The scattering of vorticity waves by an infinite cascade of flat plates in subsonic flow

Abstract

The scattering of a harmonic vorticity wave by an infinite, two-dimensional cascade of thin blades in subsonic mean flow is studied analytically, as a model problem of relevance to the question of sound generation by modern aeroengines. The work aims to extend a previous study by Koch, who considers only the scattered radiation, by deriving expressions for the detailed unsteady lift distribution on the blades. In an earlier paper, the present author has calculated this lift distribution in the asymptotic limit of large reduced frequency, but here that analysis is generalised to the case of arbitrary reduced frequency. This is achieved by the solution of two scattering problems using the Wiener-Hopf technique, one in the leading-edge region of the cascade and one in the trailing-edge region, in terms of an infinite sequence of (unknown) duct-mode coefficients, and these unknowns are then determined by matching the two solutions together inside the cascade. Exact analytical expressions for the detailed lift distribution on each blade are given, which are in closed form apart from the need to invert a single matrix numerically.