(543c) Extended Conditional Quadrature-Based Moment Method for Polydisperse Gas-Particle Flows With Size-Conditioned Velocity

Extended conditional
quadrature-based moment method for polydisperse gas-particle
flows with size-conditioned velocity

Bo Kong, Alberto Passalacqua and Rodney O. Fox

Department of
Biological and Chemical Engineering & Ames Laboratory

Iowa State
University, Ames, IA, USA

Keywords: Extended
conditional quadrature-based moment method,  
polydisperse gas-particle flows, size-conditioned velocity, generalized population balance equation

Abstract: 

            Polydisperse
gas-particle flows are common in many fields of engineering, such as in
fluidized beds and risers, which are widely used in a variety of chemical
processes. Due to the various physical and chemical interactions between
particles and gas, such as particle collisions and breakage, gasification and
chemical reactions, the individual particle size and the overall size
distribution of particles changes as the flow develops. Since different size
particles have different velocity distributions, and different particle
velocity distribution again lead to different size changes, the joint number
density function of particle size and velocity has to be modeled in a gas-particle
flow. In this work, the extended conditional quadrature method of moments
(ECQMOM) is developed to treat the size-velocity coupling in numerical
solutions to the generalized population balance equation (GPBE) for particles. ECQMOM
is a multivariate moment-inversion algorithm that combines the conditional
quadrature method of moments (CQMOM) (Yuan and Fox, 2011) and the extended quadrature
method of moments (Yuan et al., 2012). CQMOM is based on the concept of
conditional moments, which can be used to solve the distribution of a conditional
variable by using univariate inversion. EQMOM is a univariate inversion method,
which replaces the delta functions with smooth kernel density functions by
adding one additional moment. In this work, a beta kernel function was chosen
for particle size distribution and a Gaussian kernel function was used for the
particle velocity distribution. By reconstructing the size-conditioned velocity
distribution function, the spatial fluxes in the moment equations are treated
using a kinetic-based finite-volume solver. The particle-phase volume-fraction
and momentum equations were then coupled with the Eulerian
solver for the fluid phase. The computational algorithm is implemented in an
open-source CFD package and tested in one dimension and then two dimensions
with small and large standard deviations in the particle size.