Role of very large-scale motions in shock wave/turbulent boundary layer interactions

Abstract

The present study investigates the cause of low-frequency unsteadiness in shock wave/turbulent boundary layer (TBL) interactions. A supersonic turbulent flow over a compression ramp is studied using wall-resolved large eddy simulation (LES) with a freestream Mach number of 2.95 and a Reynolds number (based on δ0: the thickness of the incoming TBL) of 63 560. From the view of stability analysis, the effect of intrinsic instability on such low-frequency unsteadiness is excluded from the flow system by designing a ramp angle of 15°, and our attention is paid to the convective instability contributed by the incoming TBL. The LES results are analyzed by linear and nonlinear disambiguation optimization (LANDO), spectral proper orthogonal decomposition (SPOD), and resolvent analysis. The LANDO results reveal a streamwise scale-frequency relation of coherent structures in a very long (around 60δ0) TBL, which indicates that the dynamics of very large-scale motions (VLSMs) in the TBL are featured by a low frequency. The SPOD results reveal that the most energetic SPOD mode features a low frequency that is identical to the dominant low frequency of the wall-pressure spectrum. Additionally, coherent structures of the mode resemble the VLSMs in the incoming TBL. These consistencies imply that the dynamics of VLSMs contribute to the low-frequency unsteadiness of the present flow. A resolvent analysis then further suggests that the origins of low-frequency dynamics of the present flow are from the VLSMs, which can be optimally amplified by the forcing in the turbulent flow.