Numerical simulation of shock-microscale vortex interaction

Abstract

The interaction of a moving shock wave and a microscale vortex is numerically studied by solving the BGK-type equation with the unified gas-kinetic scheme (UGKS) and the Navier-Stokes equations with the gas-kinetic scheme (GKS-NS). Different Knudsen numbers based on the core radius of the vortex are considered. The results indicate that GKS-NS tends to overestimate the dissipation rate of kinetic energy and the amplification of stress and enstrophy caused by the fully resolved shock wave, while underestimating the amplification of heat flux through the shock wave due to rarefied effects. It is also observed that as the core size of the vortex increases, the decay of the enstrophy over time slows down, while the amplification of enstrophy by the shock wave increases. Negligible rarefied effects can be assumed when the Knudsen number is below 0.01 where the overestimation of enstrophy amplification by GKS-NS is less than 5 %. However, when the Knudsen number exceeds 0.1, the difference of the enstrophy predicted by UGKS and GKS-NS is greater than 20 %, where rarefied effects need to be considered.