Basic singular fields in the theory of impulsive supersonic leading-edge noise

Abstract

This paper determines the impulsive sound fields produced by sharp-edged gusts striking the leading edge of a supersonic blade or aerofoil, for example in a turbofan aeroengine or a counter-rotating propeller system. A full three-dimensional theory is provided, so that the gust edges can be at any orientation relative to the blade. Complete details are given of the sound fields produced by gust edges in the spanwise and streamwise directions, and by many combinations of such edges, including corners. The mathematical theory depends on singular sound fields produced by gusts with a delta- function upwash; these are used to derive exact analytical formulae for impulsive sound fields of different three-dimensional shapes, and also a Green’s function representation of the field which is especially adapted to numerical evaluation. Gusts with top-hat profiles are given particular attention, and also the effect of Gaussian-function smoothing of both delta-function and top-hat profiles. The investigation is complementary to that in a companion paper (Powles and Chapman, 2019), which determines the smooth sound fields produced by single-frequency gusts. Fourier integration provides the relation between the two types of field.