Numerical investigations of shock wave interactions with a supersonic turbulent boundary layer

Abstract

Direct numerical simulations (DNS) are conducted for a Mach 2.75 turbulent boundary layer interacting with an impinging shock at three different shock incidence angles. The accuracies of DNS calculations are established by checking the convergence of flow statistics for various grids, by comparing the generated results with those in the literature and also by the balance of contributing terms in the turbulent kinetic energy equation. Instantaneous flow visualizations show the significant effect of shock on turbulence structure in the shock-boundary layer interaction zone and also in the flow downstream of the interaction region. The separation bubbles exhibit highly unsteady and three-dimensional behavior and are larger for stronger shocks but the maximum probability of flow separation is found to be independent of the shock strength. The differences between Reynolds- and Favre-averaged quantities are also observed to be small and largely independent of the shock intensity. The turbulent kinetic energy is amplified across the shock, mainly by the production term in the turbulent kinetic energy equation. The amplification of enstrophy across the shock zone is found to be due to the vortex stretching term in the enstrophy transport equation. A detailed examination of the terms in the turbulent kinetic equation shows a strong coupling between the mean and turbulent fields in the interaction region with energy being continuously exchanged from one field to another. However, the compressibility-related terms in the transport equations for turbulent kinetic energy and enstrophy are found to be small for the simulated flows.