Abstract
This study investigated the performance of proper orthogonal decomposition (POD), discrete Fourier transformation (DFT), time-domain spectral proper orthogonal decomposition (td-SPOD), and frequency-domain spectral proper orthogonal decomposition (fd-SPOD) in the identification of the multi-dominant coherent structures of flow fields. All decompositions were conducted using experimental datasets of swirling jets obtained by tomographic particle image velocimetry (Tomo-PIV), with swirl numbers (S) of 0.0, 0.41, and 0.87 and a Reynolds number fixed at 3000. Mode decomposition, temporal flow dynamics, and the low-rank reconstruction of three-dimensional (3D) swirling jets by POD, td-SPOD, DFT, and fd-SPOD were compared. POD, td-SPOD, and DFT were implemented using the fd-SPOD framework with various filter sizes, and fd-SPOD was executed by data blocking, Fourier transformation, and POD. Modal analysis of the non-swirl jet indicates that POD, DFT, and td-SPOD did not provide sufficiently clear structures, whereas fd-SPOD performed best in identifying ring-like vortex structures and vortex ring merging. The temporal flow dynamics of a low-swirl jet with S = 0.41 show that td-SPOD improved the correlation of the mode time coefficient in linked modes and provided temporal flow dynamics that enabled monitoring of the flow process. The interactions between the double-helix structure at a Strouhal number (St) of 0.26 and the single-helix structure at St = 0.13 could be analyzed in the time evolution provided by td-SPOD. The fd-SPOD and td-SPOD for the swirl jet at S = 0.87 were directly related through a Fourier transform, and the first several modal pairs with the highest harmonic correlation intensity obtained by td-SPOD agree with the most energetic first-order mode at each frequency obtained by fd-SPOD. The reconstruction of the 3D flow field from the low-order modes shows that POD was suitable for denoising the flow field with reconstruction of the flow field through mode truncation. Overall, the results reveal that td-SPOD is suitable for investigating mode interactions between various wavelengths and the time-dynamic evolution of modes, whereas fd-SPOD is suitable for mode extraction with strict separation of the modes according to frequency.
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Acknowledgements
The authors thank Moritz Sieber for stimulating discussions and the generous provision of the open-source td-SPOD framework and Towne and Schmidt et al. for sharing the fd-SPOD code in GitHub. Financial support from the National Natural Science Foundation of China (11725209, 12002208) and the Natural Science Foundation of Shanghai (20ZR1425700) is gratefully acknowledged.
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This work was supported by the National Natural Science Foundation of China (11725209, 12002208) and the Natural Science Foundation of Shanghai (20ZR1425700).
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XZ and YZ did this experiment and analyzed experimental data; XZ wrote the main manuscript text and plotted all figures. CH guided the methods of experimental measurement and data analysis, and revised the paper. YL provided the overall idea of the paper and experiment. All authors reviewed the manuscript.
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Zeng, X., Zhang, Y., He, C. et al. Time- and frequency-domain spectral proper orthogonal decomposition of a swirling jet by tomographic particle image velocimetry. Exp Fluids 64, 5 (2023). https://doi.org/10.1007/s00348-022-03542-2
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DOI: https://doi.org/10.1007/s00348-022-03542-2