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Active Control and Modal Structures in Transitional Shear Flows
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Flow control of transitional shear flows is investigated by means of numerical simulations. The attenuation of three-dimensional wavepackets of Tollmien-Schlichting (TS) and streaks in the boundary layer is obtained using active control in combination with localised sensors and actuators distributed near the rigid wall. Due to the dimensions of the discretized Navier-Stokes operator, reduced-order models are identified, preserving the dynamics between the inputs and the outputs of the system. Balanced realizations of the system are computed using balanced truncation and system identification.

We demonstrate that the energy growth of the perturbations is substantially and efficiently mitigated, using relatively few sensors and actuators. The robustness of the controller is analysed by varying the number of actuators and sensors, the Reynolds number, the pressure gradient and by investigating the nonlinear, transitional case. We show that delay of the transition from laminar to turbulent flow can be achieved despite the fully linear approach. This configuration can be reproduced in experiments, due to the localisation of sensing and actuation devices.

The closed-loop system has been investigated for the corresponding twodimensional case by using full-dimensional optimal controllers computed by solving an iterative optimisation based on the Lagrangian approach. This strategy allows to compare the results achieved using open-loop model reduction with model-free controllers. Finally, a parametric analysis of the actuators/ sensors placement is carried-out to deepen the understanding of the inherent dynamics of the closed-loop. The distinction among two different classes of controllers – feedforward and feedback controllers - is highlighted.

A second shear flow, a confined turbulent jet, is investigated using particle image velocimetry (PIV) measurements. Proper orthogonal decomposition (POD) modes and Koopman modes via dynamic mode decomposition (DMD) 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, 2013. , vii, 72 p.
Series
Trita-MEK, ISSN 0348-467X ; 2013:03
Keyword [en]
Flow control, flat-plate boundary layer, optimal controllers, model reduction, turbulent jet, POD, DMD, Koopman modes
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-117916ISBN: 978-91-7501-640-5 (print)OAI: oai:DiVA.org:kth-117916DiVA: diva2:603876
Public defence
2013-02-22, Sal E3, Osquars Backe 14, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20130207

Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2013-02-07Bibliographically 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 a boundary layer flow using active control
Open this publication in new window or tab >>Transition delay in a boundary layer flow using active control
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 731, 288-311 p.Article in journal (Refereed) Published
Abstract [en]

Active linear control is applied to delay the onset of laminar-turbulent transition in the boundary layer over a flat plate. The analysis is carried out by numerical simulations of the nonlinear, transitional regime. A three-dimensional, localized initial condition triggering Tollmien-Schlichting waves of finite amplitude is used to numerically simulate the transition to turbulence. Linear quadratic Gaussian controllers based on reduced-order models of the linearized Navier-Stokes equations are designed, where the wall sensors and the actuators are localized in space. A parametric analysis is carried out in the nonlinear regime, for different disturbance amplitudes, by investigating the effects of the actuation on the flow due to different distributions of the localized actuators along the spanwise direction, different sizes of the actuators and the effort of the controllers. We identify the range of parameters where the controllers are effective and highlight the limits of the device for high amplitudes and strong control action. Despite the fully linear control approach, it is shown that the device is effective in delaying the onset of laminar-turbulent transition in the presence of packets characterized by amplitudes a approximate to 1% of the free stream velocity at the actuator location. Up to these amplitudes, it is found that a proper choice of the actuators positively affects the performance of the controller. For a transitional case, a approximate to 0.20 %, we show a transition delay of Delta Re-x = 3 .0 x 10(5).

Keyword
boundary layers, boundary layer control, flow control, instability
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-117917 (URN)10.1017/jfm.2013.299 (DOI)000324425800016 ()
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note

QC 20131017. Updated from submitted to published.

Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2017-12-06Bibliographically approved
3. Riccati-less approach for optimal control and estimation: An application in 2D Boundary Layers
Open this publication in new window or tab >>Riccati-less approach for optimal control and estimation: An application in 2D Boundary Layers
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The control of Tollmien-Schlichting (TS) in a 2D boundary layer is analysed by using numerical simulations. Full-dimensional optimal controllers are used in combination with a set-up of spatially localised inputs (actuators and disturbance) and outputs (sensors).

The Adjoint of the Direct-Adjoint (ADA) algorithm, recently proposed by Pralits & Luchini (2010), is used to efficiently compute the linear quadratic Regulator (LQR) controller; the method is iterative and allows to by-pass the solution of the corresponding Riccati equation, unfeasible for high-dimensional systems. We show that an analogous iteration can be cast for the estimation problem; the dual algorithm is referred to as Adjoint of the Adjoint-Direct (AAD). By combining the solutions of the estimation and control problem, full dimensional, model-free, linear gaussian Quadratic (LQG) controllers are obtained and used for the attenuation of the disturbances arising in the boundary layer flow.

The full dimensional controllers turn out to be an excellent benchmark for evaluating the performance of the optimal control/estimation design based on open-loop model reduction. We show the conditions under which the two strategies are in perfect agreement by focusing on the issues arising when feedback configurations are considered. An analysis of the finite amplitude disturbances is also carried out by addressing the limitations of the optimal controllers, the role of the estimation and the robustness to the nonlinearities arising in the flow of the control design.

National Category
Other Engineering and Technologies not elsewhere specified
Identifiers
urn:nbn:se:kth:diva-117912 (URN)
Note

QS 2013

Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2013-02-07Bibliographically approved
4. Feedback control of instabilities in the two-dimensional Blasius boundary layer: The role of sensors and actuators
Open this publication in new window or tab >>Feedback control of instabilities in the two-dimensional Blasius boundary layer: The role of sensors and actuators
2013 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 25, no 5, 054106-1-054106-17 p.Article in journal (Refereed) Published
Abstract [en]

We analyze the effects of different types and positions of actuators and sensors on controllers' performance and robustness in the linearized 2D Blasius boundary layer. The investigation is carried out using direct numerical simulations (DNS). To facilitate controller design, we find reduced-order models from the DNS data using a system identification procedure called the Eigensystem Realization Algorithm. Due to the highly convective nature of the boundary layer and corresponding time delays, the relative position of the actuator and sensor has a strong influence on the closed-loop dynamics. We address this issue by considering two different configurations. When the sensor is upstream of the actuator, corresponding to disturbance-feedforward control, good performance is observed, as in previous work. However, feedforward control can be degraded by additional disturbances or uncertainties in the plant model, and we demonstrate this. We then examine feedback controllers in which the sensor is a short distance downstream of the actuator. Sensors farther downstream of the actuator cause inherent time delays that limit achievable performance. The performance of the resulting feedback controllers depends strongly on the form of actuation introduced, the quantities sensed, and the observability of the structures deformed by the controller's action. These aspects are addressed by varying the spatial distribution of actuator and sensor. We find an actuator-sensor pair that is well-suited for feedback control, and demonstrate that it has good performance and robustness, even in the presence of unmodeled disturbances.

Keyword
Achievable performance, Actuators and sensors, Blasius boundary layer, Eigensystem realization algorithms, Reduced order models, Sensors and actuators, System identification procedure, Unmodeled disturbances
National Category
Other Engineering and Technologies not elsewhere specified
Identifiers
urn:nbn:se:kth:diva-117913 (URN)10.1063/1.4804390 (DOI)000320001200034 ()2-s2.0-84878528673 (Scopus ID)
Note

QC 20131202. Updated from submitted to published. Previous title: Feedback control of instabilities in the 2D Blasius boundary layer : the role of sensors and actuators

Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2017-12-06Bibliographically approved
5. Output feedback control of flow on a flat plate past a leading edge using plasma actuators
Open this publication in new window or tab >>Output feedback control of flow on a flat plate past a leading edge using plasma actuators
(English)In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385XArticle in journal (Refereed) Accepted
Abstract [en]

The evolution and control of a two dimensional (2D) wavepacket developing on a flat plate with a leading edge is investigated by means of direct numerical simulation (DNS).

