Machine learning and numerical investigation on drag coefficient of arbitrary polygonal particles

Abstract

The drag coefficient, as the most important parameter that characterizes particle dynamics in flows, has been the focus of a large number of investigations. Although good predictability is achieved for simple shapes, it is still challenging to accurately predict drag coefficient of complex-shaped particles even under moderate Reynolds number (Re). The problem is that the small-scale shape details of particles can still have considerable impact on the drag coefficient, but these geometrical details cannot be described by single shape factor. To address this challenge, we leverage modern deep-learning method's ability for pattern recognition, take multiple shape factors as input to better characterize particle-shape details, and use the drag coefficient as output. To obtain a high-precision data set, the discrete element method coupled with an improved velocity interpolation scheme of the lattice Boltzmann method is used to simulate and analyze the sedimentation dynamics of polygonal particles. Four different machine-learning models for predicting the drag coefficient are developed and compared. The results show that our model can well predict the drag coefficient with an average error of less than 5% for particles. These findings suggest that data-driven models can be an attractive option for the drag-coefficient prediction for particles with complex shapes.

Keywords

drag coefficient / arbitrary polygonal particle / shape factor / DEM–LBM / machine Learning

References

[1] Wang G, Tao L, Rong B, Rui X. Review of dynamics simulation methods for multi-field coupling systems. Adv Mech. 2023;53(2):468-495.

[2] Clift R, Grace J, Weber M. Bubbles, drops, and particles. Dry Technol. 1978;11:263-264.

[3] Khan AR, Richardson JF. The resistance to motion of a solid sphere in a fluid. Chem Eng Commun. 1987;62(1-6):135-150.

[4] Haider A, Levenspiel O. Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol. 1989;58(1):63-70.

[5] Willmarth WW, Hawk NE, Harvey RL. Steady and unsteady motions and wakes of freely falling disks. Phys Fluids. 1964;7(2):197-208.

[6] Leith D. Drag on nonspherical objects. Aerosol Sci Technol. 1987;6(2):153-161.

[7] Hölzer A, Sommerfeld M. Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles. Comput Fluids. 2009;38(3):572-589.

[8] Koochi H, Mac Intyre J, Korhonen M, Puisto A, Maleki-Jirsaraei N, Alava MJ. Interaction between a free-falling sphere and structure dynamics in a heterogeneous thixotropic fluid. Phys Fluids. 2023;35(8):083108.

[9] Wang Z, Xiao Y, Liu J, et al. Investigation on settling behavior of single cuboid-like particle in a quiescent fluid. Powder Technol. 2024;439:119713.

[10] Qiu Z, Xiao Q, Yuan H, Han X, Li C. Particle shape and clogging in fluid-driven flow: a coupled CFD-DEM study. Powder Technol. 2024;437:119566.

[11] Zhang H, Yu A, Zhong W, Tan Y. A combined TLBM-IBM-DEM scheme for simulating isothermal particulate flow in fluid. Int J Heat Mass Transfer. 2015;91:178-189.

[12] Jiao K, Han D, Li J, Yu B. Numerical simulations of polygonal particles settling within non-Newtonian fluids. Phys Fluids. 2022;34(7):073315.

[13] Wang M, Feng YT, Qu TM, Zhao TT. A coupled polygonal DEM-LBM technique based on an immersed boundary method and energy-conserving contact algorithm. Powder Technol. 2021;381:101-109.

[14] Cheng C, Galindo-Torres S, Zhang X, Zhang P, Scheuermann A, Li L. An improved immersed moving boundary for the coupled discrete element lattice Boltzmann method. Comput Fluids. 2018;177:12-19.

[15] Wang M, Feng YT, Owen DRJ, Qu TM. A novel algorithm of immersed moving boundary scheme for fluid-particle interactions in DEM-LBM. Comput Methods Appl Mech Eng. 2019;346:109-125.

[16] Li X, Ma H, Mei Z, Zhou D, Zhao Y. An approach to determine the solid volume fraction near solid boundaries for partially saturated method within the lattice Boltzmann method. Comput Fluids. 2024;271:106166.

[17] Zhang P, Galindo-Torres SA, Tang H, Jin G, Scheuermann A, Li L. Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles. Phys Rev E. 2016;93(6):062612.

[18] Zhou C, Su J, Chen H, Shi Z. Terminal velocity and drag coefficient models for disc-shaped particles based on the imaging experiment. Powder Technol. 2022;398:117062.

[19] Tran-Cong S, Gay M, Michaelides EE. Drag coefficients of irregularly shaped particles. Powder Technol. 2004;139(1):21-32.

[20] Yow HN, Pitt MJ, Salman AD. Drag correlations for particles of regular shape. Adv Powder Technol. 2005;16(4):363-372.

[21] Dioguardi F, Mele D, Dellino P. A new one-equation model of fluid drag for irregularly shaped particles valid over a wide range of Reynolds number. J Geophys Res Solid Earth. 2018;123(1):144-156.

[22] Luo W, Ebel H, Eberhard P. An LSTM-based approach to precise landing of a UAV on a moving platform. Int J Mech Syst Dynam. 2022;2(1):99-107.

[23] Jing J, Liu S, Wang G, Zhang W, Sun C. Recent advances on image edge detection: a comprehensive review. Neurocomputing. 2022;503:259-271.

[24] Dogra V, Verma S, Kavita I, et al. A complete process of text classification system using state-of-the-art NLP models. Comput Intell Neurosci. 2022;2022:1-26.

[25] Brunton SL, Noack BR, Koumoutsakos P. Machine learning for fluid mechanics. Annu Rev Fluid Mech. 2020;52(1):477-508.

