Influence of mean loading on noise generated by the interaction of gusts with a flat-plate cascade: upstream radiation

Abstract

The sound generated by the interaction between convected vortical and entropic disturbances and a blade row is a significant component of the total noise emitted by a modern aeroengine, and the blade geometry has an important effect on this process. As a first step in the development of a general prediction scheme, we model in this paper just the action of the blade mean loading by treating the blades as flat plates aligned at a non-zero incidence angle, δ, to the oncoming stream, and consider harmonic components of the incident field with reduced frequency k. We then use asymptotic analysis in the realistic limit k[Gt ]1, δ[Lt ]1 with kδ=O(1) to make a consistent asymptotic expansion of the compressible Euler equations. The flow is seen to consist of inner regions around each leading edge, in which sound is generated by the local gust–airfoil and gust–flow interactions, and an outer region in which both the incident gust is distorted according to rapid distortion theory and the out-going sound is refracted by the non-uniform mean flow. The complicated multiple interactions between the sound and the cascade are included to the appropriate asymptotic order, and analytical expressions for the forward radiation are derived. It is seen that even a relatively small value of δ can have a significant effect, thanks to both the O(δk^1/2) change in the amplitudes and the O(kδ) change in the phases of the various radiation components, corresponding to the additional source mechanisms associated with the flow distortion around each leading edge and the effects of propagation through the non-uniform flow, respectively. Further work will extend this analysis to include the effects of camber and thickness.