Subgrid-scale turbulence in shock–boundary layer flows

Abstract

Data generated by direct numerical simulation (DNS) for a Mach 2.75 zero-pressure gradient turbulent boundary layer interacting with shocks of different intensities are used for a priori analysis of subgrid-scale (SGS) turbulence and various terms in the compressible filtered Navier–Stokes equations. The numerical method used for DNS is based on a hybrid scheme that uses a non-dissipative central scheme in the shock-free turbulent regions and a robust monotonicity-preserving scheme in the shock regions. The behavior of SGS stresses and their components, namely Leonard, Cross and Reynolds components, is examined in various regions of the flow for different shock intensities and filter widths. The backscatter in various regions of the flow is found to be significant only instantaneously, while the ensemble-averaged statistics indicate no significant backscatter. The budgets for the SGS kinetic energy equation are examined for a better understanding of shock–tubulence interactions at the subgrid level and also with the aim of providing useful information for one-equation LES models. A term-by-term analysis of SGS terms in the filtered total energy equation indicate that while each term in this equation is significant by itself, the net contribution by all of them is relatively small. This observation is consistent with our a posteriori analysis.