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An analytical and experimental investigation of aerofoil–turbulence interaction noise for plates with spanwise-varying leading edges

Published online by Cambridge University Press:  18 February 2019

Lorna J. Ayton Open the ORCID record for Lorna J. Ayton [Opens in a new window]  and
Paruchuri Chaitanya Open the ORCID record for Paruchuri Chaitanya [Opens in a new window]
Lorna J. Ayton*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Paruchuri Chaitanya
Affiliation:
Faculty of Engineering and the Environment, University of Southampton, Burgess Road, Southampton SO16 7QF, UK
*
†Email address for correspondence: L.J.Ayton@damtp.cam.ac.uk
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Abstract

This paper presents an analytic solution for gust–aerofoil interaction noise for flat plates with spanwise-varying periodic leading edges in uniform mean flow. The solution is obtained by solving the linear inviscid equations via separation of variables and the Wiener–Hopf technique, and is suitable for calculating the far-field noise generated by any leading edge with a single-valued piecewise linear periodic spanwise geometry. Acoustic results for homogeneous isotropic turbulent flow are calculated by integrating the single-gust solution over a wavenumber spectrum. The far-sound pressure level is calculated for five test-case geometries; sawtooth serration, slitted $v$-root, slitted $u$-root, chopped peak and square wave, and compared to experimental measurements. Good agreement is seen over a range of frequencies and tip-to-root ratios (varying the sharpness of the serration). The analytic solution is then used to calculate the propagating pressure along the leading edge of the serration for fixed spanwise wavenumbers, i.e. only the contribution to the surface pressure which propagates to the far field. Using these results, two primary mechanisms for noise reduction are discussed; tip and root interference, and a redistribution of energy from cuton modes to cutoff modes. A secondary noise-reduction mechanism due to nonlinear features is also discussed and seen to be particularly important for leading edges with very narrow slits.

JFM classification

Acoustics: Aeroacoustics

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 137 - 168
Copyright
© 2019 Cambridge University Press 

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