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Vortex shedding model of a flapping flag

Published online by Cambridge University Press:  25 December 2008

SÉBASTIEN MICHELIN ,
STEFAN G. LLEWELLYN SMITH  and
BEVERLEY J. GLOVER
SÉBASTIEN MICHELIN*
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, La Jolla CA 92093-0411, USA Ecole Nationale Supérieure des Mines de Paris, 60–62 Boulevard Saint Michel, 75272 Paris cedex 06, France
STEFAN G. LLEWELLYN SMITH
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, La Jolla CA 92093-0411, USA
BEVERLEY J. GLOVER
Affiliation:
Departement of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK
*
†Email address for correspondence: [email protected]
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Abstract

A two-dimensional model for the flapping of an elastic flag under axial flow is described. The vortical wake is accounted for by the shedding of discrete point vortices with unsteady intensity, enforcing the regularity condition at the flag's trailing edge. The stability of the flat state of rest as well as the characteristics of the flapping modes in the periodic regime are compared successfully to existing linear stability and experimental results. An analysis of the flapping regime shows the co-existence of direct kinematic waves, travelling along the flag in the same direction as the imposed flow, and reverse dynamic waves, travelling along the flag upstream from the trailing edge.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 617 , 25 December 2008 , pp. 1 - 10
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Alben, S. & Shelley, M. J. 2008 Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos. Phys. Rev. Lett. 100, 074301.CrossRefGoogle Scholar
Balint, T. S. & Lucey, A. D. 2005 Instability of a cantilevered flexible plate in viscous channel flow. J. Fluids Struct. 20, 893–912.CrossRefGoogle Scholar
Barnett, T. P. 1983 Interaction of the Monsoon and Pacific trade wind system at interannual time scales. Part I: The equatorial zone. Mon. Weath. Rev. 111, 756–773.2.0.CO;2>CrossRefGoogle Scholar
Brown, C. E. & Michael, W. H. 1954 Effect of leading edge separation on the lift of a delta wing. J. Aero. Sci. 21, 690–694 & 706.Google Scholar
Connell, B. S. H. & Yue, D. K. P. 2007 Flapping dynamics of a flag in uniform stream. J. Fluid Mech. 581, 33–67.CrossRefGoogle Scholar
Cortelezzi, L. 1996 Nonlinear feedback control of the wake past a plate with a suction point on the downstream wall. J. Fluid Mech. 327, 303–324.CrossRefGoogle Scholar
Cortelezzi, L. & Leonard, A. 1993 Point vortex model of the unsteady separated flow past a semi-infinite plate with transverse motion. Fluid Dyn. Res. 11, 263–295.CrossRefGoogle Scholar
Eloy, C., Lagrange, R., Souilliez, C. & Schouveiler, L. 2008 Aeroelastic instability of a flexible plate in a uniform flow. J. Fluid Mech. 611, 97–106.CrossRefGoogle Scholar
Eloy, C., Souilliez, C. & Schouveiler, L. 2007 Flutter of a rectangular plate. J. Fluids Struct. 23, 904–919.CrossRefGoogle Scholar
Huang, L. 1995 Flutter of cantilevered plates in axial flow. J. Fluids Struct. 9, 127–147.Google Scholar
Jones, M. A. 2003 The separated flow of an inviscid fluid around a moving plate. J. Fluid Mech. 496, 405–441.CrossRefGoogle Scholar
Kornecki, A., Dowell, E. H. & O'Brien, J. 1976 On the aeroelastic instability of two-dimensional panels in uniform incompressible flow. J. Sound Vib. 47, 163–178.CrossRefGoogle Scholar
Lighthill, M. J. 1960 Note on the swimming of slender fish. J. Fluid Mech. 9, 305–317.CrossRefGoogle Scholar
Michelin, S. & Llewellyn Smith, S. G. 2008 An unsteady point vortex method for coupled fluid-solid problems. (submitted). Theor. Comp. Fluid. Dyn.CrossRefGoogle Scholar
Rayleigh, Lord 1878 On the instablity of jets. Proc. Lond. Math. Soc. 10, 4–13.CrossRefGoogle Scholar
Rott, N. 1956 Diffraction of a weak shock with vortex generation. J. Fluid Mech. 1, 111–128.CrossRefGoogle Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Shelley, M., Vandenberghe, N. & Zhang, J. 2005 Heavy flags undergo spontaneous oscillations in flowing water. Phys. Rev. Lett. 94, 094302.CrossRefGoogle ScholarPubMed
Shukla, R. K. & Eldredge, J. D. 2007 An inviscid model for vortex shedding from a deforming body. Theor. Comput. Fluid Dyn. 21, 343–368.Google Scholar
Wallace, J. M. & Dickinson, R. E. 1972 Empirical orthogonal representation of time series in the frequency domain. Part I: Theoretical considerations. J. Appl. Met. 11, 887–892.2.0.CO;2>CrossRefGoogle Scholar
Watanabe, Y., Suzuki, S., Sugihara, M. & Sueoka, Y. 2002 An experimental study of paper flutter. J. Fluids Struct. 16, 529–542.CrossRefGoogle 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, 835–839.CrossRefGoogle Scholar
Zhu, L. & Peskin, C. 2002 Simulation of flapping flexible filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 179, 452–468.CrossRefGoogle Scholar