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Flow field around a vibrating cantilever: coherent structure eduction by continuous wavelet transform and proper orthogonal decomposition

Published online by Cambridge University Press:  08 February 2011

Y.-H. KIM ,
C. CIERPKA  and
S. T. WERELEY
Y.-H. KIM
Affiliation:
Energy Business Department, Growth and Investment Division, POSCO, 892 Daechi 4-dong Gangnam-gu, Seoul 135-777, South Korea
C. CIERPKA*
Affiliation:
Institute for Fluid Dynamics and Aerodynamics, University of the Federal Arms Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
S. T. WERELEY
Affiliation:
Department of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-1288, USA
*
†Email address for correspondence: [email protected]
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Abstract

The velocity field around a vibrating cantilever plate was experimentally investigated using phase-locked particle image velocimetry. Experiments were performed at Reynolds numbers of Reh = 101, 126 and 146 based on the tip amplitude and the speed of the cantilever. The averaged vector fields indicate a pseudo-jet flow, which is dominated by vortical structures. These vortical structures are identified and characterized using the continuous wavelet transform. Three-dimensional flow features are also clearly revealed by this technique. Furthermore, proper orthogonal decomposition was used to investigate regions of vortex production and breakdown. The results show clearly that the investigation of phase-averaged data hides several key flow features. Careful data post-processing is therefore necessary to investigate the flow around the vibrating cantilever and similar highly transient periodic flows.

JFM classification

Wakes/Jets: Shear layers Vortex Flows: Vortex dynamics Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 584 - 606
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

The first and the second author contributed equally to the paper.

