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An analytic solution for the noise generated by gust–aerofoil interaction for plates with serrated leading edges

Published online by Cambridge University Press:  23 August 2018

Lorna J. Ayton Open the ORCID record for Lorna J. Ayton [Opens in a new window]  and
Jae Wook Kim Open the ORCID record for Jae Wook Kim [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
Jae Wook Kim
Affiliation:
Aerodynamics and Flight Mechanics Research Group, University Road, University of Southampton, Southampton SO17 1BJ, UK
*
†Email address for correspondence: L.J.Ayton@damtp.cam.ac.uk
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Abstract

This paper presents an analytic solution for the sound generated by an unsteady gust interacting with a semi-infinite flat plate with a serrated leading edge in a background steady uniform flow. Viscous and nonlinear effects are neglected. The Wiener–Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to permit analytical progress. The solution is obtained in terms of a modal expansion in the spanwise coordinate; however, for low- and mid-range incident frequencies only the zeroth-order mode is seen to contribute to the far-field acoustics, therefore the far-field noise can be quickly evaluated. The solution gives insight into the potential mechanisms behind the reduction of noise for plates with serrated leading edges compared to those with straight edges, and predicts a logarithmic dependence between the tip-to-root serration height and the decrease of far-field noise. The two mechanisms behind the noise reduction are proposed to be an increased destructive interference in the far field, and a redistribution of acoustic energy from low cut-on modes to higher cut-off modes as the tip-to-root serration height is increased. The analytic results show good agreement in comparison with experimental measurements. The results are also compared against nonlinear numerical predictions where good agreement is also seen between the two results as frequency and tip-to-root ratio are varied.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 853 , 25 October 2018 , pp. 515 - 536
Copyright
© 2018 Cambridge University Press 

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