Response and receptivity of the hypersonic boundary layer past a wedge to free-stream acoustic, vortical and entropy disturbances

Abstract

This paper analyses the response and receptivity of the hypersonic boundary layer over a wedge to free-stream disturbances including acoustic, vortical and entropy fluctuations. Due to the presence of an attached oblique shock, the boundary layer is known to support viscous instability modes whose eigenfunctions are oscillatory in the far field. These modes acquire a triple-deck structure. Any of three elementary types of disturbance with frequency and wavelength on the triple-deck scales interacts with the shock to generate a slow acoustic perturbation, which is reflected between the shock and the wall. Through this induced acoustic perturbation, vortical and entropy free-stream disturbances drive significant velocity and temperature fluctuations within the boundary layer, which is impossible when the shock is absent. A quasi-resonance was identified, due to which the boundary layer exhibits a strong response to a continuum of high-frequency disturbances within a narrow band of streamwise wavenumbers. Most importantly, in the vicinity of the lower-branch neutral curve the slow acoustic perturbation induced by a disturbance of suitable frequency and wavenumbers is in exact resonance with a neutral eigenmode. As a result, the latter can be generated directly by each of three types of free-stream disturbance without involving any surface roughness element. The amplitude of the instability mode is determined by analysing the disturbance evolution through the resonant region. The fluctuation associated with the eigenmode turns out to be much stronger than the free-stream disturbances due to the resonant nature of excitation, and in the case of acoustic disturbances, to the well-known amplification effect of a strong shock. Moreover, excitation at the neutral position means that the instability mode grows immediately without undergoing any decay, or missing any portion of the unstable region. All these indicate that this new mechanism is particularly efficient. The boundary-layer response and coupling coefficients are calculated for typical values of parameters.