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Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
IRPH́E, Université de Provence.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
2007 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 579, 305-314 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 579, 305-314 p.
Keyword [en]
Boundary layer flow, Eigenvalues and eigenfunctions, Feedback control, Flow control, Mathematical models, Optimization, Shear stress, Control optimization, Flow simulation, Global eigenmodes
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-9543DOI: 10.1017/S0022112007005496ISI: 000247023600011Scopus ID: 2-s2.0-34548175491OAI: oai:DiVA.org:kth-9543DiVA: diva2:117425
Note
QC 20100923Available from: 2008-11-13 Created: 2008-11-12 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Global stability and feedback control of boundary layer flows
Open this publication in new window or tab >>Global stability and feedback control of boundary layer flows
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

In this thesis the stability of generic boundary layer flows is studied from a global viewpoint using optimization methods. Global eigenmodes of the incompressible linearized Navier-Stokes equations are computed using the Krylov subspace Arnoldi method. These modes serve as a tool both to study asymptotic stability and as a reduced basis to study transient growth. Transient growth is also studied using adjoint iterations. The knowledge obtained from the stability analysis is used to device systematic feedback control in the Linear Quadratic Gaussian framework. The dynamics is assumed to be described by the linearized Navier-Stokes equations. Actuators and sensors are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier-Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier-Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. A standard method to construct a reduced order model is to perform a Galerkin projection of the full equations onto the subspace spanned by a suitable set of vectors, such as global eigenmodes and balanced truncation modes.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. viii, 58 p.
Series
Trita-MEK, ISSN 0348-467X ; 2008:09
Keyword
Stability, Global Stability, Feedback Control, Control, Estimation, Absolute/Convective Instabilities, Model Reduction
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-9547 (URN)978-91-7415-176-3 (ISBN)
Public defence
2008-12-05, E1, Lindstedtsvägen 3, Stockholm, 10:30 (English)
Opponent
Supervisors
Note
QC 20100924Available from: 2008-11-13 Created: 2008-11-12 Last updated: 2010-09-24Bibliographically approved
2. Feedback Control of Spatially Evolving Flows
Open this publication in new window or tab >>Feedback Control of Spatially Evolving Flows
2007 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

In this thesis we apply linear feedback control to spatially evolving flows in order to minimize disturbance growth. The dynamics is assumed to be described by the linearized Navier--Stokes equations. Actuators and sensor are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier--Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier--Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. One possible approach is to perform Fourier decomposition along (almost) homogeneous spatial directions and another is by constructing a reduced order model by Galerkin projection on a suitable set of vectors. The first strategy is used to control the evolution of a range of instabilities in the classical family of Falkner--Skan--Cooke flows whereas the second is applied to a more complex cavity type of geometry.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007. v, 104 p.
Series
Trita-MEK, ISSN 0348-467X ; 2007:03
Keyword
Stability, Control, Estimation, Absolute/Convective instabilities, Model reduction
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-4283 (URN)
Presentation
2007-03-08, S40, Teknikringen 8, Tekniska Högskolan, Valhallavägen, 10:30
Opponent
Supervisors
Note
QC 20101122Available from: 2007-02-22 Created: 2007-02-22 Last updated: 2010-11-22Bibliographically approved

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Henningson, Dan S.

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