monismith SG, Koweek DA, Torres WI, Dunbar RB (2016) Thermodynamics and hydrodynamics in an atoll reef system and their influence on coral cover. Limnol Oceanogr 61(6):2191–2206. https://doi.org/10.1002/lno.10365Article Google Scholar 
  45. Schleyer MH, Celliers L (2003) Coral dominance at the reef-sediment interface in marginal coral communities at Sodwana Bay, South Africa. Mar Freshw Res 54(8):967–972. https://doi.org/10.1071/MF02049Article Google Scholar 
  46. Schleyer MH, Porter SN (2018) Chapter One – drivers of soft and stony coral community distribution on the high-latitude coral reefs of South Africa. advances in marine biology, vol 80, Academic Press, pp 1–55, https://doi.org/10.1016/bs.amb.2018.09.001
  47. Scott F, Antolinez JAA, McCall R, Storlazzi C, Reniers A, Pearson S (2020) Hydro-morphological characterization of coral reefs for wave runup prediction. Front Mar Sci 7:361. https://doi.org/10.3389/fmars.2020.00361Article Google Scholar 
  48. Sebens KP, Grace SP, Helmuth B, Maney EJ Jr, Miles JS (1998) Water flow and prey capture by three scleractinian corals, Madracis mirabilis, Montastrea cavernosa and Porites porites, in a field enclosure. Mar Biol 131(2):347–360Article Google Scholar 
  49. Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91(3):99–164Article Google Scholar 
  50. Stocking J, Laforsch C, Sigl R, Reidenbach M (2018) The role of turbulent hydrodynamics and surface morphology on heat and mass transfer in corals. J R Soc Interface 15:20180448. https://doi.org/10.1098/rsif.2018.0448Article Google Scholar 
  51. Van Leer B (1977) Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow. J Comput Phys 23(3):263–275. https://doi.org/10.1016/0021-9991(77)90094-8Article Google Scholar 
  52. Wells C, Pringle J, Stretch D (2021) Cold water temperature anomalies on the Sodwana reefs and their driving mechanisms. South Afr J Sci. https://doi.org/10.17159/sajs.2021/9304Article Google Scholar 
  53. Wyatt ASJ, Lowe RJ, Humphries S, Waite AM (2010) Particulate nutrient fluxes over a fringing coral reef: relevant scales of phytoplankton production and mechanisms of supply. Mar Ecol Prog Ser 405:113–130Article Google Scholar 
  54. Yao Y, He T, Deng Z, Chen L, Guo H (2019) Large eddy simulation modeling of tsunami-like solitary wave processes over fringing reefs. Nat Hazards Earth Syst Sci 19(6):1281–1295. https://doi.org/10.5194/nhess-19-1281-2019Article Google Scholar 
  55. Zhao Q, Tanimoto K (1998) Numerical simulation of breaking waves by large eddy simulation and vof method. Coastal Engineering Proceedings 1(26), 10.9753/icce.v26.%p, https://journals.tdl.org/icce/index.php/icce/article/view/5656

Text and image taken from Deoraj, et al. (2022), On the reef scale hydrodynamics at Sodwana Bay, South Africa. Preprint courtesy the authors.

Figure 2: 3D (left) and 2D (right) views of wave elevation using case C

CFD 접근법을 사용하여 파도에서 하이드로포일의 SEAKEEPING 성능

SYAFIQ ZIKRYAND FITRIADHY*
Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala
Terengganu, Terengganu, Malaysia
*
Corresponding author: naoe.afit@gmail.com http://doi.org/10.46754/umtjur.2021.07.017

Abstract

수중익선은 일반적으로 열악한 환경 조건으로 인해 승객의 편안함에 영향을 미칠 수 있는 높은 저항과 과도한 수직 운동(히브 및 피치)을 경험합니다. 따라서 복잡한 유체역학적 현상이 존재하기 때문에 파랑에서 수중익선의 내항성능을 규명할 필요가 있다.

이를 위해 수중익선 운동에 대한 CFD(Computational Fluid Dynamic) 해석을 제안한다. Froude Number 및 포일 받음각과 같은 여러 매개변수가 고려되었습니다.

그 결과 Froude Number의 후속 증가는 히브 및 피치 운동에 반비례한다는 것이 밝혀졌습니다. 본질적으로 이것은 높은 응답 진폭 연산자(RAO)의 형태로 제공되는 수중익선 항해 성능의 업그레이드로 이어졌습니다.

또한 포일 선수의 증가하는 각도는 히브 운동에 비례하는 반면, 포일 선미는 7.5o에서 낮은 히브 운동을 보였고, 그 다음으로 5o, 10o 순으로 나타났다. 피치모션의 경우 포일 보우의 증가는 5o에서 더 낮았고, 그 다음이 10o, 7.5o 순이었다. 포일 선미의 증가는 수중익선에 의한 피치 모션 경험에 비례했습니다.

일반적으로 이 CFD 시뮬레이션은 앞서 언급한 설계 매개변수와 관련하여 공해 상태에서 수중익선 설계의 운영 효율성을 보장하는 데 매우 유용합니다.

Keywords

CFD, hydrofoil, foil angle of attack, heave, pitch.

Figure 1: Overall mesh block being used in simulation
Figure 1: Overall mesh block being used in simulation
Figure 2: 3D (left) and 2D (right) views of wave elevation using case C
Figure 2: 3D (left) and 2D (right) views of wave elevation using case C

References

Djavareshkian, M. H., & Esmaeili, A. (2014). Heuristic optimization of submerged hydrofoil
using ANFIS–PSO. Ocean Engineering, 92, 55-63.
Fitriadhy, A., & Adam, N. A. (2017). Heave and pitch motions performance of a monotricat ship in
head-seas. International Journal of Automotive and Mechanical Engineering, 14, 4243-4258.
Islam, M., Jahra, F., & Hiscock, S. (2016). Data analysis methodologies for hydrodynamic
experiments in waves. Journal of Naval Architecture and Marine Engineering, 13(1),
1-15.
Koutsourakis, N., Bartzis, J. G., & Markatos, N. C. (2012). Evaluation of Reynolds stress, k-ε and
RNG k-ε turbulence models in street canyon flows using various experimental datasets.
Environmental fluid mechanics, 1-25.
Manual, F. D. U. (2011). Flow3D User Manual, v9. 4.2, Flow Science. Inc., Santa Fe, NM. Matveev, K., & Duncan, R. (2005). Development
of the tool for predicting hydrofoil system performance and simulating motion of hydrofoil-assisted boats. Paper presented at the High Speed and High Performance Ship and Craft Symposium, Everett/WA: ASNE, USA.
Seif, M., Mehdigholi, H., & Najafi, A. (2014). Experimental and numerical modeling of the
high speed planing vessel motion. Journal of Marine Engineering & Technology, 13(2), 62-
72.
Sun, X., Yao, C., Xiong, Y., & Ye, Q. (2017). Numerical and experimental study on
seakeeping performance of a swath vehicle in head waves. Applied Ocean Research, 68, 262-
275.
Vakilabadi, K. A., Khedmati, M. R., & Seif, M.S. (2014). Experimental study on heave and
pitch motion characteristics of a wave-piercing trimaran. Transactions of FAMENA, 38(3), 13-
26.
Yakhot, A., Rakib, S., & Flannery, W. (1994). LowReynolds number approximation for turbulent
eddy viscosity. Journal of scientific computing, 9(3), 283-292.
Yakhot, V., & Orszag, S. A. (1986). Renormalization group analysis of turbulence. I. Basic theory.
Journal of scientific computing, 1(1), 3-51.

Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade and Abaunza Tabares, 2021)

Three-dimensional Numerical Evaluation of Hydraulic Efficiency and Discharge Coefficient in Grate Inlets

쇠창살 격자 유입구의 수리효율 및 배출계수에 대한 3차원 수치적 평가

Melquisedec Cortés Zambrano*, Helmer Edgardo Monroy González,
Wilson Enrique Amaya Tequia
Faculty of Civil Engineering, Santo Tomas Tunja University. Address Av. Universitaria No. 45-202.
Tunja – Boyacá – Colombia

Abstract

홍수는 지반이동 및 이동의 원인 중 하나이며, 급속한 도시화 및 도시화로 인해 이전보다 빈번하게 발생할 수 있다. 도시 배수 시스템의 특성은 집수 요소가 결정적인 역할을 하는 범람의 발생 및 범위를 정의할 수 있습니다. 이 문서는 7가지 유형의 화격자 유입구의 수력 유입 효율 및 배출 계수에 대한 수치 조사를 제시합니다. FLOW-3D® 시뮬레이터는 Q = 24, 34.1, 44, 100, 200 및 300 L/s의 유속에서 풀 스케일로 격자를 테스트하는 데 사용되며 종방향 기울기가 1.0인 실험 프로토타입의 구성을 유지합니다. %, 1.5% 및 2.0% 및 고정 횡단 경사, 총 126개 모델. 그 결과를 바탕으로 종류별 및 종단경사 조건에 따른 수력유입구 효율곡선과 토출계수를 구성하였다. 결과는 다른 조사에서 제안된 경험적 공식으로 조정되어 프로토타입의 물리적 테스트 결과를 검증하는 역할을 합니다.

Floods are one of the causes of ground movement and displacement, and due to rapid urbanization and urban growth may occur more frequently than before. The characteristics of an urban drainage system can define the occurrence and extent of flooding, where catchment elements have a determining role. This document presents the numerical investigation of the hydraulic inlet efficiency and the discharge coefficient of seven types of grate inlets. The FLOW-3D® simulator is used to test the gratings at a full scale, under flow rates of Q = 24, 34.1, 44, 100, 200 and 300 L/s, preserving the configuration of the experimental prototype with longitudinal slopes of 1.0%, 1.5% and 2.0% and a fixed cross slope, for a total of 126 models. Based on the results, hydraulic inlet efficiency curves and discharge coefficients are constructed for each type and a longitudinal slope condition. The results are adjusted with empirical formulations proposed in other investigations, serving to verify the results of physical testing of prototypes.

Keywords

grate inlet, inlet efficiency, discharge coefficient, computational fluid dynamic, 3D modelling.

Fig. 1. Physical model of the experimental campaign (source: Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 1. Physical model of the experimental campaign (source: Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade
and Abaunza Tabares, 2021)
Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 4. Comparison between the results obtained during physical experimentation in prototype 7 and simulation results with FLOW-3D® (source:
made with FlowSight® and photographic record by Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 4. Comparison between the results obtained during physical experimentation in prototype 7 and simulation results with FLOW-3D® (source: made with FlowSight® and photographic record by Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 6. Example of the results of flow depth and velocity vectors in the xy plane, for a stable flow condition in a grate inlet type and free surface
configuration and flow regime, of some grating types (source: produced with FlowSight®)
Fig. 6. Example of the results of flow depth and velocity vectors in the xy plane, for a stable flow condition in a grate inlet type and free surface configuration and flow regime, of some grating types (source: produced with FlowSight®)

References

Alia Md., S., and Sabtu, N. (2020). Comparison of Different Methodologies for Determining the Efficiency of Gully Inlets. In F. M.
Nazri (Ed.), Proceedings of AICCE‘19: Transforming the Nation
for a Sustainable Tomorrow (Vol. 53, pp. 1275-1284). Springer
Nature Switzerland AG. https://doi.org/10.1007/978-3-030-
32816-0_99
Antunes do Carmo, J. S. (2020). Physical Modelling vs. Numerical Modelling: Complementarity and Learning. July. https://doi.
org/10.20944/preprints202007.0753.v1
Aragón-Hernández, J. L. (2013). Modelación numérica integrada de los procesos hidráulicos en el drenaje urbano [Universidad Politécnica de Cataluña]. In Doctoral Tesis. https://
upcommons.upc.edu/handle/2117/95059?locale-attribute=es
Argue, J. R., and Pezzaniti, D. (1996). How reliable are inlet
(hydraulic) models at representing stormwater flow? Science
of the Total Environment, 189-190, 355-359. https://doi.org/10.1016/0048-9697(96)05231-X
Banco Mundial, O. (2019). Agua: Panorama general. https://
www.bancomundial.org/es/topic/water/overview
Cárdenas-Quintero, M., Carvajal-Serna, L. F., and Marbello-Pérez, R. (2018). Evaluación numérica tridimensional de un
sumidero de reja de fondo (Three-Dimensional Numerical Assessment of Grate Inlet). SSRN Electronic Journal, November.
https://doi.org/10.2139/ssrn.3112980
Carvalho, R. F., Lopes, P., Leandro, J., and David, L. M. (2019).
Numerical Research of Flows into Gullies with Different Outlet Locations. Water, 11(2), 794. https://doi.org/10.3390/
w11040794
Chaparro Andrade, F. G., and Abaunza Tabares, K. V. (2021). Importancia de los sumideros, su funcionamiento y diseño en redes de alcantarillado caso de estudio sector nororiental Tunja.
Universidad Santo Tomás.
Cortés Zambrano, M., Amaya Tequia, W. E., and Gamba Fernández, D. S. (2020). Implementation of the hydraulic modelling of
urban drainage in the northeast sector, Tunja, Boyacá. Revista
Facultad de Ingeniería Universidad de Antioquia. https://doi.
org/10.17533/udea.redin.20200578
Cosco, C., Gómez, M., Russo, B., Tellez-Alvarez, J., Macchione, F., Costabile, P., and Costanzo, C. (2020). Discharge coefficients for specific grated inlets. Influence of the Froude
number. Urban Water Journal, 17(7), 656-668. https://doi.org/10.1080/1573062X.2020.1811881
Despotovic, J., Plavsic, J., Stefanovic, N., and Pavlovic, D. (2005).
Inefficiency of storm water inlets as a source of urban floods.
Water Science and Technology, 51(2), 139-145. https://doi.
org/10.2166/wst.2005.0041
Ellis, J. B., and Marsalek, J. (1996). Overview of urban drainage:
Environmental impacts and concerns, means of mitigation and
implementation policies. Journal of Hydraulic Research, 34(6),
723-732. https://doi.org/10.1080/00221689609498446
Fang, X., Jiang, S., and Alam, S. R. (2010). Numerical simulations of efficiency of curb-opening inlets. Journal of Hydraulic
Engineering, 136(1), 62-66. https://doi.org/10.1061/(ASCE)
HY.1943-7900.0000131
Faram, M. G., and Harwood, R. (2000). CFD for the Water Industry; The Role of CFD as a Tool for the Development of Wastewater Treatment Systems. Hydro International, 21-22.
Faram, M. G., and Harwood, R. (2002). Assessment of the
effectiveness of stormwater treatment chambers using
computational fluid dynamics. Global Solutions for Urban Drainage, 40644(September 2002), 1-14. https://doi.
org/10.1061/40644(2002)7
Flow Science, I. (2018). FLOW-3D® Version 12.0 Users Manual.
In FLOW-3D [Computer software]. https://www.flow3d.com
Flow Science, I. (2019). FLOW-3D® Version 12.0 [Computer software] (No. 12). https://www.flow3d.com
Ghanbari, R., and Heidarnejad, M. (2020). Experimental and numerical analysis of flow hydraulics in triangular and rectangular
piano key weirs. Water Science, 00(00), 1-7. https://doi.org/10.
1080/11104929.2020.1724649

Gómez, M., and Russo, B. (2005a). Comparative study of methodologies to determine inlet efficiency from test data. HEC-12
methodology vs UPC method. Water Resources Management,
Algarve, Portugal., 80(October 2014), 623-632. https://doi.
org/10.2495/WRM050621
Gómez, M., and Russo, B. (2005b). Comparative study among
different methodologies to determine storm sewer inlet efficiency from test data. 10th International Conference on Urban
Drainage, August, 21-26. https://www.researchgate.net/publication/255602448_Comparative_study_among_different_methodologies_to_determine_storm_sewer_inlet_efficiency_
from_test_data
Gómez, M., Recasens, J., Russo, B., and Martínez-Gomariz, E.
(2016). Assessment of inlet efficiency through a 3D simulation: Numerical and experimental comparison. Water Science
and Technology, 74(8), 1926-1935. https://doi.org/10.2166/
wst.2016.326
Gómez, M., and Russo, B. (2011). Methodology to estimate hydraulic efficiency of drain inlets. Proceedings of the Institution of
Civil Engineers: Water Management, 164(2), 81-90. https://doi.
org/10.1680/wama.900070
Gómez Valentin, M. (2007). Hidrología urbana. In Hidrología Urbana (pp. 135-147). Instituto Flumen.
Jakeman, A. J., Letcher, R. A., and Norton, J. P. (2006). Ten iterative steps in development and evaluation of environmental
models. Environmental Modelling and Software, 21, 602-614.
https://doi.org/10.1016/j.envsoft.2006.01.004
Jang, J. H., Hsieh, C. T., and Chang, T. H. (2019). The importance of gully flow modelling to urban flood simulation. Urban Water Journal, 16(5), 377-388. https://doi.org/10.1080/1573062X.2019.1669198
Kaushal, D. R., Thinglas, T., Tomita, Y., Kuchii, S., and Tsukamoto, H. (2012). Experimental investigation on optimization of
invert trap configuration for sewer solid management. Powder Technology, 215-216, 1-14. https://doi.org/10.1016/j.powtec.2011.08.029
Khazaee, I., and Mohammadiun, M. (2010). Effects of flow field
on open channel flow properties using numerical investigation
and experimental comparison. International Journal of Energy
and Environment, 1(6), 1083-1096. https://doi.org/10.1016/
S0031-9384(10)00122-8
Kleidorfer, M., Tscheikner-Gratl, F., Vonach, T., and Rauch, W.
(2018). What can we learn from a 500-year event? Experiences
from urban drainage in Austria. Water Science and Technology,
77(8), 2146-2154. https://doi.org/10.2166/wst.2018.138
Leitão, J. P., Simões, N. E., Pina, R. D., Ochoa-Rodriguez, S.,
Onof, C., and Sá Marques, A. (2017). Stochastic evaluation of
the impact of sewer inlets‘ hydraulic capacity on urban pluvial
flooding. Stochastic Environmental Research and Risk Assessment, 31(8), 1907-1922. https://doi.org/10.1007/s00477-016-
1283-x
Lopes, P., Leandro, J., Carvalho, R. F., Russo, B., and Gómez, M.
(2016). Assessment of the ability of a volume of fluid model to
reproduce the efficiency of a continuous transverse gully with
grate. Journal of Irrigation and Drainage Engineering, 142(10),
1-9. https://doi.org/10.1061/(ASCE)IR.1943-4774.0001058
Mohsin, M., and Kaushal, D. R. (2016). 3D CFD validation of invert trap efficiency for sewer solid management using VOF model. Water Science and Engineering, 9(2), 106-114. https://doi.
org/10.1016/j.wse.2016.06.006
Palla, A., Colli, M., Candela, A., Aronica, G. T., and Lanza, L.
G. (2018). Pluvial flooding in urban areas: the role of surface
drainage efficiency. Journal of Flood Risk Management, 11,
S663-S676. https://doi.org/10.1111/jfr3.12246
Russo, B. (2010). Design of surface drainage systems according
to hazard criteria related to flooding of urban areas [Universitat
Politècnica de Catalunya]. https://dialnet.unirioja.es/servlet/
tesis?codigo=258828
Sedano-Cruz, K., Carvajal-Escoar, Y., and Ávila Díaz, A. J. (2013).
ANÁLISIS DE ASPECTOS QUE INCREMENTAN EL RIESGO
DE INUNDACIONES EN COLOMBIA. Luna Azul, 37, 219-218.
https://www.redalyc.org/articulo.oa?id=321729206014
Spaliviero, F., May, R. W. P., Escarameia, M. (2000). Spacing of road gullies. Hydraulic performance of BS EN 124 gully gratings. HR Walingford, 44(0). https://doi.org/10.13140/
RG.2.1.1344.0889
Téllez-Álvarez, J., Gómez, M., and Russo, B. (2020). Quantification of energy loss in two grated inlets under pressure. Water
(Switzerland), 12(6). https://doi.org/10.3390/w12061601
Téllez Álvarez, J., Gómez, V., Russo, B., and Redondo, J. M.
(2003). Performance assessment of numerical modelling
for hydraulic efficiency of a grated inlet. 1, 6-8. https://doi.org/10.16309/j.cnki.issn.1007-1776.2003.03.004
Téllez Álvarez, J., Gómez Valentin, M., Paindelli, A., and Russo,
B. (2017). ACTIVIDAD EXPERIMENTAL DE I+D+i EN INGENIERÍA
HIDRÁULICA EN ESPAÑA. In L. J. Balairón Pérez and D. López
Gómez (Eds.), Seminario 2017, Comunicaciones de las líneas prioritarias (pp. 41-43). Universitat Politècnica de València.
https://doi.org/10.1017/CBO9781107415324.004
Téllez Álvarez, J., Gómez Valentin, M., and Russo, B. (2019).
Modelling of Surcharge Flow Through Grated Inlet. In P. Gourbesville and G. Caignaert (Eds.), Advances in Hydroinformati-

cs. Springer, Singapore. https://doi.org/10.1007/978-981-
4451-42-0
UNDRR, I., and CRED, I. (2018). Pérdidas económicas, pobreza y
Desastres 1998 – 2017 (Vol. 6, Issue 1). https://doi.org/10.12962/
j23373520.v6i1.22451
Vyzikas, T., and Greaves, D. (2018). Numerial Modelling.
In D. Greaves and G. Iglesias (Eds.), Wave and Tidal Energy (pp. 289-363). John Wiley and Sons Ltd. https://doi.
org/10.1002/9781119014492
Yakhot, V., and Orszag, S. A. (1986). Renormalization Group Analysis of Turbulence. I . Basic Theory. Journal of Scientific Computing, 1(1), 3-51. https://doi.org/10.1007/BF01061452
Yakhot, V., and Smith, L. M. (1992). The renormalization group,
the ɛ-expansion and derivation of turbulence models. Journal
of Scientific Computing, 7(l), 35-61. https://doi.org/10.1007/
BF01060210
Yazdanfar, Z., and Sharma, A. (2015). Urban drainage system
planning and design – Challenges with climate change and urbanization: A review. Water Science and Technology, 72(2), 165-https://doi.org/10.2166/wst.2015.207

Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system

데이터 기반 방법을 활용한 재생 가능 에너지 변환기의 전력 및 수소 생성 예측 지속 가능한 스마트 그리드 사례 연구

Fatemehsadat Mirshafiee1, Emad Shahbazi 2, Mohadeseh Safi 3, Rituraj Rituraj 4,*
1Department of Electrical and Computer Engineering, K.N. Toosi University of Technology, Tehran 1999143344 , Iran
2Department of Mechatronic, Amirkabir University of Technology, Tehran 158754413, Iran
3Department of Mechatronic, Electrical and Computer Engineering, University of Tehran, Tehran 1416634793, Iran
4 Faculty of Informatics, Obuda University, 1023, Budapest, Hungary

  • Correspondence: rituraj88@stud.uni-obuda.hu

ABSTRACT

본 연구는 지속가능한 에너지 변환기의 전력 및 수소 발생 모델링을 위한 데이터 기반 방법론을 제안합니다. 파고와 풍속을 달리하여 파고와 수소생산을 예측합니다.

또한 이 연구는 파도에서 수소를 추출할 수 있는 가능성을 강조하고 장려합니다. FLOW-3D 소프트웨어 시뮬레이션에서 추출한 데이터와 해양 특수 테스트의 실험 데이터를 사용하여 두 가지 데이터 기반 학습 방법의 비교 분석을 수행합니다.

결과는 수소 생산의 양은 생성된 전력의 양에 비례한다는 것을 보여줍니다. 제안된 재생 에너지 변환기의 신뢰성은 지속 가능한 스마트 그리드 애플리케이션으로 추가로 논의됩니다.

This study proposes a data-driven methodology for modeling power and hydrogen generation of a sustainable energy converter. The wave and hydrogen production at different wave heights and wind speeds are predicted. Furthermore, this research emphasizes and encourages the possibility of extracting hydrogen from ocean waves. By using the extracted data from FLOW-3D software simulation and the experimental data from the special test in the ocean, the comparison analysis of two data-driven learning methods is conducted. The results show that the amount of hydrogen production is proportional to the amount of generated electrical power. The reliability of the proposed renewable energy converter is further discussed as a sustainable smart grid application.

Key words

Cavity, Combustion efficiency, hydrogen fuel, Computational Fluent and Gambit.

