Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-29T22:55:19.391Z Has data issue: false hasContentIssue false
  • English
  • Français

Synchronized flutter of two slender flags

Published online by Cambridge University Press:  26 July 2016

Jérôme Mougel ,
Olivier Doaré  and
Sébastien Michelin
Jérôme Mougel*
Affiliation:
LadHyX, Département de Mécanique, Ecole Polytechnique – CNRS, 91128 Palaiseau, France Institut de Mécanique des Fluides de Toulouse, CNRS-UPS-Université de Toulouse, Allée Camille Soula, 31400 Toulouse, France
Olivier Doaré
Affiliation:
IMSIA, ENSTA ParisTech, CNRS, CEA, EDF, Université Paris-Saclay, 828 bd des Maréchaux, 91762 Palaiseau, France
Sébastien Michelin
Affiliation:
LadHyX, Département de Mécanique, Ecole Polytechnique – CNRS, 91128 Palaiseau, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The interactions and synchronization of two parallel and slender flags in a uniform axial flow are studied in the present paper by generalizing Lighthill’s elongated body theory (EBT) and Lighthill’s large-amplitude elongated body theory (LAEBT) to account for the hydrodynamic coupling between flags. The proposed method consists of two successive steps, namely the reconstruction of the flow created by a flapping flag within the LAEBT framework and the computation of the fluid force generated by this non-uniform flow on the second flag. In the limit of slender flags in close proximity, we show that the effect of the wakes has little influence on the long-time coupled dynamics and can be neglected in the modelling. This provides a simplified framework extending LAEBT to the coupled dynamics of two flags. Using this simplified model, both linear and large-amplitude results are reported to explore the selection of the flapping regime as well as the dynamical properties of two side-by-side slender flags. Hydrodynamic coupling of the two flags is observed to destabilize the flags for most parameters, and to induce a long-term synchronization of the flags, either in-phase or out-of-phase.

JFM classification

Aerodynamics: Aerodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 801 , 25 August 2016 , pp. 652 - 669
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, vol. 55. Courier Corporation.Google Scholar
Alben, S. 2009 Wake-mediated synchronization and drafting in coupled flags. J. Fluid Mech. 641, 489–496.CrossRefGoogle Scholar
Banerjee, S., Connell, B. S. H. & Yue, D. K. P. 2015 Three-dimensional effects on flag flapping dynamics. J. Fluid Mech. 783, 103–136.CrossRefGoogle Scholar
Candelier, F., Boyer, F. & Leroyer, A. 2011 Three-dimensional extension of Lighthill’s large-amplitude elongated-body theory of fish locomotion. J. Fluid Mech. 674, 196–226.CrossRefGoogle Scholar
Candelier, F., Porez, M. & Boyer, F. 2013 Note on the swimming of an elongated body in a non-uniform flow. J. Fluid Mech. 716, 616–637.Google Scholar
Doaré, O. & Michelin, S. 2011 Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency. J. Fluids Struct. 27 (8), 1357–1375.CrossRefGoogle Scholar
Eloy, C., Doaré, O., Duchemin, L. & Schouveiler, L. 2010 A unified introduction to fluid mechanics of flying and swimming at high Reynolds number. Exp. Mech. 50 (9), 1361–1366.Google Scholar
Eloy, C., Kofman, N. & Schouveiler, L. 2012 The origin of hysteresis in the flag instability. J. Fluid Mech. 691, 583–593.CrossRefGoogle Scholar
Eloy, C., Souilliez, C. & Schouveiler, L. 2007 Flutter of a rectangular plate. J. Fluids Struct. 23 (6), 904–919.CrossRefGoogle Scholar
Farnell, D., David, T. & Barton, D. C. 2004 Coupled states of flapping flags. J. Fluids Struct. 19 (1), 29–36.CrossRefGoogle Scholar
Favier, J., Revell, A. & Pinelli, A. 2015 Numerical study of flapping filaments in a uniform fluid flow. J. Fluids Struct. 53, 26–35.Google Scholar
Giacomello, A. & Porfiri, M. 2011 Underwater energy harvesting from a heavy flag hosting ionic polymer metal composites. J. Appl. Phys. 109, 084903.CrossRefGoogle Scholar
Jackson, J. D. 1999 Classical Electrodynamics. Wiley.Google Scholar
Jia, L. B., Li, F., Yin, X. Z. & Yin, X. Y. 2007 Coupling modes between two flapping filaments. J. Fluid Mech. 581, 199–220.CrossRefGoogle Scholar
Lighthill, M. J. 1960 Note on the swimming of slender fish. J. Fluid Mech. 9 (02), 305–317.CrossRefGoogle Scholar
Lighthill, M. J. 1970 Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44 (02), 265–301.Google Scholar
Lighthill, M. J. 1971 Large-amplitude elongated-body theory of fish locomotion. Proc. R. Soc. Lond. B 179 (1055), 125–138.Google Scholar
Michelin, S. & Doaré, O. 2013 Energy harvesting efficiency of piezoelectric flags in axial flows. J. Fluid Mech. 714, 489–504.CrossRefGoogle Scholar
Michelin, S. & Llewellyn Smith, S. G. 2009 Linear stability analysis of coupled parallel flexible plates in an axial flow. J. Fluids Struct. 25 (7), 1136–1157.Google Scholar
Schouveiler, L. & Eloy, C. 2009 Coupled flutter of parallel plates. Phys. Fluids 21 (8), 081703.Google Scholar
Shelley, M. J. & Zhang, J. 2011 Flapping and bending bodies interacting with fluid flows. Annu. Rev. Fluid Mech. 43, 449–465.CrossRefGoogle Scholar
Singh, K., Michelin, S. & de Langre, E. 2012a The effect of non-uniform damping on flutter in axial flow and energy harvesting strategies. Proc. R. Soc. Lond. A 468, 3620–3635.Google Scholar
Singh, K., Michelin, S. & de Langre, E. 2012b Energy harvesting from axial fluid-elastic instabilities of a cylinder. J. Fluids Struct. 30, 159–172.Google Scholar
Tian, F.-B., Luo, H., Zhu, L., Liao, J. C. & Lu, X.-Y. 2011a An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments. J. Comput. Phys. 230, 7266–7283.Google Scholar
Tian, F.-B., Luo, H., Zhu, L. & Lu, X.-Y. 2011b Coupling modes of three filaments in side-by-side arrangement. Phys. Fluids 23, 111903.Google Scholar
Udding, E., Huang, W.-X. & Sung, H. J. 2013 Interaction modes of multiple flags in a uniform flow. J. Fluid Mech. 729, 563–583.CrossRefGoogle Scholar
Xia, Y., Michelin, S. & Doaré, O. 2015 Fluid-solid-electric lock-in of energy-harvesting piezoelectric flags. Phys. Rev. Appl. 3 (1), 014009.Google Scholar
Zhang, J., Childress, S., Libchaber, A. & Shelley, M. 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408 (6814), 835–839.Google Scholar
Zhu, L. & Peskin, C. S. 2003 Interaction of two flapping filaments in a flowing soap film. Phys. Fluids 15 (7), 1954–1960.CrossRefGoogle Scholar