Stability Analysis for High-Speed Boundary-Layer Flow with Cavities

This study uses direct numerical simulation and stability analysis methods to investigate the impact of wall cavity defects on the instability of boundary layers at Ma=5.92 and Ma=1.38. For flow at Ma=5.92, synchronization points with equal phase velocities in both fast and slow modes play a crucial role in controlling disturbance wave growth. When the inlet disturbance wave frequency (omega=0.98) approaches the synchronization point frequency, the impact of cavity size on the growth of the disturbance wave can be divided into three regions in the (L/delta(99), D/delta(99)) plane, namely, region A, region B, and region C. Region A refers to small cavities with L/delta(99)<2, which have the weakest suppression effect. Region B includes large cavities with L/delta(99)>2 and D/delta(99)<1.5 and exhibits the best suppression effect. Finally, region C covers cavities with L/delta(99)>3 and D/delta(99)>1.5 and shows a non-monotonic control effect on the growth of disturbance wave as the cavity depth varies. For flow at Ma=1.38, cavities of different sizes always enhance the growth of disturbance waves. The widest and shallowest cavities (L/delta(99)>5, D/delta(99)<2) exhibit the most significant enhancement.