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Feedback control and modal structures in transitional shear flows
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

 

Two types of shear flows are investigated in this thesis; numerical simulations are performed for the analysis and control of the perturbation arising in a boundary layer over a flat plate, whereas PIV measurements are analysed for the investigation of a confined turbulent jet. Modal structures of the flows are identified: the aim is to understand the flow phenomena and to identify reduced-order models for the feedback control design. The attenuation of three-dimensional wavepackets of streaks and Tollmien-Schlichting (TS) waves in the boundary layer is obtained using feedback control based on arrays of spatially localized sensors and actuators distributed near the rigid wall. In order to tackle the difficulties arising due to the dimension of the discretized Navier-Stokes operator, a reduced-order model is identified, preserving the dynamics between the inputs and the outputs; to this end, approximate balanced truncation is used. Thus, control theory tools can be easily handled using the low-order model. We demonstrate that the energy growth of both TS wavepackets and streak-packets is substantially and efficiently mitigated, using relatively few sensors and actuators. The robustness of the controller is investigated by varying the number of actuators and ensors, the Reynolds number and the pressure gradient. The configuration can be possibly reproduced in experiments, due to the localization of sensing and actuation devices. A complete analysis of a confined turbulent jet is carried out using timeresolved PIV measurements. Proper orthogonal decomposition (POD) modes and Koopman modes are computed and analysed for understanding the main features of the flow. The frequencies related to the dominating mechanisms are identified; the most energetic structures show temporal periodicity.

 

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology , 2011. , vii, 33 p.
Series
Trita-MEK, ISSN 0348-467X ; 2011:01
Keyword [en]
flow control, flat-plate boundary layer, laminar-turbulent transition
National Category
Other Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-29754ISBN: 978-91-7415-863-2 (print)OAI: oai:DiVA.org:kth-29754DiVA: diva2:397429
Presentation
2011-02-18, Sal E3, KTH, Osquars backe 14, Stockhkolm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish e‐Science Research Center
Note
QC 20110214Available from: 2011-02-14 Created: 2011-02-14 Last updated: 2012-05-24Bibliographically approved
List of papers
1. Feedback control of three-dimensional optimal disturbances using reduced-order models
Open this publication in new window or tab >>Feedback control of three-dimensional optimal disturbances using reduced-order models
2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 677, 63-102 p.Article in journal (Refereed) Published
Abstract [en]

The attenuation of three-dimensional wavepackets of streaks and Tollmien-Schlichting (TS) waves in a transitional boundary layer using feedback control is investigated numerically. Arrays of localized sensors and actuators (about 10-20) with compact spatial support are distributed near the rigid wall equidistantly along the spanwise direction and connected to a low-dimensional (r = 60) linear quadratic Gaussian controller. The control objective is to minimize the disturbance energy in a domain spanned by a number of proper orthogonal decomposition modes. The feedback controller is based on a reduced-order model of the linearized Navier-Stokes equations including the inputs and outputs, computed using a snapshot-based balanced truncation method. To account for the different temporal and spatial behaviour of the two main instabilities of boundary-layer flows, we design two controllers. We demonstrate that the two controllers reduce the energy growth of both TS wavepackets and streak packets substantially and efficiently, using relatively few sensors and actuators. The robustness of the controller is investigated by varying the number of actuators and sensors, the Reynolds number and the pressure gradient. This work constitutes the first experimentally feasible simulation-based control design using localized sensing and acting devices in conjunction with linear control theory in a three-dimensional setting.

Keyword
boundary layer stability, control theory, flow control
National Category
Other Engineering and Technologies not elsewhere specified
Identifiers
urn:nbn:se:kth:diva-36235 (URN)10.1017/S0022112011000620 (DOI)000292095200003 ()2-s2.0-79959256638 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note
Updated from submitted to published. QC 20120328Available from: 2011-07-11 Created: 2011-07-11 Last updated: 2017-12-11Bibliographically approved
2. Transition delay in boundary layer flow using feedback control
Open this publication in new window or tab >>Transition delay in boundary layer flow using feedback control
(English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Other academic) Submitted
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-29750 (URN)
Note
QC 20110214Available from: 2011-02-14 Created: 2011-02-14 Last updated: 2017-12-11Bibliographically approved
3. Analysis of time-resolved PIV measurements of a confined co-flowing jet using POD and Koopman modes
Open this publication in new window or tab >>Analysis of time-resolved PIV measurements of a confined co-flowing jet using POD and Koopman modes
2011 (English)Report (Other academic)
Abstract [en]

Modal analysis by proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) of experimental data from a fully turbulent flow is presented. The flow case is a turbulent confined jet with co-flow, with Reynolds number based on the jet thickness of Re=10700. Experiments are performed with time-resolved Particle Image Velocimetry (PIV). The jet is created in a square channel with the confinement ratio is 1:5. Statistics of the flow are presented in terms of mean and fluctuating fields. Analysis of spatial spectra and temporal spectra reveal the presence of dominant wavelengths and frequenciesembedded in broad-band turbulent spectrum. Frequencies in the shearlayer migrate from St ≈ 1 near the jet inlet to St < 0.1 at 18 jet thickness downstream.

This flow case provides an interesting and challenging benchmark for testing POD and DMD and discussing their efficacy in describing a fully turbulent case. At first, issues related to convergence and physical interpretation of the modes are discussed, then the results are analyzed and compared. POD analysis reveals the most energetic spatial structures that are related to the flapping of the jet; a low frequency peak (St = 0.02) is found when the associated temporalmode is analyzed. Higher order modes revealed the presence of fasteroscillating shear flow modes combined to a recirculation zone near the inner jet. The flapping of the inner jet is sustained by this region. A good agreement is found between DMD and POD; however, DMD is able to rank the modes by frequencies, isolating structures associated to harmonics of the flow.

National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-29753 (URN)
Note

QC 20110214

Available from: 2011-02-14 Created: 2011-02-14 Last updated: 2017-08-17Bibliographically approved

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