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

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. Optima...

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Bibliographic Details
Published in:Journal of fluid mechanics 2007-05, Vol.579, p.305-314
Main Authors: ÅKERVIK, ESPEN, HŒPFFNER, JÉRÔME, EHRENSTEIN, UWE, HENNINGSON, DAN S.
Format: Article
Language:English
Subjects:
Boundary layer flow
Control optimization
Eigenvalues
Eigenvalues and eigenfunctions
Engineering mechanics
Engineering Sciences
Exact sciences and technology
Feedback control
Flow control
Flow simulation
Fluid dynamics
Fluid mechanics
Fluids mechanics
Fundamental areas of phenomenology (including applications)
Global eigenmodes
Mathematical models
Mathematics
Mechanics
Optimization
Physics
Shear stress
Strömningsmekanik
TECHNOLOGY
TEKNIKVETENSKAP
Teknisk mekanik
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Summary: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.
ISSN:0022-1120
1469-7645
1469-7645
DOI:10.1017/S0022112007005496