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Global stability and resolvent analyses of laminar boundary-layer flow interacting with viscoelastic patches

Published online by Cambridge University Press:  22 February 2022

J.-L. Pfister Open the ORCID record for J.-L. Pfister [Opens in a new window] ,
N. Fabbiane Open the ORCID record for N. Fabbiane [Opens in a new window]  and
O. Marquet Open the ORCID record for O. Marquet [Opens in a new window]
J.-L. Pfister*
Affiliation:
DAAA, ONERA, Paris Saclay University, F-92190 Meudon, France
N. Fabbiane
Affiliation:
DAAA, ONERA, Paris Saclay University, F-92190 Meudon, France
O. Marquet
Affiliation:
DAAA, ONERA, Paris Saclay University, F-92190 Meudon, France
*
†Email address for correspondence: [email protected]
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Abstract

The attenuation of two-dimensional boundary-layer instabilities by a finite-length, viscoelastic patch is investigated by means of global linear stability theory. First, the modal stability properties of the coupled problem are assessed, revealing unstable fluid-elastic travelling-wave flutter modes. Second, the Tollmien–Schlichting instabilities over a rigid wall are characterised via the analysis of the fluid resolvent operator in order to determine a baseline for the fluid-structural analysis. To investigate the effect of the elastic patch on the growth of these flow instabilities, we first consider the linear frequency response of the coupled fluid-elastic system to the dominant rigid-wall forcing modes. In the frequency range of Tollmien–Schlichting waves, the energetic flow amplification is clearly reduced. However, an amplification is observed for higher frequencies, associated with travelling-wave flutter. This increased complexity requires the analysis of the coupled fluid-structural resolvent operator; the optimal, coupled, resolvent modes confirm the attenuation of the Tollmien–Schlichting instabilities, while also being able to capture the amplification at the higher frequencies. Finally, a decomposition of the fluid-structural response is proposed to reveal the wave cancellation mechanism responsible for the attenuation of the Tollmien–Schlichting waves. The viscoelastic patch, excited by the incoming rigid-wall wave, provokes a fluid-elastic wave that is out-of-phase with the former, thus reducing its amplitude.

JFM classification

Aerodynamics: Flow-structure interactions Boundary Layers: Boundary layer stability Flow Control: Instability control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 937 , 25 April 2022 , A1
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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