Figure 1. The process of power and hydrogen production with Searaser.
Figure 1. The process of power and hydrogen production with Searaser.
Figure 2. The cross-section A-A of the two essential parts of a Searaser
Figure 2. The cross-section A-A of the two essential parts of a Searaser
Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system
Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system
Figure 4. The boundary conditions of the control volume
Figure 4. The boundary conditions of the control volume
Figure 5. The wind velocity during the period of the experimental test
Figure 5. The wind velocity during the period of the experimental test

REFERENCES

  1. Kalbasi, R., Jahangiri, M., Dehshiri, S.J.H., Dehshiri, S.S.H., Ebrahimi, S., Etezadi, Z.A.S. and Karimipour, A., 2021. Finding the
    best station in Belgium to use residential-scale solar heating, one-year dynamic simulation with considering all system losses:
    economic analysis of using ETSW. Sustainable Energy Technologies and Assessments, 45, p.101097.
  2. Megura M, Gunderson R. Better poison is the cure? Critically examining fossil fuel companies, climate change framing, and
    corporate sustainability reports. Energy Research & Social Science. 2022 Mar 1;85:102388.
  3. Holechek JL, Geli HM, Sawalhah MN, Valdez R. A global assessment: can renewable energy replace fossil fuels by 2050?.
    Sustainability. 2022 Jan;14(8):4792.
  4. Ahmad M, Kumar A, Ranjan R. Recent Developments of Tidal Energy as Renewable Energy: An Overview. River and Coastal
    Engineering. 2022:329-43.
  5. Amini E, Mehdipour H, Faraggiana E, Golbaz D, Mozaffari S, Bracco G, Neshat M. Optimization of hydraulic power take-off
    system settings for point absorber wave energy converter. Renewable Energy. 2022 Jun 4.
  6. Claywell, R., Nadai, L., Felde, I., Ardabili, S. 2020. Adaptive neuro-fuzzy inference system and a multilayer perceptron model
    trained with grey wolf optimizer for predicting solar diffuse fraction. Entropy, 22(11), p.1192.
  7. McLeod I, Ringwood JV. Powering data buoys using wave energy: a review of possibilities. Journal of Ocean Engineering and
    Marine Energy. 2022 Jun 20:1-6.
  8. Olsson G. Water interactions: A systemic view: Why we need to comprehend the water-climate-energy-food-economics-lifestyle connections.
  9. Malkowska A, Malkowski A. Green Energy in the Political Debate. InGreen Energy 2023 (pp. 17-39). Springer, Cham.
  10. Mayon R, Ning D, Ding B, Sergiienko NY. Wave energy converter systems–status and perspectives. InModelling and Optimisation of Wave Energy Converters (pp. 3-58). CRC Press.
  11. Available online at: https://www.offshore-energy.biz/uk-ecotricity-introduces-wave-power-device-searaser/ (9/27/2022)
  12. Mousavi SM, et al.,. Deep learning for wave energy converter modeling using long short-term memory. Mathematics. 2021 Apr
    15;9(8):871.
  13. Mega V. The Energy Race to Decarbonisation. InHuman Sustainable Cities 2022 (pp. 105-141). Springer, Cham.
  14. Li R, Tang BJ, Yu B, Liao H, Zhang C, Wei YM. Cost-optimal operation strategy for integrating large scale of renewable energy
    in China’s power system: From a multi-regional perspective. Applied Energy. 2022 Nov 1;325:119780.
  15. Ardabili S., Abdolalizadeh L., Mako C., Torok B., Systematic Review of Deep Learning and Machine Learning for Building
    Energy, Frontiers in Energy Research, 10, 2022.
  16. Penalba M, Aizpurua JI, Martinez-Perurena A, Iglesias G. A data-driven long-term metocean data forecasting approach for the
    design of marine renewable energy systems. Renewable and Sustainable Energy Reviews. 2022 Oct 1;167:112751.
  17. Torabi, M., Hashemi, S., Saybani, M.R., 2019. A Hybrid clustering and classification technique for forecasting short‐term energy
    consumption. Environmental progress & sustainable energy, 38(1), pp.66-76.
  18. Rivera FP, Zalamea J, Espinoza JL, Gonzalez LG. Sustainable use of spilled turbinable energy in Ecuador: Three different energy
    storage systems. Renewable and Sustainable Energy Reviews. 2022 Mar 1;156:112005.
  19. Raza SA, Jiang J. Mathematical foundations for balancing single-phase residential microgrids connected to a three-phase distribution system. IEEE Access. 2022 Jan 6;10:5292-303.
  20. Takach M, Sarajlić M, Peters D, Kroener M, Schuldt F, von Maydell K. Review of Hydrogen Production Techniques from Water
    Using Renewable Energy Sources and Its Storage in Salt Caverns. Energies. 2022 Feb 15;15(4):1415.
  21. Lv Z, Li W, Wei J, Ho F, Cao J, Chen X. Autonomous Chemistry Enabling Environment-Adaptive Electrochemical Energy
    Storage Devices. CCS Chemistry. 2022 Jul 7:1-9.
  22. Dehghan Manshadi, Mahsa, Milad Mousavi, M. Soltani, Amir Mosavi, and Levente Kovacs. 2022. “Deep Learning for Modeling
    an Offshore Hybrid Wind–Wave Energy System” Energies 15, no. 24: 9484. https://doi.org/10.3390/en15249484
  23. Ishaq H, Dincer I, Crawford C. A review on hydrogen production and utilization: Challenges and opportunities. International
    Journal of Hydrogen Energy. 2022 Jul 22;47(62):26238-64.
  24. Maguire JF, Woodcock LV. On the Thermodynamics of Aluminum Cladding Oxidation: Water as the Catalyst for Spontaneous
    Combustion. Journal of Failure Analysis and Prevention. 2022 Sep 10:1-5.
  25. Mohammadi, M. R., Hadavimoghaddam, F., Pourmahdi, M., Atashrouz, S., Munir, M. T., Hemmati-Sarapardeh, A., … & Mohaddespour, A. (2021). Modeling hydrogen solubility in hydrocarbons using extreme gradient boosting and equations of state.
    Scientific reports, 11(1).
  26. Ma S, Qin J, Xiu X, Wang S. Design and performance evaluation of an underwater hybrid system of fuel cell and battery. Energy
    Conversion and Management. 2022 Jun 15;262:115672.
  27. Ahamed R, McKee K, Howard I. A Review of the Linear Generator Type of Wave Energy Converters’ Power Take-Off Systems.
    Sustainability. 2022 Jan;14(16):9936.
  28. Nejad, H.D., Nazari, M., Nazari, M., Mardan, M.M.S., 2022. Fuzzy State-Dependent Riccati Equation (FSDRE) Control of the
    Reverse Osmosis Desalination System With Photovoltaic Power Supply. IEEE Access, 10, pp.95585-95603.
  29. Zou S, Zhou X, Khan I, Weaver WW, Rahman S. Optimization of the electricity generation of a wave energy converter using
    deep reinforcement learning. Ocean Engineering. 2022 Jan 15;244:110363.
  30. Wu J, Qin L, Chen N, Qian C, Zheng S. Investigation on a spring-integrated mechanical power take-off system for wave energy
    conversion purpose. Energy. 2022 Apr 15;245:123318.
  31. Papini G, Dores Piuma FJ, Faedo N, Ringwood JV, Mattiazzo G. Nonlinear Model Reduction by Moment-Matching for a Point
    Absorber Wave Energy Conversion System. Journal of Marine Science and Engineering. 2022 May;10(5):656.
  32. Forbush DD, Bacelli G, Spencer SJ, Coe RG, Bosma B, Lomonaco P. Design and testing of a free floating dual flap wave energy
    converter. Energy. 2022 Feb 1;240:122485.
  33. Rezaei, M.A., 2022. A New Hybrid Cascaded Switched-Capacitor Reduced Switch Multilevel Inverter for Renewable Sources
    and Domestic Loads. IEEE Access, 10, pp.14157-14183.
  34. Lin Z, Cheng L, Huang G. Electricity consumption prediction based on LSTM with attention mechanism. IEEJ Transactions on
    Electrical and Electronic Engineering. 2020;15(4):556-562.
  35. Tavoosi, J., Mohammadzadeh, A., Pahlevanzadeh, B., Kasmani, M.B., 2022. A machine learning approach for active/reactive
    power control of grid-connected doubly-fed induction generators. Ain Shams Engineering Journal, 13(2), p.101564.
  36. Ghalandari, M., 2019. Flutter speed estimation using presented differential quadrature method formulation. Engineering Applications of Computational Fluid Mechanics, 13(1), pp.804-810.
  37. Li Z, Bouscasse B, Ducrozet G, Gentaz L, Le Touzé D, Ferrant P. Spectral wave explicit navier-stokes equations for wavestructure interactions using two-phase computational fluid dynamics solvers. Ocean Engineering. 2021 Feb 1;221:108513.
  38. Zhou Y. Ocean energy applications for coastal communities with artificial intelligencea state-of-the-art review. Energy and AI.
    2022 Jul 29:100189.
  39. Miskati S, Farin FM. Performance evaluation of wave-carpet in wave energy extraction at different coastal regions: an analytical
    approach (Doctoral dissertation, Department of Mechanical and Production Engineering).
  40. Gu C, Li H. Review on Deep Learning Research and Applications in Wind and Wave Energy. Energies. 2022 Feb 17;15(4):1510.
  41. Aazami, R., 2022. Optimal Control of an Energy-Storage System in a Microgrid for Reducing Wind-Power Fluctuations. Sustainability, 14(10), p.6183.
  42. Kabir M, Chowdhury MS, Sultana N, Jamal MS, Techato K. Ocean renewable energy and its prospect for developing economies.
    InRenewable Energy and Sustainability 2022 Jan 1 (pp. 263-298). Elsevier.
  43. Babajani A, Jafari M, Hafezisefat P, Mirhosseini M, Rezania A, Rosendahl L. Parametric study of a wave energy converter
    (Searaser) for Caspian Sea. Energy Procedia. 2018 Aug 1;147:334-42.
  44. He J. Coherence and cross-spectral density matrix analysis of random wind and wave in deep water. Ocean Engineering.
    2020;197:106930
  45. Ijadi Maghsoodi, A., 2018. Renewable energy technology selection problem using integrated h-swara-multimoora approach.
    Sustainability, 10(12), p.4481.
  46. Band, S.S., Ardabili, S., Sookhak, M., Theodore, A., Elnaffar, S., Moslehpour, M., Csaba, M., Torok, B., Pai, H.T., 2022. When
    Smart Cities Get Smarter via Machine Learning: An In-depth Literature Review. IEEE Access.
  47. Shamshirband, S., Rabczuk, T., Nabipour, N. and Chau, K.W., 2020. Prediction of significant wave height; comparison between
    nested grid numerical model, and machine learning models of artificial neural networks, extreme learning and support vector
    machines. Engineering Applications of Computational Fluid Mechanics, 14(1), pp.805-817.
  48. Liu, Z., Mohammadzadeh, A., Turabieh, H., Mafarja, M., 2021. A new online learned interval type-3 fuzzy control system for
    solar energy management systems. IEEE Access, 9, pp.10498-10508.
  49. Bavili, R.E., Mohammadzadeh, A., Tavoosi, J., Mobayen, S., Assawinchaichote, W., Asad, J.H. 2021. A New Active Fault Tolerant Control System: Predictive Online Fault Estimation. IEEE Access, 9, pp.118461-118471.
  50. Akbari, E., Teimouri, A.R., Saki, M., Rezaei, M.A., Hu, J., Band, S.S., Pai, H.T., 2022. A Fault-Tolerant Cascaded SwitchedCapacitor Multilevel Inverter for Domestic Applications in Smart Grids. IEEE Access.
  51. Band, S.S., Ardabili, S., 2022. Feasibility of soft computing techniques for estimating the long-term mean monthly wind speed.
    Energy Reports, 8, pp.638-648.
  52. Tavoosi, J., Mohammadzadeh, A., Pahlevanzadeh, B., Kasmani, M.B., 2022. A machine learning approach for active/reactive
    power control of grid-connected doubly-fed induction generators. Ain Shams Engineering Journal, 13(2), p.101564.
  53. Ponnusamy, V. K., Kasinathan, P., Madurai Elavarasan, R., Ramanathan, V., Anandan, R. K., Subramaniam, U., … & Hossain,
    E. A Comprehensive Review on Sustainable Aspects of Big Data Analytics for the Smart Grid. Sustainability, 2021; 13(23),
    13322.
  54. Ahmad, T., Zhang, D., Huang, C., Zhang, H., Dai, N., Song, Y., & Chen, H. Artificial intelligence in sustainable energy industry:
    Status Quo, challenges and opportunities. Journal of Cleaner Production, 2021; 289, 125834.
  55. Wang, G., Chao, Y., Cao, Y., Jiang, T., Han, W., & Chen, Z. A comprehensive review of research works based on evolutionary
    game theory for sustainable energy development. Energy Reports, 2022; 8, 114-136.
  56. Iranmehr H., Modeling the Price of Emergency Power Transmission Lines in the Reserve Market Due to the Influence of Renewable Energies, Frontiers in Energy Research, 9, 2022
  57. Farmanbar, M., Parham, K., Arild, Ø., & Rong, C. A widespread review of smart grids towards smart cities. Energies, 2019;
    12(23), 4484.
  58. Quartier, N., Crespo, A. J., Domínguez, J. M., Stratigaki, V., & Troch, P. Efficient response of an onshore Oscillating Water
    Column Wave Energy Converter using a one-phase SPH model coupled with a multiphysics library. Applied Ocean Research,
    2021; 115, 102856.
  59. Mahmoodi, K., Nepomuceno, E., & Razminia, A. Wave excitation force forecasting using neural networks. Energy, 2022; 247,
    123322.
  60. Wang, H., Alattas, K.A., 2022. Comprehensive review of load forecasting with emphasis on intelligent computing approaches.
    Energy Reports, 8, pp.13189-13198.
  61. Clemente, D., Rosa-Santos, P., & Taveira-Pinto, F. On the potential synergies and applications of wave energy converters: A
    review. Renewable and Sustainable Energy Reviews, 2021; 135, 110162.
  62. Felix, A., V. Hernández-Fontes, J., Lithgow, D., Mendoza, E., Posada, G., Ring, M., & Silva, R. Wave energy in tropical regions:
    deployment challenges, environmental and social perspectives. Journal of Marine Science and Engineering, 2019; 7(7), 219.
  63. Farrok, O., Ahmed, K., Tahlil, A. D., Farah, M. M., Kiran, M. R., & Islam, M. R. Electrical power generation from the oceanic
    wave for sustainable advancement in renewable energy technologies. Sustainability, 2020; 12(6), 2178.
  64. Guo, B., & Ringwood, J. V. A review of wave energy technology from a research and commercial perspective. IET Renewable
    Power Generation, 2021; 15(14), 3065-3090.
  65. López-Ruiz, A., Bergillos, R. J., Lira-Loarca, A., & Ortega-Sánchez, M. A methodology for the long-term simulation and uncertainty analysis of the operational lifetime performance of wave energy converter arrays. Energy, 2018; 153, 126-135.
  66. Safarian, S., Saryazdi, S. M. E., Unnthorsson, R., & Richter, C. Artificial neural network integrated with thermodynamic equilibrium modeling of downdraft biomass gasification-power production plant. Energy, 2020; 213, 118800.
  67. Kushwah, S. An oscillating water column (OWC): the wave energy converter. Journal of The Institution of Engineers (India):
    Series C, 2021; 102(5), 1311-1317.
  68. Pap, J., Mako, C., Illessy, M., Kis, N., 2022. Modeling Organizational Performance with Machine Learning. Journal of Open
    Innovation: Technology, Market, and Complexity, 8(4), p.177.
  69. Pap, J., Mako, C., Illessy, M., Dedaj, Z., Ardabili, S., Torok, B., 2022. Correlation Analysis of Factors Affecting Firm Performance
    and Employees Wellbeing: Application of Advanced Machine Learning Analysis. Algorithms, 15(9), p.300.
  70. Alanazi, A., 2022. Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method. Applied Sciences, 12(16), p.7959.
  71. Shakibjoo, A.D., Moradzadeh, M., Din, S.U., 2021. Optimized Type-2 Fuzzy Frequency Control for Multi-Area Power Systems.
    IEEE access, 10, pp.6989-7002.
  72. Zhang, G., 2021. Solar radiation estimation in different climates with meteorological variables using Bayesian model averaging
    and new soft computing models. Energy Reports, 7, pp.8973-8996.
  73. Cao, Y., Raise, A., Mohammadzadeh, A., Rathinasamy, S., 2021. Deep learned recurrent type-3 fuzzy system: Application for
    renewable energy modeling/prediction. Energy Reports, 7, pp.8115-8127.
  74. Tavoosi, J., Suratgar, A.A., Menhaj, M.B., 2021. Modeling renewable energy systems by a self-evolving nonlinear consequent
    part recurrent type-2 fuzzy system for power prediction. Sustainability, 13(6), p.3301.
  75. Bourouis, S., Band, S.S., 2022. Meta-Heuristic Algorithm-Tuned Neural Network for Breast Cancer Diagnosis Using Ultrasound
    Images. Frontiers in Oncology, 12, p.834028.
  76. Mosavi, A.H., Mohammadzadeh, A., Rathinasamy, S., Zhang, C., Reuter, U., Levente, K. and Adeli, H., 2022. Deep learning
    fuzzy immersion and invariance control for type-I diabetes. Computers in Biology and Medicine, 149, p.105975.
  77. Almutairi, K., Algarni, S., Alqahtani, T., Moayedi, H., 2022. A TLBO-Tuned Neural Processor for Predicting Heating Load in
    Residential Buildings. Sustainability, 14(10), p.5924.
  78. Ahmad, Z., Zhong, H., 2020. Machine learning modeling of aerobic biodegradation for azo dyes and hexavalent chromium.
    Mathematics, 8(6), p.913.
  79. Mosavi, A., Shokri, M., Mansor, Z., Qasem, S.N., Band, S.S. and Mohammadzadeh, A., 2020. Machine learning for modeling
    the singular multi-pantograph equations. Entropy, 22(9), p.1041.
  80. Ardabili, S., 2019, September. Deep learning and machine learning in hydrological processes climate change and earth systems
    a systematic review. In International conference on global research and education (pp. 52-62). Springer, Cham.
  81. Moayedi, H., (2021). Suggesting a stochastic fractal search paradigm in combination with artificial neural network for early
    prediction of cooling load in residential buildings. Energies, 14(6), 1649.
  82. Rezakazemi, M., et al., 2019. ANFIS pattern for molecular membranes separation optimization. Journal of Molecular Liquids,
    274, pp.470-476.
  83. Mosavi, A., Faghan, Y., Ghamisi, P., Duan, P., Ardabili, S.F., Salwana, E. and Band, S.S., 2020. Comprehensive review of deep
    reinforcement learning methods and applications in economics. Mathematics, 8(10), p.1640.
  84. Samadianfard, S., Jarhan, S., Salwana, E., 2019. Support vector regression integrated with fruit fly optimization algorithm for
    river flow forecasting in Lake Urmia Basin. Water, 11(9), p.1934.
  85. Moayedi, H., (2021). Double-target based neural networks in predicting energy consumption in residential buildings. Energies,
    14(5), 1331.
  86. Choubin, B., 2019. Earth fissure hazard prediction using machine learning models. Environmental research, 179, p.108770.
  87. Mohammadzadeh S, D., Kazemi, S.F., 2019. Prediction of compression index of fine-grained soils using a gene expression programming model. Infrastructures, 4(2), p.26.
  88. Karballaeezadeh, N., Mohammadzadeh S, D., Shamshirband, S., Hajikhodaverdikhan, P., 2019. Prediction of remaining service
    life of pavement using an optimized support vector machine (case study of Semnan–Firuzkuh road). Engineering Applications
    of Computational Fluid Mechanics, 13(1), pp.188-198.
  89. Rezaei, M. Et al., (2022). Adaptation of A Real-Time Deep Learning Approach with An Analog Fault Detection Technique for
    Reliability Forecasting of Capacitor Banks Used in Mobile Vehicles. IEEE Access v. 21 pp. 89-99.
  90. Khakian, R., et al., (2020). Modeling nearly zero energy buildings for sustainable development in rural areas. Energies, 13(10),
    2593.
Figure 5. Schematic view of flap and support structure [32]

Design Optimization of Ocean Renewable Energy Converter Using a Combined Bi-level Metaheuristic Approach

결합된 Bi-level 메타휴리스틱 접근법을 사용한 해양 재생 에너지 변환기의 설계 최적화

Erfan Amini a1, Mahdieh Nasiri b1, Navid Salami Pargoo a, Zahra Mozhgani c, Danial Golbaz d, Mehrdad Baniesmaeil e, Meysam Majidi Nezhad f, Mehdi Neshat gj, Davide Astiaso Garcia h, Georgios Sylaios i

Abstract

In recent years, there has been an increasing interest in renewable energies in view of the fact that fossil fuels are the leading cause of catastrophic environmental consequences. Ocean wave energy is a renewable energy source that is particularly prevalent in coastal areas. Since many countries have tremendous potential to extract this type of energy, a number of researchers have sought to determine certain effective factors on wave converters’ performance, with a primary emphasis on ambient factors. In this study, we used metaheuristic optimization methods to investigate the effects of geometric factors on the performance of an Oscillating Surge Wave Energy Converter (OSWEC), in addition to the effects of hydrodynamic parameters. To do so, we used CATIA software to model different geometries which were then inserted into a numerical model developed in Flow3D software. A Ribed-surface design of the converter’s flap is also introduced in this study to maximize wave-converter interaction. Besides, a Bi-level Hill Climbing Multi-Verse Optimization (HCMVO) method was also developed for this application. The results showed that the converter performs better with greater wave heights, flap freeboard heights, and shorter wave periods. Additionally, the added ribs led to more wave-converter interaction and better performance, while the distance between the flap and flume bed negatively impacted the performance. Finally, tracking the changes in the five-dimensional objective function revealed the optimum value for each parameter in all scenarios. This is achieved by the newly developed optimization algorithm, which is much faster than other existing cutting-edge metaheuristic approaches.

Keywords

Wave Energy Converter

OSWEC

Hydrodynamic Effects

Geometric Design

Metaheuristic Optimization

Multi-Verse Optimizer

1Introduction

The increase in energy demand, the limitations of fossil fuels, as well as environmental crises, such as air pollution and global warming, are the leading causes of calling more attention to harvesting renewable energy recently [1][2][3]. While still in its infancy, ocean wave energy has neither reached commercial maturity nor technological convergence. In recent decades, remarkable progress has been made in the marine energy domain, which is still in the early stage of development, to improve the technology performance level (TPL) [4][5]and technology readiness level (TRL) of wave energy converters (WECs). This has been achieved using novel modeling techniques [6][7][8][9][10][11][12][13][14] to gain the following advantages [15]: (i) As a source of sustainable energy, it contributes to the mix of energy resources that leads to greater diversity and attractiveness for coastal cities and suppliers. [16] (ii) Since wave energy can be exploited offshore and does not require any land, in-land site selection would be less expensive and undesirable visual effects would be reduced. [17] (iii) When the best layout and location of offshore site are taken into account, permanent generation of energy will be feasible (as opposed to using solar energy, for example, which is time-dependent) [18].

In general, the energy conversion process can be divided into three stages in a WEC device, including primary, secondary, and tertiary stages [19][20]. In the first stage of energy conversion, which is the subject of this study, the wave power is converted to mechanical power by wave-structure interaction (WSI) between ocean waves and structures. Moreover, the mechanical power is transferred into electricity in the second stage, in which mechanical structures are coupled with power take-off systems (PTO). At this stage, optimal control strategies are useful to tune the system dynamics to maximize power output [10][13][12]. Furthermore, the tertiary energy conversion stage revolves around transferring the non-standard AC power into direct current (DC) power for energy storage or standard AC power for grid integration [21][22]. We discuss only the first stage regardless of the secondary and tertiary stages. While Page 1 of 16 WECs include several categories and technologies such as terminators, point absorbers, and attenuators [15][23], we focus on oscillating surge wave energy converters (OSWECs) in this paper due to its high capacity for industrialization [24].

Over the past two decades, a number of studies have been conducted to understand how OSWECs’ structures and interactions between ocean waves and flaps affect converters performance. Henry et al.’s experiment on oscillating surge wave energy converters is considered as one of the most influential pieces of research [25], which demonstrated how the performance of oscillating surge wave energy converters (OSWECs) is affected by seven different factors, including wave period, wave power, flap’s relative density, water depth, free-board of the flap, the gap between the tubes, gap underneath the flap, and flap width. These parameters were assessed in their two models in order to estimate the absorbed energy from incoming waves [26][27]. In addition, Folly et al. investigated the impact of water depth on the OSWECs performance analytically, numerically, and experimentally. According to this and further similar studies, the average annual incident wave power is significantly reduced by water depth. Based on the experimental results, both the surge wave force and the power capture of OSWECs increase in shallow water [28][29]. Following this, Sarkar et al. found that under such circumstances, the device that is located near the coast performs much better than those in the open ocean [30]. On the other hand, other studies are showing that the size of the converter, including height and width, is relatively independent of the location (within similar depth) [31]. Subsequently, Schmitt et al. studied OSWECs numerically and experimentally. In fact, for the simulation of OSWEC, OpenFOAM was used to test the applicability of Reynolds-averaged Navier-Stokes (RANS) solvers. Then, the experimental model reproduced the numerical results with satisfying accuracy [32]. In another influential study, Wang et al. numerically assessed the effect of OSWEC’s width on their performance. According to their findings, as converter width increases, its efficiency decreases in short wave periods while increases in long wave periods [33]. One of the main challenges in the analysis of the OSWEC is the coupled effect of hydrodynamic and geometric variables. As a result, numerous cutting-edge geometry studies have been performed in recent years in order to find the optimal structure that maximizes power output and minimizes costs. Garcia et al. reviewed hull geometry optimization studies in the literature in [19]. In addition, Guo and Ringwood surveyed geometric optimization methods to improve the hydrodynamic performance of OSWECs at the primary stage [14]. Besides, they classified the hull geometry of OSWECs based on Figure 1. Subsequently, Whittaker et al. proposed a different design of OSWEC called Oyster2. There have been three examples of different geometries of oysters with different water depths. Based on its water depth, they determined the width and height of the converter. They also found that in the constant wave period the less the converter’s width, the less power captures the converter has [34]. Afterward, O’Boyle et al. investigated a type of OSWEC called Oyster 800. They compared the experimental and numerical models with the prototype model. In order to precisely reproduce the shape, mass distribution, and buoyancy properties of the prototype, a 40th-scale experimental model has been designed. Overall, all the models were fairly accurate according to the results [35].

Inclusive analysis of recent research avenues in the area of flap geometry has revealed that the interaction-based designs of such converters are emerging as a novel approach. An initiative workflow is designed in the current study to maximizing the wave energy extrication by such systems. To begin with, a sensitivity analysis plays its role of determining the best hydrodynamic values for installing the converter’s flap. Then, all flap dimensions and characteristics come into play to finalize the primary model. Following, interactive designs is proposed to increase the influence of incident waves on the body by adding ribs on both sides of the flap as a novel design. Finally, a new bi-level metaheuristic method is proposed to consider the effects of simultaneous changes in ribs properties and other design parameters. We hope this novel approach will be utilized to make big-scale projects less costly and justifiable. The efficiency of the method is also compared with four well known metaheuristic algorithms and out weight them for this application.

This paper is organized as follows. First, the research methodology is introduced by providing details about the numerical model implementation. To that end, we first introduced the primary model’s geometry and software details. That primary model is later verified with a benchmark study with regard to the flap angle of rotation and water surface elevation. Then, governing equations and performance criteria are presented. In the third part of the paper, we discuss the model’s sensitivity to lower and upper parts width (we proposed a two cross-sectional design for the flap), bottom elevation, and freeboard. Finally, the novel optimization approach is introduced in the final part and compared with four recent metaheuristic algorithms.

2. Numerical Methods

In this section, after a brief introduction of the numerical software, Flow3D, boundary conditions are defined. Afterwards, the numerical model implementation, along with primary model properties are described. Finally, governing equations, as part of numerical process, are discussed.

2.1Model Setup

FLOW-3D is a powerful and comprehensive CFD simulation platform for studying fluid dynamics. This software has several modules to solve many complex engineering problems. In addition, modeling complex flows is simple and effective using FLOW-3D’s robust meshing capabilities [36]. Interaction between fluid and moving objects might alter the computational range. Dynamic meshes are used in our modeling to take these changes into account. At each time step, the computational node positions change in order to adapt the meshing area to the moving object. In addition, to choose mesh dimensions, some factors are taken into account such as computational accuracy, computational time, and stability. The final grid size is selected based on the detailed procedure provided in [37]. To that end, we performed grid-independence testing on a CFD model using three different mesh grid sizes of 0.01, 0.015, and 0.02 meters. The problem geometry and boundary conditions were defined the same, and simulations were run on all three grids under the same conditions. The predicted values of the relevant variable, such as velocity, was compared between the grids. The convergence behavior of the numerical solution was analyzed by calculating the relative L2 norm error between two consecutive grids. Based on the results obtained, it was found that the grid size of 0.02 meters showed the least error, indicating that it provided the most accurate and reliable solution among the three grids. Therefore, the grid size of 0.02 meters was selected as the optimal spatial resolution for the mesh grid.

