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° [les ] α₂ [les ] 180°) of the acoustic waves on the leading-edge receptivity. The results at α₂ = 0° 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 α₂ = 90°, and an asymmetric variation in the receptivity with sound incidence angle, with minima at angles which were slightly less than α₂ = 0° and α₂ = 180°.