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Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and Koopman modes
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
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.

Place, publisher, year, edition, pages
2012. Vol. 53, no 5, 1203-1220 p.
Keyword [en]
Coherent Structures, Flows, Field
National Category
Other Materials Engineering
URN: urn:nbn:se:kth:diva-107078DOI: 10.1007/s00348-012-1354-9ISI: 000310643600003ScopusID: 2-s2.0-84868617830OAI: diva2:575171

QC 20121207

Available from: 2012-12-07 Created: 2012-12-06 Last updated: 2013-02-07Bibliographically approved
In thesis
1. Active Control and Modal Structures in Transitional Shear Flows
Open this publication in new window or tab >>Active Control and Modal Structures in Transitional Shear Flows
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.
Trita-MEK, ISSN 0348-467X ; 2013:03
Flow control, flat-plate boundary layer, optimal controllers, model reduction, turbulent jet, POD, DMD, Koopman modes
National Category
Fluid Mechanics and Acoustics
urn:nbn:se:kth:diva-117916 (URN)978-91-7501-640-5 (ISBN)
Public defence
2013-02-22, Sal E3, Osquars Backe 14, KTH, Stockholm, 10:15 (English)

QC 20130207

Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2013-02-07Bibliographically approved

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