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Transient force augmentation due to counter-rotating vortex ring pairs

Published online by Cambridge University Press:  23 November 2015

Zhidong Fu  and
Hong Liu
Zhidong Fu
Affiliation:
J. C. Wu Center for Aerodynamics, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
Hong Liu*
Affiliation:
J. C. Wu Center for Aerodynamics, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
*
†Email address for correspondence: [email protected]
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Abstract

Of particular significance to biological locomotion is vortex ring interaction. In the wakes of animals, this unsteady process determines the changes in the impulse of counter-rotating vortex ring pairs (VRPs), which consist of two vortex rings with opposite sense of rotation. In this paper, these VRPs are proposed to be of particular importance to unsteady force generation. We carry out numerical computations, simulating the piston–cylinder apparatus, to study the transient changes in the impulse of counter-rotating VRPs composed of a positive and a negative vortex ring. We model the negative vortex ring (NeVR) of a VRP by making reasonable assumptions about their vorticity distributions and spatial locations, which are initially prescribed. The result of modelling is superimposed on the flow, which has a pre-existing positive vortex ring (PoVR), leading to a VRP. The simulation quantitatively demonstrates that the unsteady force resulting from a VRP is significantly larger compared with an isolated PoVR (without an NeVR). The force enhancement is also correlated to vortex configurations. A normalised force coefficient characterising force augmentation over the entire stroke is given. The force augmentation coefficient grows significantly and then reaches a plateau as the momentum input increases. The results are consistent with those in fully unsteady vortex interaction, which involves the generation of an NeVR. It is suggested that counter-rotating VRPs could offer a new perspective to explain unconventional force generation for biological swimming and flying.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 785 , 25 December 2015 , pp. 324 - 348
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Copyright
© 2015 Cambridge University Press 

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Footnotes

‡

Present address: Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK.

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