Omega-Liutex Method

Prediction of the Vortex Evolution and Influence Analysis of Rough Bed in a Hydraulic Jump with the Omega-Liutex Method

Omega-Luitex법을 이용한 수력점프 발생시 러프 베드의 와류 진화 예측 및 영향 분석

Cong Trieu Tran, Cong Ty Trinh

Abstract

The dissipation of energy downstream of hydropower projects is a significant issue. The hydraulic jump is exciting and widely applied in practice to dissipate energy. Many hydraulic jump characteristics have been studied, such as length of jump Lj and sequent flow depth y2. However, understanding the evolution of the vortex structure in the hydraulic jump shows a significant challenge. This study uses the RNG k-e turbulence model to simulate hydraulic jumps on the rough bed. The Omega-Liutex method is compared with Q-criterion for capturing vortex structure in the hydraulic jump. The formation, development, and shedding of the vortex structure at the rough bed in the hydraulic jumper are analyzed. The vortex forms and rapidly reduces strength on the rough bed, resulting in fast dissipation of energy. At the rough block rows 2nd and 3rd, the vortex forms a vortex rope that moves downstream and then breaks. The vortex-shedding region represents a significant energy attenuation of the flow. Therefore, the rough bed dissipates kinetic energy well. Adding reliability to the vortex determined by the Liutex method, the vorticity transport equation is used to compare the vorticity distribution with the Liutex distribution. The results show a further comprehension of the hydraulic jump phenomenon and its energy dissipation.

Keywords

flow-3D; hydraulic Jump; omega-liutex method; vortex breakdown

References

[1] Viti, N., Valero, D., & Gualtieri, C. (2019). Numerical Simulation of Hydraulic Jumps. Part 2: Recent Results and Future Outlook. Water, 11(1), 28. https://doi.org/10.3390/w11010028
[2] Peterka, A. J. (1978.) Hydraulic Design of Stilling Basins and Energy Dissipators. Department of the Interior, Bureau of Reclamation.
[3] Bejestan, M. S. & Neisi, K. (2009). A new roughened bed hydraulic jump stilling basin. Asian journal of applied sciences, 2(5), 436-445. https://doi.org/10.3923/ajaps.2009.436.445
[4] Tokyay, N. D. (2005). Effect of channel bed corrugations on hydraulic jumps. Impacts of Global Climate Change, 1-9. https://doi.org/10.1061/40792(173)408
[5] Nikmehr, S. & Aminpour, Y. (2020). Numerical Simulation of Hydraulic Jump over Rough Beds. Periodica Polytechnica Civil Engineering, 64(2), 396-407. https://doi.org/10.3311/PPci.15292
[6] Hunt, J. C., Wray, A. A., & Moin, P. (1988). Eddies, streams, and convergence zones in turbulent flows. Studying turbulence using numerical simulation databases. 2. Proceedings of the 1988 summer program.
[7] Gao, Y. & Liu, C. (2018). Rortex and comparison with eigenvalue-based vortex identification criteria. Physics of Fluids, 30(8), 085107. https://doi.org/10.1063/1.5040112
[8] Liu, C., Gao, Y., Tian, S., & Dong, X. (2018). Rortex – A new vortex vector definition and vorticity tensor and vector decompositions. Physics of Fluids, 30(3), 035103. https://doi.org/10.1063/1.5023001
[9] Liu, C. et al. (2019). Third generation of vortex identification methods: Omega and Liutex/Rortex based systems. Journal of Hydrodynamics, 31(2), 205-223. https://doi.org/10.1007/s42241-019-0022-4
[10] Liu, C., Wang, Y., Yang, Y. et al (2016). New omega vortex identification method. Science China Physics, Mechanics & Astronomy, (8), 56-64. https://doi.org/10.1007/s11433-016-0022-6
[11] Tran, C. T. & Pham, D. C. (2022). Application of Liutex and Entropy Production to Analyze the Influence of Vortex Rope in the Francis-99 Turbine Draft Tube. Tehnički vjesnik, 29(4), 1177-1183. https://doi.org/10.17559/TV-20210821070801
[12] Dong, X., Gao, Y., & Liu, C. (2019). New normalized Rortex/vortex identification method. Physics of Fluids, 31(1), 011701. https://doi.org/10.1063/1.5066016
[13] Wang, L., Zheng, Z., Cai, W. et al. (2019). Extension Omega and Omega-Liutex methods applied to identify vortex structures in viscoelastic turbulent flow. Journal of Hydrodynamics, 31(5), 911-921. https://doi.org/10.1007/s42241-019-0045-x
[14] Xu, H., Cai, X., & Liu, C. (2019). Liutex (vortex) core definition and automatic identification for turbulence vortex structures. Journal of Hydrodynamics, 31(5), 857-863. https://doi.org/10.1007/s42241-019-0066-5
[15] Tran, C. T. et al. (2020). Prediction of the precessing vortex core in the Francis-99 draft tube under off-design conditions by using Liutex/Rortex method. Journal of Hydrodynamics, 32, 623-628. https://doi.org/10.1007/s42241-020-0031-3
[16] Liu, C. et al. (2019). A Liutex based definition of vortex axis line. arXiv preprint arXiv:1904.10094. https://doi.org/10.48550/arXiv.1904.10094
[17] Samadi-Boroujeni, H. et al. (2013). Effect of triangular corrugated beds on the hydraulic jump characteristics. Canadian Journal of Civil Engineering, 40(9), 841-847. https://doi.org/10.1139/cjce-2012-0019
[18] Ghaderi, A. et al. (2020). Characteristics of free and submerged hydraulic jumps over different macroroughnesses. Journal of Hydroinformatics, 22(6), 1554-1572. https://doi.org/10.2166/hydro.2020.298
[19] Wu, Z. et al. (2021). Analysis of the influence of transverse groove structure on the flow of a flat-plate surface based on Liutex parameters. Engineering Applications of Computational Fluid Mechanics, 15(1), 1282-1297. https://doi.org/10.1080/19942060.2021.1968955
[20] Ji, B., et al. (2014). Numerical simulation of threedimensional cavitation shedding dynamics with special emphasis on cavitation – vortex interaction. Ocean Engineering, 87, 64-77. https://doi.org/10.1016/j.oceaneng.2014.05.005
[21] Tran, C., Bin, J., & Long, X. (2019). Simulation and Analysis of Cavitating Flow in the Draft Tube of the Francis Turbine with Splitter Blades at Off-Design Condition. Tehnicki vjesnik – Technical Gazette, 26(6). https://doi.org/10.17559/TV-20190316042929
Computational Fluid Dynamics Study of Perforated Monopiles

Computational Fluid Dynamics Study of Perforated Monopiles

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

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


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


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


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

Abstract

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

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

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

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

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

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

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

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

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

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

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

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

Numerical Investigation of the Local Scour for Tripod Pile Foundation

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

OPEN ACCESS

Abstract: 

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

Keywords: 

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

1. Introduction

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

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

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

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

2. Numerical Model

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

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

2.1 Momentum equations

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

(1)

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

(2)

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

 (3)

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

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

2.2 Model of turbulence

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

2.3 Model of sediment scour

2.3.1 Induction and deposition

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

(4)

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

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

(5)

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

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

(6)

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

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

(7)

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

vf  stands for fluid kinematic viscosity.

2.3.2 Transportation for bed loads

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

(8)

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

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

(9)

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

(10)

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

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

3. Model Setup

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

image013.png

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

3.1 Generation of meshes

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

image014.png

Figure 2. The mesh block sketch

3.2 Conditional boundaries

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

image015.png

Figure 3. Boundary conditions of the typical problem

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

3.3 Mesh sensitivity

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

3.4 Model validation

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

image016.png

Figure 4. Cell size effect

image017.png

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

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

3.5 Dimensional analysis

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

(11)

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

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

(12)

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

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

4. Result and Discussion

4.1 Development of scour

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

4.2 Features of scour

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

image023.png

Figure 6. Results of scour depth with time

image024.png

image025.png

image026.png

image027.png

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

image028.png

image029.png

image030.png

image031.png

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

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

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

image032.png

(a)

image033.png

(b)

image034.png

(c)

image035.png

(d)

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

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

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

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

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

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

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

4.7 Keulegan-Carpenter (KC) number

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

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

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

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

image037.png

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

5. Conclusion

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

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

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

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

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

Nomenclature

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

  References

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Investigating effects of lateral inflow characteristics on main flow using numerical modeling

Investigating effects of lateral inflow characteristics on main flow using numerical modeling

수치모델링을 이용한 측면 유입특성이 본류에 미치는 영향 조사

Mohammad Raze Raeisi Dehkordi1*, Amir Hossein Yeganeh Mazhar1
, Farzaneh Kheradzare2
1– PhD. Student in the Department of Construction and Water Management, Science and Research Unit, Islamic Azad
University, Tehran, Iran
2– M.Sc. Graduate Water resource management, Department of Civil Engineering and Mechanics, Ghiaseddin Jamshid
Kashani University, Qazvin, Iran

  • Corresponding author: mohamadreza.raeisi.d@gmail.com

Keywords

Channel Confluence, Channel cross, sectional area, Cross channel angles, Modelling, Flow-3D

Abstract

Introduction

One of the key issues in river engineering is analyzing the flow properties at the intersection of natural rivers and canals. The flow of the side channel moves away from the intersection of the two channels as a result of the exchange of input force from the side channel with the main flow after coming into contact with it. One of the most evident properties of the flow in these sections is the development of a revolving region with low pressure and even negative pressure close to the inner wall of the side channel. One advantage of the whirling flow in this low-pressure region is that it gives the flow enough space to sediment, but it also increases flow speed near the channel’s bottom and outside wall by lowering the intersectional area of the flow. One of the most crucial considerations in the design of these intersections is minimizing sedimentation in the rotating region and scouring in the area above the shear plane.

Materials and methods:

The channel (flume) created in the laboratory based on Weber et al., (2001) model, was employed in the current investigation to confirm the validity and examine other study objectives. The main channel is 21. 95 meters long, while the side channel, which is at a 90-degree angle to the main channel, is 3. 66 meters long. The total downstream discharge is approximately 0. 17 m3/s, with the upstream velocities of the main channel being 0. 166 m/s and the side channel being 0. 5 m/s. In both channels, the flow depth and width are 0. 91 meters and 0. 296 meters, respectively. In this study, 6 various models’ angles of intersection between the main and side channels, inlet flow velocity, intersectional area, and side channel length have been examined. Models 2 and 3 have intersection angles of 60 and 30 degrees, respectively, and share the rest of their attributes with the fundamental model, or model number 1. Model 1 is the same as Weber’s experimental model. The length of the side channel in model 4 is different from model 1. The only difference between model 6 and the basic model is the side channel intake speed.

Results and Discussion

Analyzing the intersection angle The angle between the main channel and the side channel is investigated in this section of the findings. Models 1, 2, and 3 are assessed using the intersection angles of 90, 60, and 30 degrees, respectively. In some studies, the impact of the intersection angle has been examined, but in this study, three-dimensional investigation in transverse and longitudinal sections as well as the plan of the intersection is discussed, as can be observed from the literature review. Considering three models with intersection angles of 90, 60, and 30 degrees, the kinetic energy contours at the channel’s middle height can be obtained for each model. The channel with a 30-degree intersection angle (model 3) has the maximum kinetic energy in the flow. The channel with a 60-degree intersection has the minimum kinetic energy. As a result of the maximum deviation of the flow in the main channel caused by the flow of the side channel, the channel with a 90-degree intersection also has the maximum kinetic energy near the wall in front of the side channel.

Examining the side channel length In model 1, the side channel is 3. 66 meters long, whereas in model 4, it is 5. 52 meters long. This study aims to determine how changing the side channel’s length affects the flow pattern where two channels intersect. The kinetic energy contours were obtained for two states of the channel length, which are known to extend the lateral channel, increase the energy of the flow after the intersection, and shorten the length of the high-kinetic energy zone. When compared to model 1 with a shorter length of the side channel, the width of the flow separation zone is reduced by approximately 20%, which results in less flow sedimentation. Figure 12 illustrates the rotating zones in the flow separation area. The flow separation region’s length is essentially unchanged. Studying the intersection of the lateral channel After determining the lateral channel’s length, its width and, consequently, its intersectional area should be evaluated.

This section compares model 1 width of 0. 91 meters to model 5 width of 1. 40 meters. One of the most recent topics related to the intersection of the main and side channels is examining the intersection of the side channel. In model 5, the side channel’s flow rate has also increased due to an increase in the width or intersection of the channel. The flow rate through the intersection and the momentum of the flow from the side channel and the main channel increase when the side channel flow rate rises. The findings indicate that when flow width and side channel flow rise, energy increases after the inlet.

Investigating the value of inlet speed in the side channel Unlike the preceding sections, which were all concerned with the channel geometry, the inlet velocity in the side channel is one of the hydraulic parameters of the flow. In this section, models 1 and 6 with inlet velocities of the side channel of 0. 5 and 0. 75 m/s are evaluated. According to the modeling, the flow is somewhat horst before and immediately on the intersection of the flow level, but it undergoes a substantial prolapse just after the intersection. Model 6 has a larger volume and height of flow, but a smaller and softer prolapse after the intersection.

Conclusion

Some hydraulic and geometric properties of the intersection of channels have been examined using Flow-3D software. The RNG turbulence model was used for three-dimensional modeling. Some of the results are listed below. The flow is uniform upstream of the main and minor channels and only slightly becomes horst at the intersection. The analysis of the lengthening of the side channel revealed a 20% reduction in the separation zone’s width and a considerable reduction in the kinetic energy at the intersection. The input flow rate of this channel to the intersection increases with the speed and width of the side channel, which accounts for the local drop in the width of the main channel flow.

References

  • Azhdari, K., Talebi, Z. & Hosseini, S. H. (2020). Simulation of Subcritical Flow Distribution and Water Surface Fluctuations in Fourbranch Open Channel Junction with FLOW 3D. Irrigation and Drainage, 14(3), 1018- 1031. (In persian).
  • Behdarvandi, M., Hajipour, M., Parsi, E. & Ansari ghojghar, M. (2022). Investigation of Velocity Changes in a Straight Asymmetric pattern at river bend. Water and Soil Conservation, 22(6), 81-89. (In Persian).
  • Ghobadian, R. & Seyedi tabar, Z. (2016). Numerical investigating of the effect of lateral channel junction position on flow Rectangular Composite Channel Using Flow3D Software. Irrigation and Water Engineering, 13(1), 1-16. Doi: 10.22125/iwe.2022.158503 (In Persian).
  • Burqaʻi, S. M. & Nazari, A. (2003). Laboratory investigation of sediment pattern at the intersection of channels. 6th International Civil Engineering Conference, Amirkabir University of Technology, Tehran, Iran (In Persian).
  • Hemmati, M. & Aghazade-Soureh, T. (2018). Simulation of the Effect of Bed Discordance on Flow Pattern at the River Confluence by Flow-3D Model. Irrigation and Drainage, 11(5), 785-797.
  • Hosseini, S, M. & Abrishami, J. (2018). OpenChannel Hydraulics. 35th Edition: Imam Reza International University, 613 pages (In Persian).
  • Karami moghadam, M., Keshavarz, A. & Sabzevar, T. (2019). The Effect of Diversion Flow, Intake Inlet Shape, Topography and Bed Roughness on the Flow Separation Dimensions and Shear Stress at the Lateral Intake. Irrigation and Drainage Structures Engineering Research, 73(19), 113-126. (In Persian).
  • Khosravinia, P., Hosseini, S.H. & Hosseinzadeh Dalir, A. (2018). Numerical analyzing of flow in open channel junction with effect of side slope of channel. Irrigation and Water Engineering, 10(1), 1-16. Doi: 10.22125/iwe.2019.95871 (In Persian).
  • Kwanza, J.K., Kinyanjui, M. & Nkoroi, J.M. (2007). Modelling fluid flow in rectangular and trapezoidal open channels. Advances and Applications in Fluid Mechanics, 2(2), 149- 158.
  • Masjedi, A. & Taeedi, A. (2011). Experimental Investigations of Effect Intake Angle on Discharge in Lateral Intakes in 180 Degree Bend. World Applied Sciences Journal, 15(10), 1442-1444
  • Musavi Jahromi, S.M., & Goudarzizadeh, R. (2011). Numerical Simulation of 3D Flow Pattern at Open-Channel Junctions. Irrigation Sciences and Engineering, 34(2), 61-70 (In Persian).
  • Nikpour, M. & Khosravinia, P. (2018). Numerical Simulation of Side Slope Effect of Main Channel Wall on Flow Behavior in Open Channels Junction. Irrigation and Drainage, 11(6), 1024-1037. (In persian).
  • Raeisi Dehkordi, M. (2022). Description of types of pollution in water resources and protection of water resources, New Approaches in Civil Engineering, 6(1), 42- 52. Doi: 10.30469/jnace.2022.154373 (In Persian).
  • Ramamurthy, A.S., Carballada, L.B. & Tran, D.M. (1988). Combining Open Channel Flow at Right Angled Junctions. Journal of hydraulic engineering, 114(12), 1449-1460.
  • Tabesh, M. (2018). Advanced Modeling of Water Distribution Networks. 4th Edition: University of Tehran Press, 585 pages.
  • Taylor, E. (1944). Flow Characteristics at Rectangular Open-Channel Junctions. Journal of hydraulic engineering, 10(6), 893- 902.
  • Thiong’o, J.W. (2011). Investigations of fluid flows in open rectangular and triangular channels. Master’s thesis, Jomo Kenyatta University of Agriculture and Technology, Juja, Kenya.
  • Weber, L.J., Schumate, E.D. & Mawer, N. (2001). Experiments on Flow at a 90° Open-Channel Junction. Journal of hydraulic engineering, 127(5), 340-350.

Local Scour Depth Around Bridge Piers: Performance Evaluation of Dimensional Analysis-based Empirical Equations and AI Techniques

Local Scour Depth Around Bridge Piers: Performance Evaluation of Dimensional Analysis-based Empirical Equations and AI Techniques

Abstract

Artificial Intelligence (AI) techniques, such as Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference Systems (ANFIS), and dimensional analysis-based empirical equations (DAEEs), can estimate scour depth around bridge piers. AI’s accuracy depends on various architectures, while DAEEs’ performance depends on experimental data. This study evaluated the performance of AI and DAEEs for scour depth estimation using flow velocity, depth, size of bed sediment, critical approach velocity, and pier width. The data from a smooth rectangular (20 m × 1 m) flume and a high-precision particle image velocimetry to study the flow structure around the pier – width: 1.5 – 91.5 cm evaluated DAEEs. Various ANNs (5, 10, and 15 neurons), double layer (DL) and triple layers (TL), and different ANFIS settings were trained, tested, and verified. The Generalized Reduced Gradient optimization identified the parameters of DAEEs, and Nash–Sutcliffe efficiency (NSE) and Mean Square Error (MSE) evaluated the performance of different models. The study revealed that DL ANN-3 with 10 neurons (NSE = 0.986) outperformed ANFIS, other ANN (ANN1, ANN2, ANN4 & ANN5) models, and empirical equations with NSE values between 0.76 and 0.983. The study found pier dimensions to be the most influential parameter for pier scour.

 This is a preview of subscription content, log in via an institution  to check access.

Abdul Razzaq GhummanHusnain HaiderIbrahim Saleh Al SalamahMd. ShafiquzzamanAbdullah AlodahMohammad AlresheediRashid FarooqAfzal Ahmed & Ghufran Ahmed Pasha

Similar content being viewed by others

Prediction of local scour around bridge piers using the ANFIS method

Article 18 September 2015

Live-Bed Scour Depth Modelling Around the Bridge Pier Using ANN-PSO, ANFIS, MARS, and M5Tree

Article 22 May 2024

Artificial Intelligence Modeling for Scour Depth Prediction Upstream of Bridge Piers

Article 08 November 2023

References

Download references

Acknowledgments

Authors also thank “The US Department of the Interior,” US Geol. Surv. Reston, VA, USA” for providing access to scour data. The Researchers would like to thank the Deanship of Graduate Studies and Scientific Research at Qassim University for financial support (QU-APC-2024-9/1).

Author information

Authors and Affiliations

  1. Dept. of Civil Engineering, College of Engineering, Qassim University, Buraydah, 51452, Saudi ArabiaAbdul Razzaq Ghumman, Husnain Haider, Ibrahim Saleh Al Salamah, Md. Shafiquzzaman, Abdullah Alodah & Mohammad Alresheedi
  2. Dept. of Civil Engineering, International Islamic University, Islamabad, 44000, PakistanRashid Farooq
  3. Dept. of Civil Engineering, University of Engineering and Technology, Taxila, 47050, PakistanAfzal Ahmed & Ghufran Ahmed Pasha

  • DOIhttps://doi.org/10.1007/s12205-024-1161-x


Keywords

An investigation of the effect of the pulse width and amplitude on sand bed scouring by a vertical submerged pulsed jet

An investigation of the effect of the pulse width and amplitude on sand bed scouring by a vertical submerged pulsed jet

수직 수중 펄스 제트에 의한 모래층 정련에 대한 펄스 폭과 진폭의 영향 조사

Chuan Wang abc, Hao Yu b, Yang Yang b, Zhenjun Gao c, Bin Xi b, Hui Wang b, Yulong Yao b

aInternational Shipping Research Institute, GongQing Institute of Science and Technology, Jiujiang, 332020, ChinabCollege of Hydraulic Science and Engineering, Yangzhou University, Yangzhou, 225009, ChinacCollege of Mechanical and Power Engineering, China Three Gorges University, Yichang, 443002, China

https://doi.org/10.1016/j.oceaneng.2024.117324

Highlights

  • Numerical simulations and experiments were combined to investigate pulsed jet scour.
  • The effect mechanism of pulse amplitude on the variation of scour hole depth was analyzed.
  • Models for the prediction of relative low pulse width with the inlet pulse amplitude have been developed.

Abstract

This paper investigates the effects of the pulse width and amplitude on the scouring of sand beds by vertical submerged pulsed jets using a combination of experimental and numerical calculations. The reliability of the numerical calculations is verified through a comparison between the numerical simulations with the sedimentation scour model and the experimental data at a low pulse width T2 of 0, with the result that the various errors are within 5%. The results show that the scour hole depth |hmin| grows with the relative low pulse width T3 throughout three intervals: a slowly increasing zone I, a rapidly increasing zone II, and a decreasing zone III, producing a unique extreme value of |hmin|. The optimal scouring effect equation was obtained by analytically fitting the relationship curve between the pulse amplitude V and the relatively low pulse width T3. Including the optimal T3 and optimal duty cycle ƞ. The difference in the scour hole depth |hmin| under different pulse amplitudes is reflected in the initial period F of the jet. With an increasing pulse amplitude, |hmin| goes through three intervals: an increasing zone M, decreasing zone N, and rebound zone R. It is found that the scouring effect in the pulse jet is not necessarily always stronger with a larger amplitude. The results of the research in this paper can provide guidance for optimizing low-frequency pulsed jets for related engineering practices, such as dredging and rock-breaking projects.

