The interaction between a high-frequency gust and a blade row

Abstract

The ingestion of convected vorticity by a high-solidity rotating blade row is a potent noise source in modern aeroengines, due largely to the high level of mutual aerodynamic interactions between adjacent blades. In order to model this process we solve the problem of determining the unsteady lift on an infinite cascade of finite-chord flat plates due to an incident vorticity wave. The method of solution is the Wiener–Hopf technique, and we consider the case of the reduced frequency, Ω, being large, allowing application of asymptotic analysis in the formal limit Ω → ∞. This approach yields considerable simplification, both in allowing the truncation of an infinite reflection series to just two terms, and in allowing algebraic expressions for the Wiener–Hopf split functions to be found. The unsteady lift distribution is derived in closed form, and the accuracy of the asymptotic Wiener–Hopf factorization demonstrated for even modest values of Ω by comparison with exact (but less tractable) methods. Our formulae can easily be incorporated into existing noise prediction codes: the advantage of our scheme is that it handles a regime in which conventional numerical approaches become unwieldy, as well as providing significant physical insight into the underlying mechanisms.