Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-22T10:22:04.009Z Has data issue: false hasContentIssue false
  • English
  • Français

Flapping dynamics of an inverted flag

Published online by Cambridge University Press:  04 November 2013

Daegyoum Kim ,
Julia Cossé ,
Cecilia Huertas Cerdeira  and
Morteza Gharib
Daegyoum Kim*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Julia Cossé
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Cecilia Huertas Cerdeira
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Morteza Gharib
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of an inverted flag are investigated experimentally in order to find the conditions under which self-excited flapping can occur. In contrast to a typical flag with a fixed leading edge and a free trailing edge, the inverted flag of our study has a free leading edge and a fixed trailing edge. The behaviour of the inverted flag can be classified into three regimes based on its non-dimensional bending stiffness scaled by flow velocity and flag length. Two quasi-steady regimes, straight mode and fully deflected mode, are observed, and a limit-cycle flapping mode with large amplitude appears between the two quasi-steady regimes. Bistable states are found in both straight to flapping mode transition and flapping to deflected mode transition. The effect of mass ratio, relative magnitude of flag inertia and fluid inertia, on the non-dimensional bending stiffness range for flapping is negligible, unlike the instability of the typical flag. Because of the unsteady fluid force, a flapping sheet can produce elastic strain energy several times larger than a sheet of the deformed mode, improving the conversion of fluid kinetic energy to elastic strain energy. According to the analysis of the leading-edge vortex formation process, the time scale of optimal vortex formation correlates with efficient conversion to elastic strain energy during bending.

JFM classification

Aerodynamics: Aerodynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 736 , 10 December 2013 , R1
Copyright
©2013 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

Akaydin, H. D., Elvin, N. & Andreopoulos, Y. 2010 Wake of a cylinder: a paradigm for energy harvesting with piezoelectric materials. Exp. Fluids 49, 291–304.Google Scholar
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
Allen, J. J. & Smits, A. J. 2001 Energy harvesting eel. J. Fluids Struct. 15, 629–640.CrossRefGoogle Scholar
Argentina, M. & Mahadevan, L. 2005 Fluid-flow-induced flutter of a flag. Proc. Natl Acad. Sci. 102, 1829–1834.Google Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539–575.Google Scholar
Buchak, P., Eloy, C. & Reis, P. M. 2010 The clapping book: wind-driven oscillations in a stack of elastic sheets. Phys. Rev. Lett. 105, 194301.CrossRefGoogle Scholar
Chang, Y. B. & Moretti, P. M. 2002 Flow-induced vibration of free edges of thin films. J. Fluids Struct. 16, 989–1008.CrossRefGoogle Scholar
Connell, B. S. H. & Yue, D. K. P. 2007 Flapping dynamics of a flag in a uniform stream. J. Fluid Mech. 581, 33–68.Google Scholar
Dabiri, J. O. & Gharib, M. 2005 The role of optimal vortex formation in biological fluid transport. Proc. R. Soc. Lond. B 272, 1557–1560.Google Scholar
Eloy, C., Lagrange, R., Souilliez, C. & Schouveiler, L. 2008 Aeroelastic instability of cantilevered flexible plates in uniform flow. J. Fluid Mech. 611, 97–106.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Guo, C. Q. & Païdoussis, M. P. 2000 Stability of rectangular plates with free side-edges in two-dimensional inviscid channel flow. J. Appl. Mech. 67, 171–176.Google Scholar
Huang, L. 1995 Flutter of cantilevered plates in axial-flow. J. Fluids Struct. 9, 127–147.CrossRefGoogle Scholar
Johnson, E. & Jacob, J. 2009 Development and testing of a gust and shear wind tunnel for NAVs and MAVs. In 47th AIAA Aerospace Sciences Meeting, Orlando, Florida.Google Scholar
Krueger, P. S., Dabiri, J. O. & Gharib, M. 2003 Vortex ring pinchoff in the presence of simultaneously initiated uniform background co-flow. Phys. Fluids 15, L49–L52.Google Scholar
Li, S. G., Yuan, J. P. & Lipson, H. 2011 Ambient wind energy harvesting using cross-flow fluttering. J. Appl. Phys. 109, 026104.Google Scholar
McCroskey, W. J. 1981 The phenomenon of dynamic stall. NASA Tech. Rep. 81264.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., Smith, S. G. L. & Glover, B. J. 2008 Vortex shedding model of a flapping flag. J. Fluid Mech. 617, 1–10.CrossRefGoogle Scholar
Milano, M. & Gharib, M. 2005 Uncovering the physics of flapping flat plates with artificial evolution. J. Fluid Mech. 534, 403–409.Google Scholar
Païdoussis, M. P., Price, S. J. & de Langre, E. 2010 Fluid-Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University Press.Google Scholar
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101, 194502.Google Scholar
Shao, C. P., Chen, Y. J. & Lin, J. Z. 2012 Wind induced deformation and vibration of a platanus acerifolia leaf. Acta Mechanica Sini 28, 583–594.Google Scholar
Shiels, D., Leonard, A. & Roshko, A. 2001 Flow-induced vibration of a circular cylinder at limiting structural parameters. J. Fluids Struct. 15, 3–21.Google Scholar
Tang, D. M., Yamamoto, H. & Dowell, E. H. 2003 Flutter and limit cycle oscillations of two-dimensional panels in three-dimensional axial flow. J. Fluids Struct. 17, 225–242.Google Scholar
Taylor, G. W., Burns, J. R., Kammann, S. M., Powers, W. B. & Welsh, T. R. 2001 The energy harvesting eel: a small subsurface ocean/river power generator. IEEE J. Ocean. Engng 26, 539–547.CrossRefGoogle Scholar
Watanabe, Y., Suzuki, S., Sugihara, M. & Sueoka, Y. 2002 An experimental study of paper flutter. J. Fluids Struct. 16, 529–542.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, 835–839.Google Scholar

Kim et al. supplementary movie

Dynamics of an inverted flag at β = 0.58

Download Kim et al. supplementary movie(Video)
Video 2.3 MB

Kim et al. supplementary movie

Dynamics of an inverted flag at β = 0.26

Download Kim et al. supplementary movie(Video)
Video 2.5 MB

Kim et al. supplementary movie

Dynamics of an inverted flag at β = 0.10

Download Kim et al. supplementary movie(Video)
Video 2.5 MB

Kim et al. supplementary movie

Dynamics of an inverted flag at β = 0.06

Download Kim et al. supplementary movie(Video)
Video 2.4 MB