Introduction

Submerged jet scouring technology is widely used in marine engineering and dredging projects due to its high efficiency and low cost, and a wide range of research exists on the topic (Zhang et al., 2017; Thaha et al., 2018; Lourenço et al., 2020). Numerous scholars studied the scouring caused by different forms of jets, such as propeller jets (Curulli et al., 2023; Wei et al., 2020), plane jets (Sharafati et al., 2020; Mostaani and Azimi, 2022), free-fall jets (Salmasi and Abraham, 2022; Salmasi et al., 2023), and moving jets (Wang et al., 2021). Among them, vertical jets were more popular than inclined jets due to theirs simple equipment and good silt-scouring performance (Chen et al., 2023; Wang et al., 2017). So, a large number of scholars have proposed relevant static and dynamic empirical equations for the scour depth of submerged jets. Among them, Chen et al. (2022) and Mao et al. (2023) investigated the influence of jet diameters, jet angles, exit velocities, and impinging distances on scouring effects. Finally, based on a large amount of experimental data and theoretical analysis, a semi-empirical equation for the dynamic scour depth in equilibrium was established. Amin et al. (2021) developed semi-empirical prediction equations for asymptotic lengths and empirical equations for the temporal development of lengths. Shakya et al. (2021, 2022) found that the ANN model in dimensionless form performs better than the ANN model in dimensioned form and proposed an equation for predicting the depth of static scour under submerged vertical jets using MNLR. Kartal and Emiroglu (2021) proposed an empirical equation for predicting the maximum dynamic scour depth for a submerged vertical jet with a plate at the nozzle. The effect of soil properties on jet scour has also been studied by numerous scholars. Among them, Nguyen et al. (2017) investigated the effects of compaction dry density and water content on the scour volume, critical shear stress, linear scour coefficient, and volumetric scour coefficient using a new jet-scour test device. Dong et al. (2020) investigated the effect of water content on scour hole size through experiments with a vertical submerged jet scouring a cohesive sediment bed. It was found that the depth and width of the scour holes increased with the increasing water content of the cohesive sediments, and equations for the scour depth and width in the initial stage of scouring and the calculation of the scouring rate were proposed. Kartal and Emiroglu (2023) studied the scouring characteristics of different nozzle types produced in non-cohesive sands. The results of the study found that the air entrainment rate of venturi nozzles was 2–6.5 times higher than that of circular nozzles. Cihan et al. (2022) investigated the effect of different proportions of clay and sand on propeller water jet scouring. And finally, he proposed an estimation equation for the maximum depth and length of the scour hole under equilibrium conditions. From the above summary, it is clear that a great deal of research has been carried out on submerged jet scouring under continuous jet flows.

Pulsed jets have advantages such as higher erosion rates and entrainment rates compared to continuous jets and have therefore received more attention in the development of engineering fields such as cleaning and rock breaking (Raj et al., 2019; Zhu et al., 2019; Kang et al., 2022; Y. Zhang et al., 2023). In the study of jet structure, Li et al. (2018, 2019a, 2019b, 2023) investigated the effects of the jet hole diameter, the number of jet holes, the jet distance, and the tank pressure on pulse jet cleaning. It was found that the transient pressure below the injection hole gradually increased along the airflow direction of the injection pipe, and the peak positive pressure at the inner surface of the injection pipe also increased. Liu and Shen (2019) investigated the effect of a new venturi structure on the performance of pulse jet dust removal. It was found that the longer the length of the venturi or the shorter the throat diameter of the venturi, the greater the energy loss. Zhang et al. (2023b) studied jet scouring at different angles based on FLOW-3D. It was found that counter flow scouring is better than down flow scouring. In the study of pulsed structure, Li et al. (2020) investigated the effects of different pulse amplitudes, pulse frequencies, and circumferential pressures on the rock-breaking performance. It was found that the rock-breaking performance of the jet increased with increasing pulse amplitude. However, due to the variation in pulse frequency, the rock-breaking performance does not show a clear pattern. The effect of Reynolds number on pulsating jets impinging on a plane was systematically investigated by H. H Medina et al. (2013) It was found that pulsation leads to a shorter core region of the jet, a faster decrease in the centerline axial velocity component, and a wider axial velocity distribution. Bi and Zhu (2021) investigated the effect of nozzle geometry on jet performance at low Reynolds numbers, while Luo et al. (2020) studied pulse jet propulsion at high Reynolds numbers and finally found that higher Reynolds numbers accelerate the formation of irregular vortices and symmetry-breaking instabilities. Cao et al. (2019) investigated the effect of four different pulse flushing methods on diamond core drilling efficiency. It was found that the use of intermittent rinsing methods not only increases penetration rates but also reduces rinse fluid flow and saves power.

Previous research on vertical submerged jet scouring has primarily focused on the effect of jet structure on scouring under continuous jet conditions. However, there have been fewer studies conducted on scouring under pulsed jet conditions. We found that the pulsed jet has a high erosion rate and entrainment rate, which can significantly enhance the scouring effect of the jet. Therefore, to address the research gap, this paper utilizes a combination of numerical calculations and experiments to investigate the effects of high pulse width, low pulse width, and amplitude on the scouring of vertically submerged jets. The study includes analyzing the structure of the pulsed jet flow field, studying the evolution of the scouring effect over time, and examining the relationship between the optimal pulse width, duty cycle, and amplitude. The study’s conclusions of the study can provide a reference for optimizing the performance of pulse jets in the fields of jet scouring applications, such as dredger dredging and pulse rock breaking, as well as a theoretical basis for the development of submerged pulse jets.

Section snippets

Model and calculation settings

Fig. 1 shows the geometric model of the submerged vertical jet impinging on the sand bed, which was built in Flow-3D on a 1:1 dimensional scale corresponding to the experiment. The jet scour simulation was set up between four baffles, where the top baffle was used to ensure that the jet entered only from the brass tube, and the remaining three tank baffles were used to fix the sediment and water body. The computational domain consisted of only solid and liquid components, with the specific

The effects of the pulse width on submerged jet scouring

The blocking pulsed jet, indicated as A and C in Fig. 8(a)–is discontinuous and divided into a water section and a pulse interval section. The water section in region A is not a regular shape, due to part of the water section near the side wall being affected by the wall friction and the falling speed being lower, but this also shows that the wall plays a certain buffer role. Region B of Fig. 8(a) shows the symmetrical vortex generation that occurs below the nozzle as the water section is

conclusions

In this paper, the effects of the pulse width and pulse amplitude on jet scour under submerged low-frequency pulse conditions are discussed and investigated, and the following conclusions have been reached.

  • (1)The errors of between the Flow-3D simulation and the experimental measurements were within 5%, which proves that the sedimentation scouring model of Flow-3D can reliably perform numerical calculation of the type considered in this paper.
  • (2)The change in the high pulse width T1 in the pulse cycle 

CRediT authorship contribution statement

Chuan Wang: Data curation, Conceptualization. Hao Yu: Writing – original draft. Yang Yang: Writing – review & editing, Supervision. Zhenjun Gao: Supervision, Writing – review & editing. Bin Xi: Resources, Project administration. Hui Wang: Software, Data curation. Yulong Yao: Validation, Software.

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.

References (44)

Estimating maximum initial wave amplitude of subaerial landslide tsunamis: A three-dimensional modelling approach

Estimating maximum initial wave amplitude of subaerial landslide tsunamis: A three-dimensional modelling approach

해저 산사태 쓰나미의 최대 초기 파동 진폭 추정: 3차원 모델링 접근법

Ramtin Sabeti a, Mohammad Heidarzadeh ab

aDepartment of Architecture and Civil Engineering, University of Bath, Bath BA27AY, UK
bHydroCoast Consulting Engineers Ltd, Bath, UK

https://doi.org/10.1016/j.ocemod.2024.102360

Highlights

  • •Landslide travel distance is considered for the first time in a predictive equation.
  • •Predictive equation derived from databases using 3D physical and numerical modeling.
  • •The equation was successfully tested on the 2018 Anak Krakatau tsunami event.
  • •The developed equation using three-dimensional data exhibits a 91 % fitting quality.

Abstract

Landslide tsunamis, responsible for thousands of deaths and significant damage in recent years, necessitate the allocation of sufficient time and resources for studying these extreme natural hazards. This study offers a step change in the field by conducting a large number of three-dimensional numerical experiments, validated by physical tests, to develop a predictive equation for the maximum initial amplitude of tsunamis generated by subaerial landslides. We first conducted a few 3D physical experiments in a wave basin which were then applied for the validation of a 3D numerical model based on the Flow3D-HYDRO package. Consequently, we delivered 100 simulations using the validated model by varying parameters such as landslide volume, water depth, slope angle and travel distance. This large database was subsequently employed to develop a predictive equation for the maximum initial tsunami amplitude. For the first time, we considered travel distance as an independent parameter for developing the predictive equation, which can significantly improve the predication accuracy. The predictive equation was tested for the case of the 2018 Anak Krakatau subaerial landslide tsunami and produced satisfactory results.

Keywords

Tsunami, Subaerial landslide, Physical modelling, Numerical simulation, FLOW-3D HYDRO

1. Introduction and literature review

The Anak Krakatau landslide tsunami on 22nd December 2018 was a stark reminder of the dangers posed by subaerial landslide tsunamis (Ren et al., 2020Mulia et al. 2020a; Borrero et al., 2020Heidarzadeh et al., 2020Grilli et al., 2021). The collapse of the volcano’s southwest side into the ocean triggered a tsunami that struck the Sunda Strait, leading to approximately 450 fatalities (Syamsidik et al., 2020Mulia et al., 2020b) (Fig. 1). As shown in Fig. 1, landslide tsunamis (both submarine and subaerial) have been responsible for thousands of deaths and significant damage to coastal communities worldwide. These incidents underscored the critical need for advanced research into landslide-generated waves to aid in hazard prediction and mitigation. This is further emphasized by recent events such as the 28th of November 2020 landslide tsunami in the southern coast mountains of British Columbia (Canada), where an 18 million m3 rockslide generated a massive tsunami, with over 100 m wave run-up, causing significant environmental and infrastructural damage (Geertsema et al., 2022).

Fig 1

Physical modelling and numerical simulation are crucial tools in the study of landslide-induced waves due to their ability to replicate and analyse the complex dynamics of landslide events (Kim et al., 2020). In two-dimensional (2D) modelling, the discrepancy between dimensions can lead to an artificial overestimation of wave amplification (e.g., Heller and Spinneken, 2015). This limitation is overcome with 3D modelling, which enables the scaled-down representation of landslide-generated waves while avoiding the simplifications inherent in 2D approaches (Erosi et al., 2019). Another advantage of 3D modelling in studying landslide-generated waves is its ability to accurately depict the complex dynamics of wave propagation, including lateral and radial spreading from the slide impact zone, a feature unattainable with 2D models (Heller and Spinneken, 2015).

Physical experiments in tsunami research, as presented by authors such as Romano et al. (2020), McFall and Fritz (2016), and Heller and Spinneken (2015), have supported 3D modelling works through validation and calibration of the numerical models to capture the complexities of wave generation and propagation. Numerical modelling has increasingly complemented experimental approach in tsunami research due to the latter’s time and resource-intensive nature, particularly for 3D models (Li et al., 2019; Kim et al., 2021). Various numerical approaches have been employed, from Eulerian and Lagrangian frameworks to depth-averaged and Navier–Stokes models, enhancing our understanding of tsunami dynamics (Si et al., 2018Grilli et al., 2019Heidarzadeh et al., 20172020Iorio et al., 2021Zhang et al., 2021Kirby et al., 2022Wang et al., 20212022Hu et al., 2022). The sophisticated numerical techniques, including the Particle Finite Element Method and the Immersed Boundary Method, have also shown promising results in modelling highly dynamic landslide scenarios (Mulligan et al., 2020Chen et al., 2020). Among these methods and techniques, FLOW-3D HYDRO stands out in simulating landslide-generated tsunami waves due to its sophisticated technical features such as offering Tru Volume of Fluid (VOF) method for precise free surface tracking (e.g., Sabeti and Heidarzadeh 2022a). TruVOF distinguishes itself through a split Lagrangian approach, adeptly reducing cumulative volume errors in wave simulations by dynamically updating cell volume fractions and areas with each time step. Its intelligent adaptation of time step size ensures precise capture of evolving free surfaces, offering unparalleled accuracy in modelling complex fluid interfaces and behaviour (Flow Science, 2023).

Predictive equations play a crucial role in assessing the potential hazards associated with landslide-generated tsunami waves due to their ability to provide risk assessment and warnings. These equations can offer swift and reasonable evaluations of potential tsunami impacts in the absence of detailed numerical simulations, which can be time-consuming and expensive to produce. Among multiple factors and parameters within a landslide tsunami generation, the initial maximum wave amplitude (Fig. 1) stands out due to its critical role. While it is most likely that the initial wave generated by a landslide will have the highest amplitude, it is crucial to clarify that the term “initial maximum wave amplitude” refers to the highest amplitude within the first set of impulse waves. This parameter is essential in determining the tsunami’s impact severity, with higher amplitudes signalling a greater destructive potential (Sabeti and Heidarzadeh 2022a). Additionally, it plays a significant role in tsunami modelling, aiding in the prediction of wave propagation and the assessment of potential impacts.

In this study, we initially validate the FLOW-3D HYDRO model through a series of physical experiments conducted in a 3D wave tank at University of Bath (UK). Upon confirmation of the model’s accuracy, we use it to systematically vary parameters namely landslide volume, water depth, slope angle, and travel distance, creating an extensive database. Alongside this, we perform a sensitivity analysis on these variables to discern their impacts on the initial maximum wave amplitude. The generated database was consequently applied to derive a non-dimensional predictive equation aimed at estimating the initial maximum wave amplitude in real-world landslide tsunami events.

Two innovations of this study are: (i) The predictive equation of this study is based on a large number of 3D experiments whereas most of the previous equations were based on 2D results, and (ii) For the first time, the travel distance is included in the predictive equation as an independent parameter. To evaluate the performance of our predictive equation, we applied it to a previous real-world subaerial landslide tsunami, i.e., the Anak Krakatau 2018 event. Furthermore, we compare the performance of our predictive equation with other existing equations.

2. Data and methods

The methodology applied in this research is a combination of physical and numerical modelling. Limited physical modelling was performed in a 3D wave basin at the University of Bath (UK) to provide data for calibration and validation of the numerical model. After calibration and validation, the numerical model was employed to model a large number of landslide tsunami scenarios which allowed us to develop a database for deriving a predictive equation.

2.1. Physical experiments

To validate our numerical model, we conducted a series of physical experiments including two sets in a 3D wave basin at University of Bath, measuring 2.50 m in length (WL), 2.60 m in width (WW), and 0.60 m in height (WH) (Fig. 2a). Conducting two distinct sets of experiments (Table 1), each with different setups (travel distance, location, and water depth), provided a robust framework for validation of the numerical model. For wave measurement, we employed a twin wire wave gauge from HR Wallingford (https://equipit.hrwallingford.com). In these experiments, we used a concrete prism solid block, the dimensions of which are outlined in Table 2. In our experiments, we employed a concrete prism solid block with a density of 2600 kg/m3, chosen for its similarity to the natural density of landslides, akin to those observed with the 2018 Anak Krakatau tsunami, where the landslide composition is predominantly solid rather than granular. The block’s form has also been endorsed in prior studies (Watts, 1998Najafi-Jilani and Ataie-Ashtiani, 2008) as a suitable surrogate for modelling landslide-induced waves. A key aspect of our methodology was addressing scale effects, following the guidelines proposed by Heller et al. (2008) as it is described in Table 1. To enhance the reliability and accuracy of our experimental data, we conducted each physical experiment three times which revealed all three experimental waveforms were identical. This repetition was aimed at minimizing potential errors and inconsistencies in laboratory measurements.

Fig 2

Table 1. The locations and other information of the laboratory setups for making landslide-generated waves in the physical wave basin. This table details the specific parameters for each setup, including slope range (α), slide volume (V), kinematic viscosity (ν), water depth (h), travel distance (D), surface tension coefficient of water (σ), Reynolds number (R), Weber number (W), and the precise coordinates of the wave gauges (WG).

Labα(°)V (m³)h (m)D (m)WG’s Location(ν) (m²/s)(σ) (N/m)Acceptable range for avoiding scale effects*Observed values of W and R ⁎⁎
Lab 1452.60 × 10−30.2470.070X1=1.090 m1.01 × 10−60.073R > 3.0 × 105R1 = 3.80 × 105
Y1=1.210 m
W1 = 8.19 × 105
Z1=0.050mW >5.0 × 103
Lab 2452.60 × 10−30.2460.045X2=1.030 m1.01 × 10−60.073R2 = 3.78 × 105
Y2=1.210 mW2 = 8.13 × 105
Z2=0.050 m

The acceptable ranges for avoiding scale effects are based on the study by Heller et al. (2008).⁎⁎

The Reynolds number (R) is given by g0.5h1.5/ν, with ν denoting the kinematic viscosity. The Weber number (W) is W = ρgh2/σ, where σ represents surface tension coefficient and ρ = 1000kg/m3 is the density of water. In our experiments, conducted at a water temperature of approximately 20 °C, the kinematic viscosity (ν) and the surface tension coefficient of water (σ) are 1.01 × 10−6 m²/s and 0.073 N/m, respectively (Kestin et al., 1978).

Table 2. Specifications of the solid block used in physical experiments for generating subaerial landslides in the laboratory.

Solid-block attributesProperty metricsGeometric shape
Slide width (bs)0.26 mImage, table 2
Slide length (ls)0.20 m
Slide thickness (s)0.10 m
Slide volume (V)2.60 × 10−3 m3
Specific gravity, (γs)2.60
Slide weight (ms)6.86 kg

2.2. Numerical simulations applying FLOW-3D hydro

The detailed theoretical framework encompassing the governing equations, the computational methodologies employed, and the specific techniques used for tracking the water surface in these simulations are thoroughly detailed in the study by Sabeti et al. (2024). Here, we briefly explain some of the numerical details. We defined a uniform mesh for our flow domain, carefully crafted with a fine spatial resolution of 0.005 m (i.e., grid size). The dimensions of the numerical model directly matched those of our wave basin used in the physical experiment, being 2.60 m wide, 0.60 m deep, and 2.50 m long (Fig. 2). This design ensures comprehensive coverage of the study area. The output intervals of the numerical model are set at 0.02 s. This timing is consistent with the sampling rates of wave gauges used in laboratory settings. The friction coefficient in the FLOW-3D HYDRO is designated as 0.45. This value corresponds to the Coulombic friction measurements obtained in the laboratory, ensuring that the simulation accurately reflects real-world physical interactions.

In order to simulate the landslide motion, we applied coupled motion objects in FLOW-3D-HYDRO where the dynamics are predominantly driven by gravity and surface friction. This methodology stands in contrast to other models that necessitate explicit inputs of force and torque. This approach ensures that the simulation more accurately reflects the natural movement of landslides, which is heavily reliant on gravitational force and the interaction between sliding surfaces. The stability of the numerical simulations is governed by the Courant Number criterion (Courant et al., 1928), which dictates the maximum time step (Δt) for a given mesh size (Δx) and flow speed (U). According to Courant et al. (1928), this number is required to stay below one to ensure stability of numerical simulations. In our simulations, the Courant number is always maintained below one.

In alignment with the parameters of physical experiments, we set the fluid within the mesh to water, characterized by a density of 1000 kg/m³ at a temperature of 20 °C. Furthermore, we defined the top, front, and back surfaces of the mesh as symmetry planes. The remaining surfaces are designated as wall types, incorporating no-slip conditions to accurately simulate the interaction between the fluid and the boundaries. In terms of selection of an appropriate turbulence model, we selected the k–ω model that showed a better performance than other turbulence methods (e.g., Renormalization-Group) in a previous study (Sabeti et al., 2024). The simulations are conducted using a PC Intel® Core™ i7-10510U CPU with a frequency of 1.80 GHz, and a 16 GB RAM. On this PC, completion of a 3-s simulation required approximately 12.5 h.

2.3. Validation

The FLOW-3D HYDRO numerical model was validated using the two physical experiments (Fig. 3) outlined in Table 1. The level of agreement between observations (Oi) and simulations (Si) is examined using the following equation:(1)�=|��−����|×100where ε represents the mismatch error, Oi denotes the observed laboratory values, and Si represents the simulated values from the FLOW-3D HYDRO model. The results of this validation process revealed that our model could replicate the waves generated in the physical experiments with a reasonable degree of mismatch (ε): 14 % for Lab 1 and 8 % for Lab 2 experiments, respectively (Fig. 3). These values indicate that while the model is not perfect, it provides a sufficiently close approximation of the real-world phenomena.

Fig 3

In terms of mesh efficiency, we varied the mesh size to study sensitivity of the numerical results to mesh size. First, by halving the mesh size and then by doubling it, we repeated the modelling by keeping other parameters unchanged. This analysis guided that a mesh size of ∆x = 0.005 m is the most effective for the setup of this study. The total number of computational cells applying mesh size of 0.005 m is 9.269 × 106.

2.4. The dataset

The validated numerical model was employed to conduct 100 simulations, incorporating variations in four key landslide parameters namely water depth, slope angle, slide volume, and travel distance. This methodical approach was essential for a thorough sensitivity analysis of these variables, and for the creation of a detailed database to develop a predictive equation for maximum initial tsunami amplitude. Within the model, 15 distinct slide volumes were established, ranging from 0.10 × 10−3 m3 to 6.25 × 10−3 m3 (Table 3). The slope angle varied between 35° and 55°, and water depth ranged from 0.24 m to 0.27 m. The travel distance of the landslides was varied, spanning from 0.04 m to 0.07 m. Detailed configurations of each simulation, along with the maximum initial wave amplitudes and dominant wave periods are provided in Table 4.

Table 3. Geometrical information of the 15 solid blocks used in numerical modelling for generating landslide tsunamis. Parameters are: ls, slide length; bs, slide width; s, slide thickness; γs, specific gravity; and V, slide volume.

Solid blockls (m)bs (m)s (m)V (m3)γs
Block-10.3100.2600.1556.25 × 10−32.60
Block-20.3000.2600.1505.85 × 10−32.60
Block-30.2800.2600.1405.10 × 10−32.60
Block-40.2600.2600.1304.39 × 10−32.60
Block-50.2400.2600.1203.74 × 10−32.60
Block-60.2200.2600.1103.15 × 10−32.60
Block-70.2000.2600.1002.60 × 10−32.60
Block-80.1800.2600.0902.11 × 10−32.60
Block-90.1600.2600.0801.66 × 10−32.60
Block-100.1400.2600.0701.27 × 10−32.60
Block-110.1200.2600.0600.93 × 10−32.60
Block-120.1000.2600.0500.65 × 10−32.60
Block-130.0800.2600.0400.41 × 10−32.60
Block-140.0600.2600.0300.23 × 10−32.60
Block-150.0400.2600.0200.10 × 10−32.60

Table 4. The numerical simulation for the 100 tests performed in this study for subaerial solid-block landslide-generated waves. Parameters are aM, maximum wave amplitude; α, slope angle; h, water depth; D, travel distance; and T, dominant wave period. The location of the wave gauge is X=1.030 m, Y=1.210 m, and Z=0.050 m. The properties of various solid blocks are presented in Table 3.

