Non-equilibrium effects of diatomic and polyatomic gases on the shock-vortex interaction based on the second-order constitutive model of the Boltzmann-Curtiss equation

Abstract

The rotational mode of molecules plays a critical role in the behavior of diatomic and polyatomic gases away from equilibrium. In order to investigate the essence of the non-equilibrium effects, the shock-vortex interaction problem was investigated by employing an explicit modal discontinuous Galerkin method. In particular, the first- and second-order constitutive models for diatomic and polyatomic gases derived rigorously from the Boltzmann-Curtiss kinetic equation were solved in conjunction with the physical conservation laws. As compared with a monatomic gas, the non-equilibrium effects result in a substantial change in flow fields in both macroscale and microscale shock-vortex interactions. Specifically, the computational results showed three major effects of diatomic and polyatomic gases on the shock-vortex interaction: (i) the generation of the third sound waves and additional reflected shock waves with strong and enlarged expansion, (ii) the dominance of viscous vorticity generation, and (iii) an increase in enstrophy with increasing bulk viscosity, related to the rotational mode of gas molecules. Moreover, it was shown that there is a significant discrepancy in flow fields between the microscale and macroscale shock-vortex interactions in diatomic and polyatomic gases. The quadrupolar acoustic wave source structures, which are typically observed in macroscale shock-vortex interactions, were not found in any microscale shock-vortex interactions. The physics of the shock-vortex interaction was also investigated in detail to examine vortex deformation and evolution dynamics over an incident shock wave. A comparative study of first- and second-order constitutive models was also conducted for the enstrophy and dissipation rate. Finally, the study was extended to the shock-vortex pair interaction case to examine the effects of pair interaction on vortex deformation and evolution dynamics.