Phase difference effect on collective locomotion of two tandem autopropelled flapping foils

Xingjian Lin, Jie Wu, Tongwei Zhang, and Liming Yang
Phys. Rev. Fluids 4, 054101 – Published 17 May 2019

Abstract

The effect of phase difference on the collective locomotion of two tandem flapping foils is numerically studied in this paper. The numerical results indicate that the collective locomotion is greatly affected by the phase difference. Two distinct collective modes are observed, i.e., the fast mode and the slow mode. The fast mode is only observed in part of the range of the phase difference (ϕ), i.e., ϕ=0.00.1π and 1.5π–1.9π with appropriate initial distance, and the slow mode appears in the range of ϕ=0.3π1.4π. Meanwhile, the follower of the two foils has hydrodynamic benefit in both fast and slow modes, and it can obtain the highest efficiency in the fast mode at ϕ=1.6π. However, the leader can only achieve hydrodynamic benefit in the fast mode, and the highest efficiency occurs at ϕ=0.1π. In addition, the stable distance between two foils in the slow mode can be quantized with the phase difference. Furthermore, the fluid-structure interactions between two foils are also analyzed. Two distinct vortex interactions are observed in the fast mode, i.e., merging interaction and broken interaction, which, respectively, result in the highest propulsive efficiency for the follower and the leader. In the merging interaction, the leading edge vortex of the leader is captured by the follower, which results in the weak trailing edge vortex of the leader but a strong trailing edge vortex of the follower. In the broken interaction, the leading edge vortex of the follower sheds into the wake together with the trailing edge vortex of the leader, and induces the trailing edge vortex of the follower to be broken into two parts. Which kind of vortex interaction occurs depends on the phase difference. The results obtained here may provide some light on understanding the coordinated behavior of biological collectives.

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  • Received 24 January 2019

DOI:https://doi.org/10.1103/PhysRevFluids.4.054101

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Xingjian Lin1,2, Jie Wu3,1,2,*, Tongwei Zhang1,2, and Liming Yang4

  • 1Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China
  • 2Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China
  • 3State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China
  • 4Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

  • *wuj@nuaa.edu.cn

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Vol. 4, Iss. 5 — May 2019

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