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Interaction of turbulence with the leading-edge stagnation point of a thin aerofoil

Published online by Cambridge University Press:  03 June 2016

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

An asymptotic model is constructed to analyse the interaction of turbulence generated far upstream with a thin elliptic-nosed solid body in uniform flow. The leading-edge stagnation point causes significant deformation of incident vorticity, and hence our analysis focuses on the region of size scaling with the nose radius close to the stagnation point. Rapid distortion theory is used to separate the flow field generated by a single unsteady gust perturbation into a convective non-acoustic part, containing the evolution of the upstream vortical disturbance, and an acoustic part generated by the interaction of the vorticity with the solid surface, as is typical in gust–aerofoil interaction theory. Using single-frequency gust response solutions, along with a von Kármán energy spectrum, we find the turbulent pressure spectrum generated by homogeneous isotropic turbulence incident from far upstream. Both high- and low-frequency gusts are considered to allow approximations to be found for the turbulent pressure spectra close to the leading edge, and far from the body close to the incident stagnation streamline. Good agreement is shown between the asymptotic results for the near- and far-field leading-edge turbulent pressure spectra and recent experimental findings.

JFM classification

Acoustics: Aeroacoustics Turbulent Flows: Homogeneous turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , pp. 436 - 456
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Copyright
© 2016 Cambridge University Press 

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