Noise generation by a supersonic leading edge. Part 1: general theory

This paper concerns the calculation of the sound fields which are generated when a vortical gust, convected in a supersonic mean flow, strikes the leading edge of a fan blade or aerofoil. Inviscid linear theory is applied, with the blade modelled as an infinite-span flat rigid plate, and a gust of arbitrary form is considered. By application of Fourier transforms the boundary value problem for the velocity potential is solved, leading to an integral expression for the generated sound field. This expression is applicable everywhere inside a Mach wedge. For gusts localized in the span direction, a farfield approximation is derived which is valid inside a Mach cone, and which is of simple enough form to be evaluated analytically for specified gust shapes. The new feature of this analysis is the consideration of an arbitrary gust form: previous authors have only ever considered the properties of specific gusts, focusing principally on harmonic gusts and jets.