Vorticity suppression by multiphase effects in shock-driven variable density mixing

Abstract

Shock-driven variable density mixing has been frequently explored through the single-phase Richtmyer–Meshkov instability. Here, such mixing is considered when driven by a multiphase component, the Shock-Driven Multiphase Instability (SDMI). The simple case of a solid particle seeded gas in a cylindrical region surrounded by clean gas is studied. It has been previously shown that the particle-phase can lag behind the gas, diminishing vorticity deposition. In this letter we present theoretical analysis of the vorticity deposition, and a new model predicting the circulation deposition for an SDMI as a function of particle relaxation distance and hydrodynamic mixing strength. The theory is founded on a simplified vorticity equation, advection and multiphase source terms, using simple drag models to predict the particle dynamics, and scaling the results using existing circulation models for the Richtmyer–Meshkov instability in the small particle limit. The model is compared to new high-fidelity experimental data, and previous experiments and simulations, finding good agreement. This model provides the first theoretical prediction of mixing suppression in the SDMI.