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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]
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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 

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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

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Video 2.5 MB

Kim et al. supplementary movie

Dynamics of an inverted flag at β = 0.10

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Video 2.5 MB

Kim et al. supplementary movie

Dynamics of an inverted flag at β = 0.06

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Video 2.4 MB