On the receptivity of aerofoil tonal noise: an adjoint analysis

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Title: On the receptivity of aerofoil tonal noise: an adjoint analysis
Author(s): Fosas de Pando, M
Schmid, PJ
Sipp, D
Item Type: Journal Article
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.
Publication Date: 5-Jan-2017
Date of Acceptance: 1-Nov-2016
URI: http://hdl.handle.net/10044/1/43486
DOI: https://dx.doi.org/10.1017/jfm.2016.736
ISSN: 1469-7645
Publisher: Cambridge University Press (CUP)
Start Page: 771
End Page: 791
Journal / Book Title: Journal of Fluid Mechanics
Volume: 812
Copyright Statement: © 2017 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.Journal of Fluid Mechanics.
Keywords: Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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