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Stability and control of shear flows subject to stochastic excitations
KTH, School of Engineering Sciences (SCI), Mechanics.
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 [en]
control, estimation, stochastic excitations, feedback, model reduction
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-3929OAI: oai:DiVA.org:kth-3929DiVA: diva2:10062
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
List of papers
1. State estimation in wall-bounded flow systems: P. I Laminar flows
Open this publication in new window or tab >>State estimation in wall-bounded flow systems: P. I Laminar flows
2005 (English)In: Journal of fluid mechanics, ISSN 0022-1120, Vol. 534, 263-394 p.Article in journal (Refereed) Published
Abstract [en]

In applications involving the model-based control of transitional wall-bounded flow systems, it is often desired to estimate the interior flow state based on a history of noisy measurements from an array of flush-mounted skin-friction and pressure sensors on the wall. This paper considers this estimation problem, using a Kalman filter based on the linearized Navier-Stokes equations and appropriate stochastic models for the relevant statistics of the initial conditions, sensor noise and external disturbances acting on the system. We show that a physically relevant parameterization of these statistics is key to obtaining well-resolved feedback kernels with appropriate spatial extent for all three types of flow measurement available on the wall. The effectiveness of the resulting Kalman and extended Kalman filters that implement this feedback is verified for both infinitesimal and finite-amplitude disturbances in direct numerical simulations of a perturbed laminar channel flow. The consideration of time-varying feedback kernels is shown to be particularly advantageous in accelerating the convergencc of the estimator from unknown initial conditions. A companion paper (Part 2) considers the extension of such estimators to the case of fully developed turbulence.

Keyword
shear flows, transition
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-5626 (URN)10.1017/S0022112005004210 (DOI)000230698800012 ()2-s2.0-22244471082 (Scopus ID)
Note
QC 20100830Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2010-12-06Bibliographically approved
2. State estimation in wall-bounded flow systems: P. II Turbulent flows
Open this publication in new window or tab >>State estimation in wall-bounded flow systems: P. II Turbulent flows
2006 (English)In: Journal of fluid mechanics, ISSN 0022-1120, Vol. 552, 167-187 p.Article in journal (Refereed) Published
Abstract [en]

This work extends the estimator developed in Part I of this study to the problem of estimating a turbulent channel flow at Re-tau=100 based on a history of noisy measurements on the wall. The key advancement enabling this work is the development and implementation of an efficient technique to extract, from direct numerical simulations, the relevant statistics of an appropriately defined 'external forcing' term on the Navier-Stokes equation linearized about the mean turbulent flow profile. This forcing term is designed to account for the unmodelled (nonlinear) terms during the computation of the (linear) Kalman filter feedback gains in Fourier space. Upon inverse transform of the resulting feedback gains computed on an array of wavenumber pairs to physical space, we obtain, as in Part 1, effective and well-resolved feedback convolution kernels for the estimation problem. It is demonstrated that, by applying the feedback so determined, satisfactory correlation between the actual and estimated flow is obtained in the near-wall region. As anticipated, extended Kalman filters (with the nonlinearity of the actual system reintroduced into the estimator model after the feedback gains are determined) outperform standard (linear) Kalman filters on the full system.

Keyword
Feedback-Control, Transition, Channel
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-5627 (URN)10.1017/S0022112005008578 (DOI)000237161500009 ()2-s2.0-33645345695 (Scopus ID)
Note
QC 20100830Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2010-12-06Bibliographically approved
3. Control of cavity-driven separated boundary layer
Open this publication in new window or tab >>Control of cavity-driven separated boundary layer
2006 (English)In: Proceedings of the Conference on active flow control, Berlin, September 2006, 2006Conference paper, Published paper (Refereed)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-5629 (URN)
Note
QC 20100830Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2010-08-30Bibliographically approved
4. Transient growth on boundary layer streaks
Open this publication in new window or tab >>Transient growth on boundary layer streaks
2005 (English)In: Journal of fluid mechanics, ISSN 0022-1120, Vol. 537, 91-100 p.Article in journal (Refereed) Published
Abstract [en]

The linear perturbations evolving on streamwise boundary layer streaks which yield maximum energy growth are computed. The steady and spanwise-periodic streaks arising from the nonlinear saturation of optimally growing streamwise vortices are considered as base flow. It is shown that significant transient growth may occur for both sinuous antisymmetric perturbations and for varicose symmetric modes. The energy growth is observed at amplitudes significantly below the threshold beyond which the streaks become linearly unstable and is largest for sinuous perturbations, to which the base flow considered first become unstable. The optimal initial condition consists of velocity perturbations localized in the regions of highest shear of the streak base flow, tilted upstream from the wall. The optimal response is still localized in the areas of largest shear but it is tilted in the flow direction. The most amplified perturbations closely resemble the unstable eigenfunctions obtained for streaks of higher amplitudes. The results suggest the possibility of a transition scenario characterized by the non-modal growth of primary perturbations, the streaks, followed by the secondary transient growth of higher frequency perturbations. The implication for turbulent flow is also discussed.

Keyword
viscous shear-flow, optimal perturbations, optimal excitation, pressure-gradient, turbulence, transition, breakdown, wall; instability, subject
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-5630 (URN)10.1017/S0022112005005203 (DOI)000231935700004 ()2-s2.0-23944441154 (Scopus ID)
Note
QC 20100830Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2010-12-06Bibliographically approved
5. Modeling flow statistics using convex optimization
Open this publication in new window or tab >>Modeling flow statistics using convex optimization
2005 (English)In: 2005 44TH IEEE CONFERENCE ON DECISION AND CONTROL & EUROPEAN CONTROL CONFERENCE, VOLS 1-8, 2005, Vol. 1-8, 4287-4292 p.Conference paper, Published paper (Refereed)
Abstract [en]

A method is proposed to estimate the covariance of disturbances to a stable linear system when its state covariance is known and a dynamic model is available. This is an issue of fundamental interest for estimation and control of fluid mechanical systems whose dynamics is described by the linearized Navier-Stokes equations. The problem is formulated in terms of a matrix norm minimisation with linear matrix inequality constraint, and solved numerically by means of alternating convex projection. The method is tested on covariance estimation in a low Reynolds number channel flow.

Series
IEEE Conference on Decision and Control, ISSN 0191-2216
Keyword
Channel flow; Matrix algebra; Navier Stokes equations; Optimization; Parameter estimation; Problem solving
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-5631 (URN)10.1109/CDC.2005.1582836 (DOI)000240653704022 ()2-s2.0-33847203990 (Scopus ID)
Conference
44th IEEE Conference on Decision Control/European Control Conference (CCD-ECC). Seville, SPAIN. DEC 12-15, 2005
Note
QC 20100830 QC 20111017Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2011-10-17Bibliographically approved
6. 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: 2017-12-14Bibliographically approved

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