A dominant dimensionless number and theoretical model for the evolution of multiphase Richtmyer–Meshkov instability

Abstract

Multiphase Richtmyer–Meshkov instability (RMI) is often accompanied by a dispersed phase of particles, where the evolution of the mix zone width (MZW) is a significant issue. The Stokes number (St) is a key dimensionless parameter for particle-containing multiphase flows because it represents the ability of particles to follow the fluid. However, our theoretical analysis and numerical simulation indicate that the Stokes number is not the only dominant parameter for the evolution of multiphase RMI. This study uses the derivation of particle and fluid momentum equations to demonstrate the inability of the Stokes number to predict MZW evolution, that is, even at the same Stokes number, increasing the particle density or the radius leads to completely different MZW evolution trends. This study proposes a novel dimensionless number, Sd, to measure the effect of drag on the fluid owing to the particles. Sd is the ratio of the relaxation time of the fluid velocity affected by the particle force to the characteristic time of the shock wave. We developed theoretical models of MZW at different Sd values. Subsequently, a set of multiphase RMI numerical simulations on uniformly distributed particles with different St and Sd values was conducted. The numerical results verify the theoretical predictions and effectiveness of the proposed dimensionless number. The phase diagram containing different simulation cases demonstrates that the Stokes number cannot be used to predict MZW and must be combined with Sd to determine its evolution.