Boundary layer leading-edge receptivity to sound at incidence angles

The leading-edge receptivity to acoustic waves of two-dimensional parabolic bodies was investigated using a spatial solution of the Navier-Stokes equa tions in vorticity/streamfunction form in parabolic coordinates. The free s tream is composed of a uniform flow with a superposed periodic velocity flu ctuation of small amplitude. The method follows that of Haddad & Corke (199 8) in which the solution for the basic flow and linearized perturbation flo w are solved separately. We primarily investigated the effect of frequency and angle of incidence (-180 degrees less than or equal to alpha (2) less t han or equal to 180 degrees) of the acoustic waves on the leading-edge rece ptivity. The results at alpha (2) = 0 degrees were found to be in quantitat ive agreement with those of Haddad & Corke (1998), and substantiated the St rouhal number scaling based on the nose radius. The results with sound wave s at angles of incidence agreed qualitatively with the analysis of Hammerto n & Kerschen (1996). These included a maximum receptivity at alpha (2) = 90 degrees, and an asymmetric variation in the receptivity with sound inciden ce angle, with minima at angles which were slightly less than alpha (2) = 0 degrees and alpha (2) = 180 degrees.