The aim is to identify and suppress the wavepackets generated by freestream perturbations. A sensor is placed close to the wall in order to detect the upcoming wavepacket, while an actuator is placed further downstream to control it. A plasma actuator is modelled as an external forcing on the flow using a model based and validated on experimental investigations. A Linear Quadratic Gaussian (LQG) controller is designed and an output projection is used to build the objective function. Moreover, by appropriate selection of the Proper Orthogonal Decomposition (POD) modes, we identify the disturbances to be damped. A reduced-order model of the input-output system is constructed by using system identification via the Eigensystem Realization Algorithm (ERA) algorithm.

A limitation of the plasma actuators is the uni-directional forcing of the generated wall jet, which is predetermined by the electrodes location. In this paper, we address this limitation by proposing and comparing two different solutions: i) by introducing an offset in the control signal such that the resulting total forcing is oriented along one direction; ii) by using two plasma actuators acting in opposite directions. The results are compared with the ideal case where constraints are not accounted for the control design. We show that the resulting controllers based on plasma actuators can successfully attenuate the amplitude of the wavepacket developing inside the boundary layer.

National Category
Other Engineering and Technologies not elsewhere specified
Identifiers
urn:nbn:se:kth:diva-117914 (URN)
Note

QP 2013

Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2017-12-06Bibliographically approved
6. Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and Koopman modes
Open this publication in new window or tab >>Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and Koopman modes
2012 (English)In: Experiments in Fluids, ISSN 0723-4864, E-ISSN 1432-1114, Vol. 53, no 5, 1203-1220 p.Article in journal (Refereed) Published
Abstract [en]

We present a comparative analysis of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) computed from experimental data of a turbulent, quasi 2-D, confined jet with co-flow (Re = 11,500, co-flow ratio inner-to-outer flow approximate to 2:1). The experimental data come from high-speed 2-D particle image velocimetry. The flow is fully turbulent, and it contains geometry-dependent large-scale coherent structures; thus, it provides an interesting benchmark case for the comparison between POD and DMD. In this work, we address issues related to snapshot selections (1), convergence (2) and the physical interpretation (3) of both POD and DMD modes. We found that the convergence of POD modes follows the criteria of statistical convergence of the autocovariance matrix. For the computation of DMD modes, we suggest a methodology based on two criteria: the analysis of the residuals to optimize the sampling parameters of the snapshots, and a time-shifting procedure that allows us to identify the spurious modes and retain the modes that consistently appear in the spectrum. These modes are found to be the ones with nearly null growth rate. We then present the selected modes, and we discuss the way POD and DMD rank them. POD analysis reveals that the most energetic spatial structures are related to the large-scale oscillation of the inner jet (flapping); from the temporal analysis emerges that these modes are associated with a low-frequency peak at St = 0.02. At this frequency, DMD identifies a similar mode, where oblique structures from the walls appear together with the flapping mode. The second most energetic group of modes identified is associated with shear-layer oscillations, and to a recirculation zone near the inner jet. Temporal analysis of these modes shows that the flapping of the inner jet might be sustained by the recirculation. In the DMD, the shear-layer modes are separated from the recirculation modes. These have large amplitudes in the DMD. In conclusion, the DMD modes with eigenvalues on the unit circle are found to be similar to the most energetic POD modes, although differences appear due to the fact that DMD isolates structures associated with one frequency only.

Keyword
Coherent Structures, Flows, Field
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-107078 (URN)10.1007/s00348-012-1354-9 (DOI)000310643600003 ()2-s2.0-84868617830 (Scopus ID)
Note

QC 20121207

Available from: 2012-12-07 Created: 2012-12-06 Last updated: 2017-12-07Bibliographically approved

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