Test-Block Noα (°)h (m)D (m)T(s)aM (m)
1Block-7450.2460.0290.5100.0153
2Block-7450.2460.0300.5050.0154
3Block-7450.2460.0310.5050.0156
4Block-7450.2460.0320.5050.0158
5Block-7450.2460.0330.5050.0159
6Block-7450.2460.0340.5050.0160
7Block-7450.2460.0350.5050.0162
8Block-7450.2460.0360.5050.0166
9Block-7450.2460.0370.5050.0167
10Block-7450.2460.0380.5050.0172
11Block-7450.2460.0390.5050.0178
12Block-7450.2460.0400.5050.0179
13Block-7450.2460.0410.5050.0181
14Block-7450.2460.0420.5050.0183
15Block-7450.2460.0430.5050.0190
16Block-7450.2460.0440.5050.0197
17Block-7450.2460.0450.5050.0199
18Block-7450.2460.0460.5050.0201
19Block-7450.2460.0470.5050.0191
20Block-7450.2460.0480.5050.0217
21Block-7450.2460.0490.5050.0220
22Block-7450.2460.0500.5050.0226
23Block-7450.2460.0510.5050.0236
24Block-7450.2460.0520.5050.0239
25Block-7450.2460.0530.5100.0240
26Block-7450.2460.0540.5050.0241
27Block-7450.2460.0550.5050.0246
28Block-7450.2460.0560.5050.0247
29Block-7450.2460.0570.5050.0248
30Block-7450.2460.0580.5050.0249
31Block-7450.2460.0590.5050.0251
32Block-7450.2460.0600.5050.0257
33Block-1450.2460.0450.5050.0319
34Block-2450.2460.0450.5050.0294
35Block-3450.2460.0450.5050.0282
36Block-4450.2460.0450.5050.0262
37Block-5450.2460.0450.5050.0243
38Block-6450.2460.0450.5050.0223
39Block-7450.2460.0450.5050.0196
40Block-8450.2460.0450.5050.0197
41Block-9450.2460.0450.5050.0198
42Block-10450.2460.0450.5050.0184
43Block-11450.2460.0450.5050.0173
44Block-12450.2460.0450.5050.0165
45Block-13450.2460.0450.4040.0153
46Block-14450.2460.0450.4040.0124
47Block-15450.2460.0450.5050.0066
48Block-7450.2020.0450.4040.0220
49Block-7450.2040.0450.4040.0219
50Block-7450.2060.0450.4040.0218
51Block-7450.2080.0450.4040.0217
52Block-7450.2100.0450.4040.0216
53Block-7450.2120.0450.4040.0215
54Block-7450.2140.0450.5050.0214
55Block-7450.2160.0450.5050.0214
56Block-7450.2180.0450.5050.0213
57Block-7450.2200.0450.5050.0212
58Block-7450.2220.0450.5050.0211
59Block-7450.2240.0450.5050.0208
60Block-7450.2260.0450.5050.0203
61Block-7450.2280.0450.5050.0202
62Block-7450.2300.0450.5050.0201
63Block-7450.2320.0450.5050.0201
64Block-7450.2340.0450.5050.0200
65Block-7450.2360.0450.5050.0199
66Block-7450.2380.0450.4040.0196
67Block-7450.2400.0450.4040.0194
68Block-7450.2420.0450.4040.0193
69Block-7450.2440.0450.4040.0192
70Block-7450.2460.0450.5050.0190
71Block-7450.2480.0450.5050.0189
72Block-7450.2500.0450.5050.0187
73Block-7450.2520.0450.5050.0187
74Block-7450.2540.0450.5050.0186
75Block-7450.2560.0450.5050.0184
76Block-7450.2580.0450.5050.0182
77Block-7450.2590.0450.5050.0183
78Block-7450.2600.0450.5050.0191
79Block-7450.2610.0450.5050.0192
80Block-7450.2620.0450.5050.0194
81Block-7450.2630.0450.5050.0195
82Block-7450.2640.0450.5050.0195
83Block-7450.2650.0450.5050.0197
84Block-7450.2660.0450.5050.0197
85Block-7450.2670.0450.5050.0198
86Block-7450.2700.0450.5050.0199
87Block-7300.2460.0450.5050.0101
88Block-7350.2460.0450.5050.0107
89Block-7360.2460.0450.5050.0111
90Block-7370.2460.0450.5050.0116
91Block-7380.2460.0450.5050.0117
92Block-7390.2460.0450.5050.0119
93Block-7400.2460.0450.5050.0121
94Block-7410.2460.0450.5050.0127
95Block-7420.2460.0450.4040.0154
96Block-7430.2460.0450.4040.0157
97Block-7440.2460.0450.4040.0162
98Block-7450.2460.0450.5050.0197
99Block-7500.2460.0450.5050.0221
100Block-7550.2460.0450.5050.0233

In all these 100 simulations, the wave gauge was consistently positioned at coordinates X=1.09 m, Y=1.21 m, and Z=0.05 m. The dominant wave period for each simulation was determined using the Fast Fourier Transform (FFT) function in MATLAB (MathWorks, 2023). Furthermore, the classification of wave types was carried out using a wave categorization graph according to Sorensen (2010), as shown in Fig. 4a. The results indicate that the majority of the simulated waves are on the border between intermediate and deep-water waves, and they are categorized as Stokes waves (Fig. 4a). Four sample waveforms from our 100 numerical experiments are provided in Fig. 4b.

Fig 4

The dataset in Table 4 was used to derive a new predictive equation that incorporates travel distance for the first time to estimate the initial maximum tsunami amplitude. In developing this equation, a genetic algorithm optimization technique was implemented using MATLAB (MathWorks 2023). This advanced approach entailed the use of genetic algorithms (GAs), an evolutionary algorithm type inspired by natural selection processes (MathWorks, 2023). This technique is iterative, involving selection, crossover, and mutation processes to evolve solutions over several generations. The goal was to identify the optimal coefficients and powers for each landslide parameter in the predictive equation, ensuring a robust and reliable model for estimating maximum wave amplitudes. Genetic Algorithms excel at optimizing complex models by navigating through extensive combinations of coefficients and exponents. GAs effectively identify highly suitable solutions for the non-linear and complex relationships between inputs (e.g., slide volume, slope angle, travel distance, water depth) and the output (i.e., maximum initial wave amplitude, aM). MATLAB’s computational environment enhances this process, providing robust tools for GA to adapt and evolve solutions iteratively, ensuring the precision of the predictive model (Onnen et al., 1997). This approach leverages MATLAB’s capabilities to fine-tune parameters dynamically, achieving an optimal equation that accurately estimates aM. It is important to highlight that the nondimensionalized version of this dataset is employed to develop a predictive equation which enables the equation to reproduce the maximum initial wave amplitude (aM) for various subaerial landslide cases, independent of their dimensional differences (e.g., Heler and Hager 2014Heller and Spinneken 2015Sabeti and Heidarzadeh 2022b). For this nondimensionalization, we employed the water depth (h) to nondimensionalize the slide volume (V/h3) and travel distance (D/h). The slide thickness (s) was applied to nondimensionalize the water depth (h/s).

2.5. Landslide velocity

In discussing the critical role of landslide velocity for simulating landslide-generated waves, we focus on the mechanisms of landslide motion and the techniques used to record landslide velocity in our simulations (Fig. 5). Also, we examine how these methods were applied in two distinct scenarios: Lab 1 and Lab 2 (see Table 1 for their details). Regarding the process of landslide movement, a slide starts from a stationary state, gaining momentum under the influence of gravity and this acceleration continues until the landslide collides with water, leading to a significant reduction in its speed before eventually coming to a stop (Fig. 5) (e.g., Panizzo et al. 2005).

Fig 5

To measure the landslide’s velocity in our simulations, we attached a probe at the centre of the slide, which supplied a time series of the velocity data. The slide’s velocity (vs) peaks at the moment it enters the water (Fig. 5), a point referred to as the impact time (tImp). Following this initial impact, the slides continue their underwater movement, eventually coming to a complete halt (tStop). Given the results in Fig. 5, it can be seen that Lab 1, with its longer travel distance (0.070 m), exhibits a higher peak velocity of 1.89 m/s. This increase in velocity is attributed to the extended travel distance allowing more time for the slide to accelerate under gravity. Whereas Lab 2, featuring a shorter travel distance (0.045 m), records a lower peak velocity of 1.78 m/s. This difference underscores how travel distance significantly influences the dynamics of landslide motion. After reaching the peak, both profiles show a sharp decrease in velocity, marking the transition to submarine motion until the slides come to a complete stop (tStop). There are noticeable differences observable in Fig. 5 between the Lab-1 and Lab-2 simulations, including the peaks at 0.3 s . These variations might stem from the placement of the wave gauge, which differs slightly in each scenario, as well as the water depth’s minor discrepancies and, the travel distance.

2.6. Effect of air entrainment

In this section we examine whether it is required to consider air entrainment for our modelling or not as the FLOW-3D HYDRO package is capable of modelling air entrainment. The process of air entrainment in water during a landslide tsunami and its subsequent transport involve two key components: the quantification of air entrainment at the water surface, and the simulation of the air’s transport within the fluid (Hirt, 2003). FLOW-3D HYDRO employs the air entrainment model to compute the volume of air entrained at the water’s surface utilizing three approaches: a constant density model, a variable density model accounting for bulking, and a buoyancy model that adds the Drift-FLUX mechanism to variable density conditions (Flow Science, 2023). The calculation of the entrainment rate is based on the following equation:(2)�������=������[2(��−�����−2�/���)]1/2where parameters are: Vair, volume of air; Cair, entrainment rate coefficient; As, surface area of fluid; ρ, fluid density; k, turbulent kinetic energy; gn, gravity normal to surface; Lt, turbulent length scale; and σ, surface tension coefficient. The value of k is directly computed from the Reynolds-averaged Navier-Stokes (RANS) (kw) calculations in our model.

In this study, we selected the variable density + Drift-FLUX model, which effectively captures the dynamics of phase separation and automatically activates the constant density and variable density models. This method simplifies the air-water mixture, treating it as a single, homogeneous fluid within each computational cell. For the phase volume fractions f1and f2​, the velocities are expressed in terms of the mixture and relative velocities, denoted as u and ur, respectively, as follows:(3)��1��+�.(�1�)=��1��+�.(�1�)−�.(�1�2��)=0(4)��2��+�.(�2�)=��2��+�.(�2�)−�.(�1�2��)=0

The outcomes from this simulation are displayed in Fig. 6, which indicates that the influence of air entrainment on the generated wave amplitude is approximately 2 %. A value of 0.02 for the entrained air volume fraction means that, in the simulated fluid, approximately 2 % of the volume is composed of entrained air. In other words, for every unit volume of the fluid-air mixture at that location, 2 % is air and the remaining 98 % is water. The configuration of Test-17 (Table 4) was employed for this simulation. While the effect of air entrainment is anticipated to be more significant in models of granular landslide-generated waves (Fritz, 2002), in our simulations we opted not to incorporate this module due to its negligible impact on the results.

Fig 6

3. Results

In this section, we begin by presenting a sequence of our 3D simulations capturing different time steps to illustrate the generation process of landslide-generated waves. Subsequently, we derive a new predictive equation to estimate the maximum initial wave amplitude of landslide-generated waves and assess its performance.

3.1. Wave generation and propagation

To demonstrate the wave generation process in our simulation, we reference Test-17 from Table 4, where we employed Block-7 (Tables 34). In this configuration, the slope angle was set to 45°, with a water depth of 0.246 m and a travel distance at 0.045 m (Fig. 7). At 0.220 s, the initial impact of the moving slide on the water is depicted, marking the onset of the wave generation process (Fig. 7a). Disturbances are localized to the immediate area of impact, with the rest of the water surface remaining undisturbed. At this time, a maximum water particle velocity of 1.0 m/s – 1.2 m/s is seen around the impact zone (Fig. 7d). Moving to 0.320 s, the development of the wave becomes apparent as energy transfer from the landslide to the water creates outwardly radiating waves with maximum water particle velocity of up to around 1.6 m/s – 1.8 m/s (Fig. 7b, e). By the time 0.670 s, the wave has fully developed and is propagating away from the impact point exhibiting maximum water particle velocity of up to 2.0 m/s – 2.1 m/s. Concentric wave fronts are visible, moving outwards in all directions, with a colour gradient signifying the highest wave amplitude near the point of landslide entry, diminishing with distance (Fig. 7c, f).

Fig 7

3.2. Influence of landslide parameters on tsunami amplitude

In this section, we investigate the effects of various landslide parameters namely slide volume (V), water depth (h), slipe angle (α) and travel distance (D) on the maximum initial wave amplitude (aM). Fig. 8 presents the outcome of these analyses. According to Fig. 8, the slide volume, slope angle, and travel distance exhibit a direct relationship with the wave amplitude, meaning that as these parameters increase, so does the amplitude. Conversely, water depth is inversely related to the maximum initial wave amplitude, suggesting that the deeper the water depth, the smaller the maximum wave amplitude will be (Fig. 8b).

Fig 8

Fig. 8a highlights the pronounced impact of slide volume on the aM, demonstrating a direct correlation between the two variables. For instance, in the range of slide volumes we modelled (Fig. 8a), The smallest slide volume tested, measuring 0.10 × 10−3 m3, generated a low initial wave amplitude (aM= 0.0066 m) (Table 4). In contrast, the largest volume tested, 6.25 × 10−3 m3, resulted in a significantly higher initial wave amplitude (aM= 0.0319 m) (Table 4). The extremities of these results emphasize the slide volume’s paramount impact on wave amplitude, further elucidated by their positions as the smallest and largest aM values across all conducted tests (Table 4). This is corroborated by findings from the literature (e.g., Murty, 2003), which align with the observed trend in our simulations.

The slope angle’s influence on aM was smooth. A steady increase of wave amplitude was observed as the slope angle increased (Fig. 8c). In examining travel distance, an anomaly was identified. At a travel distance of 0.047 m, there was an unexpected dip in aM, which deviates from the general increasing trend associated with longer travel distances. This singular instance could potentially be attributed to a numerical error. Beyond this point, the expected pattern of increasing aM with longer travel distances resumes, suggesting that the anomaly at 0.047 m is an outlier in an otherwise consistent trend, and thus this single data point was overlooked while deriving the predictive equation. Regarding the inverse relationship between water depth and wave amplitude, our result (Fig. 8b) is consistent with previous reports by Fritz et al. (2003), (2004), and Watts et al. (2005).

The insights from Fig. 8 informed the architecture of the predictive equation in the next Section, with slide volume, travel distance, and slope angle being multiplicatively linked to wave amplitude underscoring their direct correlations with wave amplitude. Conversely, water depth is incorporated as a divisor, representing its inverse relationship with wave amplitude. This structure encapsulates the dynamics between the landslide parameters and their influence on the maximum initial wave amplitude as discussed in more detail in the next Section.

3.3. Predictive equation

Building on our sensitivity analysis of landslide parameters, as detailed in Section 3.2, and utilizing our nondimensional dataset, we have derived a new predictive equation as follows:(5)��/ℎ=0.015(tan�)0.10(�ℎ3)0.90(�ℎ)0.10(ℎ�)−0.11where, V is sliding volume, h is water depth, α is slope angle, and s is landslide thickness. It is important to note that this equation is valid only for subaerial solid-block landslide tsunamis as all our experiments were for this type of waves. The performance of this equation in predicting simulation data is demonstrated by the satisfactory alignment of data points around a 45° line, indicating its accuracy and reliability with regard to the experimental dataset (Fig. 9). The quality of fit between the dataset and Eq. (5) is 91 % indicating that Eq. (5) represents the dataset very well. Table 5 presents Eq. (5) alongside four other similar equations previously published. Two significant distinctions between our Eq. (5) and these others are: (i) Eq. (5) is derived from 3D experiments, whereas the other four equations are based on 2D experiments. (ii) Unlike the other equations, our Eq. (5) incorporates travel distance as an independent parameter.

Fig 9

Table 5. Performance comparison among our newly-developed equation and existing equations for estimating the maximum initial amplitude (aM) of the 2018 Anak Krakatau subaerial landslide tsunami. Parameters: aM, initial maximum wave amplitude; h, water depth; vs, landslide velocity; V, slide volume; bs, slide width; ls, slide length; s, slide thickness; α, slope angle; and ����, volume of the final immersed landslide. We considered ����= V as the slide volume.

EventPredictive equationsAuthor (year)Observed aM (m) ⁎⁎Calculated aM (m)Error, ε (%) ⁎⁎⁎⁎
2018 Anak Krakatau tsunami (Subaerial landslide) *��/ℎ=1.32���ℎNoda (1970)1341340
��/ℎ=0.667(0.5(���ℎ)2)0.334(���)0.754(���)0.506(�ℎ)1.631Bolin et al. (2014) ⁎⁎⁎13459424334
��/ℎ=0.25(������ℎ2)0.8Robbe-Saule et al. (2021)1343177
��/ℎ=0.4545(tan�)0.062(�ℎ3)0.296(ℎ�)−0.235Sabeti and Heidarzadeh (2022b)1341266
��/ℎ=0.015(tan�)0.10(�ℎ3)0.911(�ℎ)0.10(ℎ�)−0.11This study1341302.9

Geometrical and kinematic parameters of the 2018 Anak Krakatau subaerial landslide based on Heidarzadeh et al. (2020)Grilli et al. (2019) and Grilli et al. (2021)V=2.11 × 107 m3h= 50 m; s= 114 m; α= 45°; ls=1250 m; bs= 2700 m; vs=44.9 m/s; D= 2500 m; aM= 100 m −150 m.⁎⁎

aM= An average value of aM = 134 m is considered in this study.⁎⁎⁎

The equation of Bolin et al. (2014) is based on the reformatted one reported by Lindstrøm (2016).⁎⁎⁎⁎

Error is calculated using Eq. (1), where the calculated aM is assumed as the simulated value.

Additionally, we evaluated the performance of this equation using the real-world data from the 2018 Anak Krakatau subaerial landslide tsunami. Based on previous studies (Heidarzadeh et al., 2020Grilli et al., 20192021), we were able to provide a list of parameters for the subaerial landslide and associated tsunami for the 2018 Anak Krakatau event (see footnote of Table 5). We note that the data of the 2018 Anak Krakatau event was not used while deriving Eq. (5). The results indicate that Eq. (5) predicts the initial amplitude of the 2018 Anak Krakatau tsunami as being 130 m indicating an error of 2.9 % compared to the reported average amplitude of 134 m for this event. This performance indicates an improvement compared to the previous equation reported by Sabeti and Heidarzadeh (2022a) (Table 5). In contrast, the equations from Robbe-Saule et al. (2021) and Bolin et al. (2014) demonstrate higher discrepancies of 4200 % and 77 %, respectively (Table 5). Although Noda’s (1970) equation reproduces the tsunami amplitude of 134 m accurately (Table 5), it is crucial to consider its limitations, notably not accounting for parameters such as slope angle and travel distance.

It is essential to recognize that both travel distance and slope angle significantly affect wave amplitude. In our model, captured in Eq. (5), we integrate the slope angle (α) through the tangent function, i.e., tan α. This choice diverges from traditional physical interpretations that often employ the cosine or sine function (e.g., Heller and Hager, 2014Watts et al., 2003). We opted for the tangent function because it more effectively reflects the direct impact of slope steepness on wave generation, yielding superior estimations compared to conventional methods.

The significance of this study lies in its application of both physical and numerical 3D experiments and the derivation of a predictive equation based on 3D results. Prior research, e.g. Heller et al. (2016), has reported notable discrepancies between 2D and 3D wave amplitudes, highlighting the important role of 3D experiments. It is worth noting that the suitability of applying an equation derived from either 2D or 3D data depends on the specific geometry and characteristics inherent in the problem being addressed. For instance, in the case of a long, narrow dam reservoir, an equation derived from 2D data would likely be more suitable. In such contexts, the primary dynamics of interest such as flow patterns and potential wave propagation are predominantly two-dimensional, occurring along the length and depth of the reservoir. This simplification to 2D for narrow dam reservoirs allows for more accurate modelling of these dynamics.

This study specifically investigates waves initiated by landslides, focusing on those characterized as solid blocks instead of granular flows, with slope angles confined to a range of 25° to 60°. We acknowledge the additional complexities encountered in real-world scenarios, such as dynamic density and velocity of landslides, which could affect the estimations. The developed equation in this study is specifically designed to predict the maximum initial amplitude of tsunamis for the aforementioned specified ranges and types of landslides.

4. Conclusions

Both physical and numerical experiments were undertaken in a 3D wave basin to study solid-block landslide-generated waves and to formulate a predictive equation for their maximum initial wave amplitude. At the beginning, two physical experiments were performed to validate and calibrate a 3D numerical model, which was subsequently utilized to generate 100 experiments by varying different landslide parameters. The generated database was then used to derive a predictive equation for the maximum initial wave amplitude of landslide tsunamis. The main features and outcomes are:

  • •The predictive equation of this study is exclusively derived from 3D data and exhibits a fitting quality of 91 % when applied to the database.
  • •For the first time, landslide travel distance was considered in the predictive equation. This inclusion provides more accuracy and flexibility for applying the equation.
  • •To further evaluate the performance of the predictive equation, it was applied to a real-world subaerial landslide tsunami (i.e., the 2018 Anak Krakatau event) and delivered satisfactory performance.

CRediT authorship contribution statement

Ramtin Sabeti: Conceptualization, Methodology, Validation, Software, Visualization, Writing – review & editing. Mohammad Heidarzadeh: Methodology, Data curation, Software, Writing – review & editing.

Declaration of competing interest

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

Funding

RS is supported by the Leverhulme Trust Grant No. RPG-2022-306. MH is funded by open funding of State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, grant number SKHL2101. We acknowledge University of Bath Institutional Open Access Fund. MH is also funded by the Great Britain Sasakawa Foundation grant no. 6217 (awarded in 2023).

Acknowledgements

Authors are sincerely grateful to the laboratory technician team, particularly Mr William Bazeley, at the Faculty of Engineering, University of Bath for their support during the laboratory physical modelling of this research. We appreciate the valuable insights provided by Mr. Brian Fox (Senior CFD Engineer at Flow Science, Inc.) regarding air entrainment modelling in FLOW-3D HYDRO. We acknowledge University of Bath Institutional Open Access Fund.

Data availability

  • All data used in this study are given in the body of the article.

References

Numerical Investigation of the Local Scour for Tripod Pile Foundation.

Numerical Investigation of the Local Scour for Tripod Pile Foundation.

Hassan, Waqed H.; Fadhe, Zahraa Mohammad; Thiab, Rifqa F.; Mahdi, Karrar

초록

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

주제어

BUILDING foundationsSURFACE waves (Seismic waves)FLOW velocityRANDOM fieldsDIMENSIONAL analysisFROUDE numberOCEAN waves

키워드

출판물

Mathematical Modelling of Engineering Problems, 2024, Vol 11, Issue 4, p903

ISSN 2369-0739

저자 소속기관

  • 1 Civil Engineering Department, Faculty of Engineering, University of Warith Al-Anbiyaa, Kerbala 56001, Iraq
  • 2 Civil Engineering Department, Faculty of Engineering, University of Kerbala, Kerbala 56001, Iraq
  • 3 Department of Radiological Techniques, College of Health and Medical Techniques, Al-Zahraa University for Women, Karbala 56100, Iraq
  • 4 Soil Physics and Land Management Group, Wageningen University & Research, Wageningen 6708 PB, Netherlands
Figure (17): Stream Lines Indicating Average Flow Speed in the Model with Various Nose shapes, Measured at Mid-Depth and at the Flow Surface Level, at a Flow Rate of 78 Liters per Second.

