Kinetic-Based Model for Fully Compressible Polydisperse Gas-Particle Flows

Eulerian-Eulerian hyperbolic conservation equations for fully compressible, polydisperse, gas-particle flows are presented. First, a kinetic-based model is developed for the polydisperse particle phase that accounts for collisional and frictional terms between spherical particles of different sizes. Then, the particle-phase model is formulated in terms of the moments of the particle size distribution, and particle velocity moments conditioned on the particle mass. Transport equations for particle velocity moments up to fourth order are closed using the hyperbolic quadrature method of moments (HyQMOM). In the numerical implementation, the particle mass distribution is treated using quadrature-based moment methods wherein velocity moments conditioned on particle size are found with the conditional quadrature method of moments (CQMOM). The 1-D hyperbolic conservation equations for the gas and particle phases are solved using HLL numerical fluxes, and the coupling terms are treated using operator splitting to guarantee realizability of the moments. The ability of the proposed model to capture 1-D shocks interacting with dense, polydisperse, particle curtains, leading to particle size segregation, is demonstrated using numerical simulations.