Numerical Simulation of Single-Mode Richtmyer-Meshkov Instability Induced by High Mach Number Shock

Richtmyer-Meshkov (RM) instabilities are observed in various fields, including inertial confinement fusion, supernova explosions, and supersonic combustion engines. While considerable research has been conducted on the single-mode RM instability induced by low-Mach number shock waves, there is a notable gap in studies on the RM instability of a single-mode interface under high-Mach number shock waves. Additionally, the influence of thermo-chemical non-equilibrium effects resulting from high-Mach number shock waves remains unknown. In this study, a two-dimensional code for high-temperature non-equilibrium gas, based on the finite volume method with unstructured adaptive grids, was employed to simulate the single-mode RM instability caused by high-Mach number shock waves in air. In the numerical solution process, a splitting method was employed to separately solve the convective and source terms. The convective term was solved using the MUSCL-HANCOCK method for second-order space-time reconstruction and the HLL scheme for calculating numerical fluxes. The source term was solved using a single-step implicit time format with A-stability. Two scenarios were considered: light/heavy interface and heavy/light interface, with shock Mach numbers ranging from 6 to 9 and 9 to 11, respectively. The research compared the evolution of flow fields under three gas models: frozen gas, thermal non-equilibrium gas, and thermo-chemical non-equilibrium gas. This study gave the disturbance growth and the growth rate of each gas model and compared the numerical results with linear and nonlinear theories. The influence of the initial shock Mach number and the initial disturbance scale on RM instability was analyzed. Furthermore, the distribution of vorticity fields and the evolution of circulation were discussed. The findings reveal significant differences in thermo-chemical non-equilibrium flow compared to frozen flow, particularly in the transmission and reflection waves, as well as the interface velocity. Thermo-chemical non-equilibrium flow exhibits a decreased peak amplitude growth rate, weakened fluctuations in the interface growth rate, and a slowed-down growth of interface instability compared to frozen flow. Comparative analysis with multiple theoretical models indicates that the ZS model is more suitable than other models for describing single-mode interface RM instability under high-Mach number shock waves. The study of vorticity reveals two main regions with strong vorticity generation: one near the interface and the other behind the transmitted shock wave. This is notably different from RM instability induced by low-Mach number shock, where vorticity is primarily generated at the interface. Additionally, the investigation into circulation demonstrates that the amplitude of vortices in thermo-chemical non-equilibrium flow is smaller than in frozen flow, aligning with the conclusion that disturbances grow more slowly in thermo-chemical non-equilibrium flow compared to frozen flow. This study contributes valuable insights into RM instability under high-Mach number shock waves, expanding the understanding within the RM instability research community.