Time- and frequency-domain spectral proper orthogonal decomposition of a swirling jet by tomographic particle image velocimetry

• Published in: Experiments in fluids 2023, Vol.64 (1), Article 5
• Main Authors: Zeng, Xin, Zhang, Yuyao, He, Chuangxin, Liu, Yingzheng
• Format: Article
• Language: English
• Subjects: Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Evolution; Fluid flow; Fluid- and Aerodynamics; Fourier transforms; Frequency domain analysis; Heat and Mass Transfer; Image reconstruction; Modal analysis; Particle image velocimetry; Proper Orthogonal Decomposition; Research Article; Reynolds number; Strouhal number; Swirling; Three dimensional flow; Vortex rings
• ISSN: 0723-4864; 1432-1114
• DOI: 10.1007/s00348-022-03542-2

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. Graphical abstract