The interaction of Blasius boundary-layer flow with a compliant panel: global, local and transient analyses
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This article has been published in a revised form in the Journal of Fluid Mechanics http://doi.org/.10.1017/jfm.2017.453. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
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.
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Tsigklifis, Konstantinos; Lucey, Anthony (2015)We develop a hybrid of computational and theoretical approaches suited to study the fluid–structure interaction (FSI) of a compliant panel, flush between rigid upstream and downstream wall sections, with a Blasius ...
Modelling and analysis of the global stability of Blasius boundary-layer flow interacting with a compliant wallTsigklifis, Konstantinos; Lucey, Tony (2013)Theoretical and experimental studies have shown that compliant walls are able to reduce the growth rates of unstable Tollmien-Schlichting waves (TSWs) that are the conventional route to boundary layer transition in ...
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