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On high-frequency noise scattering by aerofoils in flow

Published online by Cambridge University Press:  08 October 2013

Lorna J. Ayton  and
N. Peake
Lorna J. Ayton*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
N. Peake
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: L.J.Ayton@damtp.cam.ac.uk
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Abstract

A theoretical model is developed for the sound scattered when a sound wave is incident on a cambered aerofoil at non-zero angle of attack. The model is based on the linearization of the Euler equations about a steady subsonic flow, and is an adaptation of previous work which considered incident vortical disturbances. Only high-frequency sound waves are considered. The aerofoil thickness, camber and angle of attack are restricted such that the steady flow past the aerofoil is a small perturbation to a uniform flow. The singular perturbation analysis identifies asymptotic regions around the aerofoil; local ‘inner’ regions, which scale on the incident wavelength, at the leading and trailing edges of the aerofoil; Fresnel regions emanating from the leading and trailing edges of the aerofoil due to the coalescence of singularities and points of stationary phase; a wake transition region downstream of the aerofoil leading and trailing edge; and an outer region far from the aerofoil and wake. An acoustic boundary layer on the aerofoil surface and within the transition region accounts for the effects of curvature. The final result is a uniformly-valid solution for the far-field sound; the effects of angle of attack, camber and thickness are investigated.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 734 , 10 November 2013 , pp. 144 - 182
Copyright
©2013 Cambridge University Press 

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