[26] Huang X, Cheng C, Zhang X. Machine learning and numerical investigation on drag reduction of underwater serial multi-projectiles. Defence Technol. 2022;18(2):229-237.

[27] Yoon HD, Cox DT, Kim M. Prediction of time-dependent sediment suspension in the surf zone using artificial neural network. Coastal Eng. 2013;71:78-86.

[28] Yan S, He Y, Tang T, Wang T. Drag coefficient prediction for non-spherical particles in dense gas-solid two-phase flow using artificial neural network. Powder Technol. 2019;354:115-124.

[29] Rushd S, Parvez MT, Al-Faiad MA, Islam MM. Towards optimal machine learning model for terminal settling velocity. Powder Technol. 2021;387:95-107.

[30] Let S, Maiti SB, Bar N, Basu RK, Das SK. Elutriation characteristics of binary particle mixture in pseudoplastic liquid: empirical correlation and GA-ANN modelling. Powder Technol. 2023;428:118796.

[31] Galindo-Torres SA, Scheuermann A, Li L. Numerical study on the permeability in a tensorial form for laminar flow in anisotropic porous media. Phys Rev E. 2012;86(4):046306.

[32] Galindo-Torres SA, Scheuermann A, Li L, Pedroso DM, Williams DJ. A lattice Boltzmann model for studying transient effects during imbibition-drainage cycles in unsaturated soils. Comput Phys Commun. 2013;184(4):1086-1093.

[33] Galindo-Torres SA. A coupled discrete element lattice Boltzmann method for the simulation of fluid-solid interaction with particles of general shapes. Comput Methods Appl Mech Eng. 2013;265:107-119.

[34] Mohamad A. Lattice Boltzmann method. Vol 70. Springer; 2011.

[35] Cundall PA, Strack ODL. A discrete numerical model for granular assemblies. Géotechnique. 1979;29(1):47-65.

[36] Zhang P, Qiu L, Chen Y, et al. Coupled metaball discrete element lattice Boltzmann method for fluid-particle systems with non-spherical particle shapes: a sharp interface coupling scheme. J Comput Phys. 2023;479:112005.

[37] Zhao Y, Zhang P, Lei L, Kong L, Galindo-Torres SA, Li SZ. Metaball-Imaging discrete element lattice Boltzmann method for fluid-particle system of complex morpholo-gies with case studies. Phys Fluids. 2023;35(2):023308.

[38] Wachs A. A DEM-DLM/FD method for direct numerical simulation of particulate flows: sedimentation of polygonal isometric particles in a Newtonian fluid with collisions. Comput Fluids. 2009;38(8):1608-1628.

[39] Swamee PK, Ojha CSP. Drag coefficient and fall velocity of nonspherical particles. J Hydraul Eng. 1991;117(5):660-667.

[40] Breiman L. Random forests. Mach Learn. 2001;45:5-32.

[41] Breiman L. Bagging predictors. Mach Learn. 1996;24:123-140.

[42] Forrest S. Genetic algorithms. ACM Comput Surv. 1996;28(1):77-80.

[43] Zhang Y, Pan G, Chen B, Han J, Zhao Y, Zhang C. Short-term wind speed prediction model based on GA-ANN improved by VMD. Renew Energy. 2020;156:1373-1388.

[44] Zhang H, Tan Y, Shu S, et al. Numerical investigation on the role of discrete element method in combined LBM-IBM-DEM modeling. Comput Fluids. 2014;94:37-48.

[45] Wu J, Shu C. Particulate flow simulation via a boundary condition-enforced immersed boundary-lattice Boltzmann scheme. Commun Comput Phys. 2010;7(4):793-812.

[46] Wan D, Turek S. Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method. Int J Numer Methods Fluids. 2006;51(5):531-566.

[47] Wicke E, Hedden SK. Strömungsformen und Wärmeübertragung in von Luft aufgewirbelten Schüttgutschichten. Chem Ing Tech. 1952;24(2):82-91.

[48] Feng J, Hu HH, Joseph DD. Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. J Fluid Mech. 1994;277:271-301.

[49] Yu Z, Phan-Thien N, Fan Y, Tanner RI. Viscoelastic mobility problem of a system of particles. J Non-Newtonian Fluid Mech. 2002;104(2-3):87-124.

[50] Ten Cate A, Nieuwstad CH, Derksen JJ, Van den Akker HEA. Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity. Phys Fluids. 2002;14(11):4012-4025.

[51] Feng ZG, Michaelides EE. The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems. J Comput Phys. 2004;195(2):602-628.

[52] Saha AK, Biswas G, Muralidhar K. Three-dimensional study of flow past a square cylinder at low Reynolds numbers. Int J Heat Fluid Flow. 2003;24(1):54-66.

[53] Sen S, Mittal S, Biswas G. Flow past a square cylinder at low Reynolds numbers. Int J Numer Methods Fluids. 2011;67(9):1160-1174.

[54] Sharma A, Eswaran V. Heat and fluid flow across a square cylinder in the two-dimensional laminar flow regime. Num Heat Transfer A: Appl. 2004;45(3):247-269.

[55] Pruppacher HR, Clair BPL, Hamielec AE. Some relations between drag and flow pattern of viscous flow past a sphere and a cylinder at low and intermediate Reynolds numbers. J Fluid Mech. 1970;44(4):781-790.

[56] Schetz JA, Fuhs AE. Fundamentals of Fluid Mechanics. John Wiley & Sons; 1999.

[57] Jayaweera KOLF, Mason BJ. The behaviour of freely falling cylinders and cones in a viscous fluid. J Fluid Mech. 1965;22(4):709-720.

RIGHTS & PERMISSIONS

2024 2024 The Author(s). International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.