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Lighthill quadrupole radiation in supersonic propeller acoustics

Published online by Cambridge University Press:  26 April 2006

N. Peake  and
D. G. Crighton
N. Peake
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
D. G. Crighton
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 363 - 382
Copyright
© 1991 Cambridge University Press

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