References

REFERENCES

Acikalin, T., Raman, A. & Garimella, S. V. 2003 Two-dimensional streaming flows induced by resonating thin beams. J. Acoust. Soc. Am. 114, 1785–1795.CrossRefGoogle ScholarPubMed
Acikalin, T., Wait, S. M., Garimella, S. V. & Raman, A 2004 Experimental investigation of the thermal performance of piezoelectric fans. Heat. Transfer Engng 25, 4–14.Google Scholar
Adrian, R. J. 1996 Stochastic Estimation of the Structure of Turbulent Fields, pp. 145–195. Springer.Google Scholar
Berkooz, G., Holmes, P. J. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539–575.CrossRefGoogle Scholar
Bernero, S. & Fiedler, H. E. 2000 Application of particle image velocimetry and proper orthogonal decomposition to the study of a jet in counterflow. Exp. Fluids 29 (Suppl.), S274–S281.Google Scholar
Bonnet, J. P., Delville, J., Glauser, M. N., Antonia, R. A., Bisset, D. K., Cole, D. R., Fiedler, H. E., Garem, J. H., Hilberg, D., Jeong, J., Kevlahan, N. K. R., Ukeiley, L. S. & Vincendeau, E. 1998 Collaborative testing of eddy structure identification methods in free turbulent shear flows. Exp. Fluids 25, 197–225.Google Scholar
Bourguet, R. & Braza, M. 2007 Reduced order modeling for unsteady transonic flows around an airfoil. Phys. Fluids 19, 111701.Google Scholar
Braud, C., Heitz, D., Braud, P., Arroyo, G. & Delville, J. 2004 Analysis of the wake-mixing-layer interaction using multiple plane PIV and 3D classical POD. Exp. Fluids 37, 95–104.CrossRefGoogle Scholar
Burmann, P., Raman, A. & Garimella, S. V. 2002 Dynamics and topology optimization of piezoelectric fans. IEEE Trans. Compon. Packag. Manuf. Technol. 25, 592–600.CrossRefGoogle Scholar
Cierpka, C., Weier, T. & Gerbeth, G. 2008 Evolution of vortex structures in an electromagnetically excited separated flow. Exp. Fluids 45, 943–953.Google Scholar
Cordier, L. & Bergmann, M. 2003 Proper orthogonal decomposition, an overview. In VKI LS 2003-03, Post-Processing of Experimental and Numerical Data (ed. Millan, P. & Riethmuller, M.L.), pp. 1–45. Von Kármán Institute for Fluid Dynamics.Google Scholar
Delville, J., Ukeiley, L., Cordier, L., Bonnet, J. P. & Glauser, M. 1999 Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition. J. Fluid Mech. 391, 91–122.Google Scholar
Farge, M. 1992 Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395–457.CrossRefGoogle Scholar
Hilberg, D., Lazi, W. & Fielder, H. E. 1994 The application of classical POD and snapshot POD in a turbulent shear layer with periodic structures. Appl. Sci. Res. 53, 283–290.Google Scholar
Holmes, P. J., Lumley, J. L., Berkooz, G., Mattingly, J. C. & Wittenberg, R. W. 1997 Low-dimensional models of coherent structures in turbulence. Phys. Rep. 287 (4), 337–384.Google Scholar
Ihara, A. & Watanabe, H. 1994 On the flow around flexible plates, oscillating with large amplitude. J. Fluids Struct. 8, 601–619.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google Scholar
Kim, Y-H., Wereley, S. T. & Chun, C-H. 2004 Phase-resolved flow field produced by a vibrating cantilever plate between two endplates. Phys. Fluids 16, 145–162.Google Scholar
Kimber, M. & Garimella, S. V. 2009 Measurement and prediction of the cooling characteristics of a generalized vibrating piezoelectric fan. Intl J. Heat Mass Transfer 52, 4470–4478.Google Scholar
Kostas, J., Soria, J. & Chong, M. S. 2005 A comparison between snapshot POD analysis of PIV velocity and vorticity data. Exp. Fluids 38, 146–160.Google Scholar
Lima, C. R., Vatanabe, S. L., Choi, A., Nakasone, P. H., Pires, R. F. & Silva, C. N. 2009 A biomimetic piezoelectric pump: Computational and experimental characterization. Sensors Actuator A 152, 110–118.Google Scholar
Linderman, R. J., Sett, S. & Bright, V. M. 2001 The resonant micro fan for fluidic transport, mixing and particle filtering. In 2001 ASME International Mechanical Engineering Congress and Exposition, New York.Google Scholar
Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation (2nd edn) (ed. Yaglom, A.M. & Tatarski, V.I.), pp. 166–178. Nauka, Moscow.Google Scholar
Raffel, M., Willert, C. E., Wereley, S. T. & Kompenhans, J. 2007 Particle Image Velocimetry. A Practical Guide. Springer.CrossRefGoogle Scholar
Schram, C., Rambaud, P. & Riethmuller, M. L. 2004 Wavelet based eddy structure eduction from a backward facing step flow investigated using particle image velocimetry. Exp. Fluids 36, 233–245.CrossRefGoogle Scholar
Siegel, S., Cohen, K., Seidel, J. & McLaughlin, T. 2007 State estimation of transient flow fields using double proper orthogonal decomposition. Notes Numer. Fluid Mech. Multidiscip. Des. 95, 105–118.Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part I. Coherent structures. Q. Appl. Maths 45, 561–571.Google Scholar
Smith, T. R., Moehlis, J. & Holmes, P. J. 2005 Low-dimensional modeling of turbulence using the proper orthogonal decomposition: a tutorial. Nonlinear Dyn. 41, 275–307.Google Scholar
Takato, K., Tsutsui, T., Akiyama, M. & Sugiyama, H. 1997 Numerical analysis of flow around a vibrating elastic plate. Trans. JSME B 64, 194–202.Google Scholar
Tinney, C. E. & Jordan, P. 2008 The near pressure field of co-axial subsonic jets. J. Fluid Mech. 611, 175–204.Google Scholar
Toda, M. 1979 Theory of air flow generation by a resonant type PVF2 Bimorph cantilever vibrator. Ferroelectrics 22, 911–918.Google Scholar
Toda, M. 1981 Voltage-induced large amplitude bending device – PVF2 Bimorph – its properties and applications. Ferroelectrics 32, 127–133.Google Scholar
Tsutsui, T., Akiyama, M., Sugiyama, H. & Shimanaka, K. 1996 Heat transfer enhancement around a rectangular cylinder set in near wake generated by elastically vibrating flat plate. Trans. JSME B 62, 135–142.Google Scholar
Wait, S. M., Acikalin, T., Garimella, S. V. & Raman, A. 2004 Piezoelectric fans for the thermal management of electronics. Paper no. HMT-2004-C76. In Proceedings of the 6th ISHMT/ASME Heat Mass Transfer Conference and 17th National Heat and Mass Transfer, Kalpakkam, India (ed. Vaidyanathan, , Prasad, , Balaji, & Joshi, ), pp. 447–452. New Delhi: Tata McGraw-Hill.Google Scholar
Wait, S. M., Basak, S., Garimella, S. V. & Raman, A. 2007 Piezoelectric fans using higher flexural modes for electronics cooling applications. IEEE Trans. Compon. Packag. Manuf. Technol. 30, 119–128.Google Scholar
Watanabe, H., Ihara, A., Hirama, H. & Hayashizaki, S. 1990 Measurement of the three-dimensional flow field around an oscillating flat plate with LDV. Trans. JSME B 56 (532), 122–129.CrossRefGoogle Scholar
Weier, T., Cierpka, C. & Gerbeth, G. 2008 Coherent structure eduction from PIV data of an electromagnetically forced separated flow. J. Fluids Struct. 24, 1339–1348.Google Scholar
Wereley, S. T. & Gui, L. 2003 A correlation-based central difference image correction (CDIC) method and application in a four-roll mill flow PIV measurement. Exp. Fluids 34, 42–51.Google Scholar
Yoo, J. H., Hong, J. I. & Cao, W. 2000 Piezoelectric ceramic Bimorph coupled to thin metal plate as cooling fan for electronic devices. Sensors Actuators A 79, 8–12.Google Scholar