Receptivity of a supersonic boundary layer to shock-wave oscillations

Abstract

We present a direct numerical simulation of the interaction of an oscillating oblique shock wave with a laminar boundary layer at a Mach number M = 4.8. The shock is strong enough to cause a laminar separation bubble at the wall. The incoming shock wave oscillates with a frequency within the unstable frequency range of the laminar boundary layer according to linear stability theory, such that the receptivity of the supersonic boundary layer to shock oscillations can be investigated. It is observed that acoustic pressure fluctuations which travel along the shock wave reflect in radial direction from the point of impingement on the flat plate leading to a rather complicated pattern of acoustical disturbances. Nevertheless, boundarylayer instability waves are generated by interaction with the shock wave oscillations but they are hidden by the acoustical disturbances. Because they travel slower they stand out after switching the forcing off. The spectral amplitudes of these disturbances compare well with the eigenfunctions of the most unstable mode according to linear stability theory despite the presence of other modes.