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Linear feedback control and estimation applied to instabilities in spatially developing boundary layers
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-3794-1643
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0001-7864-3071
2007 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 588, 163-187 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents the application of feedback control to spatially developing boundary layers. It is the natural follow-up of Hogberg & Henningson (J. Fluid Mech. vol. 470, 2002, p. 151), where exact knowledge of the entire flow state was assumed for the control. We apply recent developments in stochastic models for the external sources of disturbances that allow the efficient use of several wall measurements for estimation of the flow evolution: the two components of the skin friction and the pressure fluctuation at the wall. Perturbations to base flow profiles of the family of Falkner-Skan-Cooke boundary layers are estimated by use of wall measurements. The estimated state is in turn fed back for control in order to reduce the kinetic energy of the perturbations. The control actuation is achieved by means of unsteady blowing and suction at the wall. Flow perturbations are generated in the upstream region in the computational box and propagate in the boundary layer. Measurements are extracted downstream over a thin strip, followed by a second thin strip where the actuation is performed. It is shown that flow disturbances can be efficiently estimated and controlled in spatially evolving boundary layers for a wide range of base flows and disturbances.

Place, publisher, year, edition, pages
2007. Vol. 588, 163-187 p.
Keyword [en]
optimal perturbations, state estimation, flow systems, transition, wall, stability, equations
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-6803DOI: 10.1017/S0022112007007392ISI: 000250675400008Scopus ID: 2-s2.0-37749017590OAI: oai:DiVA.org:kth-6803DiVA: diva2:11616
Note
QC 20100830Available from: 2007-02-22 Created: 2007-02-22 Last updated: 2010-09-23Bibliographically approved
In thesis
1. 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
2. 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

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Chevalier, MattiasHenningson, Dan S.

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