Edge Scattering of Distributed Dipole Sources, Application to High-Lift Device Noise

Abstract

The present paper addresses the analytical modelling of the scattering of distributed sources by the edge of a rigid half-plane embedded in a uniform mean flow. The derivations are based on the exact Green's functions for the Helmholtz equation, either in two dimensions or in three di- mensions and in the mid-span plane. Jones' optional 2D correction proposed to account for the Kutta condition at the trailing edge is investigated. Dipole and quadrupole sources are consid- ered, with arbitrary edge-source and edge-observer distances. The work is aimed at quantifying the assumptions generally made in asymptotic formulations reported elsewhere and dedicated typically to aircraft installation effects and to trailing-edge noise. The Kutta condition is found to play a role at significant Mach numbers and/or for sources close to the scattering edge. The model is applied to a generic wing-flap configuration for which a standard transposition is used to relate the 2D and 3D models. The noise from the dipole sources induced on the flap by the turbulences generated in the gap is diffracted by the main part of the wing. The edge scattering is shown to produce a directivity which significantly differs from both the radiation the flap would have in free-field and the asymptotic cardioid pattern.