An Euler-Lagrange strategy for simulating particle-laden flows

In this work, a strategy capable of simulating polydisperse flows in complex geometries is employed where the fluid transport equations are solved in an Eulerian framework and the dispersed phase is represented as Lagrangian particles. Volume filtered equations for the carrier phase are derived in detail for variable density flows, and all unclosed terms are discussed. Special care is given to the interphase coupling terms that arise, in order to ensure that they are implemented consistently and that they converge under mesh refinement. This provides the flexibility of using cell sizes that are smaller than the particle diameter if necessary. Particle collisions are handled using a soft-sphere model that has been modified for parallel efficiency. Simulations are carried out for a number of laboratory-scale configurations, showing excellent agreement with experiments.

[1]  Dimitri Gidaspow,et al.  Computation of flow patterns in circulating fluidized beds , 1990 .

[2]  Hamid Arastoopour,et al.  Numerical simulation and experimental analysis of gas/solid flow systems: 1999 Fluor-Daniel Plenary lecture , 2001 .

[3]  O. Desjardins,et al.  Numerical Analysis of the Dynamics of Two- and Three-Dimensional Fluidized Bed Reactors using an Euler-Lagrange Approach , 2012 .

[4]  J. Kuipers,et al.  A numerical model of gas-fluidized beds , 1992 .

[5]  S. Subramaniam,et al.  Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows , 2007 .

[6]  Arthur T. Andrews,et al.  Multiscale modeling of gas-fluidized beds , 2006 .

[7]  F. Maio,et al.  Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes , 2004 .

[8]  Clayton T. Crowe,et al.  On Models for Turbulence Modulation in Fluid-Particle Flows , 2000 .

[9]  G. D. Byrne,et al.  VODE: a variable-coefficient ODE solver , 1989 .

[10]  M. Sommerfeld,et al.  Multiphase Flows with Droplets and Particles , 2011 .

[11]  Francesco Paolo Di Maio,et al.  Homogeneous and bubbling fluidization regimes in DEM-CFD simulations : Hydrodynamic stability of gas and liquid fluidized beds , 2007 .

[12]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[13]  H. Grad.  On the kinetic theory of rarefied gases , 1949 .

[14]  D. Zhang,et al.  Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions , 1997 .

[15]  Rodney O. Fox,et al.  Introduction and Fundamentals of Modeling Approaches for Polydisperse Multiphase Flows , 2007 .

[16]  Nikolaus A. Adams,et al.  A conservative immersed interface method for Large-Eddy Simulation of incompressible flows , 2010, J. Comput. Phys..

[17]  D. Joseph,et al.  Modeling and numerical simulation of particulate flows by the Eulerian–Lagrangian approach , 2001 .

[18]  T. Heindel,et al.  Local time-averaged gas holdup in a fluidized bed with side air injection using X-ray computed tomography , 2009 .

[19]  Haifeng Wang,et al.  Specific volume coupling and convergence properties in hybrid particle/finite volume algorithms for turbulent reactive flows , 2015, J. Comput. Phys..

[20]  Ng Niels Deen,et al.  Validation of a Discrete Particle Model in a 2D Spout-Fluid Bed Using Non-Intrusive Optical Measuring Techniques , 2008 .

[21]  J. X. Bouillard,et al.  Porosity distributions in a fluidized bed with an immersed obstacle , 1989 .

[22]  Yutaka Tsuji,et al.  Multi-scale modeling of dense phase gas–particle flow , 2007 .

[23]  C. Meneveau,et al.  A Lagrangian dynamic subgrid-scale model of turbulence , 1994, Journal of Fluid Mechanics.

[24]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[25]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[26]  S. Balachandar,et al.  Turbulent Dispersed Multiphase Flow , 2010 .

[27]  Jam Hans Kuipers,et al.  Flow regimes in a spout-fluid bed : A combined experimental and simulation study , 2005 .

[28]  T. Elperin,et al.  Monte Carlo simulation of gas-solids suspension flows in impinging streams reactors , 1990 .

[29]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[30]  H. Struchtrup.  Macroscopic transport equations for rarefied gas flows , 2005 .

[31]  D. Kilgour,et al.  The density of random close packing of spheres , 1969 .

[32]  P. J. O'rourke,et al.  Sediment flow in inclined vessels calculated using a multiphase particle-in-cell model for dense particle flows , 1998 .

