The receptivity of hypersonic boundary layers to free-stream disturbances, which
is the process of environmental disturbances initially entering the boundary layers
and generating disturbance waves, is altered considerably by the presence of bow
shocks in hypersonic flow fields. This paper presents a numerical simulation study
of the generation of boundary layer disturbance waves due to free-stream waves,
for a two-dimensional Mach 15 viscous flow over a parabola. Both steady and
unsteady flow solutions of the receptivity problem are obtained by computing the full
Navier–Stokes equations using a high-order-accurate shock-fitting finite difference
scheme. The effects of bow-shock/free-stream-sound interactions on the receptivity
process are accurately taken into account by treating the shock as a discontinuity
surface, governed by the Rankine-Hugoniot relations. The results show that the
disturbance waves generated and developed in the hypersonic boundary layer contain
both first-, second-, and third-mode waves. A parametric study is carried out on the
receptivity characteristics for different free-stream waves, frequencies, nose bluntness
characterized by Strouhal numbers, Reynolds numbers, Mach numbers, and wall
cooling. In this paper, the hypersonic boundary-layer receptivity is characterized by
a receptivity parameter defined as the ratio of the maximum induced wave amplitude
in the first-mode-dominated region to the amplitude of the free-stream forcing wave.
It is found that the receptivity parameter decreases when the forcing frequency or
nose bluntness increase. The results also show that the generation of boundary layer
waves is mainly due to the interaction of the boundary layer with the acoustic wave
field behind the bow shock, rather than interactions with the entropy and vorticity
wave fields.