In this work, the flume dimensions are 10 meters long, 0.1 meters wide, and 2.2 meters high, which are shown in figure2. In addition, input waves with linear characteristics have a height of 0.1 meters and a period of 1.4 seconds. Among the linear wave methods included in this software, RNGk-ε and k- ε are appropriate for turbulence model. The research of Lopez et al. shows that RNGk- ε provides the most accurate simulation of turbulence in OSWECs [21]. We use CATIA software to create the flap primary model and other innovative designs for this project. The flap measures 0.1 m x 0.65 m x 0.360 m in x, y and z directions, respectively. In Figure 3, the primary model of flap and its dimensions are shown. In this simulation, five boundaries have been defined, including 1. Inlet, 2. Outlet, 3. Converter flap, 4. Bed flume, and 5. Water surface, which are shown in figure 2. Besides, to avoid wave reflection in inlet and outlet zones, Flow3D is capable of defining some areas as damping zones, the length of which has to be one to one and a half times the wavelength. Therefore, in the model, this length is considered equal to 2 meters. Furthermore, there is no slip in all the boundaries. In other words, at every single time step, the fluid velocity is zero on the bed flume, while it is equal to the flap velocity on the converter flap. According to the wave theory defined in the software, at the inlet boundary, the water velocity is called from the wave speed to be fed into the model.

2.2Verification

In the current study, we utilize the Schmitt experimental model as a benchmark for verification, which was developed at the Queen’s University of Belfast. The experiments were conducted on the flap of the converter, its rotation, and its interaction with the water surface. Thus, the details of the experiments are presented below based up on the experimental setup’s description [38]. In the experiment, the laboratory flume has a length of 20m and a width of 4.58m. Besides, in order to avoid incident wave reflection, a wave absorption source is devised at the end of the left flume. The flume bed, also, includes two parts with different slops. The flap position and dimensions of the flume can be seen in Figure4. In addition, a wave-maker with 6 paddles is installed at one end. At the opposite end, there is a beach with wire meshes. Additionally, there are 6 indicators to extract the water level elevation. In the flap model, there are three components: the fixed support structure, the hinge, and the flap. The flap measures 0.1m x 0.65m x 0.341m in x, y and z directions, respectively. In Figure5, the details are given [32]. The support structure consists of a 15 mm thick stainless steel base plate measuring 1m by 1.4m, which is screwed onto the bottom of the tank. The hinge is supported by three bearing blocks. There is a foam centerpiece on the front and back of the flap which is sandwiched between two PVC plates. Enabling changes of the flap, three metal fittings link the flap to the hinge. Moreover, in this experiment, the selected wave is generated based on sea wave data at scale 1:40. The wave height and the wave period are equal to 0.038 (m) and 2.0625 (s), respectively, which are tantamount to a wave with a period of 13 (s) and a height of 1.5 (m).

Two distinct graphs illustrate the numerical and experi-mental study results. Figure6 and Figure7 are denoting the angle of rotation of flap and surface elevation in computational and experimental models, respectively. The two figures roughly represent that the numerical and experimental models are a good match. However, for the purpose of verifying the match, we calculated the correlation coefficient (C) and root mean square error (RMSE). According to Figure6, correlation coefficient and RMSE are 0.998 and 0.003, respectively, and in Figure7 correlation coefficient and RMSE are respectively 0.999 and 0.001. Accordingly, there is a good match between the numerical and empirical models. It is worth mentioning that the small differences between the numerical and experimental outputs may be due to the error of the measuring devices and the calibration of the data collection devices.

Including continuity equation and momentum conserva- tion for incompressible fluid are given as [32][39]:(1)

where P represents the pressure, g denotes gravitational acceleration, u represents fluid velocity, and Di is damping coefficient. Likewise, the model uses the same equation. to calculate the fluid velocity in other directions as well. Considering the turbulence, we use the two-equation model of RNGK- ε. These equations are:

(3)��t(��)+����(����)=����[�eff�������]+��-��and(4)���(��)+����(����)=����[�eff�������]+�1�∗����-��2��2�Where �2� and �1� are constants. In addition, �� and �� represent the turbulent Prandtl number of � and k, respectively.

�� also denote the production of turbulent kinetic energy of k under the effect of velocity gradient, which is calculated as follows:(5)��=�eff[�����+�����]�����(6)�eff=�+��(7)�eff=�+��where � is molecular viscosity,�� represents turbulence viscosity, k denotes kinetic energy, and ∊∊ is energy dissipation rate. The values of constant coefficients in the two-equation RNGK ∊-∊ model is as shown in the Table 1 [40].Table 2.

Table 1. Constant coefficients in RNGK- model

Factors�0�1�2������
Quantity0.0124.381.421.681.391.390.084

Table 2. Flap properties

Joint height (m)0.476
Height of the center of mass (m)0.53
Weight (Kg)10.77

It is worth mentioning that the volume of fluid method is used to separate water and air phases in this software [41]. Below is the equation of this method [40].(8)����+����(���)=0where α and 1 − α are portion of water phase and air phase, respectively. As a weighting factor, each fluid phase portion is used to determine the mixture properties. Finally, using the following equations, we calculate the efficiency of converters [42][34][43]:(9)�=14|�|2�+�2+(�+�a)2(�n2-�2)2where �� represents natural frequency, I denotes the inertia of OSWEC, Ia is the added inertia, F is the complex wave force, and B denotes the hydrodynamic damping coefficient. Afterward, the capture factor of the converter is calculated by [44]:(10)��=�1/2��2����gw where �� represents the capture factor, which is the total efficiency of device per unit length of the wave crest at each time step [15], �� represent the dimensional amplitude of the incident wave, w is the flap’s width, and Cg is the group velocity of the incident wave, as below:(11)��=��0·121+2�0ℎsinh2�0ℎwhere �0 denotes the wave number, h is water depth, and H is the height of incident waves.

According to previous sections ∊,����-∊ modeling is used for all models simulated in this section. For this purpose, the empty boundary condition is used for flume walls. In order to preventing wave reflection at the inlet and outlet of the flume, the length of wave absorption is set to be at least one incident wavelength. In addition, the structured mesh is chosen, and the mesh dimensions are selected in two distinct directions. In each model, all grids have a length of 2 (cm) and a height of 1 (cm). Afterwards, as an input of the software for all of the models, we define the time step as 0.001 (s). Moreover, the run time of every simulation is 30 (s). As mentioned before, our primary model is Schmitt model, and the flap properties is given in table2. For all simulations, the flume measures 15 meters in length and 0.65 meters in width, and water depth is equal to 0.335 (m). The flap is also located 7 meters from the flume’s inlet.

Finally, in order to compare the results, the capture factor is calculated for each simulation and compared to the primary model. It is worth mentioning that capture factor refers to the ratio of absorbed wave energy to the input wave energy.

According to primary model simulation and due to the decreasing horizontal velocity with depth, the wave crest has the highest velocity. Considering the fact that the wave’s orbital velocity causes the flap to move, the contact between the upper edge of the flap and the incident wave can enhance its performance. Additionally, the numerical model shows that the dynamic pressure decreases as depth increases, and the hydrostatic pressure increases as depth increases.

To determine the OSWEC design, it is imperative to understand the correlation between the capture factor, wave period, and wave height. Therefore, as it is shown in Figure8, we plot the change in capture factor over the variations in wave period and wave height in 3D and 2D. In this diagram, the first axis features changes in wave period, the second axis displays changes in wave height, and the third axis depicts changes in capture factor. According to our wave properties in the numerical model, the wave period and wave height range from 2 to 14 seconds and 2 to 8 meters, respectively. This is due to the fact that the flap does not oscillate if the wave height is less than 2 (m), and it does not reverse if the wave height is more than 8 (m). In addition, with wave periods more than 14 (s), the wavelength would be so long that it would violate the deep-water conditions, and with wave periods less than 2 (s), the flap would not oscillate properly due to the shortness of wavelength. The results of simulation are shown in Figure 8. As it can be perceived from Figure 8, in a constant wave period, the capture factor is in direct proportion to the wave height. It is because of the fact that waves with more height have more energy to rotate the flap. Besides, in a constant wave height, the capture factor increases when the wave period increases, until a given wave period value. However, the capture factor falls after this point. These results are expected since the flap’s angular displacement is not high in lower wave periods, while the oscillating motion of that is not fast enough to activate the power take-off system in very high wave periods.

As is shown in Figure 9, we plot the change in capture factor over the variations in wave period (s) and water depth (m) in 3D. As it can be seen in this diagram, the first axis features changes in water depth (m), the second axis depicts the wave period (s), and the third axis displays OSWEC’s capture factor. The wave period ranges from 0 to 10 seconds based on our wave properties, which have been adopted from Schmitt’s model, while water depth ranges from 0 to 0.5 meters according to the flume and flap dimensions and laboratory limitations. According to Figure9, for any specific water depth, the capture factor increases in a varying rate when the wave period increases, until a given wave period value. However, the capture factor falls steadily after this point. In fact, the maximum capture factor occurs when the wave period is around 6 seconds. This trend is expected since, in a specific water depth, the flap cannot oscillate properly when the wavelength is too short. As the wave period increases, the flap can oscillate more easily, and consequently its capture factor increases. However, the capture factor drops in higher wave periods because the wavelength is too large to move the flap. Furthermore, in a constant wave period, by changing the water depth, the capture factor does not alter. In other words, the capture factor does not depend on the water depth when it is around its maximum value.

3Sensitivity Analysis

Based on previous studies, in addition to the flap design, the location of the flap relative to the water surface (freeboard) and its elevation relative to the flume bed (flap bottom elevation) play a significant role in extracting energy from the wave energy converter. This study measures the sensitivity of the model to various parameters related to the flap design including upper part width of the flap, lower part width of the flap, the freeboard, and the flap bottom elevation. Moreover, as a novel idea, we propose that the flap widths differ in the lower and upper parts. In Figure10, as an example, a flap with an upper thickness of 100 (mm) and a lower thickness of 50 (mm) and a flap with an upper thickness of 50 (mm) and a lower thickness of 100 (mm) are shown. The influence of such discrepancy between the widths of the upper and lower parts on the interaction between the wave and the flap, or in other words on the capture factor, is evaluated. To do so, other parameters are remained constant, such as the freeboard, the distance between the flap and the flume bed, and the wave properties.

In Figure11, models are simulated with distinct upper and lower widths. As it is clear in this figure, the first axis depicts the lower part width of the flap, the second axis indicates the upper part width of the flap, and the colors represent the capture factor values. Additionally, in order to consider a sufficient range of change, the flap thickness varies from half to double the value of the primary model for each part.

According to this study, the greater the discrepancy in these two parts, the lower the capture factor. It is on account of the fact that when the lower part of the flap is thicker than the upper part, and this thickness difference in these two parts is extremely conspicuous, the inertia against the motion is significant at zero degrees of rotation. Consequently, it is difficult to move the flap, which results in a low capture factor. Similarly, when the upper part of the flap is thicker than the lower part, and this thickness difference in these two parts is exceedingly noticeable, the inertia is so great that the flap can not reverse at the maximum degree of rotation. As the results indicate, the discrepancy can enhance the performance of the converter if the difference between these two parts is around 20%. As it is depicted in the Figure11, the capture factor reaches its own maximum amount, when the lower part thickness is from 5 to 6 (cm), and the upper part thickness is between 6 and 7 (cm). Consequently, as a result of this discrepancy, less material will be used, and therefore there will be less cost.

As illustrated in Figure12, this study examines the effects of freeboard (level difference between the flap top and water surface) and the flap bottom elevation (the distance between the flume bed and flap bottom) on the converter performance. In this diagram, the first axis demonstrates the freeboard and the second axis on the left side displays the flap bottom elevation, while the colors indicate the capture factor. In addition, the feasible range of freeboard is between -15 to 15 (cm) due to the limitation of the numerical model, so that we can take the wave slamming and the overtopping into consideration. Additionally, based on the Schmitt model and its scaled model of 1:40 of the base height, the flap bottom should be at least 9 (cm) high. Since the effect of surface waves is distributed over the depth of the flume, it is imperative to maintain a reasonable flap height exposed to incoming waves. Thus, the maximum flap bottom elevation is limited to 19 (cm). As the Figure12 pictures, at constant negative values of the freeboard, the capture factor is in inverse proportion with the flap bottom elevation, although slightly.

Furthermore, at constant positive values of the freeboard, the capture factor fluctuates as the flap bottom elevation decreases while it maintains an overall increasing trend. This is on account of the fact that increasing the flap bottom elevation creates turbulence flow behind the flap, which encumbers its rotation, as well as the fact that the flap surface has less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, the capture factor increases by raising the freeboard. This is due to the fact that there is overtopping with adverse impacts on the converter performance when the freeboard is negative and the flap is under the water surface. Besides, increasing the freeboard makes the wave slam more vigorously, which improves the converter performance.

Adding ribs to the flap surface, as shown in Figure13, is a novel idea that is investigated in the next section. To achieve an optimized design for the proposed geometry of the flap, we determine the optimal number and dimensions of ribs based on the flap properties as our decision variables in the optimization process. As an example, Figure13 illustrates a flap with 3 ribs on each side with specific dimensions.

Figure14 shows the flow velocity field around the flap jointed to the flume bed. During the oscillation of the flap, the pressure on the upper and lower surfaces of the flap changes dynamically due to the changing angle of attack and the resulting change in the direction of fluid flow. As the flap moves upwards, the pressure on the upper surface decreases, and the pressure on the lower surface increases. Conversely, as the flap moves downwards, the pressure on the upper surface increases, and the pressure on the lower surface decreases. This results in a cyclic pressure variation around the flap. Under certain conditions, the pressure field around the flap can exhibit significant variations in magnitude and direction, forming vortices and other flow structures. These flow structures can affect the performance of the OSWEC by altering the lift and drag forces acting on the flap.

4Design Optimization

We consider optimizing the design parameters of the flap of converter using a nature-based swarm optimization method, that fall in the category of metaheuristic algorithms [45]. Accordingly, we choose four state-of-the-art algorithms to perform an optimization study. Then, based on their performances to achieve the highest capture factor, one of them will be chosen to be combined with the Hill Climb algorithm to carry out a local search. Therefore, in the remainder of this section, we discuss the search process of each algorithm and visualize their performance and convergence curve as they try to find the best values for decision variables.

4.1. Metaheuristic Approaches

As the first considered algorithm, the Gray Wolf Optimizer (GWO) algorithm simulates the natural leadership and hunting performance of gray wolves which tend to live in colonies. Hunters must obey the alpha wolf, the leader, who is responsible for hunting. Then, the beta wolf is at the second level of the gray wolf hierarchy. A subordinate of alpha wolf, beta stands under the command of the alpha. At the next level in this hierarchy, there are the delta wolves. They are subordinate to the alpha and beta wolves. This category of wolves includes scouts, sentinels, elders, hunters, and caretakers. In this ranking, omega wolves are at the bottom, having the lowest level and obeying all other wolves. They are also allowed to eat the prey just after others have eaten. Despite the fact that they seem less important than others, they are really central to the pack survival. Since, it has been shown that without omega wolves, the entire pack would experience some problems like fighting, violence, and frustration. In this simulation, there are three primary steps of hunting including searching, surrounding, and finally attacking the prey. Mathematically model of gray wolves’ hunting technique and their social hierarchy are applied in determined by optimization. this study. As mentioned before, gray wolves can locate their prey and surround them. The alpha wolf also leads the hunt. Assuming that the alpha, beta, and delta have more knowledge about prey locations, we can mathematically simulate gray wolf hunting behavior. Hence, in addition to saving the top three best solutions obtained so far, we compel the rest of the search agents (also the omegas) to adjust their positions based on the best search agent. Encircling behavior can be mathematically modeled by the following equations: [46].(12)�→=|�→·��→(�)-�→(�)|(13)�→(�+1)=��→(�)-�→·�→(14)�→=2.�2→(15)�→=2�→·�1→-�→Where �→indicates the position vector of gray wolf, ��→ defines the vector of prey, t indicates the current iteration, and �→and �→are coefficient vectors. To force the search agent to diverge from the prey, we use �→ with random values greater than 1 or less than -1. In addition, C→ contains random values in the range [0,2], and �→ 1 and �2→ are random vectors in [0,1]. The second considered technique is the Moth Flame Optimizer (MFO) algorithm. This method revolves around the moths’ navigation mechanism, which is realized by positioning themselves and maintaining a fixed angle relative to the moon while flying. This effective mechanism helps moths to fly in a straight path. However, when the source of light is artificial, maintaining an angle with the light leads to a spiral flying path towards the source that causes the moth’s death [47]. In MFO algorithm, moths and flames are both solutions. The moths are actual search agents that fly in hyper-dimensional space by changing their position vectors, and the flames are considered pins that moths drop when searching the search space [48]. The problem’s variables are the position of moths in the space. Each moth searches around a flame and updates it in case of finding a better solution. The fitness value is the return value of each moth’s fitness (objective) function. The position vector of each moth is passed to the fitness function, and the output of the fitness function is assigned to the corresponding moth. With this mechanism, a moth never loses its best solution [49]. Some attributes of this algorithm are as follows:

  • •It takes different values to converge moth in any point around the flame.
  • •Distance to the flame is lowered to be eventually minimized.
  • •When the position gets closer to the flame, the updated positions around the flame become more frequent.

As another method, the Multi-Verse Optimizer is based on a multiverse theory which proposes there are other universes besides the one in which we all live. According to this theory, there are more than one big bang in the universe, and each big bang leads to the birth of a new universe [50]. Multi-Verse Optimizer (MVO) is mainly inspired by three phenomena in cosmology: white holes, black holes, and wormholes. A white hole has never been observed in our universe, but physicists believe the big bang could be considered a white hole [51]. Black holes, which behave completely in contrast to white holes, attract everything including light beams with their extremely high gravitational force [52]. In the multiverse theory, wormholes are time and space tunnels that allow objects to move instantly between any two corners of a universe (or even simultaneously from one universe to another) [53]. Based on these three concepts, mathematical models are designed to perform exploration, exploitation, and local search, respectively. The concept of white and black holes is implied as an exploration phase, while the concept of wormholes is considered as an exploitation phase by MVO. Additionally, each solution is analogous to a universe, and each variable in the solution represents an object in that universe. Furthermore, each solution is assigned an inflation rate, and the time is used instead of iterations. Following are the universe rules in MVO:

  • •The possibility of having white hole increases with the inflation rate.
  • •The possibility of having black hole decreases with the inflation rate.
  • •Objects tend to pass through black holes more frequently in universes with lower inflation rates.
  • •Regardless of inflation rate, wormholes may cause objects in universes to move randomly towards the best universe. [54]

Modeling the white/black hole tunnels and exchanging objects of universes mathematically was accomplished by using the roulette wheel mechanism. With every iteration, the universes are sorted according to their inflation rates, then, based on the roulette wheel, the one with the white hole is selected as the local extremum solution. This is accomplished through the following steps:

Assume that

(16)���=����1<��(��)����1≥��(��)

Where ��� represents the jth parameter of the ith universe, Ui indicates the ith universe, NI(Ui) is normalized inflation rate of the ith universe, r1 is a random number in [0,1], and j xk shows the jth parameter of the kth universe selected by a roulette wheel selection mechanism [54]. It is assumed that wormhole tunnels always exist between a universe and the best universe formed so far. This mechanism is as follows:(17)���=if�2<���:��+���×((���-���)×�4+���)�3<0.5��-���×((���-���)×�4+���)�3≥0.5����:���where Xj indicates the jth parameter of the best universe formed so far, TDR and WEP are coefficients, where Xj indicates the jth parameter of the best universelbjshows the lower bound of the jth variable, ubj is the upper bound of the jth variable, and r2, r3, and r4 are random numbers in [1][54].

Finally, one of the newest optimization algorithms is WOA. The WOA algorithm simulates the movement of prey and the whale’s discipline when looking for their prey. Among several species, Humpback whales have a specific method of hunting [55]. Humpback whales can recognize the location of prey and encircle it before hunting. The optimal design position in the search space is not known a priori, and the WOA algorithm assumes that the best candidate solution is either the target prey or close to the optimum. This foraging behavior is called the bubble-net feeding method. Two maneuvers are associated with bubbles: upward spirals and double loops. A unique behavior exhibited only by humpback whales is bubble-net feeding. In fact, The WOA algorithm starts with a set of random solutions. At each iteration, search agents update their positions for either a randomly chosen search agent or the best solution obtained so far [56][55]. When the best search agent is determined, the other search agents will attempt to update their positions toward that agent. It is important to note that humpback whales swim around their prey simultaneously in a circular, shrinking circle and along a spiral-shaped path. By using a mathematical model, the spiral bubble-net feeding maneuver is optimized. The following equation represents this behavior:(18)�→(�+1)=�′→·�bl·cos(2��)+�∗→(�)

Where:(19)�′→=|�∗→(�)-�→(�)|

X→(t+ 1) indicates the distance of the it h whale to the prey (best solution obtained so far),� is a constant for defining the shape of the logarithmic spiral, l is a random number in [−1, 1], and dot (.) is an element-by-element multiplication [55].

Comparing the four above-mentioned methods, simulations are run with 10 search agents for 400 iterations. In Figure 15, there are 20 plots the optimal values of different parameters in optimization algorithms. The five parameters of this study are freeboard, bottom elevations, number of ribs on the converter, rib thickness, and rib Height. The optimal value for each was found by optimization algorithms, naming WOA, MVO, MFO, and GWO. By looking through the first row, the freeboard parameter converges to its maximum possible value in the optimization process of GWO after 300 iterations. Similarly, MFO finds the same result as GWO. In contrast, the freeboard converges to its minimum possible value in MVO optimizing process, which indicates positioning the converter under the water. Furthermore, WOA found the optimal value of freeboard as around 0.02 after almost 200 iterations. In the second row, the bottom elevation is found at almost 0.11 (m) in all algorithms; however, the curves follow different trends in each algorithm. The third row shows the number of ribs, where results immediately reveal that it should be over 4. All algorithms coincide at 5 ribs as the optimal number in this process. The fourth row displays the trends of algorithms to find optimal rib thickness. MFO finds the optimal value early and sets it to around 0.022, while others find the same value in higher iterations. Finally, regarding the rib height, MVO, MFO, and GWO state that the optimal value is 0.06 meters, but WOA did not find a higher value than 0.039.

4.2. HCMVO Bi-level Approach

Despite several strong search characteristics of MVO and its high performance in various optimization problems, it suffers from a few deficiencies in local and global search mechanisms. For instance, it is trapped in the local optimum when wormholes stochastically generate many solutions near the best universe achieved throughout iterations, especially in solving complex multimodal problems with high dimensions [57]. Furthermore, MVO needs to be modified by an escaping strategy from the local optima to enhance the global search abilities. To address these shortages, we propose a fast and effective meta-algorithm (HCMVO) to combine MVO with a Random-restart hill-climbing local search. This meta-algorithm uses MVO on the upper level to develop global tracking and provide a range of feasible and proper solutions. The hill-climbing algorithm is designed to develop a comprehensive neighborhood search around the best-found solution proposed by the upper-level (MVO) when MVO is faced with a stagnation issue or falling into a local optimum. The performance threshold is formulated as follows.(20)Δ����THD=∑�=1�����TH��-����TH��-1�where BestTHDis the best-found solution per generation, andM is related to the domain of iterations to compute the average performance of MVO. If the proposed best solution by the local search is better than the initial one, the global best of MVO will be updated. HCMVO iteratively runs hill climbing when the performance of MVO goes down, each time with an initial condition to prepare for escaping such undesirable situations. In order to get a better balance between exploration and exploitation, the search step size linearly decreases as follows:(21)��=��-����Ma�iter��+1where iter and Maxiter are the current iteration and maximum number of evaluation, respectively. �� stands for the step size of the neighborhood search. Meanwhile, this strategy can improve the convergence rate of MVO compared with other algorithms.

Algorithm 1 shows the technical details of the proposed optimization method (HCMVO). The initial solution includes freeboard (�), bottom elevation (�), number of ribs (Nr), rib thickness (�), and rib height(�).

5. Conclusion

The high trend of diminishing worldwide energy resources has entailed a great crisis upon vulnerable societies. To withstand this effect, developing renewable energy technologies can open doors to a more reliable means, among which the wave energy converters will help the coastal residents and infrastructure. This paper set out to determine the optimized design for such devices that leads to the highest possible power output. The main goal of this research was to demonstrate the best design for an oscillating surge wave energy converter using a novel metaheuristic optimization algorithm. In this regard, the methodology was devised such that it argued the effects of influential parameters, including wave characteristics, WEC design, and interaction criteria.

To begin with, a numerical model was developed in Flow 3D software to simulate the response of the flap of a wave energy converter to incoming waves, followed by a validation study based upon a well-reputed experimental study to verify the accuracy of the model. Secondly, the hydrodynamics of the flap was investigated by incorporating the turbulence. The effect of depth, wave height, and wave period are also investigated in this part. The influence of two novel ideas on increasing the wave-converter interaction was then assessed: i) designing a flap with different widths in the upper and lower part, and ii) adding ribs on the surface of the flap. Finally, four trending single-objective metaheuristic optimization methods

Empty CellAlgorithm 1: Hill Climb Multiverse Optimization
01:procedure HCMVO
02:�=30,�=5▹���������������������������������
03:�=〈F1,B1,N,R,H1〉,…〈FN,B2,N,R,HN〉⇒lb1N⩽�⩽ubN
04:Initialize parameters�ER,�DR,�EP,Best�,���ite��▹Wormhole existence probability (WEP)
05:��=����(��)
06:��=Normalize the inflation rate��
07:for iter in[1,⋯,���iter]do
08:for�in[1,⋯,�]do
09:Update�EP,�DR,Black����Index=�
10:for���[1,⋯,�]��
11:�1=����()
12:if�1≤��(��)then
13:White HoleIndex=Roulette�heelSelection(-��)
14:�(Black HoleIndex,�)=��(White HoleIndex,�)
15:end if
16:�2=����([0,�])
17:if�2≤�EPthen
18:�3=����(),�4=����()
19:if�3<0.5then
20:�1=((��(�)-��(�))�4+��(�))
21:�(�,�)=Best�(�)+�DR�
22:else
23:�(�,�)=Best�(�)-�DR�
24:end if
25:end if
26:end for
27:end for
28:�HD=����([�1,�2,⋯,�Np])
29:Bes�TH�itr=����HD
30:ΔBestTHD=∑�=1�BestTII��-BestTII��-1�
31:ifΔBestTHD<��then▹Perform hill climbing local search
32:BestTHD=����-�lim��������THD
33:end if
34:end for
35:return�,BestTHD▹Final configuration
36:end procedure

The implementation details of the hill-climbing algorithm applied in HCMPA can be seen in Algorithm 2. One of the critical parameters isg, which denotes the resolution of the neighborhood search around the proposed global best by MVO. If we set a small step size for hill-climbing, the convergence speed will be decreased. On the other hand, a large step size reinforces the exploration ability. Still, it may reduce the exploitation ability and in return increase the act of jumping from a global optimum or surfaces with high-potential solutions. Per each decision variable, the neighborhood search evaluates two different direct searches, incremental or decremental. After assessing the generated solutions, the best candidate will be selected to iterate the search algorithm. It is noted that the hill-climbing algorithm should not be applied in the initial iteration of the optimization process due to the immense tendency for converging to local optima. Meanwhile, for optimizing largescale problems, hill-climbing is not an appropriate selection. In order to improve understanding of the proposed hybrid optimization algorithm’s steps, the flowchart of HCMVO is designed and can be seen in Figure 16.

