On the radiation properties of an asymmetric cylinder

The radiation properties of an asymmetric cylinder, formed by slicing a circular cylinder with a plane making an angle π/2 ? Λ with the cylinder axis, are investigated as a model problem of relevance to noise emission by novel aeroengine intakes. We consider the scattering of incident duct modes and use asymptotic analysis in the limit Λ 1; the unsteady flow then comprises an inner incompressible region around the cylinder rim and an outer region comprising the rest of space, and the radiation in the outer region is determined using the method of matched asymptotic expansions. From this we are able to conclude that the correction to the radiation directivity is O(Λ), whilst the correction to the total integrated sound power reaching infinity is much weaker, and is in fact only O(Λ²).