A Theoretical Model for the Scaling of Low-Frequency Pressure Fluctuations in Shock Wave-Turbulent Boundary Layer Interaction

A physical model for the scaling of low-frequency wall pressure fluctuations associated with the shock motion observed in supersonic and hypersonic shock wave-turbulent boundary layer interactions for a compression ramp has been proposed. The author’s recent model [1] for the scaling of high-frequency pressure fluctuation generated due to the interaction of a shock with the vorticity (turbulence) in the upstream boundary layer has been extended to investigate low frequency pressure fluctuations associated with the shock motion. It is hypothesized that the high-frequency pressure fluctuations in the separated region drive the low-frequency pressure fluctuations through upstream propagation in the subsonic region of the boundary layer resulting in further amplification. The results show that the high-frequency pressure fluctuations in the separated flow (downstream of the shock) are amplified on account of the interaction of acoustic pressure (the separated region) with the shock wave in the near-wall region of the boundary layer. It is concluded that the high-frequency pressure fluctuations are amplified by a constant amplification factor of about 1.7 independent of the freestream Mach number.