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

Abstract

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 [Formula: see text] and [Formula: see text]. For flow at [Formula: see text], 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 ([Formula: see text]) 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 ([Formula: see text], [Formula: see text]) plane, namely, region A, region B, and region C. Region A refers to small cavities with [Formula: see text], which have the weakest suppression effect. Region B includes large cavities with [Formula: see text] and [Formula: see text] and exhibits the best suppression effect. Finally, region C covers cavities with [Formula: see text] and [Formula: see text] and shows a non-monotonic control effect on the growth of disturbance wave as the cavity depth varies. For flow at [Formula: see text], cavities of different sizes always enhance the growth of disturbance waves. The widest and shallowest cavities ([Formula: see text], [Formula: see text]) exhibit the most significant enhancement.