Boundary layer leading-edge receptivity to sound at incidence angles

Abstract

The leading-edge receptivity to acoustic waves of two-dimensional parabolic bodies was investigated using a spatial solution of the Navier-Stokes equations in vorticity/streamfunction form in parabolic coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998) in which the solution for the basic flow and linearized perturbation flow are solved separately. We primarily investigated the effect of frequency and angle of incidence (-180 degrees less than or equal to alpha (2) less than or equal to 180 degrees) of the acoustic waves on the leading-edge receptivity. The results at alpha (2) = 0 degrees were found to be in quantitative agreement with those of Haddad & Corke (1998), and substantiated the Strouhal number scaling based on the nose radius. The results with sound waves at angles of incidence agreed qualitatively with the analysis of Hammerton & Kerschen (1996). These included a maximum receptivity at alpha (2) = 90 degrees, and an asymmetric variation in the receptivity with sound incidence angle, with minima at angles which were slightly less than alpha (2) = 0 degrees and alpha (2) = 180 degrees.