Figure 17 shows the observed capture factor (which is the absorbed energy with respect to the available energy) by each optimization algorithm from iterations 1 to 400. The algorithms use ten search agents in their modified codes to find the optimal solutions. While GWO and MFO remain roughly constant after iterations 54 and 40, the other three algorithms keep improving the capture factor. In this case, HCMVO and MVO worked very well in the optimizing process with a capture factor obtained by the former as 0.594 and by the latter as 0.593. MFO almost found its highest value before the iteration 50, which means the exploration part of the algorithm works out well. Similarly, HCMVO does the same. However, it keeps finding the better solution during the optimization process until the last iteration, indicating the strong exploitation part of the algorithm. GWO reveals a weakness in exploration and exploitation because not only does it evoke the least capture factor value, but also the curve remains almost unchanged throughout 350 iterations.

Figure 18 illustrates complex interactions between the five optimization parameters and the capture factor for HCMVO (a), MPA (b), and MFO (c) algorithms. The first interesting observation is that there is a high level of nonlinear relationships among the setting parameters that can make a multi-modal search space. The dark blue lines represent the best-found configuration throughout the optimisation process. Based on both HCMVO (a) and MVO (b), we can infer that the dark blue lines concentrate in a specific range, showing the high convergence ability of both HCMVO and MVO. However, MFO (c) could not find the exact optimal range of the decision variables, and the best-found solutions per generation distribute mostly all around the search space.

Empty CellAlgorithm 1: Hill Climb Multiverse Optimization
01:procedure HCMVO
02:Initialization
03:Initialize the constraints��1�,��1�
04:�1�=Mi�1�+���1�/�▹Compute the step size,�is search resolution
05:So�1=〈�,�,�,�,�〉▹���������������
06:�������1=����So�1▹���������ℎ���������
07:Main loop
08:for iter≤���ita=do
09:���=���±��
10:while�≤���(Sol1)do
11:���=���+�,▹����ℎ���ℎ��������ℎ
12:fitness��iter=�������
13:t = t+1
14:end while
15:〈�����,������max〉=����������
16:���itev=���Inde�max▹�������ℎ�������������������������������ℎ�������
17:��=��-����Max��+1▹�����������������
18:end for
19:return���iter,����
20:end procedure

were utilized to illuminate the optimum values of the design parameters, and the best method was chosen to develop a new algorithm that performs both local and global search methods.

The correlation between hydrodynamic parameters and the capture factor of the converter was supported by the results. For any given water depth, the capture factor increases as the wave period increases, until a certain wave period value (6 seconds) is reached, after which the capture factor gradually decreases. It is expected since the flap cannot oscillate effectively when the wavelength is too short for a certain water depth. Conversely, when the wavelength is too long, the capture factor decreases. Furthermore, under a constant wave period, increasing the water depth does not affect the capture factor. Regarding the sensitivity analysis, the study found that increasing the flap bottom elevation causes turbulence flow behind the flap and limitation of rotation, which leads to less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, increasing the freeboard improves the capture factor. Overtopping happens when the freeboard is negative and the flap is below the water surface, which has a detrimental influence on converter performance. Furthermore, raising the freeboard causes the wave impact to become more violent, which increases converter performance.

In the last part, we discussed the search process of each algorithm and visualized their performance and convergence curves as they try to find the best values for decision variables. Among the four selected metaheuristic algorithms, the Multi-verse Optimizer proved to be the most effective in achieving the best answer in terms of the WEC capture factor. However, the MVO needed modifications regarding its escape approach from the local optima in order to improve its global search capabilities. To overcome these constraints, we presented a fast and efficient meta-algorithm (HCMVO) that combines MVO with a Random-restart hill-climbing local search. On a higher level, this meta-algorithm employed MVO to generate global tracking and present a range of possible and appropriate solutions. Taken together, the results demonstrated that there is a significant degree of nonlinearity among the setup parameters that might result in a multimodal search space. Since MVO was faced with a stagnation issue or fell into a local optimum, we constructed a complete neighborhood search around the best-found solution offered by the upper level. In sum, the newly-developed algorithm proved to be highly effective for the problem compared to other similar optimization methods. The strength of the current findings may encourage future investigation on design optimization of wave energy converters using developed geometry as well as the novel approach.

CRediT authorship contribution statement

Erfan Amini: Conceptualization, Methodology, Validation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Mahdieh Nasiri: Conceptualization, Methodology, Validation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Navid Salami Pargoo: Writing – original draft, Writing – review & editing. Zahra Mozhgani: Conceptualization, Methodology. Danial Golbaz: Writing – original draft. Mehrdad Baniesmaeil: Writing – original draft. Meysam Majidi Nezhad: . Mehdi Neshat: Supervision, Conceptualization, Writing – original draft, Writing – review & editing, Visualization. Davide Astiaso Garcia: Supervision. Georgios Sylaios: Supervision.

Declaration of Competing Interest

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

Acknowledgement

This research has been carried out within ILIAD (Inte-grated Digital Framework for Comprehensive Maritime Data and Information Services) project that received funding from the European Union’s H2020 programme.

Data availability

Data will be made available on request.

References

Figure 14. Defects: (a) Unmelt defects(Scheme NO.4);(b) Pores defects(Scheme NO.1); (c); Spattering defect (Scheme NO.3); (d) Low overlapping rate defects(Scheme NO.5).

Molten pool structure, temperature and velocity
flow in selective laser melting AlCu5MnCdVA alloy

용융 풀 구조, 선택적 온도 및 속도 흐름 레이저 용융 AlCu5MnCdVA 합금

Pan Lu1 , Zhang Cheng-Lin2,6,Wang Liang3, Liu Tong4 and Liu Jiang-lin5
1 Aviation and Materials College, Anhui Technical College of Mechanical and Electrical Engineering, Wuhu Anhui 241000, People’s
Republic of China 2 School of Engineering Science, University of Science and Technology of China, Hefei Anhui 230026, People’s Republic of China 3 Anhui Top Additive Manufacturing Technology Co., Ltd., Wuhu Anhui 241300, People’s Republic of China 4 Anhui Chungu 3D Printing Institute of Intelligent Equipment and Industrial Technology, Anhui 241300, People’s Republic of China 5 School of Mechanical and Transportation Engineering, Taiyuan University of Technology, Taiyuan Shanxi 030024, People’s Republic of
China 6 Author to whom any correspondence should be addressed.
E-mail: ahjdpanlu@126.com, jiao__zg@126.com, ahjdjxx001@126.com,tongliu1988@126.com and liujianglin@tyut.edu.cn

Keywords

SLM, molten pool, AlCu5MnCdVA alloy, heat flow, velocity flow, numerical simulation

Abstract

선택적 레이저 용융(SLM)은 열 전달, 용융, 상전이, 기화 및 물질 전달을 포함하는 복잡한 동적 비평형 프로세스인 금속 적층 제조(MAM)에서 가장 유망한 기술 중 하나가 되었습니다. 용융 풀의 특성(구조, 온도 흐름 및 속도 흐름)은 SLM의 최종 성형 품질에 결정적인 영향을 미칩니다. 이 연구에서는 선택적 레이저 용융 AlCu5MnCdVA 합금의 용융 풀 구조, 온도 흐름 및 속도장을 연구하기 위해 수치 시뮬레이션과 실험을 모두 사용했습니다.

그 결과 용융풀의 구조는 다양한 형태(깊은 오목 구조, 이중 오목 구조, 평면 구조, 돌출 구조 및 이상적인 평면 구조)를 나타냈으며, 용융 풀의 크기는 약 132 μm × 107 μm × 50 μm였습니다. : 용융풀은 초기에는 여러 구동력에 의해 깊이 15μm의 깊은 오목형상이었으나, 성형 후기에는 장력구배에 의해 높이 10μm의 돌출형상이 되었다. 용융 풀 내부의 금속 흐름은 주로 레이저 충격력, 금속 액체 중력, 표면 장력 및 반동 압력에 의해 구동되었습니다.

AlCu5MnCdVA 합금의 경우, 금속 액체 응고 속도가 매우 빠르며(3.5 × 10-4 S), 가열 속도 및 냉각 속도는 각각 6.5 × 107 K S-1 및 1.6 × 106 K S-1 에 도달했습니다. 시각적 표준으로 표면 거칠기를 선택하고, 낮은 레이저 에너지 AlCu5MnCdVA 합금 최적 공정 매개변수 창을 수치 시뮬레이션으로 얻었습니다: 레이저 출력 250W, 부화 공간 0.11mm, 층 두께 0.03mm, 레이저 스캔 속도 1.5m s-1 .

또한, 실험 프린팅과 수치 시뮬레이션과 비교할 때, 용융 풀의 폭은 각각 약 205um 및 약 210um이었고, 인접한 두 용융 트랙 사이의 중첩은 모두 약 65um이었다. 결과는 수치 시뮬레이션 결과가 실험 인쇄 결과와 기본적으로 일치함을 보여 수치 시뮬레이션 모델의 정확성을 입증했습니다.

Selective Laser Melting (SLM) has become one of the most promising technologies in Metal Additive Manufacturing (MAM), which is a complex dynamic non-equilibrium process involving heat transfer, melting, phase transition, vaporization and mass transfer. The characteristics of the molten pool (structure, temperature flow and velocity flow) have a decisive influence on the final forming quality of SLM. In this study, both numerical simulation and experiments were employed to study molten pool structure, temperature flow and velocity field in Selective Laser Melting AlCu5MnCdVA alloy. The results showed the structure of molten pool showed different forms(deep-concave structure, double-concave structure, plane structure, protruding structure and ideal planar structure), and the size of the molten pool was approximately 132 μm × 107 μm × 50 μm: in the early stage, molten pool was in a state of deep-concave shape with a depth of 15 μm due to multiple driving forces, while a protruding shape with a height of 10 μm duo to tension gradient in the later stages of forming. The metal flow inside the molten pool was mainly driven by laser impact force, metal liquid gravity, surface tension and recoil pressure. For AlCu5MnCdVA alloy, metal liquid solidification speed was extremely fast(3.5 × 10−4 S), the heating rate and cooling rate reached 6.5 × 107 K S−1 and 1.6 × 106 K S−1 , respectively. Choosing surface roughness as a visual standard, low-laser energy AlCu5MnCdVA alloy optimum process parameters window was obtained by numerical simulation: laser power 250 W, hatching space 0.11 mm, layer thickness 0.03 mm, laser scanning velocity 1.5 m s−1 . In addition, compared with experimental printing and numerical simulation, the width of the molten pool was about 205 um and about 210 um, respectively, and overlapping between two adjacent molten tracks was all about 65 um. The results showed that the numerical simulation results were basically consistent with the experimental print results, which proved the correctness of the numerical simulation model.

Figure 1. AlCu5MnCdVA powder particle size distribution.
Figure 1. AlCu5MnCdVA powder particle size distribution.
Figure 2. AlCu5MnCdVA powder
Figure 2. AlCu5MnCdVA powder
Figure 3. Finite element model and calculation domains of SLM.
Figure 3. Finite element model and calculation domains of SLM.
Figure 4. SLM heat transfer process.
Figure 4. SLM heat transfer process.
Figure 14. Defects: (a) Unmelt defects(Scheme NO.4);(b) Pores defects(Scheme NO.1); (c); Spattering defect (Scheme NO.3); (d) Low
overlapping rate defects(Scheme NO.5).
Figure 17. Two-pass molten tracks overlapping for Scheme NO.2.
Figure 17. Two-pass molten tracks overlapping for Scheme NO.2.

References

[1] Cuiyun H 2008 Phase diagram determination and thermodynamic study of Al–Cu–Mn, Al–Cu–Si, Al–Mg–Ni and Ni–Ti–Si systems Central South University
[2] Zhanfei Z 2017 Study on theta phase segregation and room temperature properties of high strength cast Al–Cu–Mn alloy Lanzhou University of Technology
[3] Nie X et al 2018 Analysis of processing parameters and characteristics of selective laser melted high strength Al–Cu–Mg alloys: from single tracks to cubic samplesJ. Mater. Process. Technol. 256 69–77
[4] Shenping Y et al 2017 Laser absorptance measurement of commonly used metal materials in laser additive manufacturing technology Aviation Manufacturing Technology 12 23–9
[5] Wenqing W 2007 Relationship between cooling rate and grain size of AlCu5MnCdVA alloy Harbin University of Technology
[6] Majeed M, Vural M, Raja S and Bilal Naim Shaikh M 2019 Finite element analysis of thermal behavior in maraging steel during SLM process Optik 208 113–24
[7] Khairallah S A, Anderson A T, Rubenchik A and King W E 2016 Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones Acta Mater. 108 36–45
[8] Bo C, Zhiyu X, Quanquan Z, Yuanbiao W, Liping W and Jin C 2020 Process optimization and microstructure and properties of SLM forming Cu6AlNiSnInCe imitation gold alloy Chin. J. Nonferr. Met. 30 372–82
[9] Li W 2012 Research on performance of metal parts formed by selective laser melting Huazhong University of Science and Technology
[10] Yu Q 2013 The influence of different laser heat sources on the surface shape of the molten pool in laser cladding Surf. Technol. 42 40–3

[11] Xianfeng J, Xiangchen M, Rongwei S, Xigen Y and Ming Y 2015 Research on the influence of material state change on temperature field
in SLM processing Applied Laser 35 155–9
[12] Körner C, Attar E and Heinl P 2011 Mesoscopic simulation of selective beam melting processesJ. Mater. Process. Technol. 211 978–87
[13] Yadroitsev I, Gusarov A, Yadroitsava I and Smurov I 2010 Single track formation in selective laser melting of metal powdersJ. Mater.
Process. Technol. 210 1624–31
[14] King W, Anderson A T, Ferencz R M, Hodge N E, Kamath C and Khairallah S A 2014 Overview of modelling and simulation of metal
powder bed fusion process at Lawrence Livermore National Laboratory Mater. Sci. Technol. 31 957–68
[15] Hussein A, Hao L, Yan C and Everson R 2013 Finite element simulation of the temperature and stress fields in single layers built
without-support in selective laser melting Materials & Design (1980–2015) 52 638–47
[16] Qiu C, Panwisawas C, Ward M, Basoalto H C, Brooks J W and Attallah M M 2015 On the role of melt flow into the surface structure and
porosity development during selective laser melting Acta Mater. 96 72–9
[17] Weihao Y, Hui C and Qingsong W 2020 Thermodynamic behavior of laser selective melting molten pool under the action of recoil
pressure Journal of Mechanical Engineering 56 213–9
[18] Weijuan Y 2019 Numerical simulation of melt pool temperature field and morphology evolution during laser selective melting process
Xi’an University of Technology
[19] Genwang W 2017 Research on the establishment of laser heat source model based on energy distribution and its simulation application
Harbin Institute of Technology
[20] FLOW-3D 2017 User Manual (USA: FLOW SCIENCE)
[21] Hirt C and Nichols B 1981 Volume of fluid (VOF) method for the dynamics of free boundariesJ. Comput. Phys. 39 201–25
[22] Hu Z, Zhang H, Zhu H, Xiao Z, Nie X and Zeng X 2019 Microstructure, mechanical properties and strengthening mechanisms of
AlCu5MnCdVA aluminum alloy fabricated by selective laser melting Materials Science and Engineering: A 759 154–66
[23] Ketai H, Liu Z and Lechang Y 2020 Simulation of temperature field, microstructure and mechanical properties of 316L stainless steel in
selected laser melting Progress in Laser and Optoelectronics 9 1–18
[24] Cao L 2020 Workpiece-scale numerical simulations of SLM molten pool dynamic behavior of 316L stainless steel Comput. Math. Appl.
4 22–34
[25] Dening Z, Yongping L, Tinglu H and Junyi S 2000 Numerical study of fluid flow and heat transfer in molten pool under the condition of
moving heat source J. Met. 4 387–90
[26] Chengyun C, Cui F and Wenlong Z 2018 The effect of Marangoni flow on the thermal behavior and melt flow behavior of laser cladding
Applied Laser 38 409–16
[27] Peiying B and Enhuai Y 2020 The effect of laser power on the morphology and residual stress of the molten pool of metal laser selective
melting Progress in Laser and Optoelectronics 7 1–12 http://kns.cnki.net/kcms/detail/31.1690.TN.20190717.0933.032.html
[28] Zhen L, Dongyun Z, Zhe F and Chengjie W 2017 Numerical simulation of the influence of overlap rate on the forming quality of
Inconel 718 alloy by selective laser melting processing Applied Laser 37 187–93
[29] Wei W, Qi L, Guang Y, Lanyun Q and Xiong X 2015 Numerical simulation of electromagnetic field, temperature field and flowfield of
laser melting pool under the action of electromagnetic stirring China Laser 42 48–55
[30] Hu Y, He X, Yu G and Zhao S 2016 Capillary convection in pulsed—butt welding of miscible dissimilar couple Proc. Inst. Mech. Eng.
Part C J. Mech. Eng. Sci. 231 2429–40
[31] Li R 2010 Research on the key basic problems of selective laser melting forming of metal powder Huazhong University of Science and
Technology
[32] Zijue T, Weiwei L, Zhaorui Y, Hao W and Hongchao Z 2019 Study on the shape evolution behavior of metal laser melting deposition
based on molten pool dynamic characteristicsJournal of Mechanical Engineering 55 39–47
[33] Pan L, Cheng-Lin Z, Hai-Yi L, Liang W and Tong L 2020 A new two-step selective laser remelting of 316L stainless steel: process,
density, surface roughness, mechanical properties, microstructure Mater. Res. Express 7 056503
[34] Pan L, Cheng-Lin Z, Hai-Yi L, Jiang H, Tong L and Liang W 2019 The influence and optimization of forming process parameters of
316L stainless steel prepared by laser melting on the density Forging Technology 44 103–9

Figure 15. Velocity distribution of impinging jet on a wall under different Reynolds numbers.

Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment

by Hongbo Mi 1,2, Chuan Wang 1,3, Xuanwen Jia 3,*, Bo Hu 2, Hongliang Wang 4, Hui Wang 3 and Yong Zhu 5

1College of Mechatronics Engineering, Hainan Vocational University of Science and Technology, Haikou 571126, China

2Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China

3College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou 225009, China

4School of Aerospace and Mechanical Engineering/Flight College, Changzhou Institute of Technology, Changzhou 213032, China

5National Research Center of Pumps, Jiangsu University, Zhenjiang 212013, China

*Author to whom correspondence should be addressed.Sustainability202315(6), 5159; https://doi.org/10.3390/su15065159

Received: 30 January 2023 / Revised: 4 March 2023 / Accepted: 10 March 2023 / Published: 14 March 2023(This article belongs to the Special Issue Advanced Technologies of Renewable Energy and Water Management for Sustainable Environment

Abstract

Due to their high efficiency, low heat loss and associated sustainability advantages, impinging jets have been used extensively in marine engineering, geotechnical engineering and other engineering practices. In this paper, the flow structure and impact characteristics of impinging jets with different Reynolds numbers and impact distances are systematically studied by Flow-3D based on PIV experiments. In the study, the relevant state parameters of the jets are dimensionlessly treated, obtaining not only the linear relationship between the length of the potential nucleation zone and the impinging distance, but also the linear relationship between the axial velocity and the axial distance in the impinging zone. In addition, after the jet impinges on the flat plate, the vortex action range caused by the wall-attached flow of the jet gradually decreases inward with the increase of the impinging distance. By examining the effect of Reynolds number Re on the hydraulic characteristics of the submerged impact jet, it can be found that the structure of the continuous submerged impact jet is relatively independent of the Reynolds number. At the same time, the final simulation results demonstrate the applicability of the linear relationship between the length of the potential core region and the impact distance. This study provides methodological guidance and theoretical support for relevant engineering practice and subsequent research on impinging jets, which has strong theoretical and practical significance.

Keywords: 

PIVFlow-3Dimpinging jethydraulic characteristicsimpinging distance

Sustainability 15 05159 g001 550

Figure 1. Geometric model.

Sustainability 15 05159 g002 550

Figure 2. Model grid schematic.

Sustainability 15 05159 g003 550

Figure 3. (a) Schematic diagram of the experimental setup; (b) PIV images of vertical impinging jets with velocity fields.

Sustainability 15 05159 g004 550

Figure 4. (a) Velocity distribution verification at the outlet of the jet pipe; (b) Distribution of flow angle in the mid-axis of the jet [39].

Sustainability 15 05159 g005 550

Figure 5. Along-range distribution of the dimensionless axial velocity of the jet at different impact distances.Figure 6 shows the variation of H

Sustainability 15 05159 g006 550

Figure 6. Relationship between the distribution of potential core region and the impact height H/D.

Sustainability 15 05159 g007 550

Figure 7. The relationship between the potential core length 

Sustainability 15 05159 g008 550

Figure 8. Along-range distribution of the flow angle φ of the jet at different impact distances.

Sustainability 15 05159 g009 550

Figure 9. Velocity distribution along the axis of the jet at different impinging regions.

Sustainability 15 05159 g010 550

Figure 10. The absolute value distribution of slope under different impact distances.

Sustainability 15 05159 g011a 550
Sustainability 15 05159 g011b 550

Figure 11. Velocity distribution of impinging jet on wall under different impinging distances.

Sustainability 15 05159 g012 550

Figure 12. Along-range distribution of the dimensionless axial velocity of the jet at different Reynolds numbers.

Sustainability 15 05159 g013 550

Figure 13. Along-range distribution of the flow angle φ of the jet at different Reynolds numbers.

Sustainability 15 05159 g014 550

Figure 14. Velocity distribution along the jet axis at different Reynolds numbers.

Sustainability 15 05159 g015 550

Figure 15. Velocity distribution of impinging jet on a wall under different Reynolds numbers.

