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Stabilizing effect of flexibility in the wake of a flapping foil

Published online by Cambridge University Press:  11 September 2012

C. Marais ,
B. Thiria ,
J. E. Wesfreid  and
R. Godoy-Diana
C. Marais
Affiliation:
Physique et Mécanique des Milieux Hétérogènes (PMMH) CNRS UMR7636, ESPCI ParisTech, UPMC (Paris 6), Univ. Paris Diderot (Paris 7), 10, rue Vauquelin, F-75005 Paris, France
B. Thiria
Affiliation:
Physique et Mécanique des Milieux Hétérogènes (PMMH) CNRS UMR7636, ESPCI ParisTech, UPMC (Paris 6), Univ. Paris Diderot (Paris 7), 10, rue Vauquelin, F-75005 Paris, France
J. E. Wesfreid
Affiliation:
Physique et Mécanique des Milieux Hétérogènes (PMMH) CNRS UMR7636, ESPCI ParisTech, UPMC (Paris 6), Univ. Paris Diderot (Paris 7), 10, rue Vauquelin, F-75005 Paris, France
R. Godoy-Diana*
Affiliation:
Physique et Mécanique des Milieux Hétérogènes (PMMH) CNRS UMR7636, ESPCI ParisTech, UPMC (Paris 6), Univ. Paris Diderot (Paris 7), 10, rue Vauquelin, F-75005 Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

The wake of a flexible foil undergoing pitching oscillations in a low-speed hydrodynamic tunnel is used to examine the effect of chordwise foil flexibility in the dynamical features of flapping-based propulsion. We compare the regime transitions in the wake with respect to the case of a rigid foil and show that foil flexibility inhibits the symmetry breaking of the reverse Bénard–von Kármán wake reported in the literature. A momentum balance calculation shows the average thrust to be up to three times greater for the flexible foil than for the rigid foil. We explain both of these observations by analysing the vortex dynamics in the very near wake.

JFM classification

Aerodynamics: Flow-structure interactions Biological Fluid Dynamics: Swimming/flying Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 710 , 10 November 2012 , pp. 659 - 669
Copyright
Copyright © Cambridge University Press 2012

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References

1. Bohl, D. G. & Koochesfahani, M. M. 2009 MTV measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency. J. Fluid Mech. 620, 63–88.CrossRefGoogle Scholar
2. Buchholz, J. H. J. & Smits, A. J. 2008 The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 603, 331–365.CrossRefGoogle ScholarPubMed
3. Cleaver, D. J., Gursul, I. & Wang, Z. J. 2010 Vortex mode bifurcation and lift force of a plunging aerofoil at low Reynolds numbers. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, Jan. 4–7, 2010. AIAA-2010-390.Google Scholar
4. Daniel, T. L. & Combes, S. A. 2002 Flexible wings and fins: bending by inertial or fluid-dynamic forces? Integr. Compar. Biol. 42 (5), 1044–1049.CrossRefGoogle ScholarPubMed
5. Eldredge, J. D. & Pisani, D. 2008 Passive locomotion of a simple articulated fish-like system in the wake of an obstacle. J. Fluid Mech. 607, 1–10.CrossRefGoogle Scholar
6. von Ellenrieder, K. D. & Pothos, S. 2008 PIV measurements of the asymmetric wake of a two-dimensional heaving hydrofoil. Exp. Fluids 44 (5), 733–745.CrossRefGoogle Scholar
7. Fish, F. E. 1999 Performance constraints on the maneuverability of flexible and rigid biological systems. In Proceedings of the Eleventh International Symposium on Unmanned Untethered Submersible Technology, pp. 394–406. Autonomous Undersea Systems Institute.Google Scholar
8. Godoy-Diana, R., Aider, J. L. & Wesfreid, J. E. 2008 Transitions in the wake of a flapping foil. Phys. Rev. E 77, 016308.CrossRefGoogle ScholarPubMed
9. Godoy-Diana, R., Marais, C., Aider, J. L. & Wesfreid, J. E. 2009 A model for the symmetry breaking of the reverse Bénard–von Kármán vortex street produced by a flapping foil. J. Fluid Mech. 622, 23–32.CrossRefGoogle Scholar
10. Heathcote, S. & Gursul, I. 2007a Flexible flapping airfoil propulsion at low Reynolds numbers. AIAA J. 45 (5), 1066–1079.CrossRefGoogle Scholar
11. Heathcote, S. & Gursul, I. 2007b Jet switching phenomenon for a periodically plunging airfoil. Phys. Fluids 19, 027104.CrossRefGoogle Scholar
12. Jones, K. D., Dohring, C. M. & Platzer, M. F. 1998 Experimental and computational investigation of the Knoller–Betz effect. AIAA J. 36 (7), 1240–1246.CrossRefGoogle Scholar
13. Katz, J. & Weihs, D. 1978 Hydrodynamic propulsion by large amplitude oscillation of an aerofoil with chordwise flexibility. J. Fluid Mech. 88, 713–723.CrossRefGoogle Scholar
14. Lewin, G. C. & Haj-Hariri, H. 2003 Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow. J. Fluid Mech. 492, 339–362.CrossRefGoogle Scholar
15. Marais, C. 2011 Dynamique tourbillonnaire dans le sillage d’un aileron oscillant: propulsion par ailes battantes biomimétiques. PhD thesis, Université Denis Diderot, Paris, France.Google Scholar
16. Michelin, S. & Llewellyn Smith, S. G. 2009 Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 21 (7), 071902.CrossRefGoogle Scholar
17. Moisy, F. 2007 PIVMat: a PIV post-processing and data analysis toolbox for Matlab. Version 1.60 17-Apr-2007. http://www.fast.u-psud.fr/pivmat.Google Scholar
18. Protas, B. & Wesfreid, J. E. 2003 On the relation between the global modes and the spectra of drag and lift in periodic wake flows. C. R. Mécanique 331, 49–54.CrossRefGoogle Scholar
19. 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. USA 108 (15), 5964–5969.CrossRefGoogle ScholarPubMed
20. Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
21. Schnipper, T., Andersen, A. & Bohr, T. 2009 Vortex wakes of a flapping foil. J. Fluid Mech. 633, 411–423.CrossRefGoogle Scholar
22. Shyy, W., Aono, H., Chimakurthi, S. K., Trizila, P., Kang, C.-K., Cesnik, C. E. S. & Liu, H. 2010 Recent progress in flapping wing aerodynamics and aeroelasticity. Progr. Aerosp. Sci. 46 (7), 284–327.CrossRefGoogle Scholar
23. Spagnolie, S. E., Moret, L., Shelley, M. J. & Zhang, J. 2010 Surprising behaviours in flapping locomotion with passive pitching. Phys. Fluids 22 (4), 041903.CrossRefGoogle Scholar
24. Thiria, B. & Godoy-Diana, R. 2010 How wing compliance drives the efficiency of self-propelled flapping flyers. Phys. Rev. E 82, 015303(R).CrossRefGoogle ScholarPubMed
25. Wootton, R. J. 1992 Functional morphology of insect wings. Annu. Rev. Entomol. 37 (1), 113–140.CrossRefGoogle Scholar
26. Yu, M. L., Hu, H. & Wang, Z. J. 2012 Experimental and numerical investigations on the asymmetric wake vortex structures around an oscillating airfoil. In 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA Paper 2012–0299.Google Scholar