Abstract
We present spectral analysis modal methods (SAMMs) to perform POD in the frequency domain using non-time-resolved particle image velocity (PIV) data combined with unsteady surface pressure measurements. In particular, time-resolved unsteady surface pressure measurements are synchronized with non-time-resolved planar PIV measurements acquired at 15 Hz in a Mach 0.6 cavity flow. Leveraging the spectral linear stochastic estimation (LSE) method of Tinney et al. (Exp Fluids 41:763–775, 2006), we first estimate the cross-correlations between the velocity field and the unsteady pressure sensors via sequential time shifts, followed by a Fast Fourier transform to obtain the pressure–velocity cross spectral density matrix. This leads to a linear multiple-input/multiple-output (MIMO) model that determines the optimal transfer functions between the input cavity wall pressure and the output velocity field. Two variants of SAMMs are developed and applied. The first, termed “SAMM-SPOD”, combines the MIMO model with the SPOD algorithm of Towne et al. (J Fluid Mech, https://doi.org/10.1017/jfm.2018.283, 2018). The second, called “SAMM-RR”, adds independent sources and uses a sorted eigendecomposition of the input pressure cross-spectral matrix to enable an efficient reduced-rank eigendecomposition of the velocity cross-spectral matrix. In both cases, the resulting rank-1 POD eigenvalues associated with the Rossiter frequencies exhibit very good agreement with those obtained using independent time-resolved PIV measurements. The results demonstrate that SAMMs provide a methodology to perform space-time POD without requiring a high-speed PIV system, while avoiding potential pitfalls associated with traditional time-domain LSE.
Graphic abstract
Similar content being viewed by others
References
Adrian RJ (1979) Conditional eddies in isotropic turbulence. Phys Fluids 22(11):2065–2070
Alkislar MB (2001) Flow field measurements in a screeching rectangular jet. Florida State University, Tallahassee
Arunajatesan S, Kannepalli C, Ukeiley L (2007) Three dimensional stochastic estimation applied to cavity flow fields. In: 37th AIAA fluid dynamics conference and exhibit. https://doi.org/10.2514/6.2007-422
Bendat JS, Piersol AG (2011) Random data, 4th edn. Wiley, New York
Berkooz G, Holmes P, Lumley JL (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Annu Rev Fluid Mech 25(1):539–575
Clark H, Naghib-Lahouti A, Lavoie P (2014) General perspectives on model construction and evaluation for stochastic estimation, with application to a blunt trailing edge wake. Exp Fluids. https://doi.org/10.1007/s00348-014-1756-y
Durgesh V, Naughton JW (2010) Multi-time-delay LSE-pod complementary approach applied to unsteady high-Reynolds-number near wake flow. Exp Fluids 49:571–583
Ewing D (1999) Examination of a LSE/POD complementary technique using single and multi-time information in the axisymmetric shear layer. In: IUTAM symposium on simulation and identification of organized structures in flows, vol 52, pp 375–384
George WK (1988) Insight into the dynamics of coherent structures from a proper orthogonal decomposition. In: Symposium on Near Wall Turbulence, Dubrovnik, Yugoslavia
Graham J, Kanov K, Yang XIA, Lee M, Malaya N, Lalescu CC, Burns R, Eyink G, Szalay A, Moser RD, Meneveau C (2015) A Web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES. J Turbul 17(2):181–215. https://doi.org/10.1080/14685248.2015.1088656
Griffin J, Schultz T, Holman R, Ukeiley LS, Cattafesta LN (2010) Application of multivariate outlier detection to fluid velocity measurements. Exp Fluids 49(1):305–317. https://doi.org/10.1007/s00348-010-0875-3
Heller H, Holmes D, Covert E (1971) Flow-induced pressure oscillations in shallow cavities. J Sound Vib 18(4):545–553. https://doi.org/10.1016/0022-460x(71)90105-2