[33]  Bo G Leckner,et al.  Fundamentals of turbulent gas-solid flows applied to circulating fluidized bed combustion , 1998 .

[34]  Daniele Marchisio,et al.  Solution of population balance equations using the direct quadrature method of moments , 2005 .

[35]  Christopher E. Brennen,et al.  Computer simulation of granular shear flows , 1985, Journal of Fluid Mechanics.

[36]  H. Enwald,et al.  Eulerian two-phase flow theory applied to fluidization , 1996 .

[37]  H. Arastoopour,et al.  Simulation of particles and gas flow behavior in the riser section of a circulating fluidized bed using the kinetic theory approach for the particulate phase , 2000 .

[38]  John R. Grace,et al.  Particle velocity profiles and solid flow patterns in spouted beds , 1994 .

[39]  Chidambaram Narayanan,et al.  A numerically convergent Lagrangian–Eulerian simulation method for dispersed two-phase flows , 2009 .

[40]  Mark R. Nimlos,et al.  Biomass Pyrolysis and Gasification of Varying Particle Sizes in a Fluidized-Bed Reactor , 2011 .

[41]  H. Salman,et al.  Lagrangian simulation of evaporating droplet sprays , 2004 .

[42]  S. Subramaniam,et al.  A comprehensive probability density function formalism for multiphase flows , 2009, Journal of Fluid Mechanics.

[43]  J. Eaton,et al.  The effect of small particles on fluid turbulence in a flat‐plate, turbulent boundary layer in air , 1991 .

[44]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases : an account of the kinetic theory of viscosity, thermal conduction, and diffusion in gases , 1954 .

[45]  P. Saffman.  The lift on a small sphere in a slow shear flow , 1965, Journal of Fluid Mechanics.

[46]  Andrea Prosperetti,et al.  Averaged equations for inviscid disperse two-phase flow , 1994, Journal of Fluid Mechanics.

[47]  Andrew H. Gee,et al.  Regularised marching tetrahedra: improved iso-surface extraction , 1999, Comput. Graph..

[48]  Heinz Pitsch,et al.  High order conservative finite difference scheme for variable density low Mach number turbulent flows , 2007, J. Comput. Phys..

[49]  T. B. Anderson,et al.  Fluid Mechanical Description of Fluidized Beds. Equations of Motion , 1967 .

[50]  Direct numerical simulation of dense particle-laden flows using a conservative immersed boundary technique , 2010 .

[51]  Shigeru Yonemura,et al.  Cluster Formation and Particle-Induced Instability in Gas-Solid Flows Predicted by the DSMC Method. , 1996 .

[52]  D. Lilly,et al.  A proposed modification of the Germano subgrid‐scale closure method , 1992 .

[53]  R. Illner,et al.  The mathematical theory of dilute gases , 1994 .

[54]  Ng Niels Deen,et al.  Review of discrete particle modeling of fluidized beds , 2007 .

[55]  J. Kuipers,et al.  Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: A hard-sphere approach. , 1996 .

[56]  D. Gidaspow.  Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions , 1994 .

[57]  C. Yuan,et al.  Conditional quadrature method of moments for kinetic equations , 2011, J. Comput. Phys..

[58]  R. Fox.  Large-Eddy-Simulation Tools for Multiphase Flows , 2012 .

[59]  S. Tenneti,et al.  Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres , 2011 .

[60]  P. Moin,et al.  Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , 1984 .

[61]  Dimitri Gidaspow,et al.  Hydrodynamics of fluidization using kinetic theory: an emerging paradigm: 2002 Flour-Daniel lecture , 2004 .

[62]  Jam Hans Kuipers,et al.  Digital image analysis measurements of bed expansion and segregation dynamics in dense gas-fluidized beds , 2003 .

[63]  Marcus Herrmann,et al.  A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure , 2010, J. Comput. Phys..

[64]  Olivier Desjardins,et al.  A quadrature-based moment method for dilute fluid-particle flows , 2008, J. Comput. Phys..

[65]  Y. Tsuji,et al.  Discrete particle simulation of two-dimensional fluidized bed , 1993 .

[66]  R. Fox,et al.  A fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows , 2010 .

[67]  R. D. Felice,et al.  On the apparent viscosity of a fluidized bed , 2007 .

[68]  W. Steckelmacher.  Molecular gas dynamics and the direct simulation of gas flows , 1996 .