Role of Freestream Slow Acoustic Waves in a Hypersonic Three-Dimensional Boundary Layer

Abstract

The spectrum of a hypersonic three-dimensional boundary layer at Mach 6 is investigated with linear stability theory. It is shown that the three-dimensional wave of Mode S of discrete spectrum can be excited by the slow acoustic wave of continuous spectrum near the leading edge, and Mode S can evolve into the unstable traveling wave of crossflow mode in the downstream region. Furthermore, the influences of freestream slow acoustic waves on the instability of the hypersonic three-dimensional boundary layer in the presence of stationary crossflow vortices are also studied. Specifically, the downstream evolutions of traveling crossflow waves stemming from slow acoustic waves inside the boundary layer distorted by stationary crossflow vortices are investigated through biglobal analysis. It is found that the traveling crossflow waves evolve to the low-frequency mode III when the hypersonic three-dimensional boundary-layer flow is distorted by stationary crossflow vortices. The growth rates of the traveling crossflow waves with low frequency are hindered due to the finite amplitude of the stationary crossflow vortices in the downstream region. However, the traveling crossflow waves with high frequency can be significantly amplified by stationary crossflow vortices. The mode shapes of the traveling crossflow waves with high frequency look similar to that of the secondary instability modes, indicating that the modes can extract the energy through the spanwsie shear or wall-normal shear of the modified basic state. It is concluded that the breakdown of stationary crossflow vortices can be triggered by the freestream slow acoustic waves.