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Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes

Abstract : Two-dimensional global eigenmodes are used as a projection basis both for analysing the dynamics and building a reduced model for control in a prototype separated boundary-layer flow. In the present configuration, a high aspect ratio smooth cavity-like geometry confines the separation bubble. Optimal growth analysis using the reduced basis shows that the sum of the highly non-normal global eigenmodes is able to describe a localized disturbance. Subject to this worst-case initial condition, a large transient growth associated with the development of a wavepacket along the shear layer followed by a global cycle related to the two unstable global eigenmodes is found. The flow simulation procedure is coupled to a measurement feedback controller, which senses the wall shear stress at the downstream lip of the cavity and actuates at the upstream lip. A reduced model for the control optimization is obtained by a projection on the least stable global eigenmodes, and the resulting linear-quadratic-gaussian controller is applied to the Navier--Stokes time integration. It is shown that the controller is able to damp out the global oscillations.
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https://hal.archives-ouvertes.fr/hal-00211799
Contributor : Uwe Ehrenstein Connect in order to contact the contributor
Submitted on : Monday, January 21, 2008 - 5:27:05 PM
Last modification on : Tuesday, October 19, 2021 - 10:59:31 PM

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  • HAL Id : hal-00211799, version 1

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Espen Akervik, Jérôme Hoepffner, Uwe Ehrenstein, Dan S. Henningson. Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2007, 579, pp.305-314. ⟨hal-00211799⟩

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