Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-16T09:21:43.509Z Has data issue: false hasContentIssue false

Algorithms in a Robust Hybrid CFD-DEM Solver for Particle-Laden Flows

Published online by Cambridge University Press:  20 August 2015

Heng Xiao*
Affiliation:
Institute of Fluid Dynamics, ETH Zürich, 8092 Zürich, Switzerland
Jin Sun*
Affiliation:
Institute of Fluid Dynamics, ETH Zürich, 8092 Zürich, Switzerland
*
Corresponding author.Email:[email protected]
Get access

Abstract

A robust and efficient solver coupling computational fluid dynamics (CFD) with discrete element method (DEM) is developed to simulate particle-laden flows in various physical settings. An interpolation algorithm suitable for unstructured meshes is proposed to translate between mesh-based Eulerian fields and particle-based La-grangian quantities. The interpolation scheme reduces the mesh-dependence of the averaging and interpolation procedures. In addition, the fluid-particle interaction terms are treated semi-implicitly in this algorithm to improve stability and to maintain accuracy. Finally, it is demonstrated that sub-stepping is desirable for fluid-particle systems with small Stokes numbers. A momentum-conserving sub-stepping technique is introduced into the fluid-particle coupling procedure, so that problems with a wide range of time scales can be solved without resorting to excessively small time steps in the CFD solver. Several numerical examples are presented to demonstrate the capabilities of the solver and the merits of the algorithm.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Liu, Y., Zhang, L., Wang, X. D. and Liu, W. K., Coupling of Navier-Stokes equations with protein molecular dynamics and its application to hemodynamics, Int. J. Numer. Meth. Fl., 46 (2004), 12371252.Google Scholar
[2]Osanloo, F., Kolahchi, M. R., McNamara, S. and Herrmann, H. J., Sediment transport in the saltation regime, Phys. Rev. E., 78 (2008), 011301.Google Scholar
[3]Syamlal, M., Rogers, W. and O’Brien, T., MFIX Documentation: Theory Guide, Technical report, National Energy Technology Laboratory, Department of Energy, 1993, See also URL http://www.mfix.org.CrossRefGoogle Scholar
[4]Sun, J. and Battaglia, F., Hydrodynamic modeling of particle rotation for segregation in bubbling gas-fluidized beds, Chem. Eng. Sci., 61 (5) (2006), 14701479.CrossRefGoogle Scholar
[5]Crowe, C. T., Troutt, T. R. and Chung, J. N., Numerical models for two-phase turbulent flows, Annu. Rev. Fluid. Mech., 28 (1) (1996), 1143.CrossRefGoogle Scholar
[6]Cundall, P. A. and Strack, D. L., A discrete numerical model for granular assemblies, Géotechnique, 29 (1979), 4765.CrossRefGoogle Scholar
[7]Tsuji, Y., Kawaguchi, T. and Tanaka, T, Discrete particle simulation of two-dimensional fluidized bed, Powder. Technol., 77 (1993), 7987.Google Scholar
[8]Sun, J., Battaglia, F. and Subramaniam, S., Dynamics and structures of segregation in a dense, vibrating granular bed, Phys. Rev. E., 74 (6) (2006), 061307(13).Google Scholar
[9]Feng, Y. Q. and Yu, A. B., Microdynamic modelling and analysis of the mixing and segregation of binary mixtures of particles in gas fluidization, Chem. Eng. Sci., 62 (1-2) (2007), 256268.Google Scholar
[10]Shamy, U. E. and Zeghal, M., Coupled continuum-discrete model for saturated granular soils, J. Engrg. Mech., 131 (4) (2005), 413426.Google Scholar
[11]Van Wachem, B. G. M., Schouten, J. C., Van den Bleek, C. M., Krishna, R. and Sinclair, J. L., CFD modelling of gas-fluidized beds with a bimodal particle mixture, AIChE. J., 47 (6) (2001), 12921301.Google Scholar
[12]Kafui, K. D., Thornton, C. and Adams, M. J., Discrete particle-continuum fluid modelling of gas-solid fluidised beds, Chem. Eng. Sci., 57 (13) (2002), 23952410.Google Scholar
[13]Sundaram, S. and Collins, L. R., Numerical considerations in simulating a turbulent suspension of finite-volume particles, J. Comput. Phys., 124 (1996), 337350.Google Scholar
[14]Silbert, L. E., Ertas, D., Grest, G. S., Halsey, T. C., D., Levine and Plimpton, S. J., Granular flow down an inclined plane: bagnold scaling and rheology, Phys. Rev. E, 64 (5) (2001), 051302.Google Scholar
[15]Anderson, T. B. and Jackson, R., A fluid mechanical description of fluidized beds: Equations of motion, Ind. Che. Engi. Fund., 6 (1967), 527534.CrossRefGoogle Scholar
[16]Sun, J., Battaglia, F. and Subramaniam, S., Hybrid two-fluid DEM simulation of gas–solid fluidized beds, J. Fluid. Eng., 129 (2007), 13941403.CrossRefGoogle Scholar
[17]Wen, C. and Yu, Y., Mechanics of fluidization, Chem. Eng. Prog., Symp. Ser., 62 (1966), 100– 111.Google Scholar
[18]Garside, J. and Al-Dibouni, M. R., Velocity-voidage relationships for fluidization and sedimentation, Ind. Eng. Chem. Proc. Dd., 16 (1977), 206214.Google Scholar
[19]Plimpton, J., Fast parallel algorithms for short-range molecular dynamics, J. Comp. Phys., 117 (1995), 119.Google Scholar
[20]Rusche, H., Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions, PhD thesis, Imperial College London, UK, 2002.Google Scholar
[21] OpenCFD, OpenFOAM User Guide, 2008, See also http://www.opencfd.co.uk/openfoam.Google Scholar
[22]Snider, D. M., An incompressible three-dimensional multiphase particle-in-cell model for dense particle flows, J. Comput. Phys., 170 (2001), 523549.Google Scholar
[23]Carmona, R. A., Statistical Analysis of Financial Data in S-Plus, Springer, 2004.Google Scholar
[24]Sun, J., Xiao, H. and Gao, D. H., Numerical study of segregation using multiscale models, Int. J. Comput. Fluid. D., 23 (2) (2009), 8192.Google Scholar
[25]Zhu, H. P., Zhou, Z. Y., Yang, R. Y. and Yu, A. B., Discrete particle simulation of particulate systems: theoretical developments, Chem. Eng. Sci., 62 (2007), 33783396.Google Scholar
[26]Crowe, C. T., Sharma, M. P. and Stock, D. E., The particle-source-in-cell (psi-cell) model for gas-droplet flow, J. Fluid. Eng., 99 (1977), 325332.CrossRefGoogle Scholar
[27]Hu, H. H., Joseph, D. D. and Crochet, M. J., Direct simulation of fluid particle motions, Theor. Comp. Fluid. Dyn., 3 (1992), 285306.Google Scholar
[28]Rhie, C. M. and Chow, W. L., A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation, AIAA., 21 (11) (1983), 15251532.Google Scholar
[29]Issa, R. I., Solution of the implicitly discretised fluid flow equations by operator-splitting, J. Comput. Phys., 62 (1986),40-65.CrossRefGoogle Scholar
[30]Jasak, H., Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows, PhD thesis, Imperial College London, UK, 1996.Google Scholar
[31]Ergun, S., Fluid flow through packed columns, Chem. Eng. Prog., 43 (2) (1952), 226231.Google Scholar
[32]Goldschmidt, M., Hydrodynamic Modelling of Fluidised Bed Spray Granulation, PhD thesis, Twente University, The Netherlands, 2001.Google Scholar