Abstract
Coherent structures are generally three-dimensional (3D), and while this information may be readily available from numerical simulations, obtaining 3D time resolved measurements might be technically challenging. We present a methodology to produce 3D kinematic tomographies of spatially localized coherent structures from two-dimensional sequences of snapshots. The method operates by synchronizing modal decompositions of multiple independent Particle Image Velocimetry (PIV) scans of a given flow volume. The volume should be scanned in pairs of simultaneous planes, one of which is taken as sync reference. The case study is a rectangular channel partially obstructed by a permeable media showing a linear instability producing periodic waves. The volume of interest is the downstream-facing permeable step generated by the end of the permeable media. The method is first verified using 3D numerical simulation results produced with a lattice Boltzmann scheme, comparing the kinematic tomography against the complete 3D dataset. Then the method is applied to actual experimental measurements with excellent result, which reveals non-trivial 3D features of the dominating coherent structures.
Graphical Abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data that support the findings of this study as well as the scripts used for the method implementation are available from the corresponding author upon reasonable request.
References
Antonia RA (1981) Conditional sampling in turbulence measurement. Annu Rev Fluid Mech 13(1):131–156. https://doi.org/10.1146/annurev.fl.13.010181.001023
Arroyo MP and Hinsch KD (2008) Recent developments of PIV towards 3D measurements. In: Particle image velocimetry: new developments and recent applications. Springer, Berlin, Heidelberg (Topics in Applied Physics) 127–154 https://doi.org/10.1007/978-3-540-73528-1_7.
Berkooz G, Holmes P, Lumley JL (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Annu Rev Fluid Mech 25:539–575
Boroni G, Dottori J, Rinaldi P (2017) FULL GPU implementation of lattice-Boltzmann methods with immersed boundary conditions for fast fluid simulations. The Int J Multiphys 11(1):1–14
Boroni G, Silin N, Clausse A (2020) A python implementation in graphic processing unit of a lattice Boltzmann model for unstable three-dimensional flows in immersed permeable media. Phys Fluids 32(12):127107. https://doi.org/10.1063/5.0032630
Boroni G et al (2015) Lattice-Boltzmann modeling of unstable flows amid arrays of wires. Comput Fluids 120:37–45. https://doi.org/10.1016/j.compfluid.2015.07.026
Braud C et al (2004) Analysis of the wake–mixing-layer interaction using multiple plane PIV and 3D classical POD. Exp Fluids 37(1):95–104
Braud C et al (2002) Investigation of a plane mixing layer-wake interaction by means of two 2D PIV planes and of POD. In: 11th international symposium on applications of laser techniques to fluid mechanics, Lisbon, PRT, 8–11 juillet 2002, 15 https://hal.inrae.fr/hal-02581117. Accessed 6 May 2021
Brücker C (1997) 3D scanning PIV applied to an air flow in a motored engine using digital high-speed video. Meas Sci Technol 8(12):1480. https://doi.org/10.1088/0957-0233/8/12/011
Clausse A, Silin N, Boroni G (2019) A multiscale method for producing homogenized drag laws of a permeable medium by conflating experimental data with Lattice-Boltzmann simulations. Int J Numer Meth Heat Fluid Flow 29(11):4394–4407. https://doi.org/10.1108/HFF-01-2019-0058
Decker AJ (1986) Evaluation of diffuse- illumination holographic cinematography in a flutter cascade. NASA Technical Paper 2593:33
Dellacasagrande M et al (2021) Mixed LSE and EPOD based technique for multi-plane PIV measurements synchronization in separated flow condition. Exp Thermal Fluid Sci 122:110313. https://doi.org/10.1016/j.expthermflusci.2020.110313
Drew B, Charonko J and Vlachos PP (2015) Qi-Quantitative imaging (PIV and more), SourceForge https://sourceforge.net/projects/qi-tools/.Accessed 6 Aug 2019
Druault P, Chaillou C (2007) Use of Proper Orthogonal Decomposition for reconstructing the 3D in-cylinder mean-flow field from PIV data. Comptes Rendus Méc 335(1):42–47. https://doi.org/10.1016/j.crme.2006.11.004
Hess D et al (2011) Single-view volumetric PIV using high-resolution scanning and least squares matching. In: Proceedings of the 9TH International Symposium on Particle Image Velocimetry–PIV’11. 9TH International Symposium On Particle Image Velocimetry–PIV’11, kobe, Japan 7
Higham JE, Brevis W, Keylock CJ (2018) Implications of the selection of a particular modal decomposition technique for the analysis of shallow flows. J Hydraul Res 56(6):796–805
Higham JE et al (2017) Using modal decompositions to explain the sudden expansion of the mixing layer in the wake of a groyne in a shallow flow. Adv Water Resour 107:451–459. https://doi.org/10.1016/j.advwatres.2017.05.010
Higham JE et al (2021) Modification of modal characteristics in wakes of square cylinders with multi-scale porosity. Phys Fluids 33(4):045117. https://doi.org/10.1063/5.0049528
