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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: ziniuwu@tsinghua.edu.cn
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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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