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Scaling laws for drag-to-thrust transition and propulsive performance in pitching flexible plates

Published online by Cambridge University Press:  27 April 2022

Ze-Rui Peng Open the ORCID record for Ze-Rui Peng [Opens in a new window] ,
Yuehao Sun ,
Dan Yang ,
Yongliang Xiong Open the ORCID record for Yongliang Xiong [Opens in a new window] ,
Lei Wang  and
Lin Wang
Ze-Rui Peng
Affiliation:
Department of Mechanics, School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, PR China
Yuehao Sun*
Affiliation:
Department of Mechanics, School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, PR China Department of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China
Dan Yang*
Affiliation:
Department of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China
Yongliang Xiong
Affiliation:
Department of Mechanics, School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, PR China
Lei Wang
Affiliation:
Department of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China
Lin Wang
Affiliation:
Department of Mechanics, School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, PR China
*
†Email addresses for correspondence: yhaosun@hust.edu.cn, dan_yang@hust.edu.cn
†Email addresses for correspondence: yhaosun@hust.edu.cn, dan_yang@hust.edu.cn
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Abstract

The propulsion of a pitching flexible plate in a uniform flow is investigated numerically. The effects of bending stiffness ($K$), pitching amplitude ($A_L$) and frequency ($St$) on the wake patterns, thrust generations and propulsive performances of the fluid–plate system are analysed. Four typical wake patterns, i.e. von Kármán, reversed von Kármán, deflected and chaotic wakes, emerge from various kinematics, and the $St-A_L$ wake maps are given for various $K$. The drag-to-thrust transitions (DTT) and the wake transitions (WT) between the von Kármán and reversed von Kármán wakes are examined. Results indicate that the WT and DTT boundaries can be scaled by the chord-averaged distance of travel, $\mathcal {L}$, which leads to $\mathcal {L}\times St \approx 1$ and $\mathcal {L}\times St \approx 1.2$, respectively. Further, the resonance mechanism for the performance enhancement is revealed and confirmed in a wide range of parameters. The dimensionless average speed of plate, $\mathcal {U^*}\left (=\mathcal {L}\times St\right )$, is adopted merely to characterize the propulsive performances. For the first time, the $\mathcal {U^*}$-based scaling laws for the thrust and power are revealed in pitching rigid and flexible plates for various $A_L$ and $St$. This study may deepen our understanding of biological swimming and flying, and provide a guide for bionic design.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , R2
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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