Conducting experimental and numerical studies to analyze theimpact of the base nose shape on flow hydraulics in PKW weirusing FLOW-3D

FLOW-3D를 사용하여 PKW 둑의 흐름 수력학에 대한 베이스 노즈 모양의 영향을 분석하기 위한 실험 및 수치 연구 수행

Behshad Mardasi 1
Rasoul Ilkhanipour Zeynali 2
Majid Heydari 3

Abstract

Weirs are essential structures used to manage excess water flow from behind dams to downstream areas. Enhancing discharge efficiency often involves extending the effective length of Piano Key Weirs (PKW) in dams or regulating flow within irrigation and drainage networks. This study employed both numerical and laboratory investigations to assess the impact of different base nose shapes installed beneath the outlet keys and varying Input to output key width ratios (Wi/Wo) on discharges ranging from 5 to 80 liters per second. Furthermore, the study aimed to achieve research objectives and compare the performance of Piano Key Weirs with Ogee Weir. For numerical simulation, the optimal number of cells for meshing was determined, and an appropriate turbulence model was selected. The results indicated that the numerical model accurately simulated the laboratory sample with a high degree of precision. Moreover, the numerical model closely approximated PKW for all parameters Q, H, and Cd compared to the laboratory sample. The findings revealed that in laboratory models with a maximum discharge area of 80 liters per second, the weir with Wi/Wo=1.2 and a flow head value of 285 mm exhibited the lowest value, whereas the weir with Wi/Wo=0.71 and a flow head value of 305 mm showed the highest, attributed to the higher discharge in the input-output ratio. Additionally, as the ratio of flow head to weir height H/P increased, the discharge coefficient Cd decreased. Comparing the flow conditions in weirs with different base nose shapes, it was observed that the weir with a spindle nose shape (PKW1.2S) outperformed the PKW with a flat (PKW1.2), semi-cylindrical (PKW1.2CL) and triangular base nose (PKW1.2TR). The results emphasized that models featuring semi-cylindrical and flat noses exhibited notable flow deviation and abrupt disruption upon impact with the nose. However, this effect was significantly reduced in models equipped with triangular and spindle-shaped noses. Also, the coefficient of discharge in PKW1.2S and PKW1.2TR weirs, compared to the PKW1.20 weir, increased by 27% and 20%, respectively.

웨어는 댐 뒤에서 하류 지역으로의 과도한 물 흐름을 관리하는 데 사용되는 필수 구조물입니다. 배출 효율을 높이는 데에는 댐의 피아노 키 위어(PKW) 유효 길이를 연장하거나 관개 및 배수 네트워크 내 흐름을 조절하는 것이 포함됩니다.

이 연구에서는 콘센트 키 아래에 설치된 다양한 베이스 노즈 모양과 초당 5~80리터 범위의 배출에 대한 다양한 입력 대 출력 키 너비 비율(Wi/Wo)의 영향을 평가하기 위해 수치 및 실험실 조사를 모두 사용했습니다. 또한 본 연구에서는 연구 목적을 달성하고 Piano Key Weir와 Ogee Weir의 성능을 비교하는 것을 목표로 했습니다.

수치 시뮬레이션을 위해 메시 생성을 위한 최적의 셀 수를 결정하고 적절한 난류 모델을 선택했습니다. 결과는 수치 모델이 높은 정밀도로 실험실 샘플을 정확하게 시뮬레이션했음을 나타냅니다. 더욱이, 수치 모델은 실험실 샘플과 비교하여 모든 매개변수 Q, H 및 Cd에 대해 PKW에 매우 근접했습니다.

연구 결과, 최대 배출 면적이 초당 80리터인 실험실 모델에서는 Wi/Wo=1.2, 플로우 헤드 값이 285mm인 웨어가 가장 낮은 값을 나타냈고, Wi/Wo=0.71 및 a인 웨어는 가장 낮은 값을 나타냈습니다. 플로우 헤드 값은 305mm로 가장 높은 것으로 나타났는데, 이는 입출력 비율의 높은 토출량에 기인합니다. 또한, 웨어 높이에 대한 유수두 비율 H/P가 증가함에 따라 유출계수 Cd는 감소하였다.

베이스 노즈 모양이 다른 웨어의 흐름 조건을 비교해 보면, 스핀들 노즈 모양(PKW1.2S)의 웨어가 평면(PKW1.2), 반원통형(PKW1.2CL) 및 삼각형 모양의 PKW보다 성능이 우수한 것으로 관찰되었습니다. 베이스 노즈(PKW1.2TR) 결과는 반원통형 및 편평한 노즈를 특징으로 하는 모델이 노즈에 충격을 가할 때 눈에 띄는 흐름 편차와 급격한 중단을 나타냄을 강조했습니다.

그러나 삼각형 및 방추형 노즈를 장착한 모델에서는 이러한 효과가 크게 감소했습니다. 또한 PKW1.20보에 비해 PKW1.2S보와 PKW1.2TR보의 유출계수는 각각 27%, 20% 증가하였다.

Keywords

Piano Key Weir, Base Nose Shape, Flow Hydraulics, Numerical Model, Triangular
Nose Shape, Flat Nose Shape, Semi-Cylindrical Nose Shape, Spindle Nose Shape

Figure (17): Stream Lines Indicating Average Flow Speed in the Model with Various Nose shapes, Measured at Mid-Depth and at the Flow Surface Level, at a Flow Rate of 78 Liters per Second.
Figure (17): Stream Lines Indicating Average Flow Speed in the Model with Various Nose shapes, Measured at Mid-Depth and at the Flow Surface Level, at a Flow Rate of 78 Liters per Second.

Reference

  1. Chow, V.T. (1959). “Open channel hydraulics.” McGraw-Hill Book Company, New York,
    NY.
  2. Ouamane, A., and Lempérière, F. (2006). “Design of a new economic shape of weir.” Proc.,
    Intl. Symp. on Dams in the Societies of the 21st Century, 463-470, Barcelona, Spain.
  3. Crookston, B. M., Anderson, A., Shearin-Feimster, L., and Tullis, B. P. (2014). “Mitigation
    investigation of flow-induced vibrations at a rehabilitated spillway.” Proc., 5th IAHR Intl.
    Symp. on Hydraulic Structures, Univ. of Queensland Brisbane, Brisbane, Australia.
  4. Machiels, O. (2012). “Experimental study of the hydraulic behaviour of Piano Key Weirs.”
    Ph.D. Dissertation, Faculty of Applied Science, University of Liège, Liège, Belgium.
  5. Blanc, P., and Lempérière, F. (2001). “Labyrinth spillways have a promising future.” Intl. J.
    of Hydropower and Dams, 8(4), 129-131.
  6. Muslu, Y. (2001). “Numerical analysis for lateral weir flow.” J. of Irrigation and Drainage
    Eng., ASCE, 127, 246.
  7. Erpicum, S., Machiels, O., Dewals, B., Pirotton, M., and Archambeau, P. (2012).
    “Numerical and physical hydraulic modeling of Piano Key Weirs.” Proc., ASIA 2012 – 4th
    Intl. Conf. on Water Resources and Renewable Energy Development in Asia, Chiang Mai,
    Thailand.
  8. Tullis, J.P., Amanian, N., and Waldron, D. (1995). “Design of Labyrinth Spillways.” J. of
    Hydraulic Eng., ASCE, 121.
  9. Lux, F.L., and Hinchcliff, D. (1985). “Design and construction of labyrinth spillways.”
    Proc., 15th Intl. Congress on Large Dams, ICOLD, Vol. 4, 249-274, Paris, France.
  10. Erpicum, S., Laugier, F., Ho to Khanh, M., & Pfister, M. (2017). Labyrinth and Piano Key
    Weirs III–PKW 2017. CRC Press, Boca Raton, FL.
  11. Kabiri-Samani, A., and Javaheri, A. (2012). “Discharge coefficient for free and submerged flow over Piano Key weirs.” Hydraulic Research J., 50(1), 114-120.
  12. Hien, T.C., Son, H.T., and Khanh, M.H.T. (2006). “Results of some piano Key weirs
    hydraulic model tests in Vietnam.” Proc., 22nd ICOLD Congress, CIGB/ICOLD,
    Barcelona, Spain.
  13. Laugier, F., Lochu, A., Gille, C., Leite Ribeiro, M., and Boillat, J-L. (2009). “Design and
    construction of a labyrinth PKW spillway at St-Marc Dam.” Hydropower and Dams J.,
    15(5), 100-107.
  14. Cicero, G.M., Menon, J.M., Luck, M., and Pinchard, T. (2011). “Experimental study of side
    and scale effects on hydraulic performances of a Piano Key Weir.” In: Erpicum, S., Laugier,
    F., Boillat, J-L, Pirotton, M., Reverchon, B., and Schleiss, A-J (Eds.), Labyrinth and Piano
    Key Weirs, 167-172, CRC Press, London.
  15. Pralong, J., Vermeulen, J., Blancher, B., Laugier, F., Erpicum, S., Machiels, O., Pirotton,
    M., Boillat, J.L, Leite Ribeiro, M., and Schleiss, A.J. (2011). “A naming convention for the
    piano key weirs geometrical parameters.” In: Erpicum, S., Laugier, F., Boillat, J-L, Pirotton,
    M., Reverchon, B., and Schleiss, A-J (Eds.), Labyrinth and Piano Key Weirs, 271-278,
    CRC Press, London.
  16. Denys, F. J. M., and Basson, G. R. (2018). “Transient hydrodynamics of Piano Key Weirs.”
    Proc., 7th IAHR Intl. Symp. on Hydraulic Structures, ISHS2018, 518-527,
    DigitalCommons@USU, Logan, UT.
  17. Anderson, A., and Tullis, B. P. (2018). “Finite crest length weir nappe oscillation.” J. of
    Hydraulic Eng., ASCE, 144(6), 04018020. https://doi.org/10.1061/(ASCE)HY.1943-
    7900.0001461
  18. Erpicum, S., Laugier, F., Boillat, J.-L., Pirotton, M., Reverchon, B., and Schleiss, A. J.
    (2011). “Labyrinth and Piano Key Weirs–PKW 2011.” CRC Press, Boca Raton, FL.
  19. Aydin, C.M., and Emiroglu, M.E. (2011). “Determination of capacity of labyrinth side weir
    by CFD.” Flow Measurement and Instrumentation, 29, 1-8.
  20. Cicero, G.M., Delisle, J.R., Lefebvre, V., and Vermeulen, J. (2013). “Experimental and
    numerical study of the hydraulic performance of a trapezoidal PKW.” Proc., Intl. Workshop
    on Labyrinths and Piano Key Weirs PKW II 2013, 265-272, CRC Press.
  21. Anderson, R. M. (2011). “Piano Key Weir Head Discharge Relationships.” Master’s Thesis,
    Utah State University, Logan, Utah.
  22. Crookston, B.M., Anderson, R.M., and Tullis, B.P. (2018). “Free-flow discharge estimation
    method for Piano Key weir geometries.” J. of Hydro-environment Research, 19, 160-167
Coupled CFD-DEM simulation of interfacial fluid–particle interaction during binder jet 3D printing

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

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

Joshua J. Wagner, C. Fred Higgs III

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

Abstract

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

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

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

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

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

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

Introduction

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

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

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

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

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

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

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

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

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

Section snippets

Mathematical description of interfacial fluid–particle interaction

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

CFD solver for incompressible flow with multifluid interfaces

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

DEM solver for solid particle dynamics

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

Unified CFD-DEM solver

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

Binder jet process modeling and validation experiments

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

Conclusions

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

CRediT authorship contribution statement

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

Declaration of competing interest

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

Acknowledgments

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

References (155)

그림 12: 시간 경과에 따른 속도 카운터: 30초 그림 13: 시간 경과에 따른 속도 카운터: 20초

Gemelo digital del puente de Kalix: cargas estructurales de futuros eventos climáticos extremos

Kalix Bridge 디지털 트윈: 미래 극한 기후 현상으로 인한 구조적 부하

Este documento está relacionado con un proyecto en curso para el cual se está desarrollando e implementando un gemelo digital estructural del puente de Kalix en Suecia.
이 문서는 스웨덴 Kalix 교량의 구조적 디지털 트윈이 개발 및 구현되고 있는 진행 중인 프로젝트와 관련이 있습니다.

Autores: Mahyar Kazemian1, Sajad Nikdel2, Mehrnaz MohammadEsmaeili3, Vahid Nik4, Kamyab Zandi*5

RESUMEN Las cargas ambientales, como el viento y el caudal de los ríos, juegan un papel esencial en el diseño y evaluación estructural de puentes de grandes luces. El cambio climático y los eventos climáticos extremos son amenazas para la confiabilidad y seguridad de la red de transporte.

Esto ha llevado a una creciente demanda de modelos de gemelos digitales para investigar la resistencia de los puentes en condiciones climáticas extremas. El puente de Kalix, construido sobre el río Kalix en Suecia en 1956, se utiliza como banco de pruebas en este contexto.

La estructura del puente, realizada en hormigón postensado, consta de cinco vanos, siendo el más largo de 94 m. En este estudio, las características aerodinámicas y los valores extremos de la simulación numérica del viento, como la presión en la superficie, se obtienen utilizando la simulación de remolinos desprendidos retardados (DDES) de Spalart-Allmaras como un enfoque de turbulencia RANS-LES híbrido que es práctico y computacionalmente eficiente para cerca de la pared densidad de malla impuesta por el método LES.

La presión del viento en la superficie se obtiene para tres escenarios climáticos extremos, que incluyen un clima con mucho viento, un clima extremadamente frío y el valor de cálculo para un período de retorno de 3000 años. El resultado indica diferencias significativas en la presión del viento en la superficie debido a las capas de tiempo que provienen de la simulación del flujo de viento transitorio. Para evaluar el comportamiento estructural en el escenario de viento crítico, se considera el valor más alto de presión en la superficie para cada escenario.

Además, se realiza un estudio hidrodinámico en los pilares del puente, en el que se simula el flujo del río por el método VOF, y se examina el proceso de movimiento del agua alrededor de los pilares de forma transitoria y en diferentes momentos. En cada una de las superficies del pilar se calcula la presión superficial aplicada por el caudal del río con el caudal volumétrico más alto registrado.

Para simular el flujo del río, se ha utilizado la información y las condiciones meteorológicas registradas en períodos anteriores. Los resultados muestran que la presión en la superficie en el momento en que el flujo del río golpea los pilares es mucho mayor que en los momentos posteriores. Esta cantidad de presión se puede usar como carga crítica en los cálculos de interacción fluido-estructura (FSI).

Finalmente, para ambas secciones, la presión en la superficie del viento, el campo de velocidades con respecto a las líneas de sondas auxiliares, los contornos del movimiento circunferencial del agua alrededor de los pilares y el diagrama de presión en ellos se informan en diferentes intervalos de tiempo.

요약 바람, 강의 흐름과 같은 환경 하중은 장대 교량의 설계 및 구조 평가에 필수적인 역할을 합니다. 기후 변화와 기상 이변은 교통 네트워크의 신뢰성과 보안에 위협이 됩니다.

이로 인해 극한 기상 조건에서 교량의 복원력을 조사하기 위한 디지털 트윈 모델에 대한 수요가 증가했습니다. 1956년 스웨덴 칼릭스 강 위에 건설된 칼릭스 다리는 이러한 맥락에서 테스트베드로 사용됩니다.

포스트텐션 콘크리트로 만들어진 교량 구조는 5개 경간으로 구성되며 가장 긴 길이는 94m입니다. 본 연구에서는 하이브리드 RANS-LES 난류 접근 방식인 Spalart-Allmaras 지연 분리 와류 시뮬레이션(DDES)을 사용하여 수치적 바람 시뮬레이션의 공기역학적 특성과 표면압 등 극한값을 얻습니다. LES 방법으로 부과된 벽 근처 메쉬 밀도.

바람이 많이 부는 기후, 극도로 추운 기후, 그리고 3000년의 반환 기간에 대해 계산된 값을 포함한 세 가지 극한 기후 시나리오에 대해 표면 풍압을 얻습니다. 결과는 과도 풍류 시뮬레이션에서 나오는 시간 레이어로 인해 표면 풍압에 상당한 차이가 있음을 나타냅니다. 임계 바람 시나리오에서 구조적 거동을 평가하기 위해 각 시나리오에 대해 가장 높은 표면 압력 값이 고려됩니다.

또한 교량 기둥에 대한 유체 역학 연구를 수행하여 하천의 흐름을 VOF 방법으로 시뮬레이션하고 기둥 주변의 물 이동 과정을 일시적이고 다른 시간에 조사합니다. 각 기둥 표면에서 기록된 체적 유량이 가장 높은 강의 흐름에 의해 적용되는 표면 압력이 계산됩니다.

강의 흐름을 시뮬레이션하기 위해 이전 기간에 기록된 정보와 기상 조건이 사용되었습니다. 결과는 강의 흐름이 기둥에 닿는 순간의 표면 압력이 나중에 순간보다 훨씬 높다는 것을 보여줍니다. 이 압력의 양은 유체-구조 상호작용(FSI) 계산에서 임계 하중으로 사용될 수 있습니다.

마지막으로 두 섹션 모두 바람 표면의 압력, 보조 프로브 라인에 대한 속도장, 기둥 주위 물의 원주 운동 윤곽 및 압력 다이어그램이 서로 다른 시간 간격으로 보고됩니다.

키워드: 디지털 트윈 , 풍력 공학, 콘크리트 교량, 유체역학, CFD 시뮬레이션, DDES 난류 모델, Kalix 교량

Palabras clave: Gemelo digital , Ingeniería eólica, Puente de hormigón, Hidrodinámica, Simulación CFD, Modelo de turbulencia DDES, Puente Kalix

1. Introducción

Las infraestructuras de transporte son la columna vertebral de nuestra sociedad y los puentes son el cuello de botella de la red de transporte [1]. Además, el cambio climático que da como resultado tasas de deterioro más altas y los eventos climáticos extremos son amenazas importantes para la confiabilidad y seguridad de las redes de transporte. Durante la última década, muchos puentes se han dañado o fallado por condiciones climáticas extremas como tifones e inundaciones.

Wang et al. analizó los impactos del cambio climático y mostró que se espera que el deterioro de los puentes de hormigón sea aún peor que en la actualidad, y se prevé que los eventos climáticos extremos sean más frecuentes y con mayor gravedad [2].

Además, la demanda de capacidad de carga a menudo aumenta con el tiempo, por ejemplo, debido al uso de camiones más pesados para el transporte de madera en el norte de Europa y América del Norte. Por lo tanto, existe una necesidad creciente de métodos confiables para evaluar la resistencia estructural de la red de transporte en condiciones climáticas extremas que tengan en cuenta los escenarios futuros de cambio climático.

Los activos de transporte por carretera se diseñan, construyen y explotan basándose en numerosas fuentes de datos y varios modelos. Por lo tanto, los ingenieros de diseño usan modelos establecidos proporcionados por las normas; ingenieros de construccion
documentar los datos en el material real y proporcionar planos según lo construido; los operadores recopilan datos sobre el tráfico, realizan inspecciones y planifican el mantenimiento; los científicos del clima combinan datos y modelos climáticos para
predecir eventos climáticos futuros, y los ingenieros de evaluación calculan el impacto de la carga climática extrema en la estructura.

Dadas las fuentes abrumadoras y la complejidad de los datos y modelos, es posible que la información y los cálculos actualizados no estén disponibles para decisiones cruciales, por ejemplo, con respecto a la seguridad estructural y la operabilidad de la infraestructura durante episodios de eventos extremos. La falta de una integración perfecta entre los datos de la infraestructura, los modelos estructurales y la toma de decisiones a nivel del sistema es una limitación importante de las soluciones actuales, lo que conduce a la inadaptación e incertidumbre y crea costos e ineficiencias.

El gemelo digital estructural de la infraestructura es una simulación estructural viva que reúne todos los datos y modelos y se actualiza desde múltiples fuentes para representar su contraparte física. El Digital Twin estructural, mantenido durante todo el ciclo de vida de un activo y fácilmente accesible en cualquier momento, proporciona al propietario/usuarios de la infraestructura una idea temprana de los riesgos potenciales para la movilidad inducidos por eventos climáticos, cargas de vehículos pesados e incluso el envejecimiento de un infraestructura de transporte.

En un proyecto en curso, estamos desarrollando e implementando un gemelo digital estructural para el puente de Kalix en Suecia. El objetivo general del presente artículo es presentar un método y estudiar los resultados de la cuantificación de las cargas estructurales resultantes de eventos climáticos extremos basados en escenarios climáticos futuros para el puente de Kalix. El puente de Kalix, construido sobre el río Kalix en Suecia en 1956, está hecho de una viga cajón de hormigón postensado. El puente se utiliza como banco de pruebas para la demostración de métodos de evaluación y control de la salud estructural (SHM) de última generación.

El objetivo específico de la investigación actual es dar cuenta de parámetros climáticos como el viento y el flujo de agua, que imponen cargas estáticas y dinámicas en las estructuras. Nuestro método, en el primer paso, consiste en simulaciones de flujo de viento y simulaciones de flujo de agua utilizando un modelado CFD transitorio basado en el modelo de turbulencia LES/DES para cuantificar las cargas de viento e hidráulicas; esto constituye el punto focal principal de este artículo.

En el siguiente paso, se estudiará la respuesta estructural del puente mediante la transformación de los perfiles de carga eólica e hidráulica en cargas estructurales en el análisis de EF estructural no lineal. Por último, el modelo estructural se actualizará incorporando sin problemas los datos del SHM y, por lo tanto, creando un gemelo digital estructural que refleje la verdadera respuesta de la estructura. Los dos primeros enfoques de investigación permanecen fuera del alcance inmediato del presente artículo.

2. Descripción del puente de Kalix

El puente de Kalix consta de 5 vanos largos de los cuales el más largo tiene unos 94 metros y el más corto 43,85 m. El puente es de hormigón postensado, el cual se cuela in situ de forma segmentaria y una viga cajón no prismática como se muestra en la Fig. 1. El puente es simétrico en geometría y hay una bisagra en el punto medio. El ancho del tablero del puente en la losa superior e inferior es de aproximadamente 13 my 7,5 m, respectivamente. El espesor del muro es de 45 cm y el espesor de la losa inferior varía de 20 cm a
50 cm.

Fig. 1. Geometría y secciones del puente

Fig. 1. Geometría y secciones del puente

3. Simulación de viento

Las pruebas en túnel de viento solían ser la única forma de examinar la reacción de los puentes a las cargas de viento Consulte [3]; sin embargo, estos experimentos requieren mucho tiempo y son costosos. Se requieren cerca de 6 a 8 semanas para realizar una prueba típica en un túnel de viento Consulte [4]. Los últimos logros en la capacidad computacional de las computadoras brindan oportunidades para la simulación práctica del viento alrededor de puentes utilizando la dinámica de fluidos computacional (CFD).

Es beneficioso investigar la presión del viento en los componentes del puente utilizando una simulación por computadora. Es necesario determinar los parámetros de simulación del puente y el campo de viento a su alrededor; por lo tanto, se pueden evaluar con precisión sus impactos en las fuerzas aplicadas en el puente.

Las demandas de diseño de las estructuras de puentes requieren una investigación rigurosa de la acción del viento, especialmente en condiciones climáticas extremas. Garantizar la estabilidad de los puentes de grandes luces, ya que sus características y formaciones son más propensas a la carga de viento, se encuentra entre las principales consideraciones de diseño [3].

3.1. Parámetros de simulación

La velocidad básica del viento se elige 22 m/s según el mapa de viento de Suecia y la ubicación del puente de Kalix según EN 1991-1-4 [5] y el código sueco BFS 2019: 1 EKS 11; ver figura 1. La superficie libre sobre el agua se considera un área expuesta a la carga de viento. La dirección del ataque del viento dominante se considera perpendicular al tablero del puente.

Las simulaciones actuales se basan en tres escenarios que incluyen: viento extremo, frío extremo y valor de diseño para un período de retorno de 3000 años. Cada condición tiene diferentes valores de temperatura, viento básico
velocidad, viscosidad cinemática y densidad del aire, como se muestra en la Tabla 1. Los conjuntos de datos meteorológicos se sintetizaron para dos semanas meteorológicas extremas durante el período de 30 años de 2040-2069, considerando 13 escenarios climáticos futuros diferentes con diferentes modelos climáticos globales (GCM) y rutas de concentración representativas (RCP).

