Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Matrix-free methods for the stability and control of boundary layers
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-8209-1449
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
2009 (English)In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385X, Vol. 47, no 5, 1057-1068 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents matrix-free methods for the stability analysis and control design of high-dimensional systems arising from the discretized linearized Navier-Stokes equations. The methods are applied to the two-dimensional spatially developing Blasius boundary-layer. A critical step in the process of systematically investigating stability properties and designing feedback controllers is solving very large eigenvalue problems by storing only velocity fields at different times instead of large matrices. For stability analysis, where the entire dynamics of perturbations in space and time is of interest, iterative and adjoint-based optimization techniques are employed to compute the global eigenmodes and the optimal initial conditions. The latter are the initial conditions yielding the largest possible energy growth over a finite time interval. The leading global eigenmodes take the shape of Tollmien-Schlichting wavepackets located far downstream in streamwise direction, whereas the leading optimal disturbances are tilted structures located far upstream in the boundary layer. For control design on the other hand, the input-output behavior of the system is of interest and the snapshot-method is employed to compute balanced modes that correctly capture this behavior. The inputs are external disturbances and wall actuation and the outputs are sensors that extract wall shear stress. A low-dimensional model that capture the input-output behavior is constructed by projection onto balanced modes. The reduced-order model is then used to design a feedback control strategy such that the growth of disturbances are damped as they propagate downstream.

Place, publisher, year, edition, pages
2009. Vol. 47, no 5, 1057-1068 p.
Keyword [en]
Adjoint-based optimization, Blasius boundary layer, Control design, Critical steps, Eigen modes, Eigenvalue problem, Energy growth, External disturbances, Feedback control strategies, Feedback controller, Finite time intervals, High-dimensional systems, Initial conditions, Input-output behavior, Linearized navier-stokes equations, Low-dimensional models, matrix, Optimal disturbances, Reduced order models, Snapshot method, Space and time, Stability analysis, Stability and control, Stability properties, Streamwise directions, Tollmien-schlichting wave packets, Velocity field, Wall shear stress, Aerodynamics, Boundary layers, Eigenvalues and eigenfunctions, Feedback control, Flow separation, Navier Stokes equations, Optimization, System stability
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-9546DOI: 10.2514/1.41365ISI: 000265586200001Scopus ID: 2-s2.0-67649170531OAI: oai:DiVA.org:kth-9546DiVA: diva2:117430
Note
QC 20100927 AIAA 5th Theoretical Fluid Mechanics Meeting, Seattle, WA, JUN 23-26, 2008Available from: 2008-11-12 Created: 2008-11-12 Last updated: 2017-12-14Bibliographically 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. 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

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Authority records BETA

Bagheri, ShervinBrandt, LucaHenningson, Dan S.

Search in DiVA

By author/editor
Bagheri, ShervinÅkervik, EspenBrandt, LucaHenningson, Dan S.
By organisation
Mechanics
In the same journal
AIAA Journal
Fluid Mechanics and Acoustics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 2699 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf