Boundary Layer Receptivity to Free-stream Sound on Elliptic Leading Edges of Flat Plates

Abstract

The leading edge receptivity to acoustic waves of two-dimensional bodies is investigated using a spatial solution of the Navier-Stokes equations in vorticity/stream function form in general curvilinear 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. The initial motivation for the work comes from past physical experiments for flat plates with elliptic leading edges, which indicated narrow frequency bands of higher neutral-curve Branch I receptivity. We investigated the same conditions in our simulations, as well as on a parabolic leading edge. The results document the importance of the leading edge, junction between the ellipse and flat-plate, and pressure gradient, on the receptivity coefficient at Branch I. These are compared to the past experiments and other numerical simulations. These showed the influence of the elliptic leading-edge/flat-plate joint as an additional site of receptivity which, along with the leading edge, provides a wave-length selection mechanism which favors certain frequencies through linear superposition.