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Flexibility increases lift for passive fluttering wings

Published online by Cambridge University Press:  16 January 2015

Daniel Tam
Daniel Tam*
Affiliation:
Laboratory for Aero- and Hydrodynamics, Technische Universiteit Delft, Delft, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

We examine experimentally the influence of flexibility on the side-to-side fluttering motion of passive wings settling under the influence of gravity. Our results demonstrate the existence of an optimal flexibility that allows flexible wings to remain airborne twice as long as their rigid counterparts of identical mass and size. Flow visualization and measurements allow us to elucidate the role of flexibility in generating increased lift and wing circulation by shedding additional vorticity at the turning point. Theoretical scalings are derived from a reduced model of the flight dynamics and yield quantitative agreement with experiments. These scalings rationalize the strong positive correlation between flexibility and flight time. Our experimental results and theoretical scalings represent an ideal system for the validation of computational approaches to model biologically inspired fluid–structure interaction problems.

JFM classification

Aerodynamics: Aerodynamics Biological Fluid Dynamics: Swimming/flying
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 765 , 25 February 2015 , R2
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Copyright
© 2015 Cambridge University Press 

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References

Alben, S. 2008 Optimal flexibility of a flapping appendage in an inviscid fluid. J. Fluid Mech. 614, 355–380.CrossRefGoogle Scholar
Alben, S., Shelley, M. & Zhang, J. 2002 Drag reduction through self-similar bending of a flexible body. Nature 420 (6915), 479–481.Google Scholar
Andersen, A., Pesavento, U. & Wang, Z. 2005 Analysis of transitions between fluttering, tumbling and steady descent of falling cards. J. Fluid Mech. 541 (1), 91–104.CrossRefGoogle Scholar
Belmonte, A., Eisenberg, H. & Moses, E. 1998 From flutter to tumble: inertial drag and Froude similarity in falling paper. Phys. Rev. Lett. 81, 345–348.Google Scholar
Birch, J. M. & Dickinson, M. H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412 (6848), 729–733.Google Scholar
Combes, S. A. & Daniel, T. L. 2003 Flexural stiffness in insect wings II. Spatial distribution and dynamic wing bending. J. Expl. Biol. 206 (17), 2989–2997.Google Scholar
Eloy, C., Lagrange, R., Souilliez, C. & Schouveiler, L. 2008 Aeroelastic instability of cantilevered flexible plates in uniform flow. J. Fluid Mech. 611 (1), 97–106.Google Scholar
Heathcote, S. & Gursul, I. 2007 Flexible flapping airfoil propulsion at low Reynolds numbers. AIAA J. 45 (5), 1066–1079.Google Scholar
Heisinger, L., Newton, P. & Kanso, E. 2014 Coins falling in water. J. Fluid Mech. 742, 243–253.CrossRefGoogle Scholar
Hu, R. & Wang, L. 2014 Motion transitions of falling plates via quasisteady aerodynamics. Phys. Rev. E 90 (1), 013020.Google Scholar
Huang, W., Liu, H., Wang, F., Wu, J. & Zhang, H. P. 2013 Experimetal study of a freely falling plate with an inhomogeneous mass distribution. Phys. Rev. E 88 (5), 053008.Google Scholar
Mahadevan, L. 1996 Tumbling of a falling card. C. R. Acad. Sci. Paris II 323, 729–736.Google Scholar
Masoud, H. & Alexander, A. 2010 Resonance of flexible flapping wings at low Reynolds number. Phys. Rev. E 81 (5), 056304.Google Scholar
Michelin, S. & Llewellyn-Smith, S. G. 2009 Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 21, 071902.Google Scholar
Percin, M., Hu, Y., van Oudheusden, B. W., Remes, B. & Scarano, F. 2011 Wing flexibility effects in clap-and-fling. Intl J. Micro Air Veh. 3 (4), 217–227.CrossRefGoogle Scholar
Ramananarivo, S., Godoy-Diana, R. & Thiria, B. 2011 Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance. Proc. Natl Acad. Sci. 108 (15), 5964–5969.CrossRefGoogle ScholarPubMed
Shelley, M., Vandenberghe, N. & Zhang, J. 2005 Heavy flags undergo spontaneous oscillations in flowing water. Phys. Rev. Lett. 94 (9), 094302.Google Scholar
Spagnolie, S. E., Moret, L., Shelley, M. J. & Zhang, J. 2010 Surprising behaviors in flapping locomotion with passive pitching. Phys. Fluids 22 (4), 041903.Google Scholar
Tam, D., Bush, J. W. M., Robitaille, M. & Kudrolli, A. 2010 Tumbling dynamics of passive flexible wings. Phys. Rev. Lett. 104 (18), 184504.Google Scholar
Tchoufag, J., Fabre, D. & Magnaudet, J. 2014 Global linear stability analysis of the wake and path of buoyancy-driven disks and thin cylinders. J. Fluid Mech. 740, 278–3111.Google Scholar
Zhao, L., Huang, Q., Deng, X. & Sane, S. P. 2010 Aerodynamic effects of flexibility in flapping wings. J. R. Soc. Interface 7 (44), 485–497.Google Scholar

Tam supplementary movie

Side to side movies of flexible fluttering wings falling under the influence of gravity. All wings are characterized by I*=0.1 and the flexibility ranges from Cy=0 (rigid wings) to Cy=15

Download Tam supplementary movie(Video)
Video 1.8 MB

Tam supplementary movie

Side to side movies of flexible fluttering wings falling under the influence of gravity. All wings are characterized by I*=0.1 and the flexibility ranges from Cy=0 (rigid wings) to Cy=15

Download Tam supplementary movie(Video)
Video 3.7 MB

Tam supplementary movie

Side to side movies of flexible fluttering wings falling under the influence of gravity. All wings are characterized by I*=0.1 and the flexibility ranges from Cy=22 to Cy=60

Download Tam supplementary movie(Video)
Video 1.5 MB

Tam supplementary movie

Side to side movies of flexible fluttering wings falling under the influence of gravity. All wings are characterized by I*=0.1 and the flexibility ranges from Cy=22 to Cy=60

Download Tam supplementary movie(Video)
Video 3.5 MB