A robust high-resolution algorithm for quadrature-based moment methods applied to high-speed polydisperse multiphase flows

Abstract

A high-resolution Eulerian method for simulating high-speed polydisperse granular multiphase flows has been developed. The governing equations include a compressible gas that is coupled to mass-based moment equations for a polydisperse granular flow derived from the generalized population balance equation. The model includes effects from particle collisions, drag, convective heat transfer, particle-fluid-particle pressure, and finite-size particle force terms. The mass moment integrals are closed using the generalized quadrature method of moments to allow for continuous size distributions. The governing equations are solved by using high-resolution reconstruction schemes and results from decoupled Riemann problems for the gas and particles as each quadrature node. Success of the technique is demonstrated through a variety of numerical experiments including polydisperse multiphase Riemann shock-tube problems, shock--particle-curtain interactions, dust layer dispersal, dust layer dispersal by shock waves, and dispersal of spherical particle shells by high-pressure gas.

Figures (20)

• Figure 1: Impact-velocity-dependent coefficient of restitution of aluminum particles (the black line is Eqn. \ref{['CoR_Pade']} and the blue Weir2005 and red Hassani-Gangaraj2018 symbols represent experimental data).
• Figure 2: Diagram of energy transfer within the model, demonstrating conservation of energy.
• Figure 3: Primitive variable interpolation stencil with multiple vacuum interface, generating an "island" and "lakes" within the stencil.
• Figure 4: Primitive variable interpolation stencil with a vacuum interface.
• Figure 5: Primitive variable interpolation stencil with a large variation in the first abscissae, creating the opportunity for an invalid interpolation estimate.