On sound scattering by rigid edges and wedges in a flow, with applications to high-lift device aeroacoustics

Abstract

Exact analytical solutions for the scattering of sound by the edge of a rigid half-plane and by a rigid corner in the presence of a uniform flow are considered in this work, for arbitrary source and observer locations. Exact Green׳s functions for the Helmholtz equation are first reviewed and implemented in a quiescent propagation space from reference expressions of the literature. The effect of uniform fluid motion is introduced in a second step and the properties of the field are discussed for point dipoles and quadrupoles. The asymptotic regime of a source close to the scattering edge/wedge and of an observer far from it in terms of acoustic wavelengths is derived in both cases. Its validity limits are assessed by comparing with the exact solutions. Typically the asymptotic directivity is imposed by Green׳s function but not by the source itself. This behaviour is associated with a strong enhancement of the radiation with respect to what the source would produce in free field. The amplification depends on the geometry, on the source type and on the source distance to the edge/wedge. Various applications in aeroacoustics of wall-bounded flows are addressed, more specifically dealing with high-lift device noise mechanisms, such as trailing-edge or flap side-edge noise. The asymptotic developments are used to highlight trends that are believed to play a role in airframe noise.