References

  1. Zhang, J.; Li, Y.; Zhang, Y.; Yang, F.; Liang, C.; Tan, S. Using a high-pressure water jet-assisted tunnel boring machine to break rock. Adv. Mech. Eng. 202012, 1687814020962290. [Google Scholar] [CrossRef]
  2. Shi, X.; Zhang, G.; Xu, G.; Ma, Y.; Wu, X. Inactivating Microorganism on Medical Instrument Using Plasma Jet. High Volt. Eng. 200935, 632–635. [Google Scholar]
  3. Gao, Y.; Han, P.; Wang, F.; Cao, J.; Zhang, S. Study on the Characteristics of Water Jet Breaking Coal Rock in a Drilling Hole. Sustainability 202214, 8258. [Google Scholar] [CrossRef]
  4. Xu, W.; Wang, C.; Zhang, L.; Ge, J.; Zhang, D.; Gao, Z. Numerical study of continuous jet impinging on a rotating wall based on Wray—Agarwal turbulence model. J. Braz. Soc. Mech. Sci. Eng. 202244, 433. [Google Scholar] [CrossRef]
  5. Hu, B.; Wang, C.; Wang, H.; Yu, Q.; Liu, J.; Zhu, Y.; Ge, J.; Chen, X.; Yang, Y. Numerical Simulation Study of the Horizontal Submerged Jet Based on the Wray—Agarwal Turbulence Model. J. Mar. Sci. Eng. 202210, 1217. [Google Scholar] [CrossRef]
  6. Dahiya, A.K.; Bhuyan, B.K.; Kumar, S. Perspective study of abrasive water jet machining of composites—A review. J. Mech. Sci. Technol. 202236, 213–224. [Google Scholar] [CrossRef]
  7. Abushanab, W.S.; Moustafa, E.B.; Harish, M.; Shanmugan, S.; Elsheikh, A.H. Experimental investigation on surface characteristics of Ti6Al4V alloy during abrasive water jet machining process. Alex. Eng. J. 202261, 7529–7539. [Google Scholar] [CrossRef]
  8. Hu, B.; Wang, H.; Liu, J.; Zhu, Y.; Wang, C.; Ge, J.; Zhang, Y. A numerical study of a submerged water jet impinging on a stationary wall. J. Mar. Sci. Eng. 202210, 228. [Google Scholar] [CrossRef]
  9. Peng, J.; Shen, H.; Xie, W.; Zhai, S.; Xi, G. Influence of flow fluctuation characteristics on flow and heat transfer in different regions. J. Drain. Irrig. Mach. Eng. 202240, 826–833. [Google Scholar]
  10. Zhai, S.; Xie, F.; Yin, G.; Xi, G. Effect of gap ratio on vortex-induced vibration characteristics of different blunt bodies near-wall. J. Drain. Irrig. Mach. Eng. 202139, 1132–1138. [Google Scholar]
  11. Lin, W.; Zhou, Y.; Wang, L.; Tao, L. PIV experiment and numerical simulation of trailing vortex structure of improved INTER-MIG impeller. J. Drain. Irrig. Mach. Eng. 202139, 158–164. [Google Scholar]
  12. Han, B.; Yao, Z.; Tang, R.; Xu, H. On the supersonic impinging jet by laser Doppler velocimetry. Exp. Meas. Fluid Mech. 200216, 99–103. [Google Scholar]
  13. Darisse, A.; Lemay, J.; Benaissa, A. LDV measurements of well converged third order moments in the far field of a free turbulent round jet. Exp. Therm. Fluid Sci. 201344, 825–833. [Google Scholar] [CrossRef]
  14. Kumar, S.; Kumar, A. Effect of initial conditions on mean flow characteristics of a three dimensional turbulent wall jet. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2021235, 6177–6190. [Google Scholar] [CrossRef]
  15. Tao, D.; Zhang, R.; Ying, C. Development and application of the pollutant diffusion testing apparatus based on the image analysis. J. Saf. Environ. 201616, 247–251. [Google Scholar]
  16. Seo, H.; Kim, K.C. Experimental study on flow and turbulence characteristics of bubbly jet with low void fraction. Int. J. Multiph. Flow 2021142, 103738. [Google Scholar] [CrossRef]
  17. Wen, Q.; Sha, J.; Liu, Y. TR-PIV measurement of the turbulent submerged jet and POB analysis of the dynamic structure. J. Exp. Fluid Mech. 20144, 16–24. [Google Scholar]
  18. Yang, Y.; Zhou, L.; Shi, W.; He, Z.; Han, Y.; Xiao, Y. Interstage difference of pressure pulsation in a three-stage electrical submersible pump. J. Petrol. Sci. Eng. 2021196, 107653. [Google Scholar] [CrossRef]
  19. Tang, S.; Zhu, Y.; Yuan, S. An improved convolutional neural network with an adaptable learning rate towards multi-signal fault diagnosis of hydraulic piston pump. Adv. Eng. Inform. 202150, 101406. [Google Scholar] [CrossRef]
  20. Han, Y.; Song, X.; Li, K.; Yan, X. Hybrid modeling for submergence depth of the pumping well using stochastic configuration networks with random sampling. J. Petrol. Sci. Eng. 2022208, 109423. [Google Scholar] [CrossRef]
  21. Tang, S.; Zhu, Y.; Yuan, S. A novel adaptive convolutional neural network for fault diagnosis of hydraulic piston pump with acoustic images. Adv. Eng. Inform. 202252, 101554. [Google Scholar] [CrossRef]
  22. Long, J.; Song, X.; Shi, J.; Chen, J. Optimization and CFD Analysis on Nozzle Exit Position of Two-phase Ejector. J. Refrig. 202243, 39–45. [Google Scholar]
  23. Ni, Q.; Ruan, W. Optimization design of desilting jet pump parameters based on response surface model. J. Ship Mech. 202226, 365–374. [Google Scholar]
  24. Zhang, K.; Zhu, X.; Ren, X.; Qiu, Q.; Shen, S. Numerical investigation on the effect of nozzle position for design of high performance ejector. Appl. Therm. Eng. 2017126, 594–601. [Google Scholar] [CrossRef]
  25. Fu, W.; Liu, Z.; Li, Y.; Wu, H.; Tang, Y. Numerical study for the influences of primary steam nozzle distance and mixing chamber throat diameter on steam ejector performance. Int. J. Therm. Sci. 2018132, 509–516. [Google Scholar] [CrossRef]
  26. Lucas, C.; Rusche, H.; Schroeder, A.; Koehler, J. Numerical investigation of a two-phase CO2 ejector. Int. J. Refrigeration 201443, 154–166. [Google Scholar] [CrossRef]
  27. Ma, X.; Zhu, T.; Fu, Y.; Yan, Y.; Chen, W. Numerical simulation of rock breaking by abrasive water jet. J. Coast. Res. 201993, 274–283. [Google Scholar] [CrossRef]
  28. He, L.; Liu, Y.; Shen, K.; Yang, X.; Ba, Q.; Xiong, W. Numerical research on the dynamic rock-breaking process of impact drilling with multi-nozzle water jets. J. Pet. Sci. Eng. 2021207, 109145. [Google Scholar] [CrossRef]
  29. Yu, Z.; Wang, Z.; Lei, C.; Zhou, Y.; Qiu, X. Numerical Simulation on Internal Flow Field of a Self-excited Oscillation Pulsed Jet Nozzle with Back-flow. Mech. Sci. Technol. Aerosp. Eng. 202241, 998–1002. [Google Scholar]
  30. Huang, J.; Ni, F.; Gu, L. Numerical method of FLOW-3D for sediment erosion simulation. China Harb. Eng. 201939, 6–11. [Google Scholar]
  31. Al Shaikhli, H.I.; Khassaf, S.I. Using of flow 3d as CFD materials approach in waves generation. Mater. Today Proc. 202249, 2907–2911. [Google Scholar] [CrossRef]
  32. Kosaj, R.; Alboresha, R.S.; Sulaiman, S.O. Comparison Between Numerical Flow3d Software and Laboratory Data, For Sediment Incipient Motion. IOP Conf. Ser. Earth Environ. Sci. 2022961, 012031. [Google Scholar] [CrossRef]
  33. Du, C.; Liu, X.; Zhang, J.; Wang, B.; Chen, X.; Yu, X. Long-distance water hammer protection of pipeline after pump being first lowered and then rasied. J. Drain. Irrig. Mach. Eng. 202240, 1248–1253, 1267. [Google Scholar]
  34. Gao, F.; Li, X.; Gao, Q. Experiment and numerical simulation on hydraulic characteristics of novel trapezoidal measuring weir. J. Drain. Irrig. Mach. Eng. 202240, 1104–1111. [Google Scholar]
  35. Tu, A.; Nie, X.; Li, Y.; Li, H. Experimental and simulation study on water infiltration characteristics of layered red soil. J. Drain. Irrig. Mach. Eng. 202139, 1243–1249. [Google Scholar]
  36. Chen, J.; Zeng, B.; Liu, L.; Tao, K.; Zhao, H.; Zhang, C.; Zhang, J.; Li, D. Investigating the anchorage performance of full-grouted anchor bolts with a modified numerical simulation method. Eng. Fail. Anal. 2022141, 106640. [Google Scholar] [CrossRef]
  37. Hu, B.; Yao, Y.; Wang, M.; Wang, C.; Liu, Y. Flow and Performance of the Disk Cavity of a Marine Gas Turbine at Varying Nozzle Pressure and Low Rotation Speeds: A Numerical Investigation. Machines 202311, 68. [Google Scholar] [CrossRef]
  38. Yao, J.; Wang, X.; Zhang, S.; Xu, S.; Jin, B.; Ding, S. Orthogonal test of important parameters affecting hydraulic performance of negative pressure feedback jet sprinkler. J. Drain. Irrig. Mach. Eng. 202139, 966–972. [Google Scholar]
  39. Wang, C.; Wang, X.; Shi, W.; Lu, W.; Tan, S.K.; Zhou, L. Experimental investigation on impingement of a submerged circular water jet at varying impinging angles and Reynolds numbers. Exp. Therm. Fluid Sci. 201789, 189–198. [Google Scholar] [CrossRef]
  40. Speziale, C.G.; Thangam, S. Analysis of an RNG based turbulence model for separated flows. Int. J. Eng. Sci. 199230, 1379–1388. [Google Scholar] [CrossRef]
  41. El Hassan, M.; Assoum, H.H.; Sobolik, V.; Vétel, J.; Abed-Meraim, K.; Garon, A.; Sakout, A. Experimental investigation of the wall shear stress and the vortex dynamics in a circular impinging jet. Exp. Fluids 201252, 1475–1489. [Google Scholar] [CrossRef]
  42. Fairweather, M.; Hargrave, G. Experimental investigation of an axisymmetric, impinging turbulent jet. 1. Velocity field. Exp. Fluids 200233, 464–471. [Google Scholar] [CrossRef]
  43. Ashforth-Frost, S.; Jambunathan, K. Effect of nozzle geometry and semi-confinement on the potential core of a turbulent axisymmetric free jet. Int. Commun. Heat Mass Transf. 199623, 155–162. [Google Scholar] [CrossRef]
  44. Chen, M.; Huang, H.; Wang, D.; Lv, S.; Chen, Y. PIV tests for flow characteristics of impinging jet in a semi-closed circular pipe. J. Vib. Shock 202140, 90–97, 113. [Google Scholar]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Share and Cite

      

MDPI and ACS Style

Mi, H.; Wang, C.; Jia, X.; Hu, B.; Wang, H.; Wang, H.; Zhu, Y. Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment. Sustainability 202315, 5159. https://doi.org/10.3390/su15065159

AMA Style

Mi H, Wang C, Jia X, Hu B, Wang H, Wang H, Zhu Y. Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment. Sustainability. 2023; 15(6):5159. https://doi.org/10.3390/su15065159Chicago/Turabian Style

Mi, Hongbo, Chuan Wang, Xuanwen Jia, Bo Hu, Hongliang Wang, Hui Wang, and Yong Zhu. 2023. “Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment” Sustainability 15, no. 6: 5159. https://doi.org/10.3390/su15065159

Figure 5 A schematic of the water model of reactor URO 200.

Physical and Numerical Modeling of the Impeller Construction Impact on the Aluminum Degassing Process

알루미늄 탈기 공정에 미치는 임펠러 구성의 물리적 및 수치적 모델링

Kamil Kuglin,1 Michał Szucki,2 Jacek Pieprzyca,3 Simon Genthe,2 Tomasz Merder,3 and Dorota Kalisz1,*

Mikael Ersson, Academic Editor

Author information Article notes Copyright and License information Disclaimer

Associated Data

Data Availability Statement

Go to:

Abstract

This paper presents the results of tests on the suitability of designed heads (impellers) for aluminum refining. The research was carried out on a physical model of the URO-200, followed by numerical simulations in the FLOW 3D program. Four design variants of impellers were used in the study. The degree of dispersion of the gas phase in the model liquid was used as a criterion for evaluating the performance of each solution using different process parameters, i.e., gas flow rate and impeller speed. Afterward, numerical simulations in Flow 3D software were conducted for the best solution. These simulations confirmed the results obtained with the water model and verified them.

Keywords: aluminum, impeller construction, degassing process, numerical modeling, physical modeling

Go to:

1. Introduction

Constantly increasing requirements concerning metallurgical purity in terms of hydrogen content and nonmetallic inclusions make casting manufacturers use effective refining techniques. The answer to this demand is the implementation of the aluminum refining technique making use of a rotor with an original design guaranteeing efficient refining [1,2,3,4]. The main task of the impeller (rotor) is to reduce the contamination of liquid metal (primary and recycled aluminum) with hydrogen and nonmetallic inclusions. An inert gas, mainly argon or a mixture of gases, is introduced through the rotor into the liquid metal to bring both hydrogen and nonmetallic inclusions to the metal surface through the flotation process. Appropriately and uniformly distributed gas bubbles in the liquid metal guarantee achieving the assumed level of contaminant removal economically. A very important factor in deciding about the obtained degassing effect is the optimal rotor design [5,6,7,8]. Thanks to the appropriate geometry of the rotor, gas bubbles introduced into the liquid metal are split into smaller ones, and the spinning movement of the rotor distributes them throughout the volume of the liquid metal bath. In this solution impurities in the liquid metal are removed both in the volume and from the upper surface of the metal. With a well-designed impeller, the costs of refining aluminum and its alloys can be lowered thanks to the reduced inert gas and energy consumption (optimal selection of rotor rotational speed). Shorter processing time and a high degree of dehydrogenation decrease the formation of dross on the metal surface (waste). A bigger produced dross leads to bigger process losses. Consequently, this means that the choice of rotor geometry has an indirect impact on the degree to which the generated waste is reduced [9,10].

Another equally important factor is the selection of process parameters such as gas flow rate and rotor speed [11,12]. A well-designed gas injection system for liquid metal meets two key requirements; it causes rapid mixing of the liquid metal to maintain a uniform temperature throughout the volume and during the entire process, to produce a chemically homogeneous metal composition. This solution ensures effective degassing of the metal bath. Therefore, the shape of the rotor, the arrangement of the nozzles, and their number are significant design parameters that guarantee the optimum course of the refining process. It is equally important to complete the mixing of the metal bath in a relatively short time, as this considerably shortens the refining process and, consequently, reduces the process costs. Another important criterion conditioning the implementation of the developed rotor is the generation of fine diffused gas bubbles which are distributed throughout the metal volume, and whose residence time will be sufficient for the bubbles to collide and adsorb the contaminants. The process of bubble formation by the spinning rotors differs from that in the nozzles or porous molders. In the case of a spinning rotor, the shear force generated by the rotor motion splits the bubbles into smaller ones. Here, the rotational speed, mixing force, surface tension, and fluid density have a key effect on the bubble size. The velocity of the bubbles, which depends mainly on their size and shape, determines their residence time in the reactor and is, therefore, very important for the refining process, especially since gas bubbles in liquid aluminum may remain steady only below a certain size [13,14,15].

The impeller designs presented in the article were developed to improve the efficiency of the process and reduce its costs. The impellers used so far have a complicated structure and are very pricey. The success of the conducted research will allow small companies to become independent of external supplies through the possibility of making simple and effective impellers on their own. The developed structures were tested on the water model. The results of this study can be considered as pilot.

Go to:

2. Materials and Methods

Rotors were realized with the SolidWorks computer design technique and a 3D printer. The developed designs were tested on a water model. Afterward, the solution with the most advantageous refining parameters was selected and subjected to calculations with the Flow3D package. As a result, an impeller was designed for aluminum refining. Its principal lies in an even distribution of gas bubbles in the entire volume of liquid metal, with the largest possible participation of the bubble surface, without disturbing the metal surface. This procedure guarantees the removal of gaseous, as well as metallic and nonmetallic, impurities.

2.1. Rotor Designs

The developed impeller constructions, shown in Figure 1Figure 2Figure 3 and Figure 4, were printed on a 3D printer using the PLA (polylactide) material. The impeller design models differ in their shape and the number of holes through which the inert gas flows. Figure 1Figure 2 and Figure 3 show the same impeller model but with a different number of gas outlets. The arrangement of four, eight, and 12 outlet holes was adopted in the developed design. A triangle-shaped structure equipped with three gas outlet holes is presented in Figure 4.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g001.jpg

Figure 1

A 3D model—impeller with four holes—variant B4.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g002.jpg

Figure 2

A 3D model—impeller with eight holes—variant B8.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g003.jpg

Figure 3

A 3D model—impeller with twelve holes—variant B12.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g004.jpg

Figure 4

A 3D model—‘red triangle’ impeller with three holes—variant RT3.

2.2. Physical Models

Investigations were carried out on a water model of the URO 200 reactor of the barbotage refining process (see Figure 5).

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g005.jpg

Figure 5

A schematic of the water model of reactor URO 200.

The URO 200 reactor can be classified as a cyclic reactor. The main element of the device is a rotor, which ends the impeller. The whole system is attached to a shaft via which the refining gas is supplied. Then, the shaft with the rotor is immersed in the liquid metal in the melting pot or the furnace chamber. In URO 200 reactors, the refining process lasts 600 s (10 min), the gas flow rate that can be obtained ranges from 5 to 20 dm3·min−1, and the speed at which the rotor can move is 0 to 400 rpm. The permissible quantity of liquid metal for barbotage refining is 300 kg or 700 kg [8,16,17]. The URO 200 has several design solutions which improve operation and can be adapted to the existing equipment in the foundry. These solutions include the following [8,16]:

  • URO-200XR—used for small crucible furnaces, the capacity of which does not exceed 250 kg, with no control system and no control of the refining process.
  • URO-200SA—used to service several crucible furnaces of capacity from 250 kg to 700 kg, fully automated and equipped with a mechanical rotor lift.
  • URO-200KA—used for refining processes in crucible furnaces and allows refining in a ladle. The process is fully automated, with a hydraulic rotor lift.
  • URO-200KX—a combination of the XR and KA models, designed for the ladle refining process. Additionally, refining in heated crucibles is possible. The unit is equipped with a manual hydraulic rotor lift.
  • URO-200PA—designed to cooperate with induction or crucible furnaces or intermediate chambers, the capacity of which does not exceed one ton. This unit is an integral part of the furnace. The rotor lift is equipped with a screw drive.

Studies making use of a physical model can be associated with the observation of the flow and circulation of gas bubbles. They require meeting several criteria regarding the similarity of the process and the object characteristics. The similarity conditions mainly include geometric, mechanical, chemical, thermal, and kinetic parameters. During simulation of aluminum refining with inert gas, it is necessary to maintain the geometric similarity between the model and the real object, as well as the similarity related to the flow of liquid metal and gas (hydrodynamic similarity). These quantities are characterized by the Reynolds, Weber, and Froude numbers. The Froude number is the most important parameter characterizing the process, its magnitude is the same for the physical model and the real object. Water was used as the medium in the physical modeling. The factors influencing the choice of water are its availability, relatively low cost, and kinematic viscosity at room temperature, which is very close to that of liquid aluminum.

The physical model studies focused on the flow of inert gas in the form of gas bubbles with varying degrees of dispersion, particularly with respect to some flow patterns such as flow in columns and geysers, as well as disturbance of the metal surface. The most important refining parameters are gas flow rate and rotor speed. The barbotage refining studies for the developed impeller (variants B4, B8, B12, and RT3) designs were conducted for the following process parameters:

  • Rotor speed: 200, 300, 400, and 500 rpm,
  • Ideal gas flow: 10, 20, and 30 dm3·min−1,
  • Temperature: 293 K (20 °C).

These studies were aimed at determining the most favorable variants of impellers, which were then verified using the numerical modeling methods in the Flow-3D program.

2.3. Numerical Simulations with Flow-3D Program

Testing different rotor impellers using a physical model allows for observing the phenomena taking place while refining. This is a very important step when testing new design solutions without using expensive industrial trials. Another solution is modeling by means of commercial simulation programs such as ANSYS Fluent or Flow-3D [18,19]. Unlike studies on a physical model, in a computer program, the parameters of the refining process and the object itself, including the impeller design, can be easily modified. The simulations were performed with the Flow-3D program version 12.03.02. A three-dimensional system with the same dimensions as in the physical modeling was used in the calculations. The isothermal flow of liquid–gas bubbles was analyzed. As in the physical model, three speeds were adopted in the numerical tests: 200, 300, and 500 rpm. During the initial phase of the simulations, the velocity field around the rotor generated an appropriate direction of motion for the newly produced bubbles. When the required speed was reached, the generation of randomly distributed bubbles around the rotor was started at a rate of 2000 per second. Table 1 lists the most important simulation parameters.

Table 1

Values of parameters used in the calculations.

ParameterValueUnit
Maximum number of gas particles1,000,000
Rate of particle generation20001·s−1
Specific gas constant287.058J·kg−1·K−1
Atmospheric pressure1.013 × 105Pa
Water density1000kg·m−3
Water viscosity0.001kg·m−1·s−1
Boundary condition on the wallsNo-slip
Size of computational cell0.0034m

Open in a separate window

In the case of the CFD analysis, the numerical solutions require great care when generating the computational mesh. Therefore, computational mesh tests were performed prior to the CFD calculations. The effect of mesh density was evaluated by taking into account the velocity of water in the tested object on the measurement line A (height of 0.065 m from the bottom) in a characteristic cross-section passing through the object axis (see Figure 6). The mesh contained 3,207,600, 6,311,981, 7,889,512, 11,569,230, and 14,115,049 cells.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g006.jpg

Figure 6

The velocity of the water depending on the size of the computational grid.

The quality of the generated computational meshes was checked using the criterion skewness angle QEAS [18]. This criterion is described by the following relationship:

QEAS=max{βmax−βeq180−βeq,βeq−βminβeq},

(1)

where βmaxβmin are the maximal and minimal angles (in degrees) between the edges of the cell, and βeq is the angle corresponding to an ideal cell, which for cubic cells is 90°.

Normalized in the interval [0;1], the value of QEAS should not exceed 0.75, which identifies the permissible skewness angle of the generated mesh. For the computed meshes, this value was equal to 0.55–0.65.

Moreover, when generating the computational grids in the studied facility, they were compacted in the areas of the highest gradients of the calculated values, where higher turbulence is to be expected (near the impeller). The obtained results of water velocity in the studied object at constant gas flow rate are shown in Figure 6.

The analysis of the obtained water velocity distributions (see Figure 6) along the line inside the object revealed that, with the density of the grid of nodal points, the velocity changed and its changes for the test cases of 7,889,512, 11,569,230, and 14,115,049 were insignificant. Therefore, it was assumed that a grid containing not less than 7,900,000 (7,889,512) cells would not affect the result of CFD calculations.

A single-block mesh of regular cells with a size of 0.0034 m was used in the numerical calculations. The total number of cells was approximately 7,900,000 (7,889,512). This grid resolution (see Figure 7) allowed the geometry of the system to be properly represented, maintaining acceptable computation time (about 3 days on a workstation with 2× CPU and 12 computing cores).

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g007.jpg

Figure 7

Structured equidistant mesh used in numerical calculations: (a) mesh with smoothed, surface cells (the so-called FAVOR method) used in Flow-3D; (b) visualization of the applied mesh resolution.

The calculations were conducted with an explicit scheme. The timestep was selected by the program automatically and controlled by stability and convergence. From the moment of the initial velocity field generation (start of particle generation), it was 0.0001 s.

When modeling the degassing process, three fluids are present in the system: water, gas supplied through the rotor head (impeller), and the surrounding air. Modeling such a multiphase flow is a numerically very complex issue. The necessity to overcome the liquid backpressure by the gas flowing out from the impeller leads to the formation of numerical instabilities in the volume of fluid (VOF)-based approach used by Flow-3D software. Therefore, a mixed description of the analyzed flow was used here. In this case, water was treated as a continuous medium, while, in the case of gas bubbles, the discrete phase model (DPM) model was applied. The way in which the air surrounding the system was taken into account is later described in detail.

The following additional assumptions were made in the modeling:

  • —The liquid phase was considered as an incompressible Newtonian fluid.
  • —The effect of chemical reactions during the refining process was neglected.
  • —The composition of each phase (gas and liquid) was considered homogeneous; therefore, the viscosity and surface tension were set as constants.
  • —Only full turbulence existed in the liquid, and the effect of molecular viscosity was neglected.
  • —The gas bubbles were shaped as perfect spheres.
  • —The mutual interaction between gas bubbles (particles) was neglected.

2.3.1. Modeling of Liquid Flow 

The motion of the real fluid (continuous medium) is described by the Navier–Stokes Equation [20].

dudt=−1ρ∇p+ν∇2u+13ν∇(∇⋅ u)+F,

(2)

where du/dt is the time derivative, u is the velocity vector, t is the time, and F is the term accounting for external forces including gravity (unit components denoted by XYZ).

In the simulations, the fluid flow was assumed to be incompressible, in which case the following equation is applicable:

∂u∂t+(u⋅∇)u=−1ρ∇p+ν∇2u+F.

(3)

Due to the large range of liquid velocities during flows, the turbulence formation process was included in the modeling. For this purpose, the k–ε model turbulence kinetic energy k and turbulence dissipation ε were the target parameters, as expressed by the following equations [21]:

∂(ρk)∂t+∂(ρkvi)∂xi=∂∂xj[(μ+μtσk)⋅∂k∂xi]+Gk+Gb−ρε−Ym+Sk,

(4)

∂(ρε)∂t+∂(ρεui)∂xi=∂∂xj[(μ+μtσε)⋅∂k∂xi]+C1εεk(Gk+G3εGb)+C2ερε2k+Sε,

(5)

where ρ is the gas density, σκ and σε are the Prandtl turbulence numbers, k and ε are constants of 1.0 and 1.3, and Gk and Gb are the kinetic energy of turbulence generated by the average velocity and buoyancy, respectively.

As mentioned earlier, there are two gas phases in the considered problem. In addition to the gas bubbles, which are treated here as particles, there is also air, which surrounds the system. The boundary of phase separation is in this case the free surface of the water. The shape of the free surface can change as a result of the forming velocity field in the liquid. Therefore, it is necessary to use an appropriate approach to free surface tracking. The most commonly used concept in liquid–gas flow modeling is the volume of fluid (VOF) method [22,23], and Flow-3D uses a modified version of this method called TrueVOF. It introduces the concept of the volume fraction of the liquid phase fl. This parameter can be used for classifying the cells of a discrete grid into areas filled with liquid phase (fl = 1), gaseous phase, or empty cells (fl = 0) and those through which the phase separation boundary (fl ∈ (0, 1)) passes (free surface). To determine the local variations of the liquid phase fraction, it is necessary to solve the following continuity equation:

dfldt=0.

(6)

Then, the fluid parameters in the region of coexistence of the two phases (the so-called interface) depend on the volume fraction of each phase.

ρ=flρl+(1−fl)ρg,

(7)

ν=flνl+(1−fl)νg,

(8)

where indices l and g refer to the liquid and gaseous phases, respectively.

The parameter of fluid velocity in cells containing both phases is also determined in the same way.

u=flul+(1−fl)ug.

(9)

Since the processes taking place in the surrounding air can be omitted, to speed up the calculations, a single-phase, free-surface model was used. This means that no calculations were performed in the gas cells (they were treated as empty cells). The liquid could fill them freely, and the air surrounding the system was considered by the atmospheric pressure exerted on the free surface. This approach is often used in modeling foundry and metallurgical processes [24].

2.3.2. Modeling of Gas Bubble Flow 

As stated, a particle model was used to model bubble flow. Spherical particles (gas bubbles) of a given size were randomly generated in the area marked with green in Figure 7b. In the simulations, the gas bubbles were assumed to have diameters of 0.016 and 0.02 m corresponding to the gas flow rates of 10 and 30 dm3·min−1, respectively.

Experimental studies have shown that, as a result of turbulent fluid motion, some of the bubbles may burst, leading to the formation of smaller bubbles, although merging of bubbles into larger groupings may also occur. Therefore, to be able to observe the behavior of bubbles of different sizes (diameter), the calculations generated two additional particle types with diameters twice smaller and twice larger, respectively. The proportion of each species in the system was set to 33.33% (Table 2).

Table 2

Data assumed for calculations.

NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
A2000.01610D2000.0230
0.0080.01
0.0320.04
B3000.01610E3000.0230
0.0080.01
0.0320.04
C5000.01610F5000.0230
0.0080.01
0.0320.04

Open in a separate window

The velocity of the particle results from the generated velocity field (calculated from Equation (3) in the liquid ul around it and its velocity resulting from the buoyancy force ub. The effect of particle radius r on the terminal velocity associated with buoyancy force can be determined according to Stokes’ law.

ub=29 (ρg−ρl)μlgr2,

(10)

where g is the acceleration (9.81).

The DPM model was used for modeling the two-phase (water–air) flow. In this model, the fluid (water) is treated as a continuous phase and described by the Navier–Stokes equation, while gas bubbles are particles flowing in the model fluid (discrete phase). The trajectories of each bubble in the DPM system are calculated at each timestep taking into account the mass forces acting on it. Table 3 characterizes the DPM model used in our own research [18].

Table 3

Characteristic of the DPM model.

MethodEquations
Euler–LagrangeBalance equation:
dugdt=FD(u−ug)+g(ϱg−ϱ)ϱg+F.
FD (u − up) denotes the drag forces per mass unit of a bubble, and the expression for the drag coefficient FD is of the form
FD=18μCDReϱ⋅gd2g24.
The relative Reynolds number has the form
Re≡ρdg|ug−u|μ.
On the other hand, the force resulting from the additional acceleration of the model fluid has the form
F=12dρdtρg(u−ug),
where ug is the gas bubble velocity, u is the liquid velocity, dg is the bubble diameter, and CD is the drag coefficient.

Open in a separate window

Go to:

3. Results and Discussion

3.1. Calculations of Power and Mixing Time by the Flowing Gas Bubbles

One of the most important parameters of refining with a rotor is the mixing power induced by the spinning rotor and the outflowing gas bubbles (via impeller). The mixing power of liquid metal in a ladle of height (h) by gas injection can be determined from the following relation [15]:

pgVm=ρ⋅g⋅uB,

(11)

where pg is the mixing power, Vm is the volume of liquid metal in the reactor, ρ is the density of liquid aluminum, and uB is the average speed of bubbles, given below.

uB=n⋅R⋅TAc⋅Pm⋅t,

(12)

where n is the number of gas moles, R is the gas constant (8.314), Ac is the cross-sectional area of the reactor vessel, T is the temperature of liquid aluminum in the reactor, and Pm is the pressure at the middle tank level. The pressure at the middle level of the tank is calculated by a function of the mean logarithmic difference.

