Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

ABSTRACT This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re) and Bingham number (Bn). These results reveal the flow behavior of Bingham plastics.

[1]  Cyrus K. Aidun,et al.  Parallel performance of a lattice-Boltzmann/finite element cellular blood flow solver on the IBM Blue Gene/P architecture , 2010, Comput. Phys. Commun..

[2]  B. C. Bell,et al.  p-version least squares finite element formulation for two-dimensional, incompressible, non-Newtonian isothermal and non-isothermal fluid flow , 1994 .

[3]  Tayfun E. Tezduyar,et al.  Finite element methods for flow problems with moving boundaries and interfaces , 2001 .

[4]  Q. Zou,et al.  On pressure and velocity boundary conditions for the lattice Boltzmann BGK model , 1995, comp-gas/9611001.

[5]  Zhenhua Chai,et al.  Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows , 2011 .

[6]  D. Carruthers,et al.  Comparisons between FLUENT and ADMS for atmospheric dispersion modelling , 2004 .

[7]  Andreas G. Boudouvis,et al.  Flows of viscoplastic materials: Models and computations , 1997 .

[8]  J. Derksen.  Flow-induced forces in sphere doublets , 2008, Journal of Fluid Mechanics.

[9]  Qicheng Sun,et al.  Simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model , 2014 .

[10]  Jessie P. Bitog,et al.  The past, present and future of CFD for agro-environmental applications , 2013 .

[11]  Tayfun E. Tezduyar,et al.  Space–time finite element computation of complex fluid–structure interactions , 2010 .

[12]  Masato Yoshino,et al.  A numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method , 2007 .

[13]  Nicolas Roussel,et al.  A Theoretical Frame to Study Stability of Fresh Concrete , 2005 .

[14]  A. Vikhansky,et al.  Lattice-Boltzmann method for yield-stress liquids , 2008 .

[15]  Zhenhua Chai,et al.  Effect of the forcing term in the multiple-relaxation-time lattice Boltzmann equation on the shear stress or the strain rate tensor. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Xiaoxian Zhang,et al.  Domain-decomposition method for parallel lattice Boltzmann simulation of incompressible flow in porous media. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Prashant,et al.  Direct simulations of spherical particle motion in Bingham liquids , 2011, Comput. Chem. Eng..

[18]  T. N. Smith,et al.  Motion of spherical particles in a Bingham plastic , 1967 .

[19]  Peter M. A. Sloot,et al.  Lattice-Boltzmann hydrodynamics on parallel systems , 1998 .

[20]  B. Shizgal,et al.  Generalized Lattice-Boltzmann Equations , 1994 .

[21]  J. Derksen,et al.  Direct numerical simulations of dense suspensions: wave instabilities in liquid-fluidized beds , 2007, Journal of Fluid Mechanics.

[22]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[23]  R. Byron Bird,et al.  The Rheology and Flow of Viscoplastic Materials , 1983 .

[24]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[25]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  John Tsamopoulos,et al.  Creeping motion of a sphere through a Bingham plastic , 1985, Journal of Fluid Mechanics.

[27]  Yifeng Zhang,et al.  High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems , 2012 .

[28]  Georgios C. Georgiou,et al.  Cessation of Couette and Poiseuille flows of a Bingham plastic and finite stopping times , 2005 .

[29]  M. Taghilou,et al.  LBM Simulation of a Droplet Dripping Down a Hole , 2013 .

[30]  Selahattin Kocaman,et al.  Dam-Break Flow in the Presence of Obstacle: Experiment and CFD Simulation , 2011 .

[31]  Tim Reis,et al.  The lattice Boltzmann method for complex flows , 2007 .

[32]  H. J. Herrmann,et al.  Flow Through Randomly Curved Manifolds , 2013, Scientific reports.

[33]  Jens-Uwe Repke,et al.  CFD Study on Liquid Flow Behavior on Inclined Flat Plate Focusing on Effect of Flow Rate , 2012 .

[34]  Evan Mitsoulis,et al.  Creeping motion of a sphere in tubes filled with a Bingham plastic material , 1997 .

[35]  Cheng-Hsien Lee,et al.  An extrapolation-based boundary treatment for using the lattice Boltzmann method to simulate fluid-particle interaction near a wall , 2015 .

[36]  Ulrich Rüde,et al.  A flexible Patch-based lattice Boltzmann parallelization approach for heterogeneous GPU-CPU clusters , 2010, Parallel Comput..

[37]  David R. Owen,et al.  An efficient framework for fluid–structure interaction using the lattice Boltzmann method and immersed moving boundaries , 2011 .

[38]  Panagiotis Neofytou,et al.  A 3rd order upwind finite volume method for generalised Newtonian fluid flows , 2005, Adv. Eng. Softw..