Response And Receptivity Of Hypersonic Boundary-layer Flow Past A Wedge To Free-stream Acoustic, Vortical And Entropy Disturbances

Boundary-layer receptivity refers to excitation of instability waves within the flow by external disturbances. The present work 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 types of disturbances 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 slow 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. For the external disturbances on the triple-deck scales, the response is influenced by viscosity, in contrast to short-wavelength acoustic disturbances, for which the response is primarily inviscid. Most importantly, in the vicinity of the lower-branch neutral curve the induced slow acoustic disturbance is in resonance with the nearly neutral T-S mode of the same frequency. As a result, the latter can be excited directly by each of three types of free-stream disturbances without involving any surface roughness element.The amplitude of the instability mode is determined by analysing the disturbance evolution within the resonant region. The fluctuation associated with the eigen mode turns out to be much stronger than the free-stream disturbances due to both the well-known amplification effect of strong shock and the resonance nature of excitation. Moreover, excitation at the neutral position means that the T-S mode grows immediately without undergoing any decay, or missing any portion of the unstable region. All these indicate that this new mechanism is particularly effective. The boundary-layer response and coupling coefficient are calculated for typical values of parameters.