Pm=(Pa+ρ⋅g⋅h)−Paln(Pa+ρ⋅g⋅h)Pa,

(13)

where Pa is the atmospheric pressure, and h is the the height of metal in the reactor.

Themelis and Goyal [25] developed a model for calculating mixing power delivered by gas injection.

pg=2Q⋅R⋅T⋅ln(1+m⋅ρ⋅g⋅hP),

(14)

where Q is the gas flow, and m is the mass of liquid metal.

Zhang [26] proposed a model taking into account the temperature difference between gas and alloy (metal).

pg=QRTgVm[ln(1+ρ⋅g⋅hPa)+(1−TTg)],

(15)

where Tg is the gas temperature at the entry point.

Data for calculating the mixing power resulting from inert gas injection into liquid aluminum are given below in Table 4. The design parameters were adopted for the model, the parameters of which are shown in Figure 5.

Table 4

Data for calculating mixing power introduced by an inert gas.

ParameterValueUnit
Height of metal column0.7m
Density of aluminum2375kg·m−3
Process duration20s
Gas temperature at the injection site940K
Cross-sectional area of ladle0.448m2
Mass of liquid aluminum546.25kg
Volume of ladle0.23M3
Temperature of liquid aluminum941.15K

Open in a separate window

Table 5 presents the results of mixing power calculations according to the models of Themelis and Goyal and of Zhang for inert gas flows of 10, 20, and 30 dm3·min−1. The obtained calculation results significantly differed from each other. The difference was an order of magnitude, which indicates that the model is highly inaccurate without considering the temperature of the injected gas. Moreover, the calculations apply to the case when the mixing was performed only by the flowing gas bubbles, without using a rotor, which is a great simplification of the phenomenon.

Table 5

Mixing power calculated from mathematical models.

Mathematical ModelMixing Power (W·t−1)
for a Given Inert Gas Flow (dm3·min−1)
102030
Themelis and Goyal11.4923.3335.03
Zhang0.821.662.49

Open in a separate window

The mixing time is defined as the time required to achieve 95% complete mixing of liquid metal in the ladle [27,28,29,30]. Table 6 groups together equations for the mixing time according to the models.

Table 6

Models for calculating mixing time.

AuthorsModelRemarks
Szekely [31]τ=800ε−0.4ε—W·t−1
Chiti and Paglianti [27]τ=CVQlV—volume of reactor, m3
Ql—flow intensity, m3·s−1
Iguchi and Nakamura [32]τ=1200⋅Q−0.4D1.97h−1.0υ0.47υ—kinematic viscosity, m2·s−1
D—diameter of ladle, m
h—height of metal column, m
Q—liquid flow intensity, m3·s−1

Open in a separate window

Figure 8 and Figure 9 show the mixing time as a function of gas flow rate for various heights of the liquid column in the ladle and mixing power values.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g008.jpg

Figure 8

Mixing time as a function of gas flow rate for various heights of the metal column (Iguchi and Nakamura model).

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g009.jpg

Figure 9

Mixing time as a function of mixing power (Szekly model).

3.2. Determining the Bubble Size

The mechanisms controlling bubble size and mass transfer in an alloy undergoing refining are complex. Strong mixing conditions in the reactor promote impurity mass transfer. In the case of a spinning rotor, the shear force generated by the rotor motion separates the bubbles into smaller bubbles. Rotational speed, mixing force, surface tension, and liquid density have a strong influence on the bubble size. To characterize the kinetic state of the refining process, parameters k and A were introduced. Parameters kA, and uB can be calculated using the below equations [33].

k=2D⋅uBdB⋅π−−−−−−√,

(16)

A=6Q⋅hdB⋅uB,

(17)

uB=1.02g⋅dB,−−−−−√

(18)

where D is the diffusion coefficient, and dB is the bubble diameter.

After substituting appropriate values, we get

dB=3.03×104(πD)−2/5g−1/5h4/5Q0.344N−1.48.

(19)

According to the last equation, the size of the gas bubble decreases with the increasing rotational speed (see Figure 10).

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g010.jpg

Figure 10

Effect of rotational speed on the bubble diameter.

In a flow of given turbulence intensity, the diameter of the bubble does not exceed the maximum size dmax, which is inversely proportional to the rate of kinetic energy dissipation in a viscous flow ε. The size of the gas bubble diameter as a function of the mixing energy, also considering the Weber number and the mixing energy in the negative power, can be determined from the following equations [31,34]:

  • —Sevik and Park:

dBmax=We0.6kr⋅(σ⋅103ρ⋅10−3)0.6⋅(10⋅ε)−0.4⋅10−2.

(20)

  • —Evans:

dBmax=⎡⎣Wekr⋅σ⋅1032⋅(ρ⋅10−3)13⎤⎦35 ⋅(10⋅ε)−25⋅10−2.

(21)

The results of calculating the maximum diameter of the bubble dBmax determined from Equation (21) are given in Table 7.

Table 7

The results of calculating the maximum diameter of the bubble using Equation (21).

ModelMixing Energy
ĺ (m2·s−3)
Weber Number (Wekr)
0.591.01.2
Zhang and Taniguchi
dmax
0.10.01670.02300.026
0.50.00880.01210.013
1.00.00670.00910.010
1.50.00570.00780.009
Sevik and Park
dBmax
0.10.2650.360.41
0.50.1390.190.21
1.00.1060.140.16
1.50.0900.120.14
Evans
dBmax
0.10.2470.3400.38
0.50.1300.1780.20
1.00.0980.1350.15
1.50.0840.1150.13

Open in a separate window

3.3. Physical Modeling

The first stage of experiments (using the URO-200 water model) included conducting experiments with impellers equipped with four, eight, and 12 gas outlets (variants B4, B8, B12). The tests were carried out for different process parameters. Selected results for these experiments are presented in Figure 11Figure 12Figure 13 and Figure 14.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g011.jpg

Figure 11

Impeller variant B4—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g012.jpg

Figure 12

Impeller variant B8—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g013.jpg

Figure 13

Gas bubble dispersion registered for different processing parameters (impeller variant B12).

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g014.jpg

Figure 14

Gas bubble dispersion registered for different processing parameters (impeller variant RT3).

The analysis of the refining variants presented in Figure 11Figure 12Figure 13 and Figure 14 reveals that the proposed impellers design model is not useful for the aluminum refining process. The number of gas outlet orifices, rotational speed, and flow did not affect the refining efficiency. In all the variants shown in the figures, very poor dispersion of gas bubbles was observed in the object. The gas bubble flow had a columnar character, and so-called dead zones, i.e., areas where no inert gas bubbles are present, were visible in the analyzed object. Such dead zones were located in the bottom and side zones of the ladle, while the flow of bubbles occurred near the turning rotor. Another negative phenomenon observed was a significant agitation of the water surface due to excessive (rotational) rotor speed and gas flow (see Figure 13, cases 20; 400, 30; 300, 30; 400, and 30; 500).

Research results for a ‘red triangle’ impeller equipped with three gas supply orifices (variant RT3) are presented in Figure 14.

In this impeller design, a uniform degree of bubble dispersion in the entire volume of the modeling fluid was achieved for most cases presented (see Figure 14). In all tested variants, single bubbles were observed in the area of the water surface in the vessel. For variants 20; 200, 30; 200, and 20; 300 shown in Figure 14, the bubble dispersion results were the worst as the so-called dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further applications. Interestingly, areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model. This means that the presented model had the best performance in terms of dispersion of gas bubbles in the model liquid. Its design with sharp edges also differed from previously analyzed models, which is beneficial for gas bubble dispersion, but may interfere with its suitability in industrial conditions due to possible premature wear.

3.4. Qualitative Comparison of Research Results (CFD and Physical Model)

The analysis (physical modeling) revealed that the best mixing efficiency results were obtained with the RT3 impeller variant. Therefore, numerical calculations were carried out for the impeller model with three outlet orifices (variant RT3). The CFD results are presented in Figure 15 and Figure 16.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g015.jpg

Figure 15

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 1 s: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g016.jpg

Figure 16

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 5.4 s.: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

CFD results are presented for all analyzed variants (impeller RT3) at two selected calculation timesteps of 1 and 5.40 s. They show the velocity field of the medium (water) and the dispersion of gas bubbles.

Figure 15 shows the initial refining phase after 1 s of the process. In this case, the gas bubble formation and flow were observed in an area close to contact with the rotor. Figure 16 shows the phase when the dispersion and flow of gas bubbles were advanced in the reactor area of the URO-200 model.

The quantitative evaluation of the obtained results of physical and numerical model tests was based on the comparison of the degree of gas dispersion in the model liquid. The degree of gas bubble dispersion in the volume of the model liquid and the areas of strong turbulent zones formation were evaluated during the analysis of the results of visualization and numerical simulations. These two effects sufficiently characterize the required course of the process from the physical point of view. The known scheme of the below description was adopted as a basic criterion for the evaluation of the degree of dispersion of gas bubbles in the model liquid.

  • Minimal dispersion—single bubbles ascending in the region of their formation along the ladle axis; lack of mixing in the whole bath volume.
  • Accurate dispersion—single and well-mixed bubbles ascending toward the bath mirror in the region of the ladle axis; no dispersion near the walls and in the lower part of the ladle.
  • Uniform dispersion—most desirable; very good mixing of fine bubbles with model liquid.
  • Excessive dispersion—bubbles join together to form chains; large turbulence zones; uneven flow of gas.

The numerical simulation results give a good agreement with the experiments performed with the physical model. For all studied variants (used process parameters), the single bubbles were observed in the area of water surface in the vessel. For variants presented in Figure 13 (200 rpm, gas flow 20 and dm3·min−1) and relevant examples in numerical simulation Figure 16, the worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further use. The areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model (physical model). This means that the presented impeller model had the best performance in terms of dispersion of gas bubbles in the model liquid. The worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and side walls of the vessel, which disqualifies these work parameters for further use.

Figure 17 presents exemplary results of model tests (CFD and physical model) with marked gas bubble dispersion zones. All variants of tests were analogously compared, and this comparison allowed validating the numerical model.

An external file that holds a picture, illustration, etc.
Object name is materials-15-05273-g017.jpg

Figure 17

Compilations of model research results (CFD and physical): A—single gas bubbles formed on the surface of the modeling liquid, B—excessive formation of gas chains and swirls, C—uniform distribution of gas bubbles in the entire volume of the tank, and D—dead zones without gas bubbles, no dispersion. (a) Variant B; (b) variant F.

It should be mentioned here that, in numerical simulations, it is necessary to make certain assumptions and simplifications. The calculations assumed three particle size classes (Table 2), which represent the different gas bubbles that form due to different gas flow rates. The maximum number of particles/bubbles (Table 1) generated was assumed in advance and related to the computational capabilities of the computer. Too many particles can also make it difficult to visualize and analyze the results. The size of the particles, of course, affects their behavior during simulation, while, in the figures provided in the article, the bubbles are represented by spheres (visualization of the results) of the same size. Please note that, due to the adopted Lagrangian–Eulerian approach, the simulation did not take into account phenomena such as bubble collapse or fusion. However, the obtained results allow a comprehensive analysis of the behavior of gas bubbles in the system under consideration.

The comparative analysis of the visualization (quantitative) results obtained with the water model and CFD simulations (see Figure 17) generated a sufficient agreement from the point of view of the trends. A precise quantitative evaluation is difficult to perform because of the lack of a refraction compensating system in the water model. Furthermore, in numerical simulations, it is not possible to determine the geometry of the forming gas bubbles and their interaction with each other as opposed to the visualization in the water model. The use of both research methods is complementary. Thus, a direct comparison of images obtained by the two methods requires appropriate interpretation. However, such an assessment gives the possibility to qualitatively determine the types of the present gas bubble dispersion, thus ultimately validating the CFD results with the water model.

A summary of the visualization results for impellers RT3, i.e., analysis of the occurring gas bubble dispersion types, is presented in Table 8.

Table 8

Summary of visualization results (impeller RT3)—different types of gas bubble dispersion.

No Exp.ABCDEF
Gas flow rate, dm3·min−11030
Impeller speed, rpm200300500200300500
Type of dispersionAccurateUniformUniform/excessiveMinimalExcessiveExcessive

Open in a separate window

Tests carried out for impeller RT3 confirmed the high efficiency of gas bubble distribution in the volume of the tested object at a low inert gas flow rate of 10 dm3·min−1. The most optimal variant was variant B (300 rpm, 10 dm3·min−1). However, the other variants A and C (gas flow rate 10 dm3·min−1) seemed to be favorable for this type of impeller and are recommended for further testing. The above process parameters will be analyzed in detail in a quantitative analysis to be performed on the basis of the obtained efficiency curves of the degassing process (oxygen removal). This analysis will give an unambiguous answer as to which process parameters are the most optimal for this type of impeller; the results are planned for publication in the next article.

It should also be noted here that the high agreement between the results of numerical calculations and physical modelling prompts a conclusion that the proposed approach to the simulation of a degassing process which consists of a single-phase flow model with a free surface and a particle flow model is appropriate. The simulation results enable us to understand how the velocity field in the fluid is formed and to analyze the distribution of gas bubbles in the system. The simulations in Flow-3D software can, therefore, be useful for both the design of the impeller geometry and the selection of process parameters.

Go to:

4. Conclusions

The results of experiments carried out on the physical model of the device for the simulation of barbotage refining of aluminum revealed that the worst results in terms of distribution and dispersion of gas bubbles in the studied object were obtained for the black impellers variants B4, B8, and B12 (multi-orifice impellers—four, eight, and 12 outlet holes, respectively).

In this case, the control of flow, speed, and number of gas exit orifices did not improve the process efficiency, and the developed design did not meet the criteria for industrial tests. In the case of the ‘red triangle’ impeller (variant RT3), uniform gas bubble dispersion was achieved throughout the volume of the modeling fluid for most of the tested variants. The worst bubble dispersion results due to the occurrence of the so-called dead zones in the area near the bottom and sidewalls of the vessel were obtained for the flow variants of 20 dm3·min−1 and 200 rpm and 30 dm3·min−1 and 200 rpm. For the analyzed model, areas where swirls and gas bubble chains were formed were found only for the inert gas flow of 20 and 30 dm3·min−1 and 200 rpm. The model impeller (variant RT3) had the best performance compared to the previously presented impellers in terms of dispersion of gas bubbles in the model liquid. Moreover, its design differed from previously presented models because of its sharp edges. This can be advantageous for gas bubble dispersion, but may negatively affect its suitability in industrial conditions due to premature wearing.

The CFD simulation results confirmed the results obtained from the experiments performed on the physical model. The numerical simulation of the operation of the ‘red triangle’ impeller model (using Flow-3D software) gave good agreement with the experiments performed on the physical model. This means that the presented model impeller, as compared to other (analyzed) designs, had the best performance in terms of gas bubble dispersion in the model liquid.

In further work, the developed numerical model is planned to be used for CFD simulations of the gas bubble distribution process taking into account physicochemical parameters of liquid aluminum based on industrial tests. Consequently, the obtained results may be implemented in production practice.

Go to:

Funding Statement

This paper was created with the financial support grants from the AGH-UST, Faculty of Foundry Engineering, Poland (16.16.170.654 and 11/990/BK_22/0083) for the Faculty of Materials Engineering, Silesian University of Technology, Poland.

Go to:

Author Contributions

Conceptualization, K.K. and D.K.; methodology, J.P. and T.M.; validation, M.S. and S.G.; formal analysis, D.K. and T.M.; investigation, J.P., K.K. and S.G.; resources, M.S., J.P. and K.K.; writing—original draft preparation, D.K. and T.M.; writing—review and editing, D.K. and T.M.; visualization, J.P., K.K. and S.G.; supervision, D.K.; funding acquisition, D.K. and T.M. All authors have read and agreed to the published version of the manuscript.

Go to:

Institutional Review Board Statement

Not applicable.

Go to:

Informed Consent Statement

Not applicable.

Go to:

Data Availability Statement

Data are contained within the article.

Go to:

Conflicts of Interest

The authors declare no conflict of interest.

Go to:

Footnotes

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Go to:

References

1. Zhang L., Xuewei L., Torgerson A.T., Long M. Removal of Impurity Elements from Molten Aluminium: A Review. Miner. Process. Extr. Metall. Rev. 2011;32:150–228. doi: 10.1080/08827508.2010.483396. [CrossRef] [Google Scholar]

2. Saternus M. Impurities of liquid aluminium-methods on their estimation and removal. Met. Form. 2015;23:115–132. [Google Scholar]

3. Żak P.L., Kalisz D., Lelito J., Gracz B., Szucki M., Suchy J.S. Modelling of non-metallic particle motion process in foundry alloys. Metalurgija. 2015;54:357–360. [Google Scholar]

4. Kalisz D., Kuglin K. Efficiency of aluminum oxide inclusions rmoval from liquid steel as a result of collisions and agglomeration on ceramic filters. Arch. Foundry Eng. 2020;20:43–48. [Google Scholar]

5. Kuglin K., Kalisz D. Evaluation of the usefulness of rotors for aluminium refining. IOP Conf. Ser. Mater. Sci. Eng. 2021;1178:012036. doi: 10.1088/1757-899X/1178/1/012036. [CrossRef] [Google Scholar]

6. Saternus M., Merder T. Physical modeling of the impeller construction impact o the aluminium refining process. Materials. 2022;15:575. doi: 10.3390/ma15020575. [PMC free article] [PubMed] [CrossRef] [Google Scholar]

7. Saternus M., Merder T. Physical modelling of aluminum refining process conducted in batch reactor with rotary impeller. Metals. 2018;8:726. doi: 10.3390/met8090726. [CrossRef] [Google Scholar]

8. Saternus M., Merder T., Pieprzyca J. The influence of impeller geometry on the gas bubbles dispersion in uro-200 reactor—RTD curves. Arch. Metall. Mater. 2015;60:2887–2893. doi: 10.1515/amm-2015-0461. [CrossRef] [Google Scholar]

9. Hernández-Hernández M., Camacho-Martínez J., González-Rivera C., Ramírez-Argáez M.A. Impeller design assisted by physical modeling and pilot plant trials. J. Mater. Process. Technol. 2016;236:1–8. doi: 10.1016/j.jmatprotec.2016.04.031. [CrossRef] [Google Scholar]

10. Mancilla E., Cruz-Méndez W., Garduño I.E., González-Rivera C., Ramírez-Argáez M.A., Ascanio G. Comparison of the hydrodynamic performance of rotor-injector devices in a water physical model of an aluminum degassing ladle. Chem. Eng. Res. Des. 2017;118:158–169. doi: 10.1016/j.cherd.2016.11.031. [CrossRef] [Google Scholar]

11. Michalek K., Socha L., Gryc K., Tkadleckova M., Saternus M., Pieprzyca J., Merder T. Modelling of technological parameters of aluminium melt refining in the ladle by blowing of inert gas through the rotating impeller. Arch. Metall. Mater. 2018;63:987–992. [Google Scholar]

12. Walek J., Michalek K., Tkadlecková M., Saternus M. Modelling of Technological Parameters of Aluminium Melt Refining in the Ladle by Blowing of Inert Gas through the Rotating Impeller. Metals. 2021;11:284. doi: 10.3390/met11020284. [CrossRef] [Google Scholar]

13. Michalek K., Gryc K., Moravka J. Physical modelling of bath homogenization in argon stirred ladle. Metalurgija. 2009;48:215–218. [Google Scholar]

14. Michalek K. The Use of Physical Modeling and Numerical Optimization for Metallurgical Processes. VSB; Ostrawa, Czech Republic: 2001. [Google Scholar]

15. Chen J., Zhao J. Light Metals. TMS; Warrendale, PA, USA: 1995. Bubble distribution in a melt treatment water model; pp. 1227–1231. [Google Scholar]

16. Saternus M. Model Matematyczny do Sterowania Procesem Rafinacji Ciekłych Stopów Aluminium Przy Zastosowaniu URO-200. Katowice, Poland: 2004. Research Project Nr 7 T08B 019 21. [Google Scholar]

17. Pietrewicz L., Wężyk W. Urządzenia do rafinacji gazowej typu URO-200 sześć lat produkcji i doświadczeń; Proceedings of the Aluminum Conference; Zakopane, Poland. 12–16 October 1998. [Google Scholar]

18. Flow3d User’s Guide. Flow Science, Inc.; Santa Fe, NM, USA: 2020. [Google Scholar]

19. Sinelnikov V., Szucki M., Merder T., Pieprzyca J., Kalisz D. Physical and numerical modeling of the slag splashing process. Materials. 2021;14:2289. doi: 10.3390/ma14092289. [PMC free article] [PubMed] [CrossRef] [Google Scholar]

20. White F. Fluid Mechanics. McGraw-Hill; New York, NY, USA: 2010. (McGraw-Hill Series in Mechanical Engineering). [Google Scholar]

21. Yang Z., Yang L., Cheng T., Chen F., Zheng F., Wang S., Guo Y. Fluid Flow Characteristic of EAF Molten Steel with Different Bottom-Blowing Gas Flow Rate Distributions. ISIJ. 2020;60:1957–1967. doi: 10.2355/isijinternational.ISIJINT-2019-794. [CrossRef] [Google Scholar]

22. Nichols B.D., Hirt C.W. Methods for calculating multi-dimensional, transient free surface flows past bodies; Proceedings of the First International Conference on Numerical Ship Hydrodynamics; Gaithersburg, MD, USA. 20–22 October 1975. [Google Scholar]

23. Hirt C.W., Nichols B.D. Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries. J. Comput. Phys. 1981;39:201–255. doi: 10.1016/0021-9991(81)90145-5. [CrossRef] [Google Scholar]

24. Szucki M., Suchy J.S., Lelito J., Malinowski P., Sobczyk J. Application of the lattice Boltzmann method for simulation of the mold filling process in the casting industry. Heat Mass Transf. 2017;53:3421–3431. doi: 10.1007/s00231-017-2069-5. [CrossRef] [Google Scholar]

25. Themelis N.J., Goyal P. Gas injection in steelmaking. Candian Metall. Trans. 1983;22:313–320. [Google Scholar]

26. Zhang L., Jing X., Li Y., Xu Z., Cai K. Mathematical model of decarburization of ultralow carbon steel during RH treatment. J. Univ. Sci. Technol. Beijing. 1997;4:19–23. [Google Scholar]

27. Chiti F., Paglianti A., Bujalshi W. A mechanistic model to estimate powder consumption and mixing time in aluminium industries. Chem. Eng. Res. Des. 2004;82:1105–1111. doi: 10.1205/cerd.82.9.1105.44156. [CrossRef] [Google Scholar]

28. Bouaifi M., Roustan M. Power consumption, mixing time and homogenization energy in dual-impeller agitated gas-liquid reactors. Chem. Eng. Process. 2011;40:87–95. doi: 10.1016/S0255-2701(00)00128-8. [CrossRef] [Google Scholar]

29. Kang J., Lee C.H., Haam S., Koo K.K., Kim W.S. Studies on the overall oxygen transfer rate and mixing time in pilot-scale surface aeration vessel. Environ. Technol. 2001;22:1055–1068. doi: 10.1080/09593332208618215. [PubMed] [CrossRef] [Google Scholar]

30. Moucha T., Linek V., Prokopov E. Gas hold-up, mixing time and gas-liquid volumetric mass transfer coefficient of various multiple-impeller configurations: Rushton turbine, pitched blade and techmix impeller and their combinations. Chem. Eng. Sci. 2003;58:1839–1846. doi: 10.1016/S0009-2509(02)00682-6. [CrossRef] [Google Scholar]

31. Szekely J. Flow phenomena, mixing and mass transfer in argon-stirred ladles. Ironmak. Steelmak. 1979;6:285–293. [Google Scholar]

32. Iguchi M., Nakamura K., Tsujino R. Mixing time and fluid flow phenomena in liquids of varying kinematic viscosities agitated by bottom gas injection. Metall. Mat. Trans. 1998;29:569–575. doi: 10.1007/s11663-998-0091-1. [CrossRef] [Google Scholar]

33. Hjelle O., Engh T.A., Rasch B. Removal of Sodium from Aluminiummagnesium Alloys by Purging with Cl2. Aluminium-Verlag GmbH; Dusseldorf, Germany: 1985. pp. 343–360. [Google Scholar]

34. Zhang L., Taniguchi S. Fundamentals of inclusion removal from liquid steel by bubble flotation. Int. Mat. Rev. 2000;45:59–82. doi: 10.1179/095066000101528313. [CrossRef] [Google Scholar]

Figure 4.24 - Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling

Optimization of filling systems for low pressure by Flow-3D

Dissertação de Mestrado
Ciclo de Estudos Integrados Conducentes ao
Grau de Mestre em Engenharia Mecânica
Trabalho efectuado sob a orientação do
Doutor Hélder de Jesus Fernades Puga
Professor Doutor José Joaquim Carneiro Barbosa

ABSTRACT

논문의 일부로 튜터 선택 가능성과 해결해야 할 주제가 설정되는 매개변수를 염두에 두고 개발 주제 ‘Flow- 3D ®에 의한 저압 충전 시스템 최적화’가 선택되었습니다. 이를 위해서는 달성해야 할 목표와 이를 달성하기 위한 방법을 정의하는 것이 필요했습니다.

충전 시스템을 시뮬레이션하고 검증할 수 있는 광범위한 소프트웨어에도 불구하고 Flow-3D®는 시장에서 최고의 도구 중 하나로 표시되어 전체 충전 프로세스 및 행동 표현과 관련하여 탁월한 정확도로 시뮬레이션하는 능력을 입증했습니다.

이를 위해 관련 프로세스를 더 잘 이해하고 충진 시스템 시뮬레이션을 위한 탐색적 기반 역할을 하기 위해 이 도구를 탐색하는 것이 중요합니다. 지연 및 재료 낭비에 반영되는 실제적인 측면에서 충전 장치의 치수를 완벽하게 만드는 비용 및 시간 낭비. 이러한 방식으로 저압 주조 공정에서 충진 시스템을 설계하고 물리적 모델을 탐색하여 특성화하는 방법론을 검증하기 위한 것입니다.

이를 위해 다음 주요 단계를 고려하십시오.

시뮬레이션 소프트웨어 Flow 3D® 탐색;
충전 시스템 모델링;
모델의 매개변수를 탐색하여 모델링된 시스템의 시뮬레이션, 검증 및 최적화.

따라서 연구 중인 압력 곡선과 주조 분석에서 가장 관련성이 높은 정보의 최종 마이닝을 검증하기 위한 것입니다.

사용된 압력 곡선은 수집된 문헌과 이전에 수행된 실제 작업을 통해 얻었습니다. 결과를 통해 3단계 압력 곡선이 층류 충진 체계의 의도된 목적과 관련 속도가 0.5 𝑚/𝑠를 초과하지 않는다는 결론을 내릴 수 있었습니다.

