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Article information
Optimal growth, model reduction and control in a separated
boundary-layer flow using global eigenmodes
| Authors: |
Åkervik, E.Å.,
Hoepffner, J.P.J.,
Ehrenstein, U,
Henningson, D.S.H.,
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| Type: |
Article |
| Pubstate: |
Published |
| Journal: |
J. Fluid Mech. |
| Volume: |
579
305-314 |
| Year: |
2007 |
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 are 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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