Abstract

We consider the acoustic scattering problem on an infinite cascade of finite-length blades. This problem has its origins as a model for the components in turbofan engines and is of correspondingly wide interest. Analytical studies of the problem, however, have only been successful thus far in the case of overlapping blades. We present the first analytical solution in the case of non-overlapping blades, which is found to be valid for an arbitrary choice of blade spacing. This solution exploits the Wiener-Hopf technique and is based on the use of a novel additive splitting in a system of coupled scalar Wiener-Hopf equations. The solution allows us to understand the far-field behaviour of scattered acoustic waves, as well as the lift exerted on the blades by vortex waves that are incident on the structure.