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The interaction of Blasius boundary-layer flow with a compliant panel: global, local and transient analyses

Published online by Cambridge University Press:  22 August 2017

Konstantinos Tsigklifis Open the ORCID record for Konstantinos Tsigklifis [Opens in a new window]  and
Anthony D. Lucey
Konstantinos Tsigklifis*
Affiliation:
Fluid Dynamics Research Group, Department of Mechanical Engineering, Curtin University, Western Australia 6845, Australia
Anthony D. Lucey
Affiliation:
Fluid Dynamics Research Group, Department of Mechanical Engineering, Curtin University, Western Australia 6845, Australia
*
†Email address for correspondence: [email protected]
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Abstract

We study the fluid–structure interaction (FSI) of a compliant panel with developing Blasius boundary-layer flow. The linearised Navier–Stokes equations in velocity–vorticity form are solved using a Helmholtz decomposition coupled with the dynamics of a plate-spring compliant panel couched in finite-difference form. The FSI system is written as an eigenvalue problem and the various flow- and wall-based instabilities are analysed. It is shown that global temporal instability can occur through the interaction of travelling wave flutter (TWF) with a structural mode or as a resonance between Tollmien–Schlichting wave (TSW) instability and discrete structural modes of the compliant panel. The former is independent of compliant panel length and upstream inflow disturbances while the specific behaviour arising from the latter phenomenon is dependent upon the frequency of a disturbance introduced upstream of the compliant panel. The inclusion of axial displacements in the wall model does not lead to any further global instabilities. The dependence of instability-onset Reynolds numbers with structural stiffness and damping for the global modes is quantified. It is also shown that the TWF-based global instability is stabilised as the boundary layer progresses downstream while the TSW-based global instability exhibits discrete resonance-type behaviour as Reynolds number increases. At sufficiently high Reynolds numbers, a globally unstable divergence instability is identified when the wavelength of its wall-based mode is longer than that of the least stable TSW mode. Finally, a non-modal analysis reveals a high level of transient growth when the flow interacts with a compliant panel which has structural properties capable of reducing TSW growth but which is prone to global instability through wall-based modes.

JFM classification

Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 827 , 25 September 2017 , pp. 155 - 193
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© 2017 Cambridge University Press 

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