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Journal articles
Closed-loop control of vortex breakdown: A model study
Abstract : The objective of the study is to develop a closed-loop control scheme that is capable of preserving the columnar swirling flow state in the finite-length pipe model of Wang & Rusak (1996a). The base state consists of a solid body rotation superimposed on axial plug flow, with two dimensionless parameters: the swirl O and the pipe aspect ratio L. The linear stability properties of the columnar base state are documented and shown to give rise to unstable global modes above a critical swirl O1, thereby triggering vortex breakdown. Our study focuses on the derivation of a control method in order to quench the linear development of the Wang & Rusak instability. An óptimal control approach is then devised for a reduced-order system which is obtained by a suitable projection on a low-order subspace of the N least-stable eigenmodes. The actuator consists of perturbations of the inlet circulation and its time history is selected so as to minimize a cost-functional incorporating both the state energy and the control energy. A Riccati-based formulation leads to the determination of the optimal gain matrix for the low-order system. When applied to the full linear system, the feedback law for N = 4 succeeds in maintaining the columnar base state for swirl levels as high as 13% above global onset. The control scheme is found to be robust with respect to noise and to uncertainties in parameter settings. It remains effective even under partial-state information conditions. © 2004 Cambridge University Press.
Cited literature [56 references]
https://hal-polytechnique.archives-ouvertes.fr/hal-01024951
Contributor : Denis Roura <>
Submitted on : Tuesday, July 29, 2014 - 3:16:57 PM
Last modification on : Monday, July 27, 2020 - 1:00:05 PM
Long-term archiving on: : Monday, November 24, 2014 - 5:03:56 PM
Contributor : Denis Roura <>
Submitted on : Tuesday, July 29, 2014 - 3:16:57 PM
Last modification on : Monday, July 27, 2020 - 1:00:05 PM
Long-term archiving on: : Monday, November 24, 2014 - 5:03:56 PM
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