충전 수준이 2인 압력 곡선은 0.5 𝑚/𝑠 이상의 속도로 영역을 채우는 더 난류 시스템을 갖습니다. 열전달 매개변수는 이전에 얻은 값이 주물에 대한 소산 거동을 확증하지 않았기 때문에 연구되었습니다.

이러한 방식으로 주조 공정에 더 부합하는 새로운 가치를 얻었습니다. 달성된 결과는 유사한 것으로 나타난 NovaFlow & Solid®에 의해 생성된 결과와 비교되어 시뮬레이션에서 설정된 매개변수를 검증했습니다. Flow 3D®는 주조 부품 시뮬레이션을 위한 강력한 도구로 입증되었습니다.

As part of the dissertation and bearing in mind the parameters in which the possibility of a choice of tutor and the subject to be addressed is established, the subject for development ’Optimization of filling systems for low pressure by Flow 3D ®’ was chosen. For this it was necessary to define the objectives to achieve and the methods to attain them. Despite the wide range of software able to simulate and validate filling systems, Flow 3D® has been shown as one of the best tools in the market, demonstrating its ability to simulate with distinctive accuracy with respect to the entire process of filling and the behavioral representation of the fluid obtained. To this end, it is important to explore this tool for a better understanding of the processes involved and to serve as an exploratory basis for the simulation of filling systems, simulation being one of the great strengths of the current industry due to the need to reduce costs and time waste, in practical terms, that lead to the perfecting of the dimensioning of filling devices, which are reflected in delays and wasted material. In this way it is intended to validate the methodology to design a filling system in lowpressure casting process, exploring their physical models and thus allowing for its characterization. For this, consider the following main phases: The exploration of the simulation software Flow 3D®; modeling of filling systems; simulation, validation and optimization of systems modeled by exploring the parameters of the models. Therefore, it is intended to validate the pressure curves under study and the eventual mining of the most relevant information in a casting analysis. The pressure curves that were used were obtained through the gathered literature and the practical work previously performed. Through the results it was possible to conclude that the pressure curve with 3 levels meets the intended purpose of a laminar filling regime and associated speeds never exceeding 0.5 𝑚/𝑠. The pressure curve with 2 filling levels has a more turbulent system, having filling areas with velocities above 0.5 𝑚/𝑠. The heat transfer parameter was studied due to the values previously obtained didn’t corroborate the behavior of dissipation regarding to the casting. In this way, new values, more in tune with the casting process, were obtained. The achieved results were compared with those generated by NovaFlow & Solid®, which were shown to be similar, validating the parameters established in the simulations. Flow 3D® was proven a powerful tool for the simulation of casting parts.

키워드

저압, Flow 3D®, 시뮬레이션, 파운드리, 압력-시간 관계,Low Pressure, Flow 3D®, Simulation, Foundry, Pressure-time relation

Figure 4.24 - Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling
Figure 4.24 – Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling
Figure 4.39 - Values of temperature contours using full energy heat transfer parameter for simula
Figure 4.39 – Values of temperature contours using full energy heat transfer parameter for simula
Figure 4.40 – Comparison between software simulations (a) Flow 3D® simulation,
(b) NovaFlow & Solid® simulation
Figure 4.40 – Comparison between software simulations (a) Flow 3D® simulation, (b) NovaFlow & Solid® simulation

BIBLIOGRAPHY

[1] E. Stanley and D. B. Sc, “Fluid Flow Aspects of Solidification Modelling : Simulation
of Low Pressure Die Casting .”
[2] Y. Sahin, “Computer aided foundry die-design,” Metallography, vol. 24, no. 8, pp.
671–679, 2003.
[3] F. Bonollo, J. Urban, B. Bonatto, and M. Botter, “Gravity and low pressure die casting
of aluminium alloys : a technical and economical benchmark,” La Metall. Ital., vol. 97,
no. 6, pp. 23–32, 2005.
[4] P. a and R. R, “Study of the effect of process parameters on the production of a nonsimmetric low pressure die casting part,” La Metall. Ital., pp. 57–63, 2009.
[5] “Fundição em baixa pressão | Aluinfo.” [Online]. Available:
http://www.aluinfo.com.br/novo/materiais/fundicao-em-baixa-pressao. [Accessed: 18-
Sep-2015].
[6] “Low Pressure Sand Casting by Wolverine Bronze.” [Online]. Available:
http://www.wolverinebronze.com/low-pressure-sand-casting.php. [Accessed: 18-Sep2015].
[7] A. Reikher, “Numerical Analysis of Die-Casting Process in Thin Cavities Using
Lubrication Approximation,” no. December, 2012.
[8] P. Fu, A. a. Luo, H. Jiang, L. Peng, Y. Yu, C. Zhai, and A. K. Sachdev, “Low-pressure
die casting of magnesium alloy AM50: Response to process parameters,” J. Mater.
Process. Technol., vol. 205, no. 1–3, pp. 224–234, 2008.
[9] X. Li, Q. Hao, W. Jie, and Y. Zhou, “Development of pressure control system in
counter gravity casting for large thin-walled A357 aluminum alloy components,”
Trans. Nonferrous Met. Soc. China, vol. 18, no. 4, pp. 847–851, 2008.
[10] J. a. Hines, “Determination of interfacial heat-transfer boundary conditions in an
aluminum low-pressure permanent mold test casting,” Metall. Mater. Trans. B, vol. 35,
no. 2, pp. 299–311, 2004.
[11] A. Lima, A. Freitas, and P. Magalhães, “Processos de vazamento em moldações
permanentes,” pp. 40–49, 2003.
[12] Y. B. Choi, K. Matsugi, G. Sasaki, K. Arita, and O. Yanagisawa, “Analysis of
Manufacturing Processes for Metal Fiber Reinforced Aluminum Alloy Composite
Fabricated by Low-Pressure Casting,” Mater. Trans., vol. 47, no. 4, pp. 1227–1231,
68
2006.
[13] G. Mi, X. Liu, K. Wang, and H. Fu, “Numerical simulation of low pressure die-casting
aluminum wheel,” China Foundry, vol. 6, no. 1, pp. 48–52, 2009.
[14] J. Kuo, F. Hsu, and W. Hwang, “ADVANCED Development of an interactive
simulation system for the determination of the pressure ± time relationship during the
® lling in a low pressure casting process,” vol. 2, pp. 131–145, 2001.
[15] S.-G. Liu, F.-Y. Cao, X.-Y. Zhao, Y.-D. Jia, Z.-L. Ning, and J.-F. Sun, “Characteristics
of mold filling and entrainment of oxide film in low pressure casting of A356 alloy,”
Mater. Sci. Eng. A, vol. 626, pp. 159–164, 2015.
[16] “Casting Training Class – Lecture 10 – Solidification and Shrinkage-Casting.” FLOW3D®.
[17] “UAB Casting Engineering Laboratory.” [Online]. Available:
file:///C:/Users/Jos%C3%A9 Belo/Desktop/Artigo_Software/UAB Casting
Engineering Laboratory.htm. [Accessed: 09-Nov-2015].
[18] A. Louvo, “Casting Simulation as a Tool in Concurrent Engineering,” pp. 1–12, 1997.
[19] T. R. Vijayaram and P. Piccardo, “Computers in Foundries,” vol. 30, 2012.
[20] M. Sadaiah, D. R. Yadav, P. V. Mohanram, and P. Radhakrishnan, “A generative
computer-aided process planning system for prismatic components,” Int. J. Adv.
Manuf. Technol., vol. 20, no. 10, pp. 709–719, 2002.
[21] Ministry_of_Planning, “Digital Data,” vol. 67, pp. 1–6, 2004.
[22] S. Shamasundar, D. Ramachandran, and N. S. Shrinivasan, “COMPUTER
SIMULATION AND ANALYSIS OF INVESTMENTCASTING PROCESS.”
[23] J. M. Siqueira and G. Motors, “Simulation applied to Aluminum High Pressure Die
Casting,” pp. 1–5, 1998.
[24] C. Fluid, COMPUTATIONAL FLUID DYNAMICS. Abdulnaser Sayma & Ventus
Publishing ApS, 2009.
[25] C. a. Felippa, “1 – Overview,” Adv. Finite Elem. Methods, pp. 1–9.
[26] a. Meena and M. El Mansori, “Correlative thermal methodology for castability
simulation of ductile iron in ADI production,” J. Mater. Process. Technol., vol. 212,
no. 11, pp. 2484–2495, 2012.
[27] T. R. Vijayaram, S. Sulaiman, a. M. S. Hamouda, and M. H. M. Ahmad, “Numerical
simulation of casting solidification in permanent metallic molds,” J. Mater. Process.
69
Technol., vol. 178, pp. 29–33, 2006.
[28] “General CFD FAQ — CFD-Wiki, the free CFD reference.” [Online]. Available:
http://www.cfd-online.com/Wiki/General_CFD_FAQ. [Accessed: 10-Nov-2015].
[29] “FEM | FEA | CFD.” [Online]. Available: http://fem4analyze.blogspot.pt/. [Accessed:
09-Nov-2015].
[30] “Fundição; revista da Associação portuguesa de fundição,” Fundição, vol. N
o
227.
[31] “Casting Training Class – Lecture 1 – Introduction_to_FLOW-3D – Casting.” FLOW3D®.
[32] F. Science, “FLOW-3D Cast Documentation,” no. 3.5, p. 80, 2012.
[33] “Casting Training Class – Lecture 4 – Geometry Building – General.” FLOW-3D®.
[34] F. Science, “FLOW-3D v11.0.3 User Manual,” pp. 1–132, 2015.
[35] “Casting Training Class – Lecture 5 Meshing Concept – General.” FLOW-3D®.
[36] “Casting Training Class – Lecture 6 – Boundary_Conditions – Casting.” FLOW-3D®.
[37] “Casting Training Class – Lecture 9 – Physical Models-castings.” FLOW-3D®.
[38] P. A. D. Jácome, M. C. Landim, A. Garcia, A. F. Furtado, and I. L. Ferreira, “The
application of computational thermodynamics and a numerical model for the
determination of surface tension and Gibbs–Thomson coefficient of aluminum based
alloys,” Thermochim. Acta, vol. 523, no. 1–2, pp. 142–149, 2011.
[39] J. P. Anson, R. A. L. Drew, and J. E. Gruzleski, “The surface tension of molten
aluminum and Al-Si-Mg alloy under vacuum and hydrogen atmospheres,” Metall.
Mater. Trans. B Process Metall. Mater. Process. Sci., vol. 30, no. 6, pp. XVI–1032,
1999.

Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.

Numerical modelling of air-water flows in sewer drops

하수구 방울의 공기-물 흐름 수치 모델링

Paula Beceiro (corresponding author)
Maria do Céu Almeida
Hydraulic and Environment Department (DHA), National Laboratory for Civil Engineering, Avenida do Brasil 101, 1700-066 Lisbon, Portugal
E-mail: pbeceiro@lnec.pt
Jorge Matos
Department of Civil Engineering, Arquitecture and Geosources,
Technical University of Lisbon (IST), Avenida Rovisco Pais 1, 1049-001 Lisbon, Portugal

ABSTRACT

물 흐름에 용존 산소(DO)의 존재는 해로운 영향의 발생을 방지하는 데 유익한 것으로 인식되는 호기성 조건을 보장하는 중요한 요소입니다.

하수도 시스템에서 흐르는 폐수에 DO를 통합하는 것은 공기-액체 경계면 또는 방울이나 접합부와 같은 특이점의 존재로 인해 혼입된 공기를 통한 연속 재방출의 영향을 정량화하기 위해 광범위하게 조사된 프로세스입니다. 공기 혼입 및 후속 환기를 향상시키기 위한 하수구 드롭의 위치는 하수구의 호기성 조건을 촉진하는 효과적인 방법입니다.

본 논문에서는 수직 낙하, 배경 및 계단식 낙하를 CFD(전산유체역학) 코드 FLOW-3D®를 사용하여 모델링하여 이러한 유형의 구조물의 존재로 인해 발생하는 난류로 인한 공기-물 흐름을 평가했습니다. 이용 가능한 실험적 연구에 기초한 수력학적 변수의 평가와 공기 혼입의 분석이 수행되었습니다.

이러한 구조물에 대한 CFD 모델의 결과는 Soares(2003), Afonso(2004) 및 Azevedo(2006)가 개발한 해당 물리적 모델에서 얻은 방류, 압력 헤드 및 수심의 측정을 사용하여 검증되었습니다.

유압 거동에 대해 매우 잘 맞았습니다. 수치 모델을 검증한 후 공기 연행 분석을 수행했습니다.

The presence of dissolved oxygen (DO) in water flows is an important factor to ensure the aerobic conditions recognised as beneficial to prevent the occurrence of detrimental effects. The incorporation of DO in wastewater flowing in sewer systems is a process widely investigated in order to quantify the effect of continuous reaeration through the air-liquid interface or air entrained due the presence of singularities such as drops or junctions. The location of sewer drops to enhance air entrainment and subsequently reaeration is an effective practice to promote aerobic conditions in sewers. In the present paper, vertical drops, backdrops and stepped drop was modelled using the computational fluid dynamics (CFD) code FLOW-3D® to evaluate the air-water flows due to the turbulence induced by the presence of this type of structures. The assessment of the hydraulic variables and an analysis of the air entrainment based in the available experimental studies were carried out. The results of the CFD models for these structures were validated using measurements of discharge, pressure head and water depth obtained in the corresponding physical models developed by Soares (2003), Afonso (2004) and Azevedo (2006). A very good fit was obtained for the hydraulic behaviour. After validation of numerical models, analysis of the air entrainment was carried out.

Key words | air entrainment, computational fluid dynamics (CFD), sewer drops

Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.
Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.
Figure 3. Comparison between the experimental and numerical pressure head along of the invert of the outlet pipe.
Figure 3. Comparison between the experimental and numerical pressure head along of the invert of the outlet pipe.
Figure 4. Average void fraction along the longitudinal axis of the outlet pipe for the lower discharges in the vertical drop and backdrop.
Figure 4. Average void fraction along the longitudinal axis of the outlet pipe for the lower discharges in the vertical drop and backdrop.

REFERENCES

Afonso, J. Dissipação de energia e rearejamento em quedas em colectores. M.Sc. Thesis, UTL/IST, Lisboa, Portugal.
Almeida, M. C., Butler, D. & Matos, J. S. Reaeration by sewer drops. In: 8th Int. Conf. on Urban Storm Drainage, Sydney, Australia.
Azevedo, R. I. Transferência de oxigénio em quedas guiadas em colectores. M.Sc. Thesis, IST, Lisboa, Portugal.
Beceiro, P., Almeida, M. C. & Matos, J. Numerical Modelling of air-water flows in a vertical drop and a backdrop. In: 3rd IAHR Europe Congress, Porto, Portugal.
Bombardelli, F. A., Meireles, I. & Matos, J. S. Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of step stepped spillways. Environ. Fluid Mech. 11 (3), 263–288.
Brethour, J. M. & Hirt, C. W. Drift Model for TwoComponent Flows. Flow Science, Inc., Los Alamos, NM, USA.
Chamani, M. R. Jet Flow on Stepped Spillways and Drops. M.Sc. Thesis, University of Alberta, Alberta, Canada.
Chanson, H. Air Bubble Entrainment in Free-Surface Turbulent Shear Flow. Academic Press Inc., California, USA.
Chanson, H. Air bubble entrainment in open channels: flow structure and bubble size distribution. Int. J. Multiphase 23 (1), 193–203.
Chanson, H. Hydraulics of aerated flows: qui pro quo? Journal of Hydraulic Research 51 (3), 223–243.
Dufresne, M., Vazques, J., Terfous, A., Ghenaim, A. & Poulet, J. Experimental investigation and CFD modelling of flow, sedimentation, and solids separation in a combined sewer detention tank. Computer and Fluids 38, 1042–1049.
Durve, A. P. & Patwardhan, A. W. Numerical and experimental investigation of onset of gas entrainment phenomenon. Chemical Engineering Science 73, 140–150.
Felder, S. & Chanson, H. Air–water flows and free-surface profiles on a non-uniform stepped chute. Journal of Hydraulic Research 52 (2), 253–263.
Flow Science FLOW-3D User’s Manuals Version 10.0. Vol.1/2. Flow Science Inc., Los Alamos, NM, USA.
Granata, F., Marinis, G., Gargano, R. & Hager, W. H. Energy loss in circular drop manholes. In: 33rd IAHR Congress: Water Engineering for Sustainable Environment, British
Columbia, Vancouver, Canada. Hirt, C. W. Modeling Turbulent Entrainment of air at A Free Surface. Flow Science Inc., Los Alamos, NM, USA.
Hirt, C. W. & Nichols, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39, 201–225.
Hirt, C. W. & Sicilian, J. M. A porosity technique for the definition of obstacles in rectangular cell meshes. In: Proc. 4th Int, Conf. Ship Hydro., National Academy of Science, Washington, DC, USA.
Isfahani, A. H. G. & Brethour, J. On the Implementation of Two-Equation Turbulence Models in FLOW-3D. Flow Science Inc., Los Alamos, NM, USA.
Kouyi, G. L., Bret, P., Didier, J. M., Chocat, B. & Billat, C. The use of CFD modelling to optimise measurement of overflow rates in a downstream-controlled dual-overflow structure. Water Science and Technology 64 (2), 521–527.
Lopes, P., Leandro, J., Carvalho, R. F., Páscoa, P. & Martins, R. Numerical and experimental investigation of a gully under surcharge conditions. Urban Water Journal 12 (6), 468–476.
Martins, R., Leandro, J. & Carvalho, R. F. Characterization of the hydraulic performance of a gully under drainage conditions. Water Science and Technology 69 (12), 2423–2430.
Matias, N., Nielsel, A. H., Vollertsen, J., Ferreira, F. & Matos, J. S. Reaeration and hydrogen sulfide release at drop structures. In: 8th International Conference on Sewer Processes and Networks (SPN8), Rotterdam, Netherlands.
Matos, J. S. & Sousa, E. R. Prediction of dissolved oxygen concentration along sanitary sewers. Water Science and Technology 34 (5–6), 525–532.
Mignot, E., Bonakdari, H., Knothe, P., Lipeme Kouyi, G., Bessette, A., Rivière, N. & Bertrand-Krajewski, J. L. Experiments and 3D simulations of flow structures in junctions and of their influence on location of flowmeters. In: 12th International Conference on Urban Drainage, Porto Alegre, Brazil.
Ozmen-Cagatay, H. & Kocaman, S. Dam-break flow in the presence of obstacle: experiment and CFD Simulation. Engineering Applications of Computational Fluid Mechanics 5 (4), 541–552.
Shojaee Fard, M. H. & Boyaghchi, F. A. Studies of the influence of various blade outlet angles in a centrifugal pump when handling viscous fluids. American Journal of Applied Sciences 4 (9), 718–724.
Soares, A. Rearejamento em Quedas em Colectores de Águas Residuais. M.Sc. Thesis, FCTUC, Coimbra, Portugal.
Sousa, C. M. & Lopes, R. R. Hidráulica e rearejamento em quedas verticais em colectores. Estudo Experimental. Research Report, UTL/IST, Lisboa, Portugal.
Sousa, V., Meireles, I., Matos, J. & Almeida, M. C. Numerical modelling of air-water flow in a vertical drop manhole. In: 7th International Conference on Sewer Processes and Networks (SPN7), Shefield, UK.
Stovin, V., Guymer, I. & Lau, S. D. Approaches to validating a 3D CFD manhole model. In: 11th International Conference on Urban Drainage, Edinburgh, Scotland, UK.
Tota, P. V. Turbulent Flow Over A Backward-Facing Step Using the RNG Model. Flow Science Inc., Los Alamos, NM, USA.
Valero, D. & García-Bartual, R. Calibration of an air entrainment model for CFD spillway applications. In: Advances in Hydroinformatics. Springer, Singapore, pp. 571–582.
Versteeg, H. K. & Malalasekera, W. An Introduction to Computational Fluid Dynamics. The Finite Volume Method. Longman Group limited, England.
Yang, Y., Yang, J., Zuo, J., Li, Y., He, S., Yang, X. & Zhang, K. Study on two operating conditions of a full-scale oxidation ditch for optimization of energy consumption and effluent quality by using CFD model. Water Research 45 (11), 3439–3452.
Zhai, A. J., Zhang, Z., Zhang, W. & Chen, Q. Y. Evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by CFD: part 1— summary of prevalent Turbulence models. HVAC&R Research 13 (6), 853–870.
Zhao, C., Zhu, D. Z. & Rajaratnam, N. Computational and experimental study of surcharged flow at a 90W combining sewer junction. Journal of Hydraulic Engineering 134 (6), 688–700.

Development of macro-defect-free PBF-EB-processed Ti–6Al–4V alloys with superior plasticity using PREP-synthesized powder and machine learning-assisted process optimization

Development of macro-defect-free PBF-EB-processed Ti–6Al–4V alloys with superior plasticity using PREP-synthesized powder and machine learning-assisted process optimization

Yunwei GuiabKenta Aoyagib Akihiko Chibab
aDepartment of Materials Processing, Graduate School of Engineering, Tohoku University, 6-6 Aramaki Aza Aoba, Aoba-ku, Sendai, 980-8579, Japan
bInstitute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

Received 14 October 2022, Revised 23 December 2022, Accepted 3 January 2023, Available online 5 January 2023.Show lessAdd to MendeleyShareCite

https://doi.org/10.1016/j.msea.2023.144595Get rights and content

Abstract

The elimination of internal macro-defects is a key issue in Ti–6Al–4V alloys fabricated via powder bed fusion using electron beams (PBF-EB), wherein internal macro-defects mainly originate from the virgin powder and inappropriate printing parameters. This study compares different types powders by combining support vector machine techniques to determine the most suitable powder for PBF-EB and to predict the processing window for the printing parameters without internal macro-defects. The results show that powders fabricated via plasma rotating electrode process have the best sphericity, flowability, and minimal porosity and are most suitable for printing. Surface roughness criterion was also applied to determine the quality of the even surfaces, and support vector machine was used to construct processing maps capable of predicting a wide range of four-dimensional printing parameters to obtain macro-defect-free samples, offering the possibility of subsequent development of Ti–6Al–4V alloys with excellent properties. The macro-defect-free samples exhibited good elongation, with the best overall mechanical properties being the ultimate tensile strength and elongation of 934.7 MPa and 24.3%, respectively. The elongation of the three macro-defect-free samples was much higher than that previously reported for additively manufactured Ti–6Al–4V alloys. The high elongation of the samples in this work is mainly attributed to the elimination of internal macro-defects.

Introduction

Additive manufacturing (AM) technologies can rapidly manufacture complex or custom parts, reducing process steps and saving manufacturing time [[1], [2], [3], [4]], and are widely used in the aerospace, automotive, and other precision industries [5,6]. Powder bed fusion using an electron beam (PBF-EB) is an additive manufacturing method that uses a high-energy electron beam to melt metal powders layer by layer to produce parts. In contrast to selective laser melting, PBF-EB involves the preparation of samples in a high vacuum environment, which effectively prevents the introduction of impurities such as O and N. It also involves a preheating process for the print substrate and powder, which reduces residual thermal stress on the sample and subsequent heat treatment processes [[2], [3], [4],7]. Due to these features and advantages, PBF-EB technology is a very important AM technology with great potential in metallic materials. Moreover, PBF-EB is the ideal AM technology for the manufacture of complex components made of many alloys, such as titanium alloys, nickel-based superalloys, aluminum alloys and stainless steels [[2], [3], [4],8].

Ti–6Al–4V alloy is one of the prevalent commercial titanium alloys possessing high specific strength, excellent mechanical properties, excellent corrosion resistance, and good biocompatibility [9,10]. It is widely used in applications requiring low density and excellent corrosion resistance, such as the aerospace industry and biomechanical applications [11,12]. The mechanical properties of PBF-EB-processed Ti–6Al–4V alloys are superior to those fabricated by casting or forging, because the rapid cooling rate in PBF-EB results in finer grains [[12], [13], [14], [15], [16], [17], [18]]. However, the PBF-EB-fabricated parts often include internal macro-defects, which compromises their mechanical properties [[19], [20], [21], [22]]. This study focused on the elimination of macro-defects, such as porosity, lack of fusion, incomplete penetration and unmelted powders, which distinguishes them from micro-defects such as vacancies, dislocations, grain boundaries and secondary phases, etc. Large-sized fusion defects cause a severe reduction in mechanical strength. Smaller defects, such as pores and cracks, lead to the initiation of fatigue cracking and rapidly accelerate the cracking process [23]. The issue of internal macro-defects must be addressed to expand the application of the PBF-EB technology. The main studies for controlling internal macro-defects are online monitoring of defects, remelting and hot isostatic pressing (HIP). The literatures [24,25] report the use of infrared imaging or other imaging techniques to identify defects, but the monitoring of smaller sized defects is still not adequate. And in some cases remelting does not reduce the internal macro-defects of the part, but instead causes coarsening of the macrostructure and volatilization of some metal elements [23]. The HIP treatment does not completely eliminate the internal macro-defects, the original defect location may still act as a point of origin of the crack, and the subsequent treatment will consume more time and economic costs [23]. Therefore, optimizing suitable printing parameters to avoid internal macro-defects in printed parts at source is of great industrial value and research significance, and is an urgent issue in PBF-EB related technology.

There are two causes of internal macro-defects in the AM process: gas pores trapped in the virgin powder and the inappropriate printing parameters [7,23]. Gui et al. [26] classify internal macro-defects during PBF-EB process according to their shape, such as spherical defects, elongated shape defects, flat shape defects and other irregular shape defects. Of these, spherical defects mainly originate from raw material powders. Other shape defects mainly originate from lack of fusion or unmelted powders caused by unsuitable printing parameters, etc. The PBF-EB process requires powders with good flowability, and spherical powders are typically chosen as raw materials. The prevalent techniques for the fabrication of pre-alloyed powders are gas atomization (GA), plasma atomization (PA), and the plasma rotating electrode process (PREP) [27,28]. These methods yield powders with different characteristics that affect the subsequent fabrication. The selection of a suitable powder for PBF-EB is particularly important to produce Ti–6Al–4V alloys without internal macro-defects. The need to optimize several printing parameters such as beam current, scan speed, line offset, and focus offset make it difficult to eliminate internal macro-defects that occur during printing [23]. Most of the studies [11,12,22,[29], [30], [31], [32], [33]] on the optimization of AM processes for Ti–6Al–4V alloys have focused on samples with a limited set of parameters (e.g., power–scan speed) and do not allow for the guidance and development of unknown process windows for macro-defect-free samples. In addition, process optimization remains a time-consuming problem, with the traditional ‘trial and error’ method demanding considerable time and economic costs. The development of a simple and efficient method to predict the processing window for alloys without internal macro-defects is a key issue. In recent years, machine learning techniques have increasingly been used in the field of additive manufacturing and materials development [[34], [35], [36], [37]]. Aoyagi et al. [38] recently proposed a novel and efficient method based on a support vector machine (SVM) to optimize the two-dimensional process parameters (current and scan speed) and obtain PBF-EB-processed CoCr alloys without internal macro-defects. The method is one of the potential approaches toward effective optimization of more than two process parameters and makes it possible for the machine learning techniques to accelerate the development of alloys without internal macro-defects.

