Free surface flow of a suspension of rigid particles in a non-Newtonian fluid: A lattice Boltzmann approach

Abstract A numerical framework capable of predicting the free surface flow of a suspension of rigid particles in a non-Newtonian fluid is described. The framework is a combination of the lattice Boltzmann method for fluid flow, the mass tracking algorithm for free surface representation, the immersed boundary method for two-way coupled interactions between fluid and rigid particles and an algorithm for the dynamics and mutual interactions of rigid particles. The framework is able to simulate the flow of suspensions at the level of the largest suspended particles and, at the same time, the model is very efficient, allowing simulations of tens of thousands of rigid particles within a reasonable computational time. Furthermore, the framework does not require any fitting constants or parameters devoid of a clear physical meaning and it is stable, robust and can be easily generalized to a variety of problems from many fields.

[1]  Cyrus K. Aidun,et al.  Lattice-Boltzmann Method for Complex Flows , 2010 .

[2]  David R. Owen,et al.  Numerical rheometry of bulk materials using a power law fluid and the lattice Boltzmann method , 2011 .

[3]  Xiaolei Yang,et al.  A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations , 2009, J. Comput. Phys..

[4]  J. Wu,et al.  Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications , 2009 .

[5]  Michael C. Sukop,et al.  Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers , 2005 .

[6]  John Forbes Olesen,et al.  Flow simulation of fiber reinforced self compacting concrete using Lattice Boltzmann method , 2011 .

[7]  Chang Shu,et al.  A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder , 2007, J. Comput. Phys..

[8]  G. Batchelor,et al.  The determination of the bulk stress in a suspension of spherical particles to order c2 , 1972, Journal of Fluid Mechanics.

[9]  A. Louisa,et al.  コロイド混合体における有効力 空乏引力から集積斥力へ | 文献情報 | J-GLOBAL 科学技術総合リンクセンター , 2002 .

[10]  R. V. D. Sman,et al.  Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow , 2006 .

[11]  A. Ladd Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation , 1993, Journal of Fluid Mechanics.

[12]  U. Rüde,et al.  Lattice Boltzmann Model for Free Surface Flow for Modeling Foaming , 2005 .

[13]  Nicolas Roussel,et al.  “Fifty-cent rheometer” for yield stress measurements: From slump to spreading flow , 2005 .

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

[15]  Jonas Latt,et al.  Hydrodynamic limit of lattice Boltzmann equations , 2007 .

[16]  Abdulmajeed A. Mohamad,et al.  A critical evaluation of force term in lattice Boltzmann method, natural convection problem , 2010 .

[17]  A. Ladd,et al.  Lattice-Boltzmann Simulations of Particle-Fluid Suspensions , 2001 .

[18]  N. Martys,et al.  Critical properties and phase separation in lattice Boltzmann fluid mixtures. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Orestis Malaspinas,et al.  Straight velocity boundaries in the lattice Boltzmann method. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Stefano Longhi Spiral waves in optical parametric oscillators , 2001 .

[21]  L. Luo,et al.  Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model , 1997 .

[22]  D. Wolf-Gladrow Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction , 2000 .

[23]  M. Markus,et al.  On-off intermittency and intermingledlike basins in a granular medium. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Z. Feng,et al.  Robust treatment of no-slip boundary condition and velocity updating for the lattice-Boltzmann simulation of particulate flows , 2009 .

[25]  P. Lallemand,et al.  Lattice Boltzmann method for moving boundaries , 2003 .

[26]  Duggento Andrea,et al.  非定常動力学に対する推論の枠組 II 生理学的シグナリングモデルへの応用 , 2008 .

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

[28]  A. Ladd Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results , 1993, Journal of Fluid Mechanics.

[29]  D. Baraff An Introduction to Physically Based Modeling: Rigid Body Simulation I—Unconstrained Rigid Body Dynamics , 1997 .

[30]  M. Uhlmann An immersed boundary method with direct forcing for the simulation of particulate flows , 2005, 1809.08170.

[31]  B. Shi,et al.  Discrete lattice effects on the forcing term in the lattice Boltzmann method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Wei Shyy,et al.  Regular Article: An Accurate Curved Boundary Treatment in the Lattice Boltzmann Method , 1999 .

[33]  Thomas J. Dougherty,et al.  A Mechanism for Non‐Newtonian Flow in Suspensions of Rigid Spheres , 1959 .

[34]  Z. Feng,et al.  Proteus: a direct forcing method in the simulations of particulate flows , 2005 .

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

[36]  A. Ladd,et al.  Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Mitsuhiro Ohta,et al.  Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels , 2011 .

[38]  D. H. Rothman,et al.  Microscopic modeling of immiscible fluids in three dimensions by a lattice Boltzmann method , 1992 .

[39]  Takaji Inamuro,et al.  A lattice kinetic scheme for incompressible viscous flows with heat transfer , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[40]  Wei Shyy,et al.  Force evaluation in the lattice Boltzmann method involving curved geometry. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  J. Wu,et al.  An improved immersed boundary-lattice Boltzmann method for simulating three-dimensional incompressible flows , 2010, J. Comput. Phys..