A volume-filtered description of compressible particle-laden flows. (January 2020) - Shallcross, Gregory S.; Fox, Rodney O.; Capecelatro, Jesse
Highlights: Rigorous derivation of the volume-filtered compressible equations for two-phase flows. Evaluate unclosed terms via a posteriori filtering of particle-resolved simulations. Propose a transport equation for PTKE and closure model for the dissipation rate. Grid convergence of the Euler-Lagrange framework is demonstrated on compressible flow. The model captures pseudo-turbulent Reynolds stresses independently of the drag law. Abstract: In this work, we present a rigorous derivation of the volume-filtered viscous compressible Navier–Stokes equations for disperse two-phase flows. Compared to incompressible flows, many new unclosed terms appear. These terms are quantified via a posteriori filtering of two-dimensional direct simulations of shock-particle interactions. We demonstrate that the pseudo-turbulent kinetic energy (PTKE) systematically acts to reduce the local gas-phase pressure and consequently increase the local Mach number. Its magnitude varies with volume fraction and filter size, which can be characterized using a Knudsen number based on the filter size and inter-particle spacing. A transport equation for PTKE is derived and closure models are proposed to accurately capture its evolution. The resulting set of volume-filtered equations are implemented within a high-order Eulerian–Lagrangian framework. An interphase coupling strategy consistent with the volume filtered formulation is employed to ensure grid convergence. Finally PTKE obtained from the volume-filtered Eulerian–Lagrangian simulations are compared to a series of two- and three-dimensional direct simulations of shocks passing through stationary particles.