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Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and Koopman modes

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Abstract

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 ≈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.

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Acknowledgments

Gabriele Bellani and Fredrik Lundell thank the Swedish energy agency for funding. Computer time was provided by SNIC (Swedish National Infrastructure for Computing). We also wish to acknowledge the following persons: Prof. Hiroshi Higuchi for helpful discussion on the design and development of the experimental setup, as well as comments on the analysis of the experimental results; Dr. Ramis Örlü for helpful comments and suggestions on the manuscript; Dr. Shervin Bagheri, Dr. Francesco Picano and Dr. Johan Malm for fruitful discussions.

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  1. Gabriele Bellani

    Present address: Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720, USA

Authors and Affiliations

  1. Linné Flow Centre, KTH Mechanics, Osquars Backe 18, 100 44, Stockholm, Sweden

    Onofrio Semeraro, Gabriele Bellani & Fredrik Lundell

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  1. Onofrio Semeraro
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  2. Gabriele Bellani
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  3. Fredrik Lundell
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Correspondence to Onofrio Semeraro.

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Semeraro, O., Bellani, G. & Lundell, F. Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and Koopman modes. Exp Fluids 53, 1203–1220 (2012). https://doi.org/10.1007/s00348-012-1354-9

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