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Lift force reduction due to body image of vortex for a hovering flight model

Published online by Cambridge University Press:  20 August 2012

X. X. Wang  and
Z. N. Wu
X. X. Wang
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Z. N. Wu*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The effect of the body on the lift force in hovering flight is studied here by including the effect of image vortex rings (IVRs) in the inviscid vortex ring model proposed by Rayner (J. Fluid Mech., vol. 91, 1979, pp. 697–730) and used by Wang & Wu (J. Fluid Mech., vol. 654, 2010, pp. 453–472) to study lift force due to wakes. The body is treated simply as an equivalent sphere following the data of Ellington (Phil. Trans. R. Soc. Lond. B, vol. 305, 1984a, pp. 17–40). It is shown that the body image reduces the lift by inducing a further downwash near the wing tip and an additional contraction to the real vortex rings (RVRs). The amount of force reduction due to body image is found to grow cubically with relative body size, defined by the equivalent radius relative to the wing span, and approximately linearly with the feathering parameter. For Apis and Bombus with large relative body size and large feathering parameter, the body images reduce lift by an amount near 8 % according to the present simplified analysis.

JFM classification

Biological Fluid Dynamics: Swimming/flying Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 709 , 25 October 2012 , pp. 648 - 658
Copyright
Copyright © Cambridge University Press 2012

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References

1. Allen, J. J., Jouanne, Y. & Shashikanth, B. N. 2007 Vortex interaction with a moving sphere. J. Fluid Mech. 587, 337–346.CrossRefGoogle Scholar
2. Altshuler, D. L., Princevac, M., Pan, H. & Lozano, J. 2009 Wake patterns of the wings and tail of hovering hummingbirds. Expl. Fluids 46, 835–846.CrossRefGoogle Scholar
3. Aono, H., Liang, F. & Liu, H. 2008 Near- and far-field aerodynamics in insect hovering flight: an integrated computational study. J. Expl. Biol. 211, 239–257.Google ScholarPubMed
4. Bolster, D., Hershberger, R. & Donnelly, R. J. 2011 An appreciation of the 1939 paper ‘on an experimentally observed phenomenon on vortex rings…’ by Carl-Heinz Krutzsch. Ann. Phys. (Berlin) 523, 380–382.CrossRefGoogle Scholar
5. Bomphrey, R. J., Lawson, N. J., Harding, N. J., Taylor, G. K. & Thomas, A. L. R. 2005 The aerodynamics of Manduca sexta: digital particle image velocimetry analysis of the leading-edge vortex. J. Expl. Biol. 208, 1079–1094.CrossRefGoogle ScholarPubMed
6. Dickinson, M. H., Lehmann, F.-O. & Sane, S. P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284, 1954–1960.CrossRefGoogle ScholarPubMed
7. Ellington, C. P. 1984a The aerodynamics of hovering insect flight. Part 2. Morphological parameters. Phil. Trans. R. Soc. Lond. Ser. B 305, 17–40.Google Scholar
8. Ellington, C. P. 1984b The aerodynamics of hovering insect flight. Part 5. A vortex theory. Phil. Trans. R. Soc. Lond. Ser. B 305, 115–144.Google Scholar
9. Krutzsch, C.-H. 1939 On an experimentally observed phenomenon on vortex rings during their translational movement in a real liquid. Ann. Phys. (Berlin) 427, 497.CrossRefGoogle Scholar
10. Lehmann, F.-O. 2008 When wings touch wakes: understanding locomotor force control by wake–wing interference in insect wings. J. Expl. Biol. 211, 224–233.CrossRefGoogle ScholarPubMed
11. Liu, H., Ellington, C. P., Kawachi, K., van Den Berg, C. & Willmott, A. P. 1998 A computational fluid dynamics study of hawkmoth hovering. J. Expl. Biol. 201, 461–477.CrossRefGoogle ScholarPubMed
12. Ramamurti, R. & Sandberg, W. C. 2007 A computational investigation of the three-dimensional unsteady aerodynamics of Drosophila hovering and maneuvering. J. Expl. Biol. 210, 881–896.CrossRefGoogle ScholarPubMed
13. Rayner, J. M. V. 1979 A vortex theory of animal flight. Part 1. The vortex wake of a hovering animal. J. Fluid Mech. 91, 697–730.CrossRefGoogle Scholar
14. Riskin, D. K., Iriarte-Díaz, J., Middleton, K. M., Breuer, K. S. & Swartz, S. M. 2010 The effect of body size on the wing movements of pteropodid bats, with insights into thrust and lift production. J. Expl. Biol. 213, 4110–4122.CrossRefGoogle ScholarPubMed
15. Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
16. Samejima, Y. & Tsubaki, Y. 2010 Body temperature and body size affect flight performance in a damselfly. Behav. Ecology Sociobiology 64, 685–692.CrossRefGoogle Scholar
17. Sane, S. P. 2003 The aerodynamics of insect flight. J. Expl. Biol. 206, 4191–4208.CrossRefGoogle ScholarPubMed
18. Sun, M. & Tang, J. 2002 Unsteady aerodynamics force generation by a model fruit-fly wing. J. Expl. Biol. 205, 55–70.CrossRefGoogle ScholarPubMed
19. Sun, M. & Wu, J. H. 2003 Aerodynamic force generation and power requirements in forward flight in a fruit fly with modeled wing motion. J. Expl. Biol. 206, 3065–3083.CrossRefGoogle Scholar
20. Wang, X. X. & Wu, Z. N. 2010 Stroke-averaged lift forces due to vortex rings and their mutual interactions for a flapping flight model. J. Fluid Mech. 654, 453–472.Google Scholar
21. Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19, 432–441.CrossRefGoogle Scholar