Modeling and verification of the Richtmyer-Meshkov instability linear growth rate of the dense gas-particle flow

The multiphase Richtmyer-Meshkov instability (RMI) often occurs in supernova events and inertial confinement fusion processes, where it plays a critical role. In the evolution of the RMI process, the particle phase may have either a dilute or a dense pattern. Previous studies have mainly focused on the dilute pattern. Currently, there is no published research on the theoretical growth model of the dense gas-particle flow. In this work, a new Atwood number model was developed with the assumption of a small Stokes number and shown to be effective for the RMI of the dense gas-particle flow. The Atwood number model was characterized by the moment coupling parameters and the ratio of the volume fractions of the two phases. Further derivation showed that it was consistent with the original Richtmyer's model and the dilute gas-particle flow model. In addition, the theoretical growth rate was modeled to predict the evolution law of the mix zone width for the dense gas-particle flow. The presence of the particle phase inhibited the growth rate of the RMI, which emphasized the effect of the solid phase. The corresponding numerical simulations were also performed based on the compressible multiphase particle-in-cell method for different cases of the particle volume fraction. The numerical results demonstrated the accuracy of the theoretical growth rate model. Additionally, a brief analysis of the flow structures and cloud motion during the RMI process was performed.