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Input-output analysis, model reduction and control of the flat-plate boundary layer
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-8209-1449
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-4346-4732
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
2009 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 620, 263-298 p.Article in journal (Refereed) Published
Abstract [en]

The dynamics and control of two-dimensional disturbances in the spatially evolving boundary layer oil a flat plate are investigated from an input output viewpoint. A set-up of spatially localized inputs (external disturbances and actuators) and Outputs (objective functions and sensors) is introduced for the control design of convectively unstable flow configurations. From the linearized Navier Stokes equations with the inputs and outputs, controllable, observable and balanced modes are extracted using the snapshot method. A balanced reduced-order model (ROM) is constructed and shown to capture the input output behaviour of the linearized Navier Stokes equations. This model is finally used to design H-2-feedback controller to suppress the growth or two-dimensional perturbations inside the boundary layer.

Place, publisher, year, edition, pages
2009. Vol. 620, 263-298 p.
Keyword [en]
Control design, Dynamics and control, External disturbances, Feedback controller, Flat plate, Input output analysis, Input-output, Linearized navier-stokes equations, Model reduction, Objective functions, Reduced order models, Snapshot method, Two-dimensional perturbation, Unstable flows, Aerodynamics, Boundary layers, Fluid dynamics, Linearization, Two dimensional, Viscous flow
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-8500DOI: 10.1017/S0022112008004394ISI: 000263384700012Scopus ID: 2-s2.0-65649154530OAI: oai:DiVA.org:kth-8500DiVA: diva2:13843
Note
QC 20101103 Submitted 2008Available from: 2008-05-23 Created: 2008-05-23 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Analysis and control of transitional shear flows using global modes
Open this publication in new window or tab >>Analysis and control of transitional shear flows using global modes
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis direct numerical simulations are used to investigate two phenomenain shear flows: laminar-turbulent transition over a flat plate and periodicvortex shedding induced by a jet in cross flow. The emphasis is on understanding and controlling the flow dynamics using tools from dynamical systems and control theory. In particular, the global behavior of complex flows is describedand low-dimensional models suitable for control design are developed; this isdone by decomposing the flow into global modes determined from spectral analysisof various linear operators associated with the Navier–Stokes equations.Two distinct self-sustained global oscillations, associated with the sheddingof vortices, are identified from direct numerical simulations of the jet incrossflow. The investigation is split into a linear stability analysis of the steadyflow and a nonlinear analysis of the unsteady flow. The eigenmodes of theNavier–Stokes equations, linearized about an unstable steady solution revealthe presence of elliptic, Kelvin-Helmholtz and von K´arm´an type instabilities.The unsteady nonlinear dynamics is decomposed into a sequence of Koopmanmodes, determined from the spectral analysis of the Koopman operator. Thesemodes represent spatial structures with periodic behavior in time. A shearlayermode and a wall mode are identified, corresponding to high-frequency andlow-frequency self-sustained oscillations in the jet in crossflow, respectively.The knowledge of global modes is also useful for transition control, wherethe objective is to reduce the growth of small-amplitude disturbances to delaythe transition to turbulence. Using a particular basis of global modes, knownas balanced modes, low-dimensional models that capture the behavior betweenactuator and sensor signals in a flat-plate boundary layer are constructed andused to design optimal feedback controllers. It is shown that by using controltheory in combination with sensing/actuation in small, localized, regionsnear the rigid wall, the energy of disturbances may be reduced by an order of magnitude.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. viii, 82 p.
Series
Trita-MEK, ISSN 0348-467X ; 2010:01
Keyword
Fluid mechanics, flow control, hydrodynamic stability, global modes, jet in crossflow, flat-plate boundary layer, laminar-turbulent transition, Arnoldi method, Koopman modes, balanced truncation, direct numerical simulations.
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-11894 (URN)978-91-7415-540-2 (ISBN)
Public defence
2010-02-12, F3, Lindsedsv, 26, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Available from: 2010-01-26 Created: 2010-01-20 Last updated: 2010-11-03
2. Stability analysis and control design of spatially developing flows
Open this publication in new window or tab >>Stability analysis and control design of spatially developing flows
2008 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

Methods in hydrodynamic stability, systems and control theory are applied to spatially developing flows, where the flow is not required to vary slowly in the streamwise direction. A substantial part of the thesis presents a theoretical framework for the stability analysis, input-output behavior, model reduction and control design for fluid dynamical systems using examples on the linear complex Ginzburg-Landau equation. The framework is then applied to high dimensional systems arising from the discretized Navier–Stokes equations. In particular, global stability analysis of the three-dimensional jet in cross flow and control design of two-dimensional disturbances in the flat-plate boundary layer are performed. Finally, a parametric study of the passive control of two-dimensional disturbances in a flat-plate boundary layer using streamwise streaks is presented.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. vii, 15 p.
Series
Trita-MEK, ISSN 0348-467X ; 2008:04
Keyword
Global modes, transient growth, model reduction, feedback control
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-4769 (URN)
Presentation
2008-05-06, D41, D, Lindstedsvägen 17, Stockholm, 14:00 (English)
Opponent
Supervisors
Note
QC 20101103Available from: 2008-05-23 Created: 2008-05-23 Last updated: 2010-11-03Bibliographically approved

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Bagheri, ShervinBrandt, LucaHenningson, Dan

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