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Global two-dimensional stability measures of the flat plate boundary-layer flow
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
IRPHÉ, Université de Provence.
Laboratoire J.A. Dieudonné.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
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.

Place, publisher, year, edition, pages
2008. Vol. 27, no 5, 501-513 p.
Keyword [en]
boundary layer stability, global modes, convective instabilities, non-modal stability
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-9542DOI: 10.1016/j.euromechflu.2007.09.004ISI: 000258752500001Scopus ID: 2-s2.0-47549119097OAI: oai:DiVA.org:kth-9542DiVA: diva2:117423
Note
QC 20100923Available from: 2008-11-12 Created: 2008-11-12 Last updated: 2010-11-22Bibliographically 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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