Modeling and simulation of a single-mode multiphase Richtmyer–Meshkov instability with a large Stokes number

Abstract

This study focuses on the effects of a large Stokes number (St) on the perturbation growth in linear and nonlinear stages of a Richtmyer–Meshkov instability (RMI) in a gas-particle system, which to the best of our knowledge has not been previously reported. A linear growth model is developed by linear stability analysis and numerically verified by the compressible multiphase particle-in-cell (CMP-PIC) method. Additionally, the RMI growth characteristics in the nonlinear stage are also investigated by CMP-PIC. For the linear growth model, two major differences characterize the effects of a large St. The first one is that an RMI with a large St, which performs significantly different from the RMI with a small St, is induced and driven only by the density difference of the gas-phase and totally independent of particle density. Second, due to the significant momentum coupling effects between gas and particle phases, which govern the gas-particle flow, the growth rate experiences exponential decay, even in the linear RMI stage. The decay behavior performs markedly different from any previous RMI models, especially those of the original single-phase RMI and the gas-particle RMI with a small St. Notably, in the nonlinear stage of the RMI with a large particle volume fraction, the decay effects are much more pronounced and lead to a fall in the growth rate to almost zero, which is not found in any other type of RMI. These findings offer the possibility to develop a new method to control the development of hydrodynamic instability.