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Steady solutions of the Navier-Stokes equations by selective frequency damping
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-4346-4732
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0001-7864-3071
KTH, School of Engineering Sciences (SCI), Mechanics.
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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.

Place, publisher, year, edition, pages
2006. Vol. 18, no 6, 068102- p.
Keyword [en]
approximate deconvolution model, flows, simulation
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-6804DOI: 10.1063/1.2211705ISI: 000238731500045Scopus ID: 2-s2.0-33745610422OAI: oai:DiVA.org:kth-6804DiVA: diva2:11617
Note
QC 20100830Available from: 2008-11-13 Created: 2008-11-13 Last updated: 2017-12-14Bibliographically 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
3. Stability and control of shear flows subject to stochastic excitations
Open this publication in new window or tab >>Stability and control of shear flows subject to stochastic excitations
2006 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

In this thesis, we adapt and apply methods from linear control theory to shear flows. The challenge of this task is to build a linear dynamic system that models the evolution of the flow, using the Navier--Stokes equations, then to define sensors and actuators, that can sense the flow state and affect its evolution. We consider flows exposed to stochastic excitations. This framework allows to account for complex sources of excitations, often present in engineering applications. Once the system is built, including dynamic model, sensors, actuators, and sources of excitations, we can use standard optimization techniques to derive a feedback law. We have used feedback control to stabilize unstable flows, and to reduce the energy level of sensitive flows subject to external excitations.

Place, publisher, year, edition, pages
Stockholm: KTH, 2006. 86 p.
Series
Trita-MEK, ISSN 0348-467X ; 2006:08
Keyword
control, estimation, stochastic excitations, feedback, model reduction
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-3929 (URN)
Public defence
2006-05-05, Sal F3, Lindstedtsvägen 26, Stockholm, 10:15
Opponent
Supervisors
Note
QC 20100830Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2011-12-16Bibliographically approved

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Brandt, LucaHenningson, Dan S.Schlatter, Philipp

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