Krishna CV, Wang M, Hemati MS, Luhar M (2020) Reconstructing the time evolution of wall-bounded turbulent flows from non-time-resolved PIV measurements. Phys Rev Fluids 5(5):054604. https://doi.org/10.1103/physrevfluids.5.054604
Lumley JL (1967) The structure of inhomogeneous turbulent flows. In: Yaglom AM, Tatarski VI (eds) Proceedings of the international colloquium on the fine scale structure of the atmosphere and its influence on radio wave propagation. Doklady Akademii Nauk SSSR, Nauka, Moscow
McKeon BJ, Sharma AS (2010) A critical-layer framework for turbulent pipe flow. J Fluid Mech 658:336–382. https://doi.org/10.1017/s002211201000176x
Pinnau R (2008) Model reduction via proper orthogonal decomposition. Springer, Berlin, pp 95–109
Schmidt OT, Colonius T (2020) Guide to spectral proper orthogonal decomposition. AIAA J 58(3):1023–1033. https://doi.org/10.2514/1.j058809
Schmid PJ, Li L, Juniper MP, Pust O (2010) Applications of the dynamic mode decomposition. Theor Comput Fluid Dyn 25(1):249–259
Singh S, Ukeiley L (2020) Proper orthogonal decomposition of high-speed particle image velocimetry in an open cavity. AIAA J 58(7):1–16. https://doi.org/10.2514/1.j059046
Sirovich L (1987) Turbulence and the dynamics of coherent structures, part I–III. Q Appl Math 45(3):561–590
Taira K, Brunton SL, Dawson STM, Rowley CW, Colonius T, McKeon BJ, Schmidt OT, Gordeyev S, Theofilis V, Ukeiley LS (2017) Modal analysis of fluid flows: an overview. AIAA J 55(12):4013–4041. https://doi.org/10.2514/1.j056060
Taira K, Hemati MS, Brunton SL, Sun Y, Duraisamy K, Bagheri S, Dawson STM, Yeh CA (2019) Modal analysis of fluid flows: applications and outlook. AIAA J 22(11):1–25. https://doi.org/10.2514/1.j058462
Taylor JA, Glauser MN (2004) Towards practical flow sensing and control via POD and LSE based low-dimensional tools. J Fluids Eng 126(3):337–345. https://doi.org/10.1115/1.1760540
Tinney CE, Coiffet F, Delville J, Hall AM, Jordan P, Glauser MN (2006) On spectral linear stochastic estimation. Exp Fluids 41(5):763–775. https://doi.org/10.1007/s00348-006-0199-5
Towne A, Schmidt OT, Colonius T (2018) Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J Fluid Mech. https://doi.org/10.1017/jfm.2018.283
Tu JH, Griffin J, Hart A, Rowley CW, Cattafesta LN, Ukeiley LS (2013) Integration of non-time-resolved PIV and time-resolved velocity point sensors for dynamic estimation of velocity fields. Exp Fluids 54(2):1429
Tu JH, Rowley CW, Kutz JN, Shang JK (2014) Spectral analysis of fluid flows using sub-nyquist-rate PIV data. Exp Fluids 55(9):297. https://doi.org/10.1007/s00348-014-1805-6
Westerweel J, Scarano F (2005) Universal outlier detection for PIV data. Exp Fluids 39(6):1096–1100. https://doi.org/10.1007/s00348-005-0016-6
Zhang Y, Cattafesta L, Ukeiley L (2019a) A spectral analysis modal method applied to cavity flow oscillations. In: 11th international symposium on turbulence and shear flow phenomena (TSFP11), UK
Zhang Y, Sun Y, Arora N, Cattafesta III LN, Taira K, Ukeiley LS (2019b) Suppression of cavity flow oscillations via three-dimensional steady blowing. AIAA J 57(1):90–105. https://doi.org/10.2514/1.j057012
Acknowledgements
This research was supported by the US Air Force Office of Scientific Research (Grant FA9550-17-1-0380, Program Manager: Dr. Gregg Abate). The authors also gratefully acknowledge fruitful conversations with Profs. Peter Schmidt and Kunihiko Taira.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhang, Y., Cattafesta, L.N. & Ukeiley, L. Spectral analysis modal methods (SAMMs) using non-time-resolved PIV. Exp Fluids 61, 226 (2020). https://doi.org/10.1007/s00348-020-03057-8
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-020-03057-8