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Feedback Control of Spatially Evolving Flows
KTH, School of Engineering Sciences (SCI), Mechanics.
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 [en]
Stability, Control, Estimation, Absolute/Convective instabilities, Model reduction
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-4283OAI: oai:DiVA.org:kth-4283DiVA: diva2:11620
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
List of papers
1. Linear feedback control and estimation applied to instabilities in spatially developing boundary layers
Open this publication in new window or tab >>Linear feedback control and estimation applied to instabilities in spatially developing boundary layers
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.

Keyword
optimal perturbations, state estimation, flow systems, transition, wall, stability, equations
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-6803 (URN)10.1017/S0022112007007392 (DOI)000250675400008 ()2-s2.0-37749017590 (Scopus ID)
Note
QC 20100830Available from: 2007-02-22 Created: 2007-02-22 Last updated: 2010-09-23Bibliographically approved
2. Steady solutions of the Navier-Stokes equations by selective frequency damping
Open this publication in new window or tab >>Steady solutions of the Navier-Stokes equations by selective frequency damping
Show others...
2006 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 18, no 6, 068102- p.Article in journal (Refereed) Published
Abstract [en]

A new method, enabling the computation of steady solutions of the Navier-Stokes equations in globally unstable configurations, is presented. We show that it is possible to reach a steady state by damping the unstable (temporal) frequencies. This is achieved by adding a dissipative relaxation term proportional to the high-frequency content of the velocity fluctuations. Results are presented for cavity-driven boundary-layer separation and a separation bubble induced by an external pressure gradient.

Keyword
approximate deconvolution model, flows, simulation
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-6804 (URN)10.1063/1.2211705 (DOI)000238731500045 ()2-s2.0-33745610422 (Scopus ID)
Note
QC 20100830Available from: 2008-11-13 Created: 2008-11-13 Last updated: 2011-12-16Bibliographically approved
3. Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes
Open this publication in new window or tab >>Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes
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.

Keyword
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:nbn:se:kth:diva-9543 (URN)10.1017/S0022112007005496 (DOI)000247023600011 ()2-s2.0-34548175491 (Scopus ID)
Note
QC 20100923Available from: 2008-11-13 Created: 2008-11-12 Last updated: 2010-09-23Bibliographically approved
4. Global two-dimensional stability measures of the flat plate boundary-layer flow
Open this publication in new window or tab >>Global two-dimensional stability measures of the flat plate boundary-layer flow
2008 (English)In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 27, no 5, 501-513 p.Article in journal (Refereed) Published
Abstract [en]

The stability of the two-dimensional flat plate boundary-layer is studied by means of global eigenmodes. These eigenmodes depend both on the streamwise and wall-normal coordinate, hence there are no assumptions on the streamwise length scales of the disturbances. Expanding the perturbation velocity field in the basis of eigenmodes yields a reduced order model from which the stability characteristics of the flow, i.e. the initial condition and forcing function leading to the largest energy growth, are extracted by means of non-modal analysis. In this paper we show that, even when performing stability analysis using global eigenmodes, it is not sufficient to consider only a few of the least damped seemingly relevant eigenmodes. Instead it is the task of the optimization procedure, inherent in the non-modal analysis, to decide which eigenmodes are relevant. We show that both the optimal initial condition and the optimal forcing structure have the form of upstream tilted structures. Time integration reveals that these structures gain energy through the so called Orr mechanism, where the instabilities extract energy from the mean shear. This provides the optimal way of initiating Tollmien-Schlichting waves in the boundary layer. The optimal initial condition results in a localized Tollmien-Schlichting wavepacket that propagates downstream, whereas the optimal forcing results in a persistent Tollmien-Schlichting wave train.

Keyword
boundary layer stability, global modes, convective instabilities, non-modal stability
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-9542 (URN)10.1016/j.euromechflu.2007.09.004 (DOI)000258752500001 ()2-s2.0-47549119097 (Scopus ID)
Note
QC 20100923Available from: 2008-11-12 Created: 2008-11-12 Last updated: 2010-11-22Bibliographically approved

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Citation style
  • apa
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