Boundary-layer receptivity for a parabolic leading edge

The effect of the nose radius of a body on boundary-layer receptivity is analysed for the case of a symmetric mean flow past a body with a parabolic leading edge. Asymptotic methods based on large Reynolds number are used, supplemented by numerical results. The Mach number is assumed small, and acoustic free-stream disturbances are considered. The case of free-stream acoustic waves, propagating obliquely to the symmetric mean flow is considered. The body nose radius, r_n, enters the theory through a Strouhal number, S = ωr_n/U, where ω is the frequency of the acoustic wave and U is the mean flow speed. The finite nose radius dramatically reduces the receptivity level compared to that for a flat plate, the amplitude of the instability waves in the boundary layer being decreased by an order of magnitude when S = 0.3. Oblique acoustic waves produce much higher receptivity levels than acoustic waves propagating parallel to the body chord.