Shock-induced turbulence amplification on a supersonic compression ramp: a DNS investigation*

The turbulence amplification mechanism on the shock-turbulent boundary layer interaction (STBLI) using direct numerical simulation (DNS) is investigated. The STBLI is generated by a  compression ramp at an inflow Mach number of 2.9. An in-house code based on a compact finite difference scheme for solving compressible flow has been developed and extensively validated using experimental and existing DNS data. The turbulent kinetic energy (TKE) distribution analysis reveals two distinct hotspots and in which the second TKE peak is located within the shear layer near the reattachment point. An investigation of the power spectral density of the pressure at the second TKE hotspots reveals the presence of mid-frequencies characteristic, indicating a secondary shock dynamic behavior. The amplification of turbulence at the second hotspot is found to be influenced not solely by the free shear layer, but rather by the mean flow deceleration attributed to the secondary shock. Detailed TKE budget analysis provides that the turbulence production due to the velocity gradient is notably greater around the second TKE hotspot, and intriguingly, the strongest production region is slightly displaced above the actual TKE maximum region. Furthermore, our findings indicate that the transfer of the turbulent energy is primarily influenced by transport through velocity fluctuation and pressure-velocity gradient interaction, serving as the dominant mechanism for the formation of the TKE maximum region.