Freeze out of multi-mode Richtmyer-Meshkov instability using particles

Richtmyer-Meshkov instability (RMI) occurs when a shock wave traverses an interface separated by two fluids with different densities. Achieving “freeze out” (i.e., “killing” of RMI), a critical objective in RMI research for engineering applications, remains an open problem in the context of multi-mode RMI. Here, we introduce particles into the flow field to achieve freeze out, which is attributed to the momentum non-equilibrium effect inherent in the gas-particle phases. This effect facilitates the transfer of momentum and energy from the fluid to the particles, thereby mitigating the amplification of initial perturbations within the mixing zone. We developed a one-dimensional model to predict the velocities of the mixing zone boundaries in multiphase RMI. The growth of RMI was suppressed by controlling the velocities of the mixing zone boundaries through particle effects. A non-dimensional freeze out criterion was derived, incorporating the gas-particle coupling along with the particle volume fraction effect. The condition for freezing a multi-mode RMI was specially designed to estimate the required particle volume fraction to achieve the freeze out. A series of simulations were conducted using a well-verified compressible multiphase particle-in-cell method to validate the realization of freeze out. Further analysis reveals that the designed condition exhibits applicability across a spectrum of multi-mode perturbations, including both broadband and narrowband perturbations, as well as various initial Mach numbers.