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On the receptivity of aerofoil tonal noise: an adjoint analysis

Published online by Cambridge University Press:  05 January 2017

Miguel Fosas de Pando ,
Peter J. Schmid  and
Denis Sipp
Miguel Fosas de Pando*
Affiliation:
Departamento de Ingeniería Mecánica y Diseño Industrial, Escuela Superior de Ingeniería, Universidad de Cádiz, Avenida de la Universidad de Cádiz, 10, 11519 Puerto Real, Spain
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Denis Sipp
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
*
†Email address for correspondence: [email protected]
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Abstract

For moderate-to-high Reynolds numbers, aerofoils are known to produce substantial levels of acoustic radiation, known as tonal noise, which arises from a complex interplay between laminar boundary-layer instabilities, trailing-edge acoustic scattering and upstream receptivity of the boundary layers on both aerofoil surfaces. The resulting acoustic spectrum is commonly characterised by distinct equally spaced peaks encompassing the frequency range of convectively amplified instability waves in the pressure-surface boundary layer. In this work, we assess the receptivity and sensitivity of the flow by means of global stability theory and adjoint methods which are discussed in light of the spatial structure of the adjoint global modes, as well as the wavemaker region. It is found that for the frequency range corresponding to acoustic tones the direct global modes capture the growth of instability waves on the suction surface and the near wake together with acoustic radiation into the far field. Conversely, it is shown that the corresponding adjoint global modes, which capture the most receptive region in the flow to external perturbations, have compact spatial support in the pressure surface boundary layer, upstream of the separated flow region. Furthermore, we find that the relative spatial amplitude of the adjoint modes is higher for those modes whose real frequencies correspond to the acoustic peaks. Finally, analysis of the wavemaker region points at the pressure surface near 30 % of the chord as the preferred zone for the placement of actuators for flow control of tonal noise.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 771 - 791
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Copyright
© 2017 Cambridge University Press 

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