Compressibility and vibrational-excitation effects in hypersonic shock-turbulence interaction*

The interaction of turbulence with shock waves significantly modulates the frequency and amplitude of hydrodynamic fluctuations encountered by aerospace vehicles in low-altitude hypersonic flight. In these high-speed flows, intrinsic compressibility effects emerge together with high-enthalpy phenomena in the form of internal-energy excitation. The present study directly compares direct numerical simulation (DNS) and linear interaction analysis (LIA) to characterize the impact of density fluctuations and endothermic processes on Mach-5 canonical shock-turbulence interaction. Whereas the computational effort entails directly resolving all relevant length scales and nonlinear interactions, the LIA framework models the upstream compressible turbulence as a superposition of weakly vortical, entropic, and acoustic fluctuations. Both the numerical and theoretical approaches reveal that increasing upstream compressibility serves to augment the turbulent kinetic energy (TKE) across the shock-turbulence interaction for varying turbulent Mach numbers. The effect of endothermicity is likewise assessed in each framework by introducing equilibrium vibrational excitation, which is shown to further amplify the TKE downstream of the shock.