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Effects of Reynolds number on leading-edge vortex formation dynamics and stability in revolving wings

Published online by Cambridge University Press:  23 November 2021

Long Chen Open the ORCID record for Long Chen [Opens in a new window] ,
Luyao Wang ,
Chao Zhou ,
Jianghao Wu  and
Bo Cheng Open the ORCID record for Bo Cheng [Opens in a new window]
Long Chen*
Affiliation:
College of Sciences, Northeastern University, Shenyang, Liaoning 110819, PR China
Luyao Wang
Affiliation:
College of Sciences, Northeastern University, Shenyang, Liaoning 110819, PR China
Chao Zhou
Affiliation:
School of Transportation Science and Engineering, Beihang University, Beijing 100191, PR China
Jianghao Wu
Affiliation:
School of Transportation Science and Engineering, Beihang University, Beijing 100191, PR China
Bo Cheng
Affiliation:
Department of Mechanical Engineering, Pennsylvania State University, University Park, PA 16801, USA
*
†Email address for correspondence: chenlong@mail.neu.edu.cn
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Abstract

The mechanisms of leading-edge vortex (LEV) formation and its stable attachment to revolving wings depend highly on Reynolds number ($\textit {Re}$). In this study, using numerical methods, we examined the $\textit {Re}$ dependence of LEV formation dynamics and stability on revolving wings with $\textit {Re}$ ranging from 10 to 5000. Our results show that the duration of the LEV formation period and its steady-state intensity both reduce significantly as $