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Stability analysis and control design of spatially developing flows
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-8209-1449
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 [en]
Global modes, transient growth, model reduction, feedback control
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-4769OAI: oai:DiVA.org:kth-4769DiVA: diva2:13846
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
List of papers
1. Input-Output Analysis and Control Design Applied to a Linear Model of Spatially Developing Flows
Open this publication in new window or tab >>Input-Output Analysis and Control Design Applied to a Linear Model of Spatially Developing Flows
2009 (English)In: Applied Mechanics Review, ISSN 0003-6900, E-ISSN 1088-8535, Vol. 62, no 2Article in journal (Refereed) Published
Abstract [en]

This review presents a framework for the input-output analysis, model reduction, and control design for fluid dynamical systems using examples applied to the linear complex Ginzburg-Landau equation. Major advances in hydrodynamics stability, such as global modes in spatially inhomogeneous systems and transient growth of non-normal systems, are reviewed. Input-output analysis generalizes hydrodynamic stability analysis by considering a finite-time horizon over which energy amplification, driven by a specific input (disturbances/actuator) and measured at a specific output (sensor), is observed. In the control design the loop is closed between the output and the input through a feedback gain. Model reduction approximates the system with a low-order model, making modern control design computationally tractable for systems of large dimensions. Methods from control theory are reviewed and applied to the Ginzburg-Landau equation in a manner that is readily generalized to fluid mechanics problems, thus giving a fluid mechanics audience an accessible introduction to the subject.

Keyword
control system synthesis, feedback, flow control, flow instability, flow simulation, Ginzburg-Landau theory, hydrodynamics, reduced order systems
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-8499 (URN)10.1115/1.3077635 (DOI)000263717800003 ()2-s2.0-77950642067 (Scopus ID)
Note
QC 20101103Available from: 2008-05-23 Created: 2008-05-23 Last updated: 2010-11-03Bibliographically approved
2. Input-output analysis, model reduction and control of the flat-plate boundary layer
Open this publication in new window or tab >>Input-output analysis, model reduction and control of the flat-plate boundary layer
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.

Keyword
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:nbn:se:kth:diva-8500 (URN)10.1017/S0022112008004394 (DOI)000263384700012 ()2-s2.0-65649154530 (Scopus ID)
Note
QC 20101103 Submitted 2008Available from: 2008-05-23 Created: 2008-05-23 Last updated: 2010-11-03Bibliographically approved
3. The global stability of the jet in crossflow
Open this publication in new window or tab >>The global stability of the jet in crossflow
2008 (English)Report (Other academic)
Series
Internal report
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-25889 (URN)
Note
QC 20101103Available from: 2010-11-03 Created: 2010-11-03 Last updated: 2010-11-03Bibliographically approved
4. The stabilizing effect of streaks on Tollmien-Schlichting and oblique waves: A parametric study
Open this publication in new window or tab >>The stabilizing effect of streaks on Tollmien-Schlichting and oblique waves: A parametric study
2007 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 19, no 7, 078103-1-078103-4 p.Article in journal (Refereed) Published
Abstract [en]

The stabilizing effect of finite amplitude streaks on the linear growth of unstable perturbations [Tollmien-Schlichting (TS) and oblique waves] is numerically investigated by means of the nonlinear parabolized stability equations. We have found that for stabilization of a TS-wave, there exists an optimal spanwise spacing of the streaks. These streaks reach their maximum amplitudes close to the first neutral point of the TS-wave and induce the largest distortion of the mean flow in the unstable region of the TS-wave. For such a distribution, the required streak amplitude for complete stabilization of a given TS-wave is considerably lower than for beta=0.45, which is the optimal for streak growth and used in previous studies. We have also observed a damping effect of streaks on the growth rate of oblique waves in Blasius boundary layer and for TS-waves in Falkner-Skan boundary layers.

Keyword
blasius boundary-layer, transition
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-16836 (URN)10.1063/1.2746047 (DOI)000248486100047 ()2-s2.0-34547814063 (Scopus ID)
Note
QC 20100525 Tidigare titel: The stabilizing effect of streaks on TS-waves: A parametric studyAvailable from: 2010-08-05 Created: 2010-08-05 Last updated: 2010-11-03Bibliographically approved

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