Numerical simulations and analyses of shock wave - boundary layer interactions

Shock-boundary layer interaction (SBLI) is becoming one of the benchmark problems in the high-speed flow modeling and simulation community. The interaction of shock wave with the boundary layer is a very complex phenomenon that requires high-fidelity numerical methods like direct numerical simulation (DNS) and large-eddy simulation (LES) to capture the flow physics. In this study, SBLI is examined for various flow conditions using DNS and LES. In the first part of this study, DNSs are conducted for a Mach 2.75 turbulent boundary layer interacting with an impinging shock at three different shock incidence angles. Instantaneous flow visualizations show the 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. A detailed examination of the terms in the turbulent kinetic equation shows a strong coupling exists 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. In the second part of this study, data generated by 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 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 the 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. In the third part of the study, assessments of several existing SGS LES models along with a new model are made for SBLI through systematic a priori and a posteriori analyses. In the problem chosen for this study, the incident shock is strong enough to generate a marginal separation of the boundary layer near the interaction region, hence providing the SGS models with a non-trivial challenge. The effect of SGS stress term on the resolved velocity field is found to be significant and shock-dependent. The subgrid-scale models tested include the mixed-time-scale model, the dynamic Smagorinsky model, the dynamic mixed model and a new dynamic model, termed the compressible serial decomposition model. A priori analysis indicate that the new dynamic model is more accurate than other SGS closures. A posteriori tests also indicate better predictions of DNS results by the LES employing the compressible serial decomposition model.