(493c) A Numerical Method for Large-Scale Dense Particulate Flows Based On an Improved MP-PIC Method and Extended Lattice-Boltzmann Scheme

         Detailed
simulation of large-scale, dense particulate flows is extremely demanding.
Prohibitively high computational expenses arise from large numbers of particles
and their interactions. In order to be able to gain insight into such flows,
numerical methods have been proposed in the literature. A multiphase
particle-in-cell (MP-PIC) method offers a satisfactory level of accuracy with
reasonable computational expenses [1]. In the MP-PIC method, particles with
identical properties (e.g., particle diameter, velocity) are represented by a
parcel and tracked in a Lagrangian manner. At the
particle volume fraction near close-packing,
conditions are imposed to prevent the particle volume fraction beyond
close-packing. Effects of particle collisions are modeled based on the local
particle distribution and their properties. Recently, O'Rourke et al.
[2] proposed a collision procedure based on a Bhatnagar,
Gross, and Krook (BGK) approximation to the collision
terms in a particle distribution function transport equation. A collision
damping time which represents the rate toward the local
average particle velocity was introduced.

         We
present a numerical method for large-scale dense particulate flows with
applications to sedimenting suspensions. The locally
averaged conservation equations for the fluid phase are discretized using an
extended lattice-Boltzmann (LB) scheme. A MP-PIC method with an improved  collision
procedure is used to track parcels of particles. A new collision damping time
is derived from the discrete kinetic equation for the particle distribution
function. The LB scheme and the MP-PIC method are coupled resulting in the
so-called four-way coupling. The computer code for the present method is
implemented and parallelized using the message passing interface (MPI) library.

         The
present method is used to carry out simulations of dense sedimenting
suspensions in a cubic periodic domain. In order to evaluate the accuracy of
the present method, the predicted average and variance of particle settling
velocity are compared to the experimental data from the literature [3]. In
addition, the excellent speedup on a parallel computing platform of the present
method demonstrates its potential for simulations of industrial-scale
particulate flows.

References

[1]
Snider D. M. An incompressible three-dimensional multiphase particle-in-cell
model for dense particle flows. J. Comp. Phys. 2001;170:523-549.

[2] O'Rourke
P. J., Snider D. M. An improved collision damping time for MP-PIC calculations
of dense particle flows with applications to polydisperse
sedimenting beds and colliding particle jets. Chem.
Eng. Sci. 2010;65:6014-6028.

[3] Guazzelli
E., Hinch J. Fluctuations and instability in
sedimentation. Annu. Rev. Fluid.
Mech. 2011;43:97-116.