Herein, we focus on the elimination of internal macro-defects, such as pores, lack of fusion, etc., caused by raw powders and printing parameters. The Ti–6Al–4V powders produced by three different methods were compared, and the powder with the best sphericity, flowability, and minimal porosity was selected as the feedstock for subsequent printing. The relationship between the surface roughness and internal macro-defects in the Ti–6Al–4V components was also investigated. The combination of SVM and surface roughness indices (Sdr) predicted a wider four-dimensional processing window for obtaining Ti–6Al–4V alloys without internal macro-defects. Finally, we investigated the tensile properties of Ti–6Al–4V alloys at room temperature with different printing parameters, as well as the corresponding microstructures and fracture types.

Section snippets

Starting materials

Three types of Ti–6Al–4V alloy powders, produced by GA, PA, and PREP, were compared. The particle size distribution of the powders was determined using a laser particle size analyzer (LS230, Beckman Coulter, USA), and the flowability was measured using a Hall flowmeter (JIS-Z2502, Tsutsui Scientific Instruments Co., Ltd., Japan), according to the ASTM B213 standard. The powder morphology and internal macro-defects were determined using scanning electron microscopy (SEM, JEOL JCM-6000) and X-ray 

Comparison of the characteristics of GA, PA, and PREP Ti–6Al–4V powders

The particle size distributions (PSDs) and flowability of the three types of Ti–6Al–4V alloy powders produced by GA, PA, and PREP are shown in Fig. 2. Although the average particle sizes are similar (89.4 μm for GA, 82.5 μm for PA, and 86.1μm for PREP), the particle size range is different for the three types of powder (6.2–174.8 μm for GA, 27.3–139.2 μm for PA, and 39.4–133.9 μm for PREP). The flowability of the GA, PA, and PREP powders was 30.25 ± 0.98, 26.54 ± 0.37, and 25.03 ± 0.22 (s/50

Conclusions

The characteristics of the three types of Ti–6Al–4V alloy powders produced via GA, PA, and PREP were compared. The PREP powder with the best sphericity, flowability, and low porosity was found to be the most favorable powder for subsequent printing of Ti–6Al–4V alloys without internal macro-defects. The quantitative criterion of Sdr <0.015 for even surfaces was also found to be applicable to Ti–6Al–4V alloys. The process maps of Ti–6Al–4V alloys include two regions, high beam current/scan speed 

Uncited references

[55]; [56]; [57]; [58]; [59]; [60]; [61]; [62]; [63]; [64]; [65].

CRediT authorship contribution statement

Yunwei Gui: Writing – original draft, Visualization, Validation, Investigation. Kenta Aoyagi: Writing – review & editing, Supervision, Resources, Methodology, Funding acquisition, Conceptualization. Akihiko Chiba: Supervision, Funding acquisition.

Declaration of competing interest

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

Acknowledgments

This study was based on the results obtained from project JPNP19007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO). This work was also supported by JSPS KAKENHI (Proposal No. 21K03801) and the Inter-University Cooperative Research Program (Proposal nos. 18G0418, 19G0411, and 20G0418) of the Cooperative Research and Development Center for Advanced Materials, Institute for Materials Research, Tohoku University. It was also supported by the Council for

References (65)

View more references

Cited by (0)

Recommended articles (6)

Figure 2. Different PKW Types.

A review of Piano Key Weir as a superior alternative for dam rehabilitation

댐 복구를 위한 우수한 대안으로서의 Piano Key Weir에 대한 검토

Amiya Abhash &

K. K. Pandey

Pages 541-551 | Received 03 Mar 2020, Accepted 07 May 2020, Published online: 21 May 2020

ABSTRACT

Dams fall in ‘installations containing dangerous forces’ because of their massive impact on the environment and civilian life and property as per International humanitarian law. As such, it becomes vital for hydraulic engineers to refurbish various solutions for dam rehabilitation. This paper presents a review of a new type of weir installation called Piano Key Weir (PKW), which is becoming popular around the world for its higher spillway capacity both for existing and new dam spillway installations. This paper reviews the geometry along with structural integrity, discharging capacity, economic aspects, aeration requirements, sediment transport and erosion aspects of Piano Key Weir (PKW) as compared with other traditional spillway structures and alternatives from literature. The comparison with other alternatives shows PKW to be an excellent alternative for dam risk mitigation owing to its high spillway capabilities and economy, along with its use in both existing and new hydraulic structures.

댐은 국제 인도법에 따라 환경과 민간인 생활 및 재산에 막대한 영향을 미치기 때문에 ‘위험한 힘을 포함하는 시설물’에 속합니다. 따라서 유압 엔지니어는 댐 복구를 위한 다양한 솔루션을 재정비해야 합니다.

이 백서에서는 PKW(Piano Key Weir)라는 새로운 유형의 둑 설치에 대한 검토를 제공합니다. PKW는 기존 및 신규 댐 방수로 설치 모두에서 더 높은 방수로 용량으로 전 세계적으로 인기를 얻고 있습니다.

이 백서에서는 구조적 무결성, 배출 용량, 경제적 측면, 폭기 요구 사항, 퇴적물 운반 및 PKW(Piano Key Weir)의 침식 측면과 함께 다른 전통적인 여수로 구조 및 문헌의 대안과 비교하여 기하학을 검토합니다.

다른 대안과의 비교는 PKW가 높은 여수로 기능과 경제성으로 인해 댐 위험 완화를 위한 탁월한 대안이며 기존 및 새로운 수력 구조물 모두에 사용됨을 보여줍니다.

KEYWORDS: 

Figure 2. Different PKW Types.
Figure 2. Different PKW Types.

References

  • Anderson, R., and Tullis, B. (2011). Influence of Piano Key Weir geometry on discharge. Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B. Liège, Belgium. [Crossref][Google Scholar]
  • Anderson, R., and Tullis, B. (2012a). “Piano key weir hydraulics and labyrinth weir comparison”. J. Irrig. Drain. Eng., 139(3), 246–253. doi:https://doi.org/10.1061/(ASCE)IR.1943-4774.0000530 [Crossref][Web of Science ®][Google Scholar]
  • Anderson, R., and Tullis, B. (2012b). “Piano key weir: Reservoir versus channel application”. J. Irrig. Drain. Eng., 138(8), 773–776. doi:https://doi.org/10.1061/(ASCE)IR.1943-4774.0000464 [Crossref][Web of Science ®][Google Scholar]
  • Anderson, R.M. 2011. Piano key weir head discharge relationships, M.S. Thesis, Utah State University, Logan, Utah. [Google Scholar]
  • Bashiri, H., Dewals, B., Pirotton, M., Archambeau, P., and Erpicum, S. (2016). “Towards a new design equation for piano key weirs discharge capacity.” Proc. of the 6th International Symposium on Hydraulic Structures. Portland, USA. [Google Scholar]
  • Bianucci, S.P., Sordo Ward, Á.F., Pérez Díaz, J.I., García-Palacios, J.H., Mediero Orduña, L.J., and Garrote de Marcos, L. (2013). “Risk-based methodology for parameter calibration of a reservoir flood control model”. Natl. Hazard Earth Syst. Sci., 13(4), 965–981. doi:https://doi.org/10.5194/nhess-13-965-2013 [Crossref][Web of Science ®][Google Scholar]
  • Blancher, B., Montarros, F., and Laugier, F. (2011). Hydraulic comparison between Piano Key Weirs and labyrinth spillways. Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B. Liège, Belgium. [Crossref][Google Scholar]
  • Botha, A., Fitz, I., Moore, A., Mulder, F., and Van Deventer, N. 2013. “Application of the Piano Key Weir spillway in the Republic of South Africa”. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs, Chatou, Paris, France, 20–22, 185. [Crossref][Google Scholar]
  • Chahartaghi, M.K., Nazari, S., and Shooshtari, M.M. 2019. “Experimental and numerical simulation of arced trapezoidal Piano Key Weirs”. Flow Meas. Instrum., 68, 101576. doi:https://doi.org/10.1016/j.flowmeasinst.2019.101576 [Crossref][Web of Science ®][Google Scholar]
  • Chi Hien, T., Thanh Son, H., and Ho Ta Khanh, M. (2006). Results of some ‘piano keys’ weir hydraulic model tests in Vietnam. Proc., 22nd Int. Congress of Large Dams, Question 87, Response 39, International Commission on Large Dams (ICOLD). Barcelona, Spain. [Google Scholar]
  • Cicero, G., Barcouda, M., Luck, M., and Vettori, E. (2011). Study of a piano key morning glory to increase the spillway capacity of the Bage dam. Proc. Int. Conf. Labyrinth Piano Key Weirs-PKW2011, Taylor & Francis, London. [Crossref][Google Scholar]
  • Cicero, G., De Miranda, D., and Luck, M. (2012). “Assessment of the code Wolf 1D PKW for predicting the hydraulic behaviour of PK-Weirs.” Congrès SHF-33èmes journées de l’hydraulique “Grands aménagements hydrauliques 2012”, Paris, France. [Google Scholar]
  • Cicero, G., and Delisle, J. (2013). “Discharge characteristics of Piano Key weirs under submerged flow”. Labyrinth and Piano Key Weirs II–PKW 2013, 101–109. [Crossref][Google Scholar]
  • Cicero, G., Delisle, J., Lefebvre, V., and Vermeulen, J. (2013). “Experimental and numerical study of the hydraulic performance of a trapezoidal Piano Key weir.” Labyrinth and Piano Key Weirs II: Proceedings of the Second International Workshop on Labyrinth and Piano key weirs, Chatou, Paris, France, 20–22, 265. [Crossref][Google Scholar]
  • Cicéro, G., Guene, C., Luck, M., Pinchard, T., Lochu, A., and Brousse, P. (2010). “Experimental optimization of a Piano Key Weir to increase the spillway capacity of the Malarce dam.” 1st IAHR European Congress, Edinbourgh, Mai 4–6, 2010. [Google Scholar]
  • Crookston, B., Anderson, R., and Tullis, B. (2018). “Free-flow discharge estimation method for Piano Key weir geometries.” J. Hydro. Environ. Res., 19, 160–167. doi:https://doi.org/10.1016/j.jher.2017.10.003 [Crossref][Web of Science ®][Google Scholar]
  • Das Singhal, G., and Sharma, N. 2011. “Rehabilitation of Sawara Kuddu Hydroelectric Project–Model studies of Piano Key Weir in India”. Proc. Int. Workshop on Labyrinths and Piano Key Weirs PKW 2011. Taylor & Francis, London. [Crossref][Google Scholar]
  • Denys, F., Basson, G., and Strasheim, J. (2017). Fluid Structure Interaction of Piano Key Weirs. Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam. [Crossref][Google Scholar]
  • Eichenberger, P. (2013). “The first commercial piano key weir in Switzerland.” Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 227. [Crossref][Google Scholar]
  • Erpicum, S., Laugier, F., Pfister, M., Pirotton, M., Cicero, G.-M., and Schleiss, A.J. 2013. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, CRC Press. [Crossref][Google Scholar]
  • Erpicum, S., Machiels, O., Dewals, B., Pirotton, M., and Archambeau, P. (2012). “Numerical and physical hydraulic modelling of Piano Key Weirs.” Proceedings of the 4th Int. Conf. on Water Resources and Renewable Energy Development in Asia. Chiang Mai, Thailande. [Google Scholar]
  • Erpicum, S., Nagel, V., and Laugier, F. (2011). “Piano Key Weir design study at Raviege dam”. Labyrinth and Piano Key Weirs–PKW 2011, 43–50. [Crossref][Google Scholar]
  • Ervine, D., and Elsawy, E. (1975). “The effect of a falling nappe on river aeration.” Proc. 16th IAHR Congress, Sao Paulo, Brazil. [Google Scholar]
  • Falvey, H.T. 1980. “Air-water flow in hydraulic structures”. NASA STI/Recon Technical Report N, 81. [Google Scholar]
  • Gabriel-Martin, I., Sordo-Ward, A., Garrote, L., and Castillo, L.G. (2017). “Influence of initial reservoir level and gate failure in dam safety analysis. Stochastic approach.” J. Hydrol., 550, 669–684. doi:https://doi.org/10.1016/j.jhydrol.2017.05.032 [Crossref][Web of Science ®][Google Scholar]
  • Gebhardt, M., Herbst, J., Merkel, J., and Belzner, F. (2019). “Sedimentation at labyrinth weirs–an experimental study of the self-cleaning process”. J. Hydraulic Res., 57(4), 579–590. doi:https://doi.org/10.1080/00221686.2018.1494053 [Taylor & Francis Online][Web of Science ®][Google Scholar]
  • Hu, H., Qian, Z., Yang, W., Hou, D., and Du, L. (2018). “Numerical study of characteristics and discharge capacity of piano key weirs.” Flow Meas. Instrum., 62, 27–32. doi:https://doi.org/10.1016/j.flowmeasinst.2018.05.004 [Crossref][Web of Science ®][Google Scholar]
  • Javaheri, A., and Kabiri-Samani, A. (2012). “Threshold submergence of flow over PK weirs”. Int. J. Civil Geol. Eng., 6, 46–49. [Google Scholar]
  • Jayatillake, H., and Perera, K. (2013). “Design of a Piano-Key Weir for Giritale Dam spillway in Sri Lanka.” Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 151. [Crossref][Google Scholar]
  • Jayatillake, H., and Perera, K. (2017). “Adoption of a type D Piano Key Weir spillway with tapered noses at Rambawa Tank, Sri Lanka.” Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam. [Crossref][Google Scholar]
  • Jüstrich, S., Pfister, M., and Schleiss, A.J. (2016). “Mobile riverbed scour downstream of a Piano Key weir”. J. Hydraulic Eng., 142(11), 04016043. doi:https://doi.org/10.1061/(ASCE)HY.1943-7900.0001189 [Crossref][Google Scholar]
  • Kabiri-Samani, A., and Javaheri, A. (2012). “Discharge coefficients for free and submerged flow over Piano Key weirs”. J. Hydraulic Res., 50(1), 114–120. doi:https://doi.org/10.1080/00221686.2011.647888 [Taylor & Francis Online][Web of Science ®][Google Scholar]
  • Karimi, M., Attari, J., Saneie, M., and Jalili Ghazizadeh, M.R. (2018). “Side weir flow characteristics: comparison of piano key, labyrinth, and linear types”. J. Hydraulic Eng., 144(12), 04018075. doi:https://doi.org/10.1061/(ASCE)HY.1943-7900.0001539 [Crossref][Google Scholar]
  • Karimi, M., Attari, J., Saneie, M., and Jalili-Ghazizadeh, M. (2017). “Experimental study of discharge coefficient of a piano key side weir.” Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017). Proceedings of the Third International Workshop on Labyrinth and Piano key weirs 2017, Qui Nhon, Vietnam, 22–24. [Crossref][Google Scholar]
  • Khanh, M.H.T. (2013). “The Piano Key Weirs: 15 years of Research & Development–Prospect.” Labyrinth and piano key weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 3. [Crossref][Google Scholar]
  • Khanh, M.H.T. (2017). “History and development of Piano Key Weirs in Vietnam from 2004 to 2016.” Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam. [Google Scholar]
  • Khanh, M.H.T., Hien, T.C., and Hai, N.T. (2011). “Main results of the PK weir model tests in Vietnam (2004 to 2010).” Labyrinth and Piano Key Weirs, 191. Liège, Belgium. [Crossref][Google Scholar]
  • Khassaf, S.I., Aziz, L.J., and Elkatib, Z.A. (2016). “Hydraulic behavior of piano key weir type B under free flow conditions”. Int. J. Sci. Technol. Res., 5(3), 158–163. [Google Scholar]
  • Khassaf, S.I., and Al-Baghdadi, M.B. (2015). “Experimental study of non-rectangular piano key weir discharge coefficient”. J. Homepage, 6(5), 425–436. [Google Scholar]
  • Khassaf, S.I., and Al-Baghdadi, M.B.N. (2018). “Experimental investigation of submerged flow over piano key weir”. Int. J. Energy Environ., 9(3), 249–260. [Google Scholar]
  • Kwon, -H.-H., and Moon, Y.-I. (2006). “Improvement of overtopping risk evaluations using probabilistic concepts for existing dams”. Stochastic Environ. Res. Risk Assess., 20(4), 223. doi:https://doi.org/10.1007/s00477-005-0017-2 [Crossref][Web of Science ®][Google Scholar]
  • Laugier, F. (2007). “Design and construction of the first Piano Key Weir spillway at Goulours dam”. Int. J. Hydropower Dams, 14(5), 94. [Google Scholar]
  • Laugier, F., Lochu, A., Gille, C., Leite Ribeiro, M., and Boillat, J.-L. (2009). “Design and construction of a labyrinth PKW spillway at Saint-Marc dam, France”. Hydropower Dams, 16(LCH–ARTICLE–2009–023), 100–107. [Google Scholar]
  • Laugier, F., Pralong, J., and Blancher, B. (2011). “Influence of structural thickness of sidewalls on PKW spillway discharge capacity.” Proc. Intl Workshop on Labyrinths and Piano Key Weirs PKW 2011. Liège, Belgium. [Crossref][Google Scholar]
  • Le Blanc, M., Spinazzola, U., and Kocahan, H. (2011). “Labyrinth fusegate applications on free overflow spillways–Overview of recent projects.” Labyrinth and Piano Key Weirs, 261, Liège, Belgium. [Crossref][Google Scholar]
  • Leite Ribeiro, M., Bieri, M., Boillat, J.-L., Schleiss, A., Delorme, F., and Laugier, F. (2009). “Hydraulic capacity improvement of existing spillways–design of a piano key weirs.” Proc. (on CD) of the 23rd Congress of the Int. Commission on Large Dams CIGB-ICOLD. Brasilia, Brazil. [Google Scholar]
  • Leite Ribeiro, M., Bieri, M., Boillat, J.-L., Schleiss, A., Singhal, G., and Sharma, N. (2011). “Discharge capacity of piano key weirs”. J. Hydraulic Eng., 138(2), 199–203. doi:https://doi.org/10.1061/(ASCE)HY.1943-7900.0000490 [Crossref][Google Scholar]
  • Lempérière, F., and Ouamane, A. (2003). “The Piano Keys weir: a new cost-effective solution for spillways”. Int. J. Hydropower Dams, 10(5), 144–149. [Google Scholar]
  • Lempérière, F., and Vigny, J. (2011). “General comments on labyrinth and Piano Keys Weirs–The future”. Labyrinth and Piano Key weirs–PKW 2011, 289–294. [Crossref][Google Scholar]
  • Lempérière, F., Vigny, J., and Ouamane, A. (2011). General comments on Labyrinth and Piano Key Weirs: The past and present. Proc. Intl. Conf. Labyrinth and Piano Key Weirs, Liège B. Liège, Belgium. [Crossref][Google Scholar]
  • Lewin, J., Ballard, G., and Bowles, D.S. (2003). “Spillway gate reliability in the context of overall dam failure risk.” USSD Annual Lecture, Charleston, South Carolina. [Google Scholar]
  • Lodomez, M., Pirotton, M., Dewals, B., Archambeau, P., and Erpicum, S. (2017). “Could piano key weirs be subject to nappe oscillations?” Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam [Crossref][Google Scholar]
  • Machiels, O., Erpicum, S., Archambeau, P., Dewals, B., and Pirotton, M. (2009). “Large scale experimental study of piano key weirs.” Proc. 33rd IAHR Congress: Water Engineering for a Sustainable Environment, IAHR. Vancouver, Canada [Google Scholar]
  • Machiels, O., Erpicum, S., Archambeau, P., Dewals, B., and Pirotton, M. (2011a). “Piano Key Weir preliminary design method–Application to a new dam project.” Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B. Liège, Belgium. [Crossref][Google Scholar]
  • Machiels, O., Erpicum, S., Dewals, B., Archambeau, P., and Pirotton, M. (2010). “Piano Key Weirs: The experimental study of an efficient solution for rehabilitation”. WIT Trans. Ecol., 133, 95–106. [Crossref][Google Scholar]
  • Machiels, O., Erpicum, S., Dewals, B.J., Archambeau, P., and Pirotton, M. (2011b). “Experimental observation of flow characteristics over a Piano Key Weir”. J Hydraulic Res, 49(3), 359–366. doi:https://doi.org/10.1080/00221686.2011.567761 [Taylor & Francis Online][Web of Science ®][Google Scholar]
  • Machiels, O., Pirotton, M., Pierre, A., Dewals, B., and Erpicum, S. (2014). “Experimental parametric study and design of Piano Key Weirs”. J. Hydraulic Res., 52(3), 326–335. doi:https://doi.org/10.1080/00221686.2013.875070 [Taylor & Francis Online][Web of Science ®][Google Scholar]
  • Mehboudi, A., Attari, J., and Hosseini, S. (2016). “Experimental study of discharge coefficient for trapezoidal piano key weirs.” Flow Meas. Instrum., 50, 65–72. doi:https://doi.org/10.1016/j.flowmeasinst.2016.06.005 [Crossref][Web of Science ®][Google Scholar]
  • Micovic, Z., Hartford, D.N., Schaefer, M.G., and Barker, B.L. (2016). “A non-traditional approach to the analysis of flood hazard for dams”. Stochastic Environ. Res. Risk Assess., 30(2), 559–581. doi:https://doi.org/10.1007/s00477-015-1052-2 [Crossref][Web of Science ®][Google Scholar]
  • Monjezi, R., Heidarnejad, M., Masjedi, A., Purmohammadi, M.H., and Kamanbedast, A. (2018). “Laboratory investigation of the discharge coefficient of flow in arced labyrinth weirs with triangular plans.” Flow Meas. Instrum., 64, 64–70. doi:https://doi.org/10.1016/j.flowmeasinst.2018.10.011 [Crossref][Web of Science ®][Google Scholar]
  • Noseda, M., Stojnic, I., Pfister, M., and Schleiss, A.J. (2019). “Upstream Erosion and sediment passage at piano key weirs”. J. Hydraulic Eng., 145(8), 04019029. doi:https://doi.org/10.1061/(ASCE)HY.1943-7900.0001616 [Crossref][Google Scholar]
  • Oertel, M. (2015). “Discharge coefficients of piano key weirs from experimental and numerical modelS.” E= proceedings of the 36th IAHR world congress. 28 June – 3 July, The Hague, The Netherlands. [Google Scholar]
  • Ouamane, A. (2011). Nine years of study of the Piano Key Weir in the university laboratory of Biskra “lessons and reflections”. Proc. Int. Conf. Labyrinth Piano Key Weirs-PKW2011, Taylor & Francis, London. [Crossref][Google Scholar]
  • Ouamane, A., Debabeche, M., Lempérière, F., and Vigny, J. (2017). Twenty years of research in Biskra University for Labyrinths and Piano Key Weirs and associated fuse plugs. Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam. [Crossref][Google Scholar]
  • Ouamane, A., and Lempérière, F. (2006). Design of a new economic shape of weir. Proc. Int. Symp. on Dams in the Societies of the 21st Century. Barcelona, Spain. [Crossref][Google Scholar]
  • Patev, R., and Putcha, C. (2005). “Development of fault trees for risk assessment of dam gates and associated operating equipment”. Int. J. Modell. Simul., 25(3), 190–201. doi:https://doi.org/10.1080/02286203.2005.11442336 [Taylor & Francis Online][Google Scholar]
  • Paxson, G., Tullis, B., and Hertel, D. 2013. “Comparison of Piano Key Weirs with labyrinth and gated spillways: Hydraulics, cost, constructability and operations”. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 123–130. [Crossref][Google Scholar]
  • Pfister, M., Capobianco, D., Tullis, B., and Schleiss, A.J. (2013). “Debris-blocking sensitivity of piano key weirs under reservoir-type approach flow”. J. Hydraulic Eng., 139(11), 1134–1141. doi:https://doi.org/10.1061/(ASCE)HY.1943-7900.0000780 [Crossref][Google Scholar]
  • Phillips, M., and Lesleighter, E. 2013. “Piano Key Weir spillway: Upgrade option for a major dam”. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 159–168. [Crossref][Google Scholar]
  • Pinchard, T., Boutet, J., and Cicero, G. (2011). “Spillway capacity upgrade at Malarce dam: design of an additional Piano Key Weir spillway.” Proc. Int. Workshop on Labyrinths and Piano Key Weirs PKW. Liège, Belgium. [Crossref][Google Scholar]
  • Pralong, J., J. Vermeulen, B. Blancher, F. Laugier, S. Erpicum, O. Machiels, M. Pirotton, J.-L. Boillat, M. Leite Ribeiro and A. Schleiss (2011). “A naming convention for the piano key weirs geometrical parameters.” Labyrinth and piano key weirs, 271–278. [Crossref][Google Scholar]
  • Ribeiro, M.L., Boillat, J.-L., Schleiss, A., Laugier, F., and Albalat, C. (2007). “Rehabilitation of St-Marc dam.” Experimental optimization of a piano key weir. Proc. of 32nd Congress of IAHR, Vince, Italy. [Google Scholar]
  • Ribeiro, M.L., Pfister, M., and Schleiss, A.J. (2013). “Overview of Piano Key weir prototypes and scientific model investigations”. Labyrinth and Piano Key Weirs II, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 273. [Crossref][Google Scholar]
  • Ribeiro, M.L., Pfister, M., Schleiss, A.J., and Boillat, J.-L. (2012). “Hydraulic design of A-type piano key weirs”. J. Hydraulic Res., 50(4), 400–408. doi:https://doi.org/10.1080/00221686.2012.695041 [Taylor & Francis Online][Web of Science ®][Google Scholar]
  • Ribi, J., Spahni, B., Dorthe, D., and Pfister, M. (2017). Piano Key Weir as overflow on sedimentation basin of wastewater treatment plant. Labyrinth and Piano Key Weirs III: Proceedings of the 3rd International Workshop on Labyrinth and Piano Key Weirs (PKW 2017), Feb 22–24, 2017, CRC Press, Qui Nhon, Vietnam [Crossref][Google Scholar]
  • Schleiss, A. (2011). “From labyrinth to piano key weirs: a historical review.” Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B. Liège, Belgium. [Crossref][Google Scholar]
  • Sharma, N., and Tiwari, H. (2013). “Experimental study on vertical velocity and submergence depth near Piano Key Weir.” Labyrinth and Piano Key Weirs II-PKW, Proceedings of the Second International Workshop on Labyrinth and Piano key weirs 2013, Chatou, Paris, France, 20–22, 93–100.