Lighthill quadrupole radiation in supersonic propeller acoustics

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Abstract
Sound generation by the Lighthill quadrupole is an important mechanism in the noise of supersonic and transonic propellers. Full numerical calculation of the quadrupole radiation must, however, require knowledge of the flow at all points exterior to the blades (involving transonic aerodynamics) and the evaluation of special functions. We describe how these difficulties may be largely avoided, using an asymptotic approximation that the number of blades, B, is large, and prove that to leading order the problem of the radiation in a given direction reduces to one of determining the (two-dimensional) flow field at just one radial station, legitimately achieved by linearized supersonic analysis. Simple formulae are derived for the far-field acoustic pressure generated by unswept blades, from which absolute level predictions can be made accurately and quickly. These formulae predict a significantly greater intensity, over broad angular ranges, than is predicted by the linear theory for thickness noise sources.

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