Se seleccionaron una semana de frío extremo y una semana de viento extremo utilizando el enfoque desarrollado
de Nik [7]. El planteamiento se adaptó a las necesidades de este trabajo, considerando el horario semanal en lugar de mensual. Se ha verificado la aplicación del enfoque para simulaciones complejas, incluidos los sistemas de energía Consulte [7] Consulte [8], hidrotermal Consulte [ 9] y simulaciones de microclimas Consulte [10].

Para considerar las condiciones climáticas extremas de una infraestructura muy importante, el valor de la velocidad básica del viento debe transferirse del período de retorno de 50 años a 3000 años como se indica en la ecuación 1 [6]. El perfil de velocidad y turbulencia se crea en base a EN 1991-1-4 [5] para la categoría de terreno 0 (Z0 = 0,003 my Zmín = 1 m), donde Z0 y Zmín son la longitud de rugosidad y la altura mínima, respectivamente. La variación de la velocidad del viento con la altura se define en la ecuación 2, donde co (z) es el factor de orografía tomado como 1, vm (z) es la velocidad media del viento a la altura z, kr es el factor del terreno que depende de la longitud de la rugosidad , e Iv (z) es la intensidad de la turbulencia; ver ecuación 3.���50=[0.36+0.1ln12�]     1�����=��·ln��0·���  [2]���=�����=�1�0�·ln�/�0  ��� ����≤�≤����  [3]���=������                                ��� �<����                   [4]

Velocidad del viento, variación de la velocidad del viento con la altura, intensidad de la turbulencia

Se calcula que el valor de la velocidad del viento para T = período de retorno de 3000 años es de 31 m/s; por lo tanto, los diagramas de velocidad del viento e intensidad de turbulencia se obtienen como se muestra en la figura 2.

Tabla. 1. Información meteorológica para tres escenarios

Tabla. 1. Información meteorológica para tres escenarios

Fig.  2. Valor de cálculo para la información del periodo de retorno de 3000 años: (a) Velocidad del viento y (b) Perfil de intensidad de turbulencia, y (c) Especificaciones del modelo

Fig. 2. Valor de cálculo para la información del periodo de retorno de 3000 años: (a) Velocidad del viento y (b) Intensidad de la turbulencia perfil, y (c) Especificaciones del modelo

3.2. Modelo de turbulencia

Para que las investigaciones sean precisas en el flujo alrededor de estructuras importantes como puentes, se aplica un enfoque híbrido que incluye simulaciones de remolinos desprendidos retardados (DDES) y es computacionalmente eficiente [11] [12]. Este modelo de turbulencia usa un método RANS cerca de las capas límite y el método LES lejos de las capas límite y en el área del flujo de la región separada ‘.

En el primer paso, el enfoque de simulación de remolinos separados se ha ampliado para adquirir predicciones de fuerza fiables en los modelos con un gran impacto del flujo separado. Hay varios ejemplos en la parte de revisión de Spalart Consulte [11] para varios casos que usan la aplicación del modelo de turbulencia de simulación de remolino separado (DES).

La formulación DES inicial [13] se desarrolla utilizando el enfoque de Spalart-Allmaras. Con respecto a la transición del enfoque RANS al LES, se revisa el término de destrucción en la ecuación de transporte de viscosidad modificada: la distancia entre un punto en el dominio y la superficie sólida más cercana (d) se sustituye por el factor introducido por:�~=���(�.����·∆)

Factor que sustituye la distancia entre el punto en el dominio y la superficie sólida más cercana (d)

donde CDES es un coeficiente, se considera como 0,65 y Δ es una escala de longitud asociada con el espaciado de la rejilla local:�=���(��.��.��)

Escala de longitud asociada con el espaciado de rejilla local

Se ha empleado un enfoque modificado de DES, conocido como simulación de remolinos desprendidos retardados (DDES), para dominar el probable problema de la “separación inducida por la rejilla” (GIS) que está relacionado con la geometría de la rejilla. El objetivo de este nuevo enfoque es confirmar que el modelado de turbulencia se mantiene en modo RANS en todas las capas de contorno [14]. Por lo tanto, la definición del parámetro se modifica como se define:�~=�-�����(0. �-����·�)   6

Modificación del parámetro d

donde fd es una función de filtro que considera un valor de 0 en las capas límite cercanas al muro (zona RANS) y un valor de 1 en las áreas donde se realizó la separación del flujo (zona LES).

3.3. Rejilla computacional y resultados

RWIND 2.01 Pro se emplea para la simulación de viento CFD, que usa el código CFD externo OpenFOAM® versión 17.10. La simulación CFD tridimensional se realiza como una simulación de viento transitorio para flujo turbulento incompresible utilizando el algoritmo SIMPLE (Método semi-implícito para ecuaciones vinculadas a presión).

En la simulación actual, el solucionador de estado estacionario se considera como la condición inicial, lo que significa que cuando se está calculando el flujo transitorio, el cálculo del estado estacionario de la condición inicial comienza en la primera parte de la simulación y tan pronto como se calcula. completado, el cálculo de transitorios se iniciará automáticamente.

Fig.  3. Dominio del túnel de viento y rejilla computacional de referencia (8.057.279 celdas)

Fig. 3. Dominio del túnel de viento y rejilla computacional de referencia (8.057.279 celdas)

La cuadrícula computacional se realiza mediante 8.057.279 celdas tridimensionales y 8.820.901 nudos, también se consideran las dimensiones del dominio del túnel de viento 2000 m * 1000 m * 100 m (largo, ancho, alto) como se muestra en la figura 3. El volumen mínimo de la celda es de 6,34 * 10-5 m3, el volumen máximo es de 812,30 m3 y la desviación máxima es de 1,80.

La presión residual final se considera 5 * 10-5. El proceso de generación de mallas e independencia de la rejilla se ha realizado utilizando los cuatro tamaños de malla que se muestran en la figura 4 para la malla de referencia, y finalmente se ha conseguido la independencia de la rejilla.

Fig.  4. Estudio de rejilla de cuatro tamaños de malla computacional a través de la línea de sondeo.

Fig. 4. Estudio de rejilla de cuatro tamaños de malla computacional a través de la línea de sondeo.

Se han realizado tres simulaciones para obtener el valor de la presión del viento para condiciones climáticas extremas y el valor de cálculo del viento que se muestra en la Fig. 5. Para cada escenario, el resultado de la presión del viento se obtiene utilizando el modelo de turbulencia transitoria DDES con respecto a 30 (s) de duración que incluye 60 capas de tiempo (Δt = 0,5 s).

Se puede observar que el área frontal del puente está expuesta a la presión del viento positiva y la cantidad de presión aumenta en la altura cerca del borde del tablero para todos los escenarios. Además, la Fig. 5. ilustra los valores negativos de la presión del viento en su totalidad en la superficie de la cubierta. El valor de pertenencia para el período de 3000 años es mucho más alto que los otros escenarios.

Es importante tener en cuenta que el intervalo de la velocidad del viento de entrada tiene un gran impacto en el valor de la presión en la superficie más que en los otros parámetros. Además, para cada escenario, el intervalo más alto de presión del viento y succión durante el tiempo total debe considerarse como una carga de viento crítica impuesta a la estructura. El valor más bajo de la presión en la superficie se obtiene en el escenario de condiciones de frío extremo, mientras que en condiciones de mucho viento, el valor de la presión se vuelve un orden de magnitud más alto.

Fig.  5. Contorno de presión superficial y diagrama para 60 capas de tiempo (Δt = 0.5 s) a través de una línea de sondeo para tres escenarios.

Fig. 5. Contorno de presión superficial y diagrama para 60 capas de tiempo (Δt = 0.5 s) a través de una línea de sondeo para tres escenarios.

Además, es importante tener en cuenta que el comportamiento del puente sería completamente diferente debido a las diferentes temperaturas del aire, y puede ocurrir un posible caso crítico en el escenario que experimente una presión menor. Con respecto al valor de entrada de cada escenario, el rango más alto de presión del viento pertenece al nivel de diseño debido al período de retorno de 3000 años, que ha recibido la velocidad del viento más alta como velocidad de entrada.

4. Simulación hidráulica

Los pilares de los puentes a través del río pueden bloquear el flujo al reducir la sección transversal del río, crear corrientes parásitas locales y cambiar la velocidad del flujo, lo que puede ejercer presión en las superficies de los pilares. Cuando el río fluye hacia los pilares del puente, el proceso del flujo de agua alrededor de la base se puede dividir en dos partes: aplicando presión en el momento en que el agua golpea el pilar del puente y después de la presión inicial cuando el agua fluye alrededor de los pilares [15].

Cuando el agua alcanza los pilares del puente a una cierta velocidad, el efecto de la presión sobre los pilares es mucho mayor que la presión del fluido que queda a su alrededor. Debido a los desarrollos de la ciencia de la computación, así como al desarrollo cada vez mayor de los códigos dinámicos de fluidos computacionales, se han utilizado ampliamente varias simulaciones numéricas y se ha demostrado que los resultados de muchas simulaciones son consistentes con los resultados experimentales [16].

Por ello, en esta investigación se ha utilizado el método de la dinámica de fluidos computacional para simular los fenómenos que gobiernan el comportamiento del flujo de los ríos. Para este estudio se ha seleccionado una solución tridimensional basada en cálculos numéricos utilizando el modelo de turbulencia LES. La simulación tridimensional del flujo del río en diferentes direcciones y velocidades nos permite calcular y analizar todas las presiones en la superficie de los pilares del puente en diferentes intervalos de tiempo.

4.1. Parámetros de simulación

El flujo del río se puede definir como un flujo de dos fases, que incluye agua y aire, en un canal abierto. El flujo de canal abierto es un flujo de fluido con una superficie libre en la que la presión atmosférica se distribuye uniformemente y se crea por el peso del fluido. Para simular este tipo de flujo se utiliza el método multifase VOF.

El programa Flow3D, disponible en el mercado, utiliza los métodos de fracciones volumétricas VOF y FAVOF. En el método VOF, el dominio de modelado se divide primero en celdas de elementos o volúmenes de controles más pequeños. Para los elementos que contienen fluidos, se mantienen valores numéricos para cada una de las variables de flujo dentro de ellos.

Estos valores representan la media volumétrica de los valores en cada elemento. En las corrientes superficiales libres, no todas las celdas están llenas de líquido; algunas celdas en la superficie de flujo están medio llenas. En este caso, se define una cantidad llamada volumen de fluido, F, que representa la parte de la celda que se llena con el fluido.

Después de determinar la posición y el ángulo de la superficie del flujo, será posible aplicar las condiciones de contorno apropiadas en la superficie del flujo para calcular el movimiento del fluido. A medida que se mueve el fluido, el valor de F también cambia con él. Las superficies libres son monitoreadas automáticamente por el movimiento de fluido dentro de una red fija. El método FAVOR se usa para determinar la geometría.

También se puede usar otra cantidad de fracción volumétrica para determinar el nivel de un cuerpo rígido desocupado ( Vf ). Cuando se conoce el volumen que ocupa el cuerpo rígido en cada celda, el límite del fluido dentro de la red fija se puede determinar como VOF. Este límite se usa para determinar las condiciones de contorno del muro que sigue el arroyo. En general, la ecuación de continuidad de masa es la siguiente:��𝜕�𝜕�+𝜕𝜕�(����)+�𝜕𝜕�(����)+𝜕𝜕�(����)+������=����   10

Ecuación de continuidad de masa

Las ecuaciones de movimiento para los componentes de la velocidad de un fluido en coordenadas 3D, o en otras palabras, las ecuaciones de Navier-Stokes, son las siguientes:𝜕�𝜕�+1�����𝜕�𝜕�+���𝜕�𝜕�+���𝜕�𝜕�+��2�����=-1�𝜕�𝜕�+��+��-��-��������-��-���    11𝜕�𝜕�+1�����𝜕�𝜕�+���𝜕�𝜕�+���𝜕�𝜕�+��������=-�1�𝜕�𝜕�+��+��-��-��������-��-���  12𝜕�𝜕�+1�����𝜕�𝜕�+���𝜕�𝜕�+���𝜕�𝜕�=-1�𝜕�𝜕�+��+��-��-��������-��-���              13

Ecuaciones de Navier-Stokes

Donde VF es la relación del volumen abierto al flujo, ρ es la densidad del fluido, (u, v, w) son las componentes de la velocidad en las direcciones x, y y z, respectivamente, R SOR es la función de la fuente, (Ax, Ay, Az ) son las áreas fraccionales, (Gx, Gy, Gz ) son las fuerzas gravitacionales, (fx, fy, fz ) son las aceleraciones de la viscosidad y (bx, by, bz ) son las pérdidas de flujo en medios porosos en las direcciones x, y, z, respectivamente [17].

La zona de captación del río Kalix es grande y amplia, por lo que tiene un clima subpolar con inviernos fríos y largos y veranos suaves y cortos. Aproximadamente el 50% de las precipitaciones en esta zona es nieve. En mayo, por lo general, el deshielo provoca un aumento significativo en el caudal del río. Las condiciones climáticas del río se resumen en la Tabla 2, [18].

Contrariamente a la tendencia general de este estudio, la previsión de las condiciones meteorológicas mencionadas está utilizando la información meteorológica registrada en los períodos pasados. En función de la información meteorológica disponible, definimos las condiciones de contorno al realizar los cálculos.

Tabla 2: Parámetros del modelo y tabla 3:Condiciones de contorno del modelo

Tabla 2: Parámetros del modelo y tabla 3:Condiciones de contorno del modelo

4.2 Cuadrícula computacional y resultados

Primero, según las dimensiones de los pilares en tres direcciones X, Y, Z, y según la dimensión longitudinal de los pilares (D = 8,5 m; véase la figura 7), el dominio se extiende 10D aguas arriba y 20D aguas abajo. Se ha utilizado el método de mallado estructurado (cartesiano) y el software Flow3D para resolver este problema. Para una cuadrícula correcta, el dominio se debe dividir en diferentes secciones.

Esta división se basa en lugares con fuertes pendientes. Usando la creación de una nueva superficie, el dominio se puede dividir en varias secciones para crear una malla regular con las dimensiones correctas y apropiadas, se puede especificar el número de celdas en cada superficie.

Fig. 6: Estudio de rejilla para el dominio hídrico

Fig. 6: Estudio de rejilla para el dominio hídrico

Esto aumenta el volumen final de las células. Por esta razón, hemos dividido este dominio en tres niveles: Grueso, medio y fino. Los resultados de los estudios de independencia de la red se muestran en la figura 6. Para comprobar los resultados calculados, primero debemos asegurarnos de que la corriente de entrada sea la correcta. Para hacer esto, el caudal de entrada se mide en el dominio de la solución y se compara con el valor base. Las dimensiones del dominio de la solución se especifican en la figura 7. Esta figura también contribuye al reconocimiento de los pilares del puente y su denominación de superficies.

Como se muestra en la Fig. 8, el caudal del río se encuentra dentro del intervalo admisible durante el 90% del tiempo de simulación y el caudal de entrada se ha simulado correctamente. Además, en la Fig. 9, la velocidad media del río se calcula en función del caudal y del área de la sección transversal del río.

Para extraer la cantidad de presión aplicada a los diferentes lados de las columnas, hemos seleccionado el intervalo de tiempo de simulación de 10 a 25 segundos (tiempo de estabilización de descarga en la cantidad de 1800 metros cúbicos por segundo). Los resultados calculados para cada lado se muestran en la Fig. 10 y 11. Los contornos de velocidad también se muestran en las Figuras 12 y 13. Estos contornos se ajustan en función de la velocidad del fluido en un momento dado.

Debido a las dimensiones del dominio de la solución y al caudal del río, el flujo de agua llega a los pilares del puente en el décimo segundo y la presión inicial del flujo del río afecta las superficies de los pilares del puente. Esta presión inicial decrece con el tiempo y se estabiliza en un rango determinado para cada lado según el área y el porcentaje de interacción con el flujo. Para los cálculos de interacción fluido-estructura (FSI), se puede usar la presión crítica calculada en el momento en que la corriente golpea los pilares.

Fig. 7: Dibujo del dominio hidrostático

Fig. 7: Dibujo del dominio hidrostático

Fig. 8: caudal del río; La figura 9: Caudal de la velocidad del río; La figura 10: Presión en la pila del puente - I; La figura 11: Presión en la pila del puente – II

Fig. 8: caudal del río; La figura 9: Caudal de la velocidad del río; La figura 10: Presión en la pila del puente – I; La figura 11: Presión en la pila del puente – II

Fig. 12: Contador de velocidad en el tiempo: 30s Fig. 13: Contador de velocidad en el tiempo: 20 s

Fig. 12: Contador de velocidad en el tiempo: 30s Fig. 13: Contador de velocidad en el tiempo: 20 s

5. Conclusión

Los efectos de las condiciones meteorológicas extremas, incluido el viento dinámico y el flujo de agua, se investigaron numéricamente para el puente de Kalix. Se definieron tres escenarios para las simulaciones dinámicas de viento, incluido el clima con mucho viento, el clima extremadamente frío y el valor de diseño para un período de retorno de 3.000 años. Aprovechando las simulaciones CFD, se determinaron las presiones del viento en pasos de 60 tiempos (30 segundos) utilizando el modelo de turbulencia transitoria DDES.

Los resultados indican diferencias significativas entre los escenarios, lo que implica la importancia de los datos de entrada, especialmente el diagrama de velocidades del viento. Se observó que el valor de diseño para el período de devolución de 3000 años tiene un impacto mucho mayor que los otros escenarios. Además, se mostró la importancia de considerar el rango más alto de presión del viento en la superficie a través de los pasos de tiempo para evaluar el comportamiento estructural del puente en la condición más crítica.

Además, se consideró el caudal máximo del río para una simulación transitoria según las condiciones meteorológicas registradas, y los pilares del puente se sometieron al caudal máximo del río durante 30 segundos. Por lo tanto, además de las condiciones físicas del flujo del río y cómo cambia la dirección del flujo aguas abajo, se cuantificaron las presiones máximas del agua en el momento en que el flujo golpea los pilares.

En el trabajo futuro, el rendimiento estructural del puente de Kalix será evaluado por
imposición de la carga del viento, la presión del agua y la carga del tráfico, creando así un gemelo digital estructural que refleja la verdadera respuesta de la estructura.

6. Reconocimiento

Los autores agradecen enormemente el apoyo de Dlubal Software por proporcionar la licencia de RWIND Simulation, así como de Flow Sciences Inc. por proporcionar la licencia de FLOW-3D.

Autores: Mahyar Kazemian1, Sajad Nikdel2, Mehrnaz MohammadEsmaeili3, Vahid Nik4, Kamyab Zandi*5

Candidato a doctorado, becario en el Departamento de Ingeniería de Timezyx Inc., Canadá.

M.Sc. estudiante, pasante en el Departamento de Ingeniería, Timezyx Inc., Canadá.

Estudiante de licenciatura, pasante en el Departamento de Ingeniería, Timezyx Inc., Canadá.

4 Profesor adjunto en la división de Física de la construcción de la Universidad de Lund y la Universidad Tecnológica de Chalmers, Suecia.

* 5 Director, Timezyx Inc., Vancouver, BC V6N 2R2, Canadá. E-mail: kamyab.zandi@timezyx.com


Referencias

  1. Jančula, M., Jošt, J., & Gocál, J. (2021). Influencia de las acciones ambientales agresivas en las estructuras de los puentes. Transportation Research Procedia, 55 , 1229–1235. https://doi.org/10.1016/j.trpro.2021.07.104
  2. Wang, X., Nguyen, M., Stewart, MG, Syme, M. y Leitch, A. (2010). Análisis de los impactos del cambio climático en el deterioro de la infraestructura de hormigón – Informe de síntesis. CSIRO, Canberra.
  3. Kemayou, BTM (2016). Análisis de secciones de tableros de puentes por el método de la pseudocompresibilidad basado en FDM y LES: Mejora del rendimiento mediante la implementación de la computación en paralelo (tesis). Universidad de Arkansas.
  4. Larsen, A. y Walther, JH (1997). Análisis aeroelástico de secciones de vigas de puentes basado en simulaciones discretas de vórtices. Journal of Wind Engineering and Industrial Aerodynamics, 67–68 , 253–265. https://doi.org/10.1016/s0167-6105(97)00077-9
  5. Eurocódigo 1: Acciones en estructuras. (2006). Instituto Británico de Normas.
  6. ASCE. Cargas mínimas de cálculo para edificios y otras estructuras. (2013). Sociedad Estadounidense de Ingenieros Civiles.
  7. Nik, VM (2016). Facilitación de la simulación energética para el clima futuro: síntesis de conjuntos de datos meteorológicos típicos y extremos a partir de modelos climáticos regionales (RCM). Applied Energy, 177 , 204–226. https://doi.org/10.1016/j.apenergy.2016.05.107
  8. Perera, AT, Nik, VM, Chen, D., Scartezzini, J.‑L. y Hong, T. (2020). Cuantificación de los impactos del cambio climático y los eventos climáticos extremos en los sistemas energéticos. Nature Energy, 5 (2), 150–159. https://doi.org/10.1038/s41560-020-0558-0
  9. Nik, VM (2017). Aplicación de conjuntos de datos meteorológicos típicos y extremos en la simulación higrotérmica de componentes de construcción para el clima futuro: un estudio de caso para un muro de entramado de madera. Energy and Buildings, 154 , 30–45. https://doi.org/10.1016/j.enbuild.2017.08.042
  10. Hosseini, M., Javanroodi, K. y Nik, VM (2022). Evaluación de impacto de alta resolución del cambio climático en el rendimiento energético de los edificios considerando los eventos meteorológicos extremos y el microclima – Investigando las variaciones en el confort térmico interior y los grados-día. Ciudades sostenibles y sociedad, 78 , 103634. https://doi.org/10.1016/j.scs.2021.103634
  11. Spalart, P. R. (2009). Simulación de remolinos separados. Revisión anual de mecánica de fluidos, 41 , 181–202. https://doi.org/10.1146/annurev.fluid.010908.165130
  12. Spalart, PR, et al. (2006) Una nueva versión de simulación de remolinos separados, resistente a densidades de rejilla ambiguas. Dinámica de fluidos teórica y computacional, 2006. 20 (3), 181-195. https://doi.org/10.1007/s00162-006-0015-0
  13. Spalart, PR (1997). Comentarios sobre la viabilidad de LES para alas y sobre una aproximación híbrida RANS/LES. En Actas de la Primera Conferencia Internacional de AFOSR sobre DNS/LES. Prensa de Greyden.
  14. Boudreau, M., Dumas, G. y Veilleux, J.-C. (2017). Evaluación de la capacidad del enfoque de modelado de turbulencia DDES para simular la estela de un cuerpo de farol. Aeroespacial, 4 (3), 41. https://doi.org/10.3390/aerospace4030041
  15. Wang, Y., Zou, Y., Xu, L. y Luo, Z. (2015). Análisis de la presión del flujo de agua en pilas de puentes considerando el efecto del impacto. Problemas matemáticos en ingeniería, 2015 , 1–8. https://doi.org/10.1155/2015/687535
  16. Qi, H., Zheng, J. y Zhang, C. (2020). Simulación numérica del campo de velocidades alrededor de dos pilares de pilas en tándem del puente longitudinal. Fluidos, 5 (1), 32. https://doi.org/10.3390/fluids5010032
  17. Jalal, H. K. y Hassan, W. H (2020). Simulación numérica tridimensional de la socavación local alrededor de la pila de un puente circular utilizando el software flow-3d. Ciclo de conferencias de IOP: Ciencia e ingeniería de materiales, 745 , 012150. https://doi.org/10.1088/1757-899x/745/1/012150
  18. Herzog, S. D., Conrad, S., Ingri, J., Persson, P. y Kritzberg, E. S (2019). Cambios inducidos por crecidas de primavera en la especiación y destino del Fe a mayor salinidad. Geoquímica aplicada, 109 , 104385. https://doi.org/10.1016/j.apgeochem.2019.104385

The impacts of profile concavity on turbidite deposits: Insights from the submarine canyons on global continental margins

The impacts of profile concavity on turbidite deposits: Insights from the submarine canyons on global continental margins

프로필 오목부가 탁도 퇴적물에 미치는 영향: 전 세계 대륙 경계에 대한 해저 협곡의 통찰력

Kaiqi Yu a, Elda Miramontes bc, Matthieu J.B. Cartigny d, Yuping Yang a, Jingping Xu a
aDepartment of Ocean Science and Engineering, Southern University of Science and Technology, 1088 Xueyuan Rd., Shenzhen 518055, Guangdong, China
bMARUM-Center for Marine Environmental Sciences, University of Bremen, Bremen, Germanyc
Faculty of Geosciences, University of Bremen, Bremen, Germany
dDepartment of Geography, Durham University, South Road, Durham DH1 3LE, UK

Received 10 August 2023, Revised 13 March 2024, Accepted 13 March 2024, Available online 17 March 2024, Version of Record 20 March 2024.