Holmes P et al (2012) Turbulence, coherent structures, dynamical systems and symmetry | nonlinear science and fluid dynamics. (Cambridge Monographs on Mechanics). https://www.cambridge.org/ar/academic/subjects/physics/nonlinear-science-and-fluid-dynamics/turbulence-coherent-structures-dynamical-systems-and-symmetry-2nd-edition, https://www.cambridge.org/ar/academic/subjects/physics/nonlinear-science-and-fluid-dynamics. Accessed 8 Dec 2021
Hussain AKMF (1986) Coherent structures and turbulence. J Fluid Mech 173:303–356. https://doi.org/10.1017/S0022112086001192
Keller Y, Averbuch A, Miller O (2004) Robust phase correlation. ICPR 2:740–743
Lawson JM, Dawson JR (2014) A scanning PIV method for fine-scale turbulence measurements. Exp Fluids 55(12):1857. https://doi.org/10.1007/s00348-014-1857-7
Noack BR (2016) From snapshots to modal expansions–bridging low residuals and pure frequencies. J Fluid Mech 802:1–4. https://doi.org/10.1017/jfm.2016.416
Noack BR et al (2016) Recursive dynamic mode decomposition of transient and post-transient wake flows. J Fluid Mech 809:843–872. https://doi.org/10.1017/jfm.2016.678
Norouzi S et al (2021) Flow examination in abdominal aortic aneurysms: reduced-order models driven by in vitro data and spectral proper orthogonal decomposition. Phys Fluids 33(11):111708. https://doi.org/10.1063/5.0069560
Partridge JL, Lefauve A, Dalziel SB (2019) A versatile scanning method for volumetric measurements of velocity and density fields. Meas Sci Technol 30(5):055203. https://doi.org/10.1088/1361-6501/ab0bfd
Perrin R et al. (2006) Phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD. In: Proceedings of the 13th International Symposium Applications of Laser Techniques to Fluid Mechanics. Lisbon, Portugal
Pick S, Lehmann F-O (2009) Stereoscopic PIV on multiple color-coded light sheets and its application to axial flow in flapping robotic insect wings. Exp Fluids 47(6):1009. https://doi.org/10.1007/s00348-009-0687-5
Raffel M et al (2018) Particle image velocimetry: a practical guide. Springer, Berlin
Rowley CW, Dawson STM (2017) Model reduction for flow analysis and control. Annu Rev Fluid Mech 49(1):387–417. https://doi.org/10.1146/annurev-fluid-010816-060042
Rowley CW et al (2009) Spectral analysis of nonlinear flows. J Fluid Mech 641:115–127. https://doi.org/10.1017/S0022112009992059
Schmid PJ (2010) Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 656:5–28. https://doi.org/10.1017/S0022112010001217
Schmidt OT, Schmid PJ (2019) A conditional space–time POD formalism for intermittent and rare events: example of acoustic bursts in turbulent jets. J Fluid Mech 867:R2. https://doi.org/10.1017/jfm.2019.200
Silin N et al (2011) Flow instabilities between two parallel planes semi-obstructed by an easily penetrable porous medium. J Fluid Mech 689:417–433. https://doi.org/10.1017/jfm.2011.422
Sirovich L (1987) Turbulence and the dynamics of coherent structures. i. coherent structures. Q Appl Math 45(3):561–571
Taira K et al (2017) Modal analysis of fluid flows: an overview. AIAA J 55(12):4013–4041. https://doi.org/10.2514/1.J056060
Tang T, et al (2019) The formation mechanism of recirculating wake for steady flow through and around arrays of cylinders. Phys Fluids 31(4):043607. https://doi.org/10.1063/1.5090817
Tokovinin A et al (2001) Optimized modal tomography in adaptive optics. Astron Astrophys 378(2):710–721. https://doi.org/10.1051/0004-6361:20011213
Towne A, Schmidt OT, Colonius T (2018) Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J Fluid Mech 847:821–867. https://doi.org/10.1017/jfm.2018.283
Tropea C, Yarin AL, Foss JF (eds) (2007) Handbook of experimental fluid mechanics. Springer, Berlin
Vernet R, Thomas L, David L (2009) Analysis and reconstruction of a pulsed jet in crossflow by multi-plane snapshot POD. Exp Fluids 47(4):707. https://doi.org/10.1007/s00348-009-0730-6
Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8(12):1379. https://doi.org/10.1088/0957-0233/8/12/002
Xiong J et al. (2018) ‘Reconfigurable rainbow PIV for 3D flow measurement’, In: 2018 IEEE International Conference on Computational Photography (ICCP). 2018 IEEE International Conference on Computational Photography (ICCP) https://doi.org/10.1109/ICCPHOT.2018.8368475.
Acknowledgements
The authors wish to thank Diego Dalponte for the construction of the test section.
Funding
The experimental work was partly funded by the Secretaría de Investigación, Internacionales y Posgrado research project number 06/C595.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no conflicts of interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Silin, N., Boroni, G.A., Higham, J.E. et al. Kinematic tomography of oscillatory coherent structures through synchronized mode decomposition. J Vis 26, 563–576 (2023). https://doi.org/10.1007/s12650-022-00902-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12650-022-00902-2