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Self-organization of multiple self-propelling flapping foils: energy saving and increased speed

Published online by Cambridge University Press:  05 December 2019

Xingjian Lin ,
Jie Wu Open the ORCID record for Jie Wu [Opens in a new window] ,
Tongwei Zhang  and
Liming Yang
Xingjian Lin
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China Key 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
Jie Wu*
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China Key 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
Tongwei Zhang
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China Key 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
Liming Yang
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
*
†Email address for correspondence: wuj@nuaa.edu.cn
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Abstract

The collective hydrodynamics in fish schools and bird flocks, which includes self-organization of multiple dynamic bodies, is complex and lacks sufficient exploration. In this paper, we study the performance of multiple self-propelled foils in tandem formation, whose flapping motions are asynchronous with a phase difference. It is shown that a compact formation, in which all of the foils perform like a complete anguilliform swimmer, can be spontaneously formed by multiple foils via hydrodynamic interactions. Both velocity enhancement and energy saving can be achieved by multiple foils in anguilliform-like swimming. Furthermore, such anguilliform-like swimming behaviour can be observed over a wide range of parameters, including the number of foils, the phase difference, the initial distance, the heaving amplitude and the pitching amplitude. The results obtained here may provide some light on understanding the self-organization behaviour of biological collectives.

JFM classification

Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex dynamics Wakes/Jets: Vortex streets
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , R1
Copyright
© 2019 Cambridge University Press

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Lin et al. supplementary movie 1

Anguilliform-like swimming of five flapping foils.

Download Lin et al. supplementary movie 1(Video)
Video 2.6 MB

Lin et al. supplementary movie 2

Anguilliform-like swimming of ten flapping foils.

Download Lin et al. supplementary movie 2(Video)
Video 3.4 MB

Lin et al. supplementary movie 3

Anguilliform-like swimming of fifteen flapping foils.

Download Lin et al. supplementary movie 3(Video)
Video 3.5 MB