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.