What do these dates mean?Show lessAdd to MendeleyShareCite

https://doi.org/10.1016/j.geomorph.2024.109157Get rights and content

Highlights

  • •The impact of submarine canyon concavity on turbidite deposition was assessed.
  • •Distribution of turbidite deposits varies with changes in canyon concavity.
  • •Three distinct deposition patterns were identified.
  • •The recognized deposition patterns align well with the observed turbidite deposits.

Abstract

Submarine canyons are primary conduits for turbidity currents transporting terrestrial sediments, nutrients, pollutants and organic carbon to the deep sea. The concavity in the longitudinal profile of these canyons (i.e. the downstream flattening rate along the profiles) influences the transport processes and results in variations in turbidite thickness, impacting the transfer and burial of particles. To better understand the controlling mechanisms of canyon concavity on the distribution of turbidite deposits, here we investigate the variation in sediment accumulation as a function of canyon concavity of 20 different modern submarine canyons, distributed on global continental margins. In order to effectively assess the isolated impact of the concavity of 20 different canyons, a series of two-dimensional, depth-resolved numerical simulations are conducted. Simulation results show that the highly concave profile (e.g. Surveyor and Horizon) tends to concentrate the turbidite deposits mainly at the slope break, while nearly straight profiles (e.g. Amazon and Congo) result in deposition focused at the canyon head. Moderately concave profiles with a smoother canyon floor (e.g. Norfolk-Washington and Mukluk) effectively facilitate the downstream transport of suspended sediments in turbidity currents. Furthermore, smooth and steep upper reaches of canyons commonly contribute to sediment bypass (i.e. Mukluk and Chirikof), while low slope angles lead to deposition at upper reaches (i.e. Bounty and Valencia). At lower reaches, the distribution of turbidite deposits is consistent with the occurrence of hydraulic jumps. Under the influence of different canyon concavities, three types of deposition patterns are inferred in this study, and verified by comparison with observed turbidite deposits on the modern or paleo-canyon floor. This study demonstrates a potential difference in sediment transport efficiency of submarine canyons with different concavities, which has potential consequences for sediment and organic carbon transport through submarine canyons.

Introduction

Submarine canyons are pivotal links in source-to-sink systems on continental margins (Sømme et al., 2009; Nyberg et al., 2018; Pope et al., 2022a, Pope et al., 2022b) that provide efficient pathways for moving prodigious volumes of terrestrial materials to the abyssal basin (Spychala et al., 2020; Heijnen et al., 2022). When turbidity currents, the main force that transports the above mentioned sediments (Xu et al., 2004; Xu, 2010; Talling et al., 2013; Stevenson et al., 2015), slow down after entering a flatter and/or wider stretch of the canyon downstream, the laden sediments settle, often rapidly, to form a deposit called turbidite that is known for organic carbon burial, hydrocarbon reserves and the accumulation of microplastics (Galy et al., 2007; Pohl et al., 2020a; Pope et al., 2022b; Pierdomenico et al., 2023). A set of flume experiments by Pohl et al. (2020b) revealed that the variation of bed slope plays a dominant role in controlling the sizes and locations of the deposit: a) a more gently dipping upper slope leads to upstream migration of upslope pinch-out; b) the increase of lower slope results in a decrease of the deposit thickness (Fig. 1a).

From upper continental slopes to deepwater basins, turbidity currents are commonly confined by submarine canyons that facilitate the longer distance transport of sediments (Eggenhuisen et al., 2022; Pope et al., 2022a; Wahab et al., 2022, Li et al., 2023a). The concavity, defined here as the downstream flattening rate of profiles (Covault et al., 2011; Chen et al., 2019; Seybold et al., 2021; Soutter et al., 2021a), of the longitudinal bed profile of the submarine canyons is therefore a key factor that determines hydrodynamic processes of turbidity currents, including the accumulation of sediments along the canyon thalweg (Covault et al., 2014; de Leeuw et al., 2016; Heerema et al., 2022; Heijnen et al., 2022). Due to the comprehensive impacts of sediment supply, grain size, climate change, regional tectonics, associated river and self-incision, the concavity of submarine canyons on global continental margins varies greatly (Parker et al., 1986; Harris and Whiteway, 2011; Casalbore et al., 2018; Nyberg et al., 2018; Soutter et al., 2021a, Li et al., 2023b), which is much more complex than the two constant slope setup of Pohl et al. (2020b)’s flume experiment (Fig. 1a). This raises the question of how the more complex concavity influences the dynamics of turbidity currents and the resultant distribution of turbidite deposits. For instance, the longitudinal profile concavity can also be increased by steepening the upper slope and/or gentling the lower slope of canyons (Fig. 1b). Parameters, known as significant factors influencing flow dynamics, include dip angle (Pohl et al., 2019), bed roughness (Baghalian and Ghodsian, 2020), obstacle presence (Howlett et al., 2019), and confinement conditions (Soutter et al., 2021b). However, the role of channel concavity in determining the downstream evolution of flow dynamics remains poorly understood (Covault et al., 2011; Georgiopoulou and Cartwright, 2013), and it is still unclear whether changes in concavity can result in different locations of pinch-out points and variations in turbidite deposit thicknesses (Pohl et al., 2020b).

In this study, we hypothesize that a more concave profile resulting from a steeper upper slope and a gentler lower slope may lead to a downstream migration of the upslope pinch-out and an increase of deposit thickness (Fig. 1b). This hypothesis is tested in 20 modern submarine canyons (shown in Fig. 2) whose longitudinal profiles are extracted from the GEBCO_2022 grid. Due to the lack of data describing the turbidite thickness trends in these canyons, we used a numerical model (FLOW-3D® software) to simulate the depositional process. The simulation results allow us to address at least two questions: (1) How does the concavity affect the distribution and thickness of turbidite deposits along the canyon thalwegs? (2) What is the impact of canyon concavity on the dynamics of the turbidity currents? Such answers on a global scale are undoubtedly helpful in understanding not only the sediment transport processes but also the efficient transfer and burial of organic carbon along global continental margins.

Section snippets

Submarine canyons used in this study

The longitudinal profiles of 20 modern submarine canyons are obtained using Global Mapper® from a public domain database GEBCO_2022 (doi:https://doi.org/10.5285/e0f0bb80-ab44-2739-e053-6c86abc0289c). The GEBCO_2022 grid provides elevation data, in meters, on a 15 arc-second interval grid. The 20 selected submarine canyons, which span the typical distance covered by turbidity currents, have been chosen from a diverse range of submarine canyon and channel systems that extend at least 250 km

Concavity of longitudinal canyon profiles

The NCI and α values of all 20 canyon profiles utilized in this study are plotted in Fig. 4, indicating the majority of these submarine canyons typically exhibit a concave profile, characterized by a negative NCI, except for the Amazon. In most of the profiles, the NCI is lower than −0.08, with the most concave point (indicated by the minimum ratio α) located closer to the canyon head than to the profile end, and their upper reaches are steeper than lower reaches, typically observed as the

Validation of the hypothesis

As previously mentioned in this paper, one of the primary objectives of this study is to evaluate the hypothesis inferred from the flume tank experiment of Pohl et al. (2020b): whether a more concave canyon profile can exert a comparable influence on turbidite deposits as the steepness of the lower and upper slopes in a slope-break system (Fig. 1). Shown as the modeling results, the deposition pattern of this study is more ‘irregular’ compared with the flume tank experiment (Pohl et al., 2020b

Conclusion

Based on global bathymetry, this study simulates the depositional behavior of turbidity currents flowing through the 20 different submarine canyons on the margins of open ocean and marginal sea. Influenced by the different concavities, the resulted deposition patterns are characterized by a variable distribution of turbidite deposits.

  • 1)The simulation results demonstrate that the accumulation of turbidite deposits is primarily observed in downstream regions near the slope break for highly concave

CRediT authorship contribution statement

Kaiqi Yu: Writing – review & editing, Writing – original draft, Validation, Software, Methodology, Investigation, Conceptualization. Elda Miramontes: Writing – review & editing, Supervision, Conceptualization. Matthieu J.B. Cartigny: Writing – review & editing, Supervision. Yuping Yang: Software, Methodology. Jingping Xu: Writing – review & editing, Supervision, Funding acquisition, Conceptualization.

Declaration of competing interest

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

Acknowledgements

This study is supported by the Shenzhen Natural Science Foundation (JCYJ20210324105211031). Matthieu J. B. Cartigny was supported by Royal Society Research Fellowship (DHF/R1/180166). We thank the Chief Editor Zhongyuan Chen, the associate editor and two reviewers for their constructive comments that helped us improve our manuscript.

References (70)

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

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

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

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

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

Abstract

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

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

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

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

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

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

Keywords

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

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

REFERENCES

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

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

홍수 시즌에 하수구를 운영할 때 흐름 회로를 제어하는 ​​기술, 푸토코무네 제방을 통해 제방에 적용

요약

대규모 홍수 구호 작업에 대한 일반적인 흐름 회로 현상의 영향은 많은 보고서에서 연구되었으며 비교적 자세하게 연구되었습니다. 그러나 유량 변동이 제방 암거 작동에 미치는 악영향에 대해서는 많이 언급되지 않았습니다.

실제 운영에 따르면 에너지 소산 탱크 또는 뒷마당의 국부적 불안정성, 운하 지붕의 부력 또는 붕괴, 하류 또는 제방 본체 일부 등 암거 구조 및 제방 시스템에 영향을 미치는 흐름 회로의 부정적인 영향이 많이 있음을 알 수 있습니다.

홍수기 운영 시 암거 및 제방의 안전성을 확보하기 위해서는 유동현상으로 인한 사업에 미치는 유해영향을 최소화할 필요가 있으며 본 연구에서는 이를 검증하고자 합니다.

제방을 통과하는 암거의 동적 회로 현상은 FLOW-3D 소프트웨어를 사용하여 수학적 모델로 시뮬레이션됩니다. 제방을 통한 암거 작동에 잠재적으로 영향을 미칠 수 있는 동맥 유형이 연구에서 구체적으로 논의됩니다.

동시에 암거와 제방 위치는 이 기사에서 지적한 흐름 회로 현상에 의해 부정적인 영향을 받을 가능성이 더 높습니다. 또한 Phuc Tho 마을의 제방을 가로지르는 암거 게이트 뒤의 회로 현상을 줄이기 위한 구조적, 비구조적 조치도 연구되고 평가됩니다.

이를 토대로 운영하수관로의 구조를 저해하지 않고 회로를 축소할 수 있는 방안을 제안한다.

The flow fluctuation has been studied in quite extensively for large-scale flood control works, however, this issue has been less addressed for culverts through levee. The operational experience has shown that there are many negative impacts of flow dynamics on the culvert structure and levee system such as the uplift instability, the local surface erosion of the stilling basin or the downstream channel, collapsing of part of the levee system, etc. According to the requirement of sluice and levee safety during flood season, the task of reducing fluctuation needs to be performed. The article not only pointed out the types of fluctuation that need to pay attention behind the operation gate, but also specified the locations where the sluice and levee could be destructively affected by the fluctuation. In addition, structural and non-structural countermeasures reducing negative impacts of fluctuation are also mentioned. Research has proposed measures to reduce flow dynamics for operating culverts without interfering with their structure.

키워드

Fluctuation, sluice, stilling basin, 흐름회로, 제방암거, 에너지소산조, Flow3D, 회로저감솔루션.

그림 10. 수문이 고르지 않게 열리는 경우의 시뮬레이션 결과
그림 10. 수문이 고르지 않게 열리는 경우의 시뮬레이션 결과

References

Hệ thống giám sát thiên tai Việt Nam (2023). http://vndms.dmc.gov.vn/ (Accessed: 28 February 2023).
Viện Thủy Công (2015) Nghiên cứu đánh giá các sự cố đê, cống dưới đê và đề xuất giải pháp
xử lý. HyCI.
Nguyễn Phương Dung (2017) Thí nghiệm xác định ảnh hưởng của áp lực thủy động tới độ dày bản
đáy bể tiêu năng và sân sau ở công trình tháo. TLU.
Nguyễn Chiến (2015) Tính toán thủy lực công trình tháo nước. NXB Xây dựng.
Nguyễn Ngọc Thắng (2019) Đề cương Đề tài cấp Bộ ‘Nghiên cứu đánh giá nguyên nhân, các biện
pháp đã áp dụng và đề xuất giải pháp xử lý sự cố cống dưới đê đảm bảo an toàn chống lũ’.
‘Flow 3D’ (2023). (User’s Manual).
Yong Peng (2018) ‘Experimental Optimization of Gate-Opening Modes to Minimize Near-Field
Vibrations in Hydropower Stations’, Water, 10(1435). Available at:
https://doi.org/doi:10.3390/w10101435.
Guibing HUANG (2021) ‘Pressure Fluctuations Characteristics of the Stilling Basin with a
Negative Step’, Hydraulic and Civil Engineering Technology VI [Preprint]. Available at:
https://doi.org/doi:10.3233/ATDE210196.
O. Fecarotta (2016) Experimental results on the physical model of an USBR type II stilling basin.
Taylor & Francis Group.

Figure 1. Experimental setup and materials. (a) Schematic of the DED process, where three types of base materials were adopted—B1 (IN718), B2 (IN625), and B3 (SS316L), and two types of powder materials were adopted—P1 (IN718) and P2 (SS316L). (b) In situ high-speed imaging of powder flow and the SEM images of IN718 and SS316L powder particle. (c) Powder size statistics, and (d) element composition of powder IN718 (P1) and SS316L (P2).

Printability disparities in heterogeneous materialcombinations via laser directed energy deposition:a comparative stud

Jinsheng Ning1,6, Lida Zhu1,6,∗, Shuhao Wang2, Zhichao Yang1, Peihua Xu1,Pengsheng Xue3, Hao Lu1, Miao Yu1, Yunhang Zhao1, Jiachen Li4, Susmita Bose5 and Amit Bandyopadhyay5,∗

Abstract

적층 제조는 바이메탈 및 다중 재료 구조의 제작 가능성을 제공합니다. 그러나 재료 호환성과 접착성은 부품의 성형성과 최종 품질에 직접적인 영향을 미칩니다. 적합한 프로세스를 기반으로 다양한 재료 조합의 기본 인쇄 가능성을 이해하는 것이 중요합니다.

여기에서는 두 가지 일반적이고 매력적인 재료 조합(니켈 및 철 기반 합금)의 인쇄 적성 차이가 레이저 지향 에너지 증착(DED)을 통해 거시적 및 미시적 수준에서 평가됩니다.

증착 프로세스는 현장 고속 이미징을 사용하여 캡처되었으며, 용융 풀 특징 및 트랙 형태의 차이점은 특정 프로세스 창 내에서 정량적으로 조사되었습니다. 더욱이, 다양한 재료 쌍으로 처리된 트랙과 블록의 미세 구조 다양성이 비교적 정교해졌고, 유익한 다중 물리 모델링을 통해 이종 재료 쌍 사이에 제시된 기계적 특성(미세 경도)의 불균일성이 합리화되었습니다.

재료 쌍의 서로 다른 열물리적 특성에 의해 유발된 용융 흐름의 차이와 응고 중 결과적인 요소 혼합 및 국부적인 재합금은 재료 조합 간의 인쇄 적성에 나타난 차이점을 지배합니다.

이 작업은 서로 다른 재료의 증착에서 현상학적 차이에 대한 심층적인 이해를 제공하고 바이메탈 부품의 보다 안정적인 DED 성형을 안내하는 것을 목표로 합니다.

Additive manufacturing provides achievability for the fabrication of bimetallic and
multi-material structures; however, the material compatibility and bondability directly affect the
parts’ formability and final quality. It is essential to understand the underlying printability of
different material combinations based on an adapted process. Here, the printability disparities of
two common and attractive material combinations (nickel- and iron-based alloys) are evaluated
at the macro and micro levels via laser directed energy deposition (DED). The deposition
processes were captured using in situ high-speed imaging, and the dissimilarities in melt pool
features and track morphology were quantitatively investigated within specific process
windows. Moreover, the microstructure diversity of the tracks and blocks processed with varied
material pairs was comparatively elaborated and, complemented with the informative
multi-physics modeling, the presented non-uniformity in mechanical properties (microhardness)
among the heterogeneous material pairs was rationalized. The differences in melt flow induced
by the unlike thermophysical properties of the material pairs and the resulting element
intermixing and localized re-alloying during solidification dominate the presented dissimilarity
in printability among the material combinations. This work provides an in-depth understanding
of the phenomenological differences in the deposition of dissimilar materials and aims to guide
more reliable DED forming of bimetallic parts.

Figure 1. Experimental setup and materials. (a) Schematic of the DED process, where three types of base materials were adopted—B1
(IN718), B2 (IN625), and B3 (SS316L), and two types of powder materials were adopted—P1 (IN718) and P2 (SS316L). (b) In situ
high-speed imaging of powder flow and the SEM images of IN718 and SS316L powder particle. (c) Powder size statistics, and (d) element
composition of powder IN718 (P1) and SS316L (P2).
Figure 1. Experimental setup and materials. (a) Schematic of the DED process, where three types of base materials were adopted—B1 (IN718), B2 (IN625), and B3 (SS316L), and two types of powder materials were adopted—P1 (IN718) and P2 (SS316L). (b) In situ high-speed imaging of powder flow and the SEM images of IN718 and SS316L powder particle. (c) Powder size statistics, and (d) element composition of powder IN718 (P1) and SS316L (P2).
Figure 2. Deposition process and the track morphology. (a)–(c) Display the in situ captured tableaux of melt propagation and some physical
features during depositing for P1B1, P1B2, and P1B3, respectively. (d) The profiles of the melt pool at a frame of (t0 + 1) ms, and the flow
streamlines in the molten pool of each case. (e) The outer surface of the formed tracks, in which the colored arrows mark the scanning
direction. (f) Cross-section of the tracks. The parameter set used for in situ imaging was P-1000 W, S-600 mm·min–1, F-18 g·min–1. All the
scale bars are 2 mm.
Figure 2. Deposition process and the track morphology. (a)–(c) Display the in situ captured tableaux of melt propagation and some physical features during depositing for P1B1, P1B2, and P1B3, respectively. (d) The profiles of the melt pool at a frame of (t0 + 1) ms, and the flow streamlines in the molten pool of each case. (e) The outer surface of the formed tracks, in which the colored arrows mark the scanning direction. (f) Cross-section of the tracks. The parameter set used for in situ imaging was P-1000 W, S-600 mm·min–1, F-18 g·min–1. All the scale bars are 2 mm.

References

[1] Tan C L, Weng F, Sui S, Chew Y and Bi G J 2021 Progress and perspectives in laser additive manufacturing of key aeroengine materials Int. J. Mach. Tools Manuf. 170 103804
[2] Bandyopadhyay A, Traxel K D, Lang M, Juhasz M, Eliaz N and Bose S 2022 Alloy design via additive manufacturing: advantages, challenges, applications and perspectives Mater. Today 52 207–24
[3] Sui S, Chew Y, Weng F, Tan C L, Du Z L and Bi G J 2022 Study of the intrinsic mechanisms of nickel additive for grain refinement and strength enhancement of laser aided additively manufactured Ti–6Al–4V Int. J. Extrem. Manuf. 4 035102
[4] Xue P S, Zhu L D, Xu P H, Ren Y, Xin B, Meng G R, Yang Z C and Liu Z 2021 Research on process optimization and microstructure of CrCoNi medium-entropy alloy formed by laser metal deposition Opt. Laser Technol. 142 107167
[5] Bandyopadhyay A, Traxel K D and Bose S 2021 Nature-inspired materials and structures using 3D printing Mater. Sci. Eng. R 145 100609
[6] Zuback J S, Palmer T A and DebRoy T 2019 Additive manufacturing of functionally graded transition joints between ferritic and austenitic alloys J. Alloys Compd. 770 995–1003
[7] Feenstra D R, Banerjee R, Fraser H L, Huang A, Molotnikov A and Birbilis N 2021 Critical review of the state of the art in multi-material fabrication via directed energy deposition Curr. Opin. Solid State Mater. Sci. 25 100924
[8] Wei C, Zhang Z Z, Cheng D X, Sun Z, Zhu M H and Li L 2021 An overview of laser-based multiple metallic material additive manufacturing: from macro- to micro-scales Int. J. Extrem. Manuf. 3 012003
[9] Gu D D, Shi X Y, Poprawe R, Bourell D L, Setchi R and Zhu J H 2021 Material-structure-performance integrated laser-metal additive manufacturing Science 372 eabg1487
[10] Bandyopadhyay A and Heer B 2018 Additive manufacturing of multi-material structures Mater. Sci. Eng. R 129 1–16
[11] Tammas-Williams S and Todd I 2017 Design for additive manufacturing with site-specific properties in metals and alloys Scr. Mater. 135 105–10
[12] Chen W, Gu D D, Yang J K, Yang Q, Chen J and Shen X F 2022 Compressive mechanical properties and shape memory effect of NiTi gradient lattice structures fabricated by laser powder bed fusion Int. J. Extrem. Manuf. 4 045002
[13] Svetlizky D, Das M, Zheng B L, Vyatskikh A L, Bose S, Bandyopadhyay A, Schoenung J M, Lavernia E J and Eliaz N 2021 Directed energy deposition (DED) additive manufacturing: physical characteristics, defects, challenges and applications Mater. Today 49 271–95
[14] Panwisawas C, Tang Y T and Reed R C 2020 Metal 3D printing as a disruptive technology for superalloys Nat. Commun. 11 2327
[15] Wang S H, Ning J S, Zhu L D, Yang Z C, Yan W T, Dun Y C, Xue P S, Xu P H, Bose S and Bandyopadhyay A 2022 Role of porosity defects in metal 3D printing: formation mechanisms, impacts on properties and mitigation strategies Mater. Today 59 133–60
[16] DebRoy T, Mukherjee T, Milewski J O, Elmer J W, Ribic B, Blecher J J and Zhang W 2019 Scientific, technological and economic issues in metal printing and their solutions Nat. Mater. 18 1026–32
[17] Afrouzian A, Groden C J, Field D P, Bose S and Bandyopadhyay A 2022 Additive manufacturing of Ti-Ni bimetallic structures Mater. Des. 215 110461
[18] Bandyopadhyay A, Zhang Y N and Onuike B 2022 Additive manufacturing of bimetallic structures Virtual Phys. Prototyp. 17 256–94
[19] Onuike B, Heer B and Bandyopadhyay A 2018 Additive manufacturing of Inconel 718—copper alloy bimetallic structure using laser engineered net shaping (LENSTM) Addit. Manuf. 21 133–40
[20] Sahasrabudhe H, Harrison R, Carpenter C and Bandyopadhyay A 2015 Stainless steel to titanium bimetallic structure using LENSTM Addit. Manuf. 5 1–8
[21] Li B Y, Han C J, Lim C W J and Zhou K 2022 Interface formation and deformation behaviors of an additively manufactured nickel-aluminum-bronze/15-5 PH multimaterial via laser-powder directed energy deposition Mater. Sci. Eng. A 829 142101
[22] Zhang X C, Pan T, Chen Y T, Li L, Zhang Y L and Liou F 2021 Additive manufacturing of copper-stainless steel hybrid components using laser-aided directed energy deposition J. Mater. Sci. Technol. 80 100–16
[23] Shinjo J and Panwisawas C 2022 Chemical species mixing during direct energy deposition of bimetallic systems using titanium and dissimilar refractory metals for repair and biomedical applications Addit. Manuf. 51 102654
[24] Wang D et al 2022 Recent progress on additive manufacturing of multi-material structures with laser powder bed fusion Virtual Phys. Prototyp. 17 329–65
[25] Lin X, Yue T M, Yang H O and Huang W D 2005 Laser rapid forming of SS316L/Rene88DT graded material Mater. Sci. Eng. A 391 325–36
[26] Melzer D, Dˇzugan J, Koukolíková M, Rzepa S and Vavˇrík J 2021 Structural integrity and mechanical properties of the functionally graded material based on 316L/IN718 processed by DED technology Mater. Sci. Eng. A 811 141038
[27] Melzer D, Dˇzugan J, Koukolíková M, Rzepa S, Dlouh´y J, Brázda M and Bucki T 2022 Fracture characterisation of vertically build functionally graded 316L stainless steel with Inconel 718 deposited by directed energy deposition process Virtual Phys. Prototyp. 17 821–40
[28] Zhang Y N and Bandyopadhyay A 2018 Direct fabrication of compositionally graded Ti-Al2O3 multi-material structures using laser engineered net shaping Addit. Manuf. 21 104–11
[29] Ben-Artzy A, Reichardt A, Borgonia P J, Dillon R P, McEnerney B, Shapiro A A and Hosemann P 2021 Compositionally graded SS316 to C300 maraging steel using additive manufacturing Mater. Des. 201 109500
[30] Tan C L, Liu Y C, Weng F, Ng F L, Su J L, Xu Z K, Ngai X D and Chew Y 2022 Additive manufacturing of voxelized heterostructured materials with hierarchical phases Addit. Manuf. 54 102775
[31] Chen J, Yang Y Q, Song C H, Zhang M K, Wu S B and Wang D 2019 Interfacial microstructure and mechanical properties of 316L/CuSn10 multi-material bimetallic structure fabricated by selective laser melting Mater. Sci. Eng. A 752 75–85
[32] Wei C, Gu H, Gu Y C, Liu L C, Huang Y H, Cheng D X, Li Z Q and Li L 2022 Abnormal interfacial bonding mechanisms of multi-material additive-manufactured tungsten–stainless steel sandwich structure Int. J. Extrem. Manuf. 4 025002
[33] Zhang Y N and Bandyopadhyay A 2021 Influence of compositionally graded interface on microstructure and compressive deformation of 316L stainless steel to Al12Si aluminum alloy bimetallic structures ACS Appl. Mater. Interfaces 13 9174–85
[34] Wei C et al 2022 Cu10Sn to Ti6Al4V bonding mechanisms in laser-based powder bed fusion multiple material additive 15 Int. J. Extrem. Manuf. 6 (2024) 025001 J Ning et al manufacturing with different build strategies Addit. Manuf. 51 102588
[35] Li W, Karnati S, Kriewall C, Liou F, Newkirk J, Brown Taminger K M and Seufzer W J 2017 Fabrication and characterization of a functionally graded material from Ti-6Al-4V to SS316 by laser metal deposition Addit. Manuf. 14 95–104
[36] Shi Q M, Zhong G Y, Sun Y, Politis C and Yang S F 2021 Effects of laser melting+remelting on interfacial macrosegregation and resulting microstructure and microhardness of laser additive manufactured H13/IN625 bimetals J. Manuf. Process. 71 345–55
[37] Zhang W X, Hou W Y, Deike L and Arnold C 2022 Understanding the Rayleigh instability in humping phenomenon during laser powder bed fusion process Int. J. Extrem. Manuf. 4 015201
[38] Chen Y W, Zhang X, Li M M, Xu R Q, Zhao C and Sun T 2020 Laser powder bed fusion of Inconel 718 on 316 stainless steel Addit. Manuf. 36 101500
[39] Yang Z C, Wang S H, Zhu L D, Ning J S, Xin B, Dun Y C and Yan W T 2022 Manipulating molten pool dynamics during metal 3D printing by ultrasound Appl. Phys. Rev. 9 021416
[40] Hofmann D C, Roberts S, Otis R, Kolodziejska J, Dillon R P, Suh J O, Shapiro A A, Liu Z K and Borgonia J P 2014 Developing gradient metal alloys through radial deposition additive manufacturing Sci. Rep. 4 5357
[41] Tumkur T U et al 2021 Nondiffractive beam shaping for enhanced optothermal control in metal additive manufacturing Sci. Adv. 7 eabg9358
[42] Scipioni Bertoli U, Guss G, Wu S, Matthews M J and Schoenung J M 2017 In-situ characterization of laser-powder interaction and cooling rates through high-speed imaging of powder bed fusion additive manufacturing Mater. Des. 135 385–96
[43] Siva Prasad H, Brueckner F and Kaplan A F H 2020 Powder incorporation and spatter formation in high deposition rate blown powder directed energy deposition Addit. Manuf. 35 101413
[44] Ebrahimi A, Kleijn C R and Richardson I M 2021 Numerical study of molten metal melt pool behaviour during conduction-mode laser spot melting J. Appl. Phys. 54 105304
[45] Mumtaz K A and Hopkinson N 2010 Selective laser melting of thin wall parts using pulse shaping J. Mater. Process. Technol. 210 279–87
[46] Sikandar Iquebal A, Yadav A, Botcha B, Krishna Gorthi R and Bukkapatnam S 2022 Tracking and quantifying spatter characteristics in a laser directed energy deposition process using Kalman filter Manuf. Lett. 33 692–700
[47] Criales L E, Arısoy Y M, Lane B, Moylan S, Donmez A and Özel T 2017 Laser powder bed fusion of nickel alloy 625: experimental investigations of effects of process parameters on melt pool size and shape with spatter analysis Int. J. Mach. Tools Manuf. 121 22–36
[48] Coen V, Goossens L and van Hooreweder B 2022 Methodology and experimental validation of analytical melt pool models for laser powder bed fusion J. Mater. Process. Technol. 304 117547
[49] Zhao C, Shi B, Chen S L, Du D, Sun T, Simonds B J, Fezzaa K and Rollett A D 2022 Laser melting modes in metal powder bed fusion additive manufacturing Rev. Mod. Phys. 94 045002
[50] Wang J H, Han F Z, Chen S F and Ying W S 2019 A novel model of laser energy attenuation by powder particles for laser solid forming Int. J. Mach. Tools Manuf. 145 103440
[51] Haley J C, Schoenung J M and Lavernia E J 2018 Observations of particle-melt pool impact events in directed energy deposition Addit. Manuf. 22 368–74
[52] Chen Y H et al 2021 Correlative synchrotron x-ray imaging and diffraction of directed energy deposition additive manufacturing Acta Mater. 209 116777
[53] Khorasani M, Ghasemi A, Leary M, Cordova L, Sharabian E, Farabi E, Gibson I, Brandt M and Rolfe B 2022 A comprehensive study on meltpool depth in laser-based powder bed fusion of Inconel 718 Int. J. Adv. Manuf. Technol. 120 2345–62
[54] Shamsaei N, Yadollahi A, Bian L and Thompson S M 2015 An overview of direct laser deposition for additive manufacturing; part II: mechanical behavior, process parameter optimization and control Addit. Manuf. 8 12–35
[55] Ghanavati R, Naffakh-Moosavy H, Moradi M and Eshraghi M 2022 Printability and microstructure of directed energy deposited SS316l-IN718 multi-material: numerical modeling and experimental analysis Sci. Rep. 12 16600
[56] Galbusera F, Demir A G, Platl J, Turk C, Schnitzer R and Previtali B 2022 Processability and cracking behaviour of novel high-alloyed tool steels processed by laser powder bed fusion J. Mater. Process. Technol. 302 117435
[57] Wang A et al 2023 Effects of processing parameters on pore defects in blue laser directed energy deposition of aluminum by in and ex situ observation J. Mater. Process. Technol. 319 118068
[58] Hinojos A, Mireles J, Reichardt A, Frigola P, Hosemann P, Murr L E and Wicker R B 2016 Joining of Inconel 718 and 316 stainless steel using electron beam melting additive manufacturing technology Mater. Des. 94 17–27
[59] Yang Z C, Zhu L D, Wang S H, Ning J S, Dun Y C, Meng G R, Xue P S, Xu P H and Xin B 2021 Effects of ultrasound on multilayer forming mechanism of Inconel 718 in directed energy deposition Addit. Manuf. 48 102462
[60] Yao L M, Huang S, Ramamurty U and Xiao Z M 2021 On the formation of “Fish-scale” morphology with curved grain interfacial microstructures during selective laser melting of dissimilar alloys Acta Mater. 220 117331
[61] Ghanavati R, Naffakh-Moosavy H and Moradi M 2021 Additive manufacturing of thin-walled SS316L-IN718 functionally graded materials by direct laser metal deposition J. Mater. Res. Technol. 15 2673–85
[62] Chen N N, Khan H A, Wan Z X, Lippert J, Sun H, Shang S L, Liu Z K and Li J J 2020 Microstructural characteristics and crack formation in additively manufactured bimetal material of 316L stainless steel and Inconel 625 Addit. Manuf. 32 101037
[63] Xiao Y H, Wan Z X, Liu P W, Wang Z, Li J J and Chen L 2022 Quantitative simulations of grain nucleation and growth at additively manufactured bimetallic interfaces of SS316L and IN625 J. Mater. Process. Technol. 302 117506
[64] Mukherjee T, DebRoy T, Lienert T J, Maloy S A and Hosemann P 2021 Spatial and temporal variation of hardness of a printed steel part Acta Mater. 209 116775
[65] Dinda G P, Dasgupta A K and Mazumder J 2021 Texture control during laser deposition of nickel-based superalloy Scr. Mater. 67 503–6
[66] Tan Z E, Pang J H L, Kaminski J and Pepin H 2019 Characterisation of porosity, density, and microstructure of directed energy deposited stainless steel AISI 316L Addit. Manuf. 25 286–96
[67] Wolff S J, Gan Z T, Lin S, Bennett J L, Yan W T, Hyatt G, Ehmann K F, Wagner G J, Liu W K and Cao J 2019 Experimentally validated predictions of thermal history and microhardness in laser-deposited Inconel 718 on carbon steel Addit. Manuf. 27 540–51 16 Int. J. Extrem. Manuf. 6 (2024) 025001 J Ning et al
[68] Zhang L, Wen M, Imade M, Fukuyama S and Yokogawa K 2008 Effect of nickel equivalent on hydrogen gas embrittlement of austenitic stainless steels based on type 316 at low temperatures Acta Mater. 56 3414–21
[69] Zuback J S and DebRoy T 2018 The hardness of additively manufactured alloys Materials 11 2070
[70] Adomako N K, Lewandowski J J, Arkhurst B M, Choi H, Chang H J and Kim J H 2022 Microstructures and mechanical properties of multi-layered materials composed of Ti-6Al-4V, vanadium, and 17–4PH stainless steel produced by directed energy deposition Addit. Manuf. 59 103174

FLOW-3D World Users Conference 2024

FLOW-3D World Users Conference 2024

FLOW-3D World Users Conference 2024 에 전 세계 고객을 초대합니다.  이 컨퍼런스는 독일 함부르크의 Steigenberger Hotel Hamburg 에서 2024년 6월 10~12일에 개최됩니다 . 세계에서 가장 유명한 기업 및 기관의 동료 엔지니어, 연구자 및 과학자들과 함께 시뮬레이션 기술을 연마하고, 새로운 모델링 접근 방식을 탐색하고, 최신 소프트웨어 개발에 대해 알아보세요. 컨퍼런스에서는 응용 분야별 트랙, 무료 고급 교육 세션, 고객의 기술 프레젠테이션, Flow Science의 수석 기술 직원이 발표하는 최신 제품 개발 등을 선보일 예정입니다. 이번 컨퍼런스는 Flow Science Deutschland가 공동 주최합니다. 

지금 등록하세요!

컨퍼런스 참석자

올해 FLOW-3D 세계 사용자 컨퍼런스에 점점 더 많은 참석자가 참여하기를 바랍니다. 우리는 BMW, Hydro-Québec, Mott MacDonald 등의 사용자를 환영하기를 기대합니다. 

Alfa Srl, Bocar GmbH, Böllinger-Group / Koncast gmbH, Brembo Spa, Cranfield University, DIETECH INDIA PRIVATE LIMITED, Fichtner Water + Transportation, Gazi University, IIT (ISM) Dhanbad, IITCA, Istanbul Technical University, KS HUAYU AluTech GmbH, MIT , 오레곤 주립 대학교, Università degli studi della Basilicata, VAW, ETH Zürich.

고급 교육

Flow Science는 FLOW-3D World Users Conference를 시작하기 위해 6월 10일 월요일 오후에 세 가지 고급 교육 세션을 개최할 예정입니다 . 모든 컨퍼런스 등록자에게는 교육이 무료로 제공됩니다. 교육 후에는 컨퍼런스 호텔 레스토랑에서 개회 리셉션이 열립니다.

더 알아보기

사교 행사

오프닝 리셉션

6월 10일 월요일 18:30-21:00에 열리는 개회 리셉션에 모든 컨퍼런스 참석자와 손님들을 초대합니다. 컨퍼런스 호텔 레스토랑에서는 음료와 다과가 제공됩니다.

컨퍼런스 디너

VLET 로고

6월 11일 화요일 저녁 함부르크의 유명한 레스토랑인 슈파이셔슈타트의 VLET 에서 열리는 컨퍼런스 만찬에 모든 컨퍼런스 참석자와 손님들을 초대하게 된 것을 매우 기쁘게 생각합니다 . 레스토랑은 컨퍼런스 호텔에서 도보로 가까운 거리에 있습니다. 지침은 회의 자료에서 제공됩니다.

VLE T  in der Speicherstadt
Am Sandtorkai 23/24
20457 함부르크

전화: +49 40 200064-222

컨퍼런스 등록

6월 10일부터 12일까지 독일 함부르크에서 열리는 FLOW-3D 세계 사용자 컨퍼런스 2024 에 등록하세요 ! 전 세계 FLOW-3D 사용자 와 연결하세요 . 사교 행사, 포스터 세션, 기술 프레젠테이션, 제품 개발 강연 및 무료 고급 교육을 즐겨보세요.

Fig. 3. (a–c) Snapshots of the CtFD simulation of laser-beam irradiation: (a) Top, (b) longitudinal vertical cross-sectional, and (c) transversal vertical cross-sectional views. (d) z-position of the solid/liquid interface during melting and solidification.

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

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

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

Get rights and content Under a Creative Commons license open access

Abstract

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

Graphical abstract

Keywords

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

1. Introduction

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

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

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

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

2. Methods

2.1. Laser-beam irradiation experiments

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

2.2. CtFD simulation

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

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

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

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

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

Table 1. Parameters used in the CtFD simulations.

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

Calculated using JMatPro v11.

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

2.3. MPF simulation

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

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

3. Results

3.1. Experimental observation of melt pool

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

Fig. 1

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

Fig. 2

3.2. CtFD simulation

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

Fig. 3

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

Fig. 4

3.3. MPF simulations coupled with CtFD simulation

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

Fig. 5
Fig. 6

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

Fig. 7

3.4. Remelting and resolidification simulation

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

Fig. 8
Fig. 9

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

Fig. 10

4. Discussion

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

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

Fig. 11

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

Fig. 12

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

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

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

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

5. Conclusions

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

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

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

CRediT authorship contribution statement

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

Declaration of Competing Interest

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

Acknowledgments

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

Appendix A. Supplementary material

Download : Download Word document (654KB)

Supplementary material.

Data availability

Data will be made available on request.

References

Figure 5. Simulation of the molten pool under low-speed scanning (1.06 m/s). (a) Sequential solidification of the molten pool at the end of the melt track for laser powers of 190 and 340 W, respectively. (b) Recoil pressure on the molten pool at the keyhole for laser powers of 190 and 340 W, respectively. (c) The force diagram of the melt at the back of the keyhole at t = 750 μs in case B. (d) Temperature gradient at the solid–liquid interface of the molten pool at the moment the laser is deactivated in case A. (e) Temperature gradient at the solid–liquid interface of the molten pool at the moment the laser is deactivated in case B.

Revealing formation mechanism of end of processdepression in laser powder bed fusion by multiphysics meso-scale simulation

다중물리 메조 규모 시뮬레이션을 통해 레이저 분말층 융합에서 공정 종료의 함몰 형성 메커니즘 공개

Haodong Chen a,b, Xin Lin a,b,c, Yajing Sund, Shuhao Wanga,b, Kunpeng Zhu a,b,c and Binbin Dana,b

To link to this article: https://doi.org/10.1080/17452759.2024.2326599

ABSTRACT

Unintended end-of-process depression (EOPD) commonly occurs in laser powder bed fusion (LPBF), leading to poor surface quality and lower fatigue strength, especially for many implants. In this study, a high-fidelity multi-physics meso-scale simulation model is developed to uncover the forming mechanism of this defect. A defect-process map of the EOPD phenomenon is obtained using this simulation model. It is found that the EOPD formation mechanisms are different under distinct regions of process parameters. At low scanning speeds in keyhole mode, the long-lasting recoil pressure and the large temperature gradient easily induce EOPD. While at high scanning speeds in keyhole mode, the shallow molten pool morphology and the large solidification rate allow the keyhole to evolve into an EOPD quickly. Nevertheless, in the conduction mode, the Marangoni effects along with a faster solidification rate induce EOPD. Finally, a ‘step’ variable power strategy is proposed to optimise the EOPD defects for the case with high volumetric energy density at low scanning speeds. This work provides a profound understanding and valuable insights into the quality control of LPBF fabrication.

의도하지 않은 공정 종료 후 함몰(EOPD)은 LPBF(레이저 분말층 융합)에서 흔히 발생하며, 특히 많은 임플란트의 경우 표면 품질이 떨어지고 피로 강도가 낮아집니다. 본 연구에서는 이 결함의 형성 메커니즘을 밝히기 위해 충실도가 높은 다중 물리학 메조 규모 시뮬레이션 모델을 개발했습니다.

이 시뮬레이션 모델을 사용하여 EOPD 현상의 결함 프로세스 맵을 얻습니다. EOPD 형성 메커니즘은 공정 매개변수의 별개 영역에서 서로 다른 것으로 밝혀졌습니다.

키홀 모드의 낮은 스캔 속도에서는 오래 지속되는 반동 압력과 큰 온도 구배로 인해 EOPD가 쉽게 유발됩니다. 키홀 모드에서 높은 스캐닝 속도를 유지하는 동안 얕은 용융 풀 형태와 큰 응고 속도로 인해 키홀이 EOPD로 빠르게 진화할 수 있습니다.

그럼에도 불구하고 전도 모드에서는 더 빠른 응고 속도와 함께 마랑고니 효과가 EOPD를 유발합니다. 마지막으로, 낮은 스캐닝 속도에서 높은 체적 에너지 밀도를 갖는 경우에 대해 EOPD 결함을 최적화하기 위한 ‘단계’ 가변 전력 전략이 제안되었습니다.

이 작업은 LPBF 제조의 품질 관리에 대한 심오한 이해와 귀중한 통찰력을 제공합니다.

Figure 5. Simulation of the molten pool under low-speed scanning (1.06 m/s). (a) Sequential solidification of the molten pool at the
end of the melt track for laser powers of 190 and 340 W, respectively. (b) Recoil pressure on the molten pool at the keyhole for laser
powers of 190 and 340 W, respectively. (c) The force diagram of the melt at the back of the keyhole at t = 750 μs in case B. (d) Temperature gradient at the solid–liquid interface of the molten pool at the moment the laser is deactivated in case A. (e) Temperature
gradient at the solid–liquid interface of the molten pool at the moment the laser is deactivated in case B.
Figure 5. Simulation of the molten pool under low-speed scanning (1.06 m/s). (a) Sequential solidification of the molten pool at the end of the melt track for laser powers of 190 and 340 W, respectively. (b) Recoil pressure on the molten pool at the keyhole for laser powers of 190 and 340 W, respectively. (c) The force diagram of the melt at the back of the keyhole at t = 750 μs in case B. (d) Temperature gradient at the solid–liquid interface of the molten pool at the moment the laser is deactivated in case A. (e) Temperature gradient at the solid–liquid interface of the molten pool at the moment the laser is deactivated in case B.

References

[1] Zhang C, Li Z, Zhang J, et al. Additive manufacturing of magnesium matrix composites: comprehensive review of recent progress and research perspectives. J Mag
Alloys. 2023. doi:10.1016/j.jma.2023.02.005
[2] Webster S, Lin H, Carter III FM, et al. Physical mechanisms in hybrid additive manufacturing: a process design framework. J Mater Process Technol. 2022;291:117048. doi:10. 1016/j.jmatprotec.2021.117048
[3] Wang S, Ning J, Zhu L, et al. Role of porosity defects in metal 3D printing: formation mechanisms, impacts on properties and mitigation strategies. Mater Today. 2022. doi:10.1016/j.mattod.2022.08.014
[4] Wei C, Li L. Recent progress and scientific challenges in multi-material additive manufacturing via laser-based powder bed fusion. Virtual Phys Prototyp. 2021;16 (3):347–371. doi:10.1080/17452759.2021.1928520
[5] Lin X, Wang Q, Fuh JYH, et al. Motion feature based melt pool monitoring for selective laser melting process. J Mater Process Technol. 2022;303:117523. doi:10.1016/j. jmatprotec.2022.117523
[6] Gockel J, Sheridan L, Koerper B, et al. The influence of additive manufacturing processing parameters on surface roughness and fatigue life. Int J Fatigue. 2019;124:380–388. doi:10.1016/j.ijfatigue.2019.03.025
[7] Nicoletto G. Influence of rough as-built surfaces on smooth and notched fatigue behavior of L-PBF AlSi10Mg. Addit Manuf. 2020;34:101251. doi:10.1016/j. addma.2020.101251
[8] Spece H, Yu T, Law AW, et al. 3D printed porous PEEK created via fused filament fabrication for osteoconductive orthopaedic surfaces. J Mech Behav Biomed Mater. 2020;109:103850. doi:10.1115/1.0004270v
[9] Andrukhov O, Huber R, Shi B, et al. Proliferation, behavior, and differentiation of osteoblasts on surfaces of different microroughness. Dent Mater. 2016;32(11):1374–1384. doi:10.1016/j.dental.2016.08.217
[10] Dai N, Zhang LC, Zhang J, et al. Corrosion behavior of selective laser melted Ti-6Al-4 V alloy in NaCl solution. Corros Sci. 2016;102:484–489. doi:10.1016/j.corsci.2015. 10.041
[11] Li EL, Wang L, Yu AB, et al. A three-phase model for simulation of heat transfer and melt pool behaviour in laser powder bed fusion process. Powder Technol. 2021;381:298–312. doi:10.1016/j.powtec.2020.11.061
[12] Liao B, Xia RF, Li W, et al. 3D-printed ti6al4v scaffolds with graded triply periodic minimal surface structure for bone tissue engineering. J Mater Eng Perform. 2021;30:4993– 5004. doi:10.1007/s11665-021-05580-z
[13] Li E, Zhou Z, Wang L, et al. Melt pool dynamics and pores formation in multi-track studies in laser powder bed fusion process. Powder Technol. 2022;405:117533. doi:10.1016/j.powtec.2022.117533
[14] Guo L, Geng S, Gao X, et al. Numerical simulation of heat transfer and fluid flow during nanosecond pulsed laser processing of Fe78Si9B13 amorphous alloys. Int J Heat Mass Transfer. 2021;170:121003. doi:10.1016/j.ijheatma sstransfer.2021.121003
[15] Guo L, Li Y, Geng S, et al. Numerical and experimental analysis for morphology evolution of 6061 aluminum alloy during nanosecond pulsed laser cleaning. Surf Coat Technol. 2022;432:128056. doi:10.1016/j.surfcoat. 2021.128056
[16] Li S, Liu D, Mi H, et al. Numerical simulation on evolution process of molten pool and solidification characteristics of melt track in selective laser melting of ceramic powder. Ceram Int. 2022;48(13):18302–18315. doi:10. 1016/j.ceramint.2022.03.089
[17] Aboulkhair NT, Maskery I, Tuck C, et al. On the formation of AlSi10Mg single tracks and layers in selective laser melting: microstructure and nano-mechanical properties. J Mater Process Technol. 2016;230:88–98. doi:10.1016/j. jmatprotec.2015.11.016
[18] Thijs L, Kempen K, Kruth JP, et al. Fine-structured aluminium products with controllable texture by selective laser melting of pre-alloyed AlSi10Mg powder. Acta Mater. 2013;61(5):1809–1819. doi:10.1016/j.actamat.2012.11.052
[19] Qiu C, Adkins NJE, Attallah MM. Microstructure and tensile properties of selectively laser-melted and of HIPed laser-melted Ti–6Al–4 V. Mater Sci Eng A. 2013;578:230–239. doi:10.1016/j.msea.2013.04.099
[20] Kazemi Z, Soleimani M, Rokhgireh H, et al. Melting pool simulation of 316L samples manufactured by selective laser melting method, comparison with experimental results. Int J Therm Sci. 2022;176:107538. doi:10.1016/j. ijthermalsci.2022.107538
[21] Cao L. Workpiece-scale numerical simulations of SLM molten pool dynamic behavior of 316L stainless steel. Comput Math Appl. 2021;96:209–228. doi:10.1016/j. camwa.2020.04.020
[22] Liu B, Fang G, Lei L, et al. Predicting the porosity defects in selective laser melting (SLM) by molten pool geometry. Int J Mech Sci. 2022;228:107478. doi:10.1016/j.ijmecsci. 2022.107478
[23] Ur Rehman A, Pitir F, Salamci MU. Full-field mapping and flow quantification of melt pool dynamics in laser powder bed fusion of SS316L. Materials. 2021;14(21):6264. doi:10. 3390/ma14216264
[24] Chia HY, Wang L, Yan W. Influence of oxygen content on melt pool dynamics in metal additive manufacturing: high-fidelity modeling with experimental validation. Acta Mater. 2023;249:118824. doi:10.1016/j.actamat. 2023.118824
[25] Cheng B, Loeber L, Willeck H, et al. Computational investigation of melt pool process dynamics and pore formation in laser powder bed fusion. J Mater Eng Perform. 2019;28:6565–6578. doi:10.1007/s11665-019- 04435-y
[26] Li X, Guo Q, Chen L, et al. Quantitative investigation of gas flow, powder-gas interaction, and powder behavior under different ambient pressure levels in laser powder bed fusion. Int J Mach Tools Manuf. 2021;170:103797. doi:10.1016/j.ijmachtools.2021.103797
[27] Wu Y, Li M, Wang J, et al. Powder-bed-fusion additive manufacturing of molybdenum: process simulation, optimization, and property prediction. Addit Manuf. 2022;58:103069. doi:10.1016/j.addma.2022.103069
[28] Wu S, Yang Y, Huang Y, et al. Study on powder particle behavior in powder spreading with discrete element method and its critical implications for binder jetting additive manufacturing processes. Virtual Phys Prototyp. 2023;18(1):e2158877. doi:10.1080/17452759.2022.2158877
[29] Klassen A, Schakowsky T, Kerner C. Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods. J Phys D Appl Phys. 2014;47 (27):275303. doi:10.1088/0022-3727/47/27/275303
[30] Cao L. Mesoscopic-scale numerical simulation including the influence of process parameters on slm single-layer multi-pass formation. Metall Mater Trans A. 2020;51:4130–4145. doi:10.1007/s11661-020-05831-z
[31] Zhuang JR, Lee YT, Hsieh WH, et al. Determination of melt pool dimensions using DOE-FEM and RSM with process window during SLM of Ti6Al4V powder. Opt Laser Technol. 2018;103:59–76. doi:10.1016/j.optlastec.2018. 01.013
[32] Li Y, Gu D. Thermal behavior during selective laser melting of commercially pure titanium powder: numerical simulation and experimental study. Addit Manuf. 2014;1–4:99–109. doi:10.1016/j.addma.2014.09.001
[33] Dai D, Gu D. Thermal behavior and densification mechanism during selective laser melting of copper matrix composites: simulation and experiments. Mater Des. 2014;55 (0):482–491. doi:10.1016/j.matdes.2013.10.006
[34] Wang S, Zhu L, Dun Y, et al. Multi-physics modeling of direct energy deposition process of thin-walled structures: defect analysis. Comput Mech. 2021;67:c1229– c1242. doi:10.1007/s00466-021-01992-9
[35] Wu J, Zheng J, Zhou H, et al. Molten pool behavior and its mechanism during selective laser melting of polyamide 6 powder: single track simulation and experiments. Mater Res Express. 2019;6. doi:10.1088/2053-1591/ab2747
[36] Cho JH, Farson DF, Milewski JO, et al. Weld pool flows during initial stages of keyhole formation in laser welding. J Phys D Appl Phys. 2009;42. doi:10.1088/0022- 3727/42/17/175502
[37] Sinha KN. Identification of a suitable volumetric heat source for modelling of selective laser melting of Ti6Al4V powder using numerical and experimental validation approach. Int J Adv Manuf Technol. 2018;99:2257–2270. doi:10.1007/s00170-018-2631-4
[38] Fu CH, Guo YB. Three-dimensional temperature gradient mechanism in selective laser melting of Ti-6Al-4V. J Manuf Sci Eng. 2014;136(6):061004. doi:10.1115/1.4028539
[39] Ansari P, Rehman AU, Pitir F, et al. Selective laser melting of 316 l austenitic stainless steel: detailed process understanding using multiphysics simulation and experimentation. Metals. 2021;11(7):1076. doi:10.3390/met11071076
[40] Zhao C, Shi B, Chen S, et al. Laser melting modes in metal powder bed fusion additive manufacturing. Rev Mod Phys. 2022;94(4):045002. doi:10.1103/revmodphys.94. 045002
[41] Bertoli US, Wolfer AJ, Matthews MJ, et al. On the limitations of volumetric energy density as a design parameter for selective laser melting. Mater Des. 2017;113:331–340. doi:10.1016/j.matdes.2016.10.037
[42] Dash A, Kamaraj A. Prediction of the shift in melting mode during additive manufacturing of 316L stainless steel. Mater Today Commun. 2023: 107238. doi:10.1016/j. mtcomm.2023.107238
[43] Majeed M, Khan HM, Rasheed I. Finite element analysis of melt pool thermal characteristics with passing laser in SLM process. Optik. 2019;194:163068. doi:10.1016/j.ijleo. 2019.163068

Schematic diagram of HP-LPBF melting process.

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

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

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

Topics

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

I. INTRODUCTION

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

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

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

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

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

II. MODELING

A. 3D powder bed modeling

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

1. DEM

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

(1)����¨=∑�(�ij×�ij),

(2)

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

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

(3)

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

FIG. 1.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of overlapping powder particles.

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

(4)1�*=(1−��2)��+(1−��2)��,

(5)1�*=1��+1��,

(6)

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

2. Model building

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

FIG. 2.

VIEW LARGEDOWNLOAD SLIDE

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

FIG. 3.

VIEW LARGEDOWNLOAD SLIDE

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

B. Modeling of fluid mechanics simulation

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

1. VOF

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

(7)

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

FIG. 4.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of VOF.

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

(8)

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

2. Control equations and boundary conditions

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

FIG. 5.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of HP-LPBF melting process.

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

3. Assumptions

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

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

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

4. Initial conditions

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

5. Material parameters

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

TABLE I.

SS316L-related parameters.

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

III. RESULTS AND DISCUSSION

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

FIG. 6.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of observation position.

A. Single-track simulation

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

FIG. 7.

VIEW LARGEDOWNLOAD SLIDE

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

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

FIG. 8.

VIEW LARGEDOWNLOAD SLIDE

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

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

FIG. 9.

VIEW LARGEDOWNLOAD SLIDE

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

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

(17)

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

FIG. 10.

VIEW LARGEDOWNLOAD SLIDE

Schematic of contact angle.

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

B. Double-track simulation

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

FIG. 11.

VIEW LARGEDOWNLOAD SLIDE

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

FIG. 12.

VIEW LARGEDOWNLOAD SLIDE

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

FIG. 13.

VIEW LARGEDOWNLOAD SLIDE

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

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

FIG. 14.

VIEW LARGEDOWNLOAD SLIDE

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

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

FIG. 15.

VIEW LARGEDOWNLOAD SLIDE

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

C. Simulation analysis of molten pool under different process parameters

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

1. Laser power

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

FIG. 16.

VIEW LARGEDOWNLOAD SLIDE

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

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

TABLE II.

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

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

2. Scanning speed

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

FIG. 17.

VIEW LARGEDOWNLOAD SLIDE

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

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

TABLE III.

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

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

3. Hatch spacing

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

FIG. 18.

VIEW LARGEDOWNLOAD SLIDE

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

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

TABLE IV.

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

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

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

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

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

FIG. 19.

VIEW LARGEDOWNLOAD SLIDE

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

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

TABLE V.

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

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

IV. CONCLUSIONS

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

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

REFERENCES

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

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

Ali Poorkarimi1
Khaled Mafakheri2
Shahrzad Maleki2

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

Abstract

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

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

Keywords

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

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

References

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

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

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

경사 낙하의 수력학적 성능: 하류 거시 거칠기 요소의 영향

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

ABSTRACT

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

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

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

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

Key words

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

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

REFERENCES

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

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

Effects of ramp slope and discharge on hydraulic performance of submerged hump weirs

Effects of ramp slope and discharge on hydraulic performance of submerged hump weirs

Arash Ahmadi a, Amir H. Azimi b

Abstract

험프 웨어는 수위 제어 및 배출 측정을 위한 기존의 수력 구조물 중 하나입니다. 상류 및 하류 경사로의 경사는 자유 및 침수 흐름 조건 모두에서 험프 웨어의 성능에 영향을 미치는 설계 매개변수입니다.

침수된 험프보의 유출 특성 및 수위 변화에 대한 램프 경사 및 유출의 영향을 조사하기 위해 일련의 수치 시뮬레이션이 수행되었습니다. 1V:1H에서 1V:5H까지의 5개 램프 경사를 다양한 업스트림 방전에서 테스트했습니다.

수치모델의 검증을 위해 수치결과를 실험실 데이터와 비교하였다. 수면수위 예측과 유출계수의 시뮬레이션 불일치는 각각 전체 범위의 ±10%와 ±5% 이내였습니다.

모듈 한계 및 방전 감소 계수의 변화에 대한 램프 경사의 영향을 연구했습니다. 험프보의 경사로 경사가 증가함에 따라 상대적으로 높은 침수율에서 모듈러 한계가 발생함을 알 수 있었다.

침수 시작은 방류 수위를 작은 증분으로 조심스럽게 증가시켜 모델링되었으며 그 결과는 모듈 한계의 고전적인 정의와 비교되었습니다. 램프 경사와 방전이 증가함에 따라 모듈러 한계가 증가하는 것으로 밝혀졌지만, 모듈러 한계의 고전적인 정의는 모듈러 한계가 방전과 무관하다는 것을 나타냅니다.

Hump weir 하류의 속도와 와류장은 램프 경사에 의해 제어되는 와류 구조 형성을 나타냅니다. 에너지 손실은 수치 출력으로부터 계산되었으며 정규화된 에너지 손실은 침수에 따라 선형적으로 감소하는 것으로 나타났습니다.

Hump weirs are amongst conventional hydraulic structures for water level control and discharge measurement. The slope in the upstream and downstream ramps is a design parameter that affects the performance of Hump weirs in both free and submerged flow conditions. A series of numerical simulations was performed to investigate the effects of ramp slope and discharge on discharge characteristics and water level variations of submerged Hump weirs. Five ramp slopes ranging from 1V:1H to 1V:5H were tested at different upstream discharges. The numerical results were compared with the laboratory data for verifications of the numerical model. The simulation discrepancies in prediction of water surface level and discharge coefficient were within ±10 % and ±5 % of the full range, respectively. The effects of ramp slope on variations of modular limit and discharge reduction factor were studied. It was found that the modular limit occurred at relatively higher submergence ratios as the ramp slope in Hump weirs increased. The onset of submergence was modeled by carefully increasing tailwater level with small increments and the results were compared with the classic definition of modular limit. It was found that the modular limit increases with increasing the ramp slope and discharge while the classic definition of modular limit indicated that the modular limit is independent of the discharge. The velocity and vortex fields in the downstream of Hump weirs indicated the formation vortex structure, which is controlled by the ramp slope. The energy losses were calculated from the numerical outputs, and it was found that the normalized energy losses decreased linearly with submergence.

Introduction

Weirs have been utilized predominantly for discharge measurement, flow diversion, and water level control in open channels, irrigation canal, and natural streams due to their simplicity of operation and accuracy. Several research studies have been conducted to determine the head-discharge relationship in weirs as one of the most common hydraulic structures for flow measurement (Rajaratnam and Muralidhar, 1969 [[1], [2], [3]]; Vatankhah, 2010, [[4], [5], [6]]; b [[7], [8], [9]]; Azimi and Seyed Hakim, 2019; Salehi et al., 2019; Salehi and Azimi, 2019, [10]. Weirs in general are classified into two major categories named as sharp-crested weirs and weirs of finite-crest length (Rajaratnam and Muralidhar, 1969; [11]. Sharp-crested weirs are typically used for flow measurement in small irrigation canals and laboratory flumes. In contrast, weirs of finite crest length are more suitable for water level control and flow diversion in rivers and natural streams [7,[12], [13], [14]].

The head-discharge relationship in sharp-crested weirs is developed by employing energy equation between two sections in the upstream and downstream of the weir and integration of the velocity profile at the crest of the weir as:

where Qf is the free flow discharge, B is the channel width, g is the acceleration due to gravity, ho is the water head in free-flow condition, and Cd is the discharge coefficient. Rehbock [15] proposed a linear correlation between discharge coefficient and the ratio of water head, ho, and the weir height, P as Cd = 0.605 + 0.08 (ho/P).

Upstream and/or downstream ramp(s) can be added to sharp-crested weirs to enhance the structural stability of the weir. A sharp-crested weir with upstream and/or downstream ramp(s) are known as triangular weirs in the literature. Triangular weirs with both upstream and downstream ramps are also known as Hump weirs and are first introduced in the experimental study of Bazin [16]. The ramps are constructed upstream and downstream of sharp-crested weirs to enhance the weir’s structural integrity and improve the hydraulic performance of the weir. In free-flow condition, the discharge coefficient of Hump weirs increases with increasing downstream ramp slope but decreases as upstream ramp slope increases (Azimi et al., 2013).

The hydraulic performance of weirs is evaluated in both free and submerged flow conditions. In free flow condition, water freely flows over weirs since the downstream water level is lower than that of the crest level of the weir. Channel blockage or flood in the downstream of weirs can raise the tailwater level, t. As tailwater passes the crest elevation in sharp-crested weirs, the upstream flow decelerates due to the excess pressure force in the downstream and the upstream water level increases. The onset of water level raise due to tailwater raise is called the modular limit. Once the tailwater level passes the modular limit, the weir is submerged. In sharp-crested weirs, the submerged flow regime may occur even before the tailwater reaches the crest elevation [8,14], whereas, in weirs of finite crest length, the upstream water level remains unchanged even if the tailwater raises above the crest elevation and it normally causes submergence once the tailwater level passes the critical depth at the crest of the weir [7,17]. The degree of submergence can be estimated by careful observation of the water surface profile. Observations of water surface at different submergence levels indicated two distinct flow patterns in submerged sharp-crested weirs that was initially classified as impinging jet and surface flow regimes [14]. [8] analyzed the variations of water surface profiles over submerged sharp-crested weirs with different submergence ratios and defined four distinct regimes of impinging jet, surface jump, surface wave, and surface jet.

[18] characterized the onset of submergence by defining the modular limit as a stage when the free flow head increases by +1 mm due to tailwater rise. The definition of modular limit is somewhat arbitrary, and it is difficult to identify for large discharges because the upstream water surface begins to fluctuate. This definition did not consider the effects of channel and weir geometries. The experimental data in triangular weirs and weirs finite-crest length with upstream and downstream ramp(s) revealed that the modular limit varied with the ratio of the free-flow head to the total streamwise length of the weir [17]. Weirs of finite crest length with upstream and downstream ramps are known as embankment weirs in literature [1,19,20] and Azimi et al., 2013) [19]. conducted two series of laboratory experiments to study the hydraulics of submerged embankment weirs with the upstream and downstream ramps of 1V:1H and 1V:2H. Empirical correlations were proposed to directly estimate the flow discharge in submerged embankment weirs for t/h > 0.7 where h is the water head in submerged flow condition. He found that the free flow discharge is a function of upstream water head, but the submerged discharge is a function of submergence level, t/h [21]. studied the hydraulics of four embankment weirs with different weir heights ranging from 0.09 m to 0.36 m. It was found that submerged embankments with a higher ho/P, where P is the height of the weir, have a smaller discharge reduction due to submergence. Effects of crest length in embankment weirs with both upstream and downstream ramps of 1V:2H was studied in both free and submerged flow conditions [1]. It was found that the modular limit in submerged embankment weirs decreased linearly with the relative crest length, Ho/(Ho + L), where Ho is the total head and L is the crest length.

In submerged flow condition, the performance of weirs is quantified by the discharge reduction factor, ψ, which is a ratio of the submerged discharge, Qs, to the corresponding free-flow discharge, Qf, based on the upstream head, h [12]. In submerged-flow conditions, flow discharge can be estimated as:��=���

[1] proposed a formula to predict ψ that could be used for embankment weirs with different crest lengths ranging from 0 to 0.3 m as:�=(1−��)�where n is an exponent varying from 4 to 7 and Yt is the normalized submergence defined as:��=�ℎ−[0.85−(0.5��+�)]1−[0.85−(0.5��+�)]where H is the total upstream head in submerged-flow conditions [7]. proposed a simpler formula to predict ψ for weirs of finite-crest length as:�=[1−(�ℎ)�]�where m and n are exponents varying for different types of weirs. Hakim and Azimi (2017) employed regression analysis to propose values of n = 0.25 and m = 0.28 (ho/L)−2.425 for triangular weirs.

The discharge capacity of weirs decreases in submerged flow condition and the onset of submergence occurs at the modular limit. Therefore, the determination of modular limit in weirs with different geometries is critical to understanding the sensitivity of a particular weir model with tailwater level variations. The available definition of modular limit as when head water raises by +1 mm due to tailwater rise does not consider the effects of channel and weir geometries. Therefore, a new and more accurate definition of modular limit is proposed in this study to consider the effect of other geometry and approaching flow parameters. The second objective of this study is to evaluate the effects of upstream and downstream ramps and ramps slopes on the hydraulic performance of submerged Hump weirs. The flow patterns, velocity distributions, and energy dissipation rates were extracted from validated numerical data to better understand the discharge reduction mechanism in Hump weirs in both free and submerged flow conditions.

Section snippets

Governing equations

Numerical simulation has been employed as an efficient and effective method to analyze free surface flow problems and in particular investigating on the hydraulics of flow over weirs [22]. The weir models were developed in numerical domain and the water pressure and velocity field were simulated by employing the FLOW-3D solver (Flow Science, Inc., Santa Fe, USA). The numerical results were validated with the laboratory measurements and the effects of ramps slopes on the performance of Hump

Verification of numerical model

The experimental observations of Bazin [16,17] were used for model validation in free and submerged flow conditions, respectively. The weir height in the study of Bazin was P = 0.5 m and two ramp slopes of 1V:1H and 1V:2H were tested. The bed and sides of the channel were made of glass, and the roughness distribution of the bed and walls were uniform. The Hump weir models in the study of Seyed Hakim and Azimi (2017) had a weir height of 0.076 m and ramp slopes of 1V:2H in both upstream and

Conclusions

A series of numerical simulations was performed to study the hydraulics and velocity pattern downstream of a Hump weir with symmetrical ramp slopes. Effects of ramp slope and discharge on formation of modular limit and in submerged flow condition were tested by conducting a series of numerical simulations on Hump weirs with ramp slopes varying from 1V:1H to 1V:5H. A comparison between numerical results and experimental data indicated that the proposed numerical model is accurate with a mean

Author contributions

Arash Ahmadi: Software, Validation, Visualization, Writing – original draft. Amir Azimi: Conceptualization, Funding acquisition, Investigation, Project administration, Supervision, Writing – review & editing

Uncited References

[30]; [31]; [32]; [33].

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.

References (33)

  • H.M. Fritz et al.Hydraulics of embankment weirsJ. Hydraul. Eng.(1998)
  • P.K. Swamee et al.Viscosity and surface tension effects on rectangular weirsThe ISH Journal of Hydraulic Engineering(2001)
  • R. BaddourHead-discharge equation for the sharp-crested polynomial weirJ. Irrigat. Drain. Eng.(2008)
  • A.R. VatankhahHead-discharge equation for sharp-crested weir with piecewise-linear sidesJ. Irrigat. Drain. Eng.(2012)
  • A.H. Azimi et al.A note on sharp-crested weirs and weirs of finite crest lengthCan. J. Civ. Eng.(2012)
  • A.H. Azimi et al.Discharge characteristics of weirs of finite crest length with upstream and downstream rampsJ. Irrigat. Drain. Eng.(2013)
  • A.H. Azimi et al.Submerged flows over rectangular weirs of finite crest lengthJ. Irrigat. Drain. Eng.(2014)
  • A.H. Azimi et al.Water surface characteristics of submerged rectangular sharp-crested weirsJ. Hydraul. Eng.(2016)
  • M. Bijankhan et al.Experimental study and numerical simulation of inclined rectangular weirsJ. Irrigat. Drain. Eng.(2018)
  • A.H. AzimiAn Introduction to Hydraulic Structure” in Water Engineering Modeling and Mathematic Tools(2021)

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