On the receptivity of aerofoil tonal noise: An adjoint analysis

Miguel Fosas De Pando, Peter J. Schmid, Denis Sipp

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)771-791
Number of pages21
JournalJournal of Fluid Mechanics
StatePublished - Feb 10 2017
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2022-09-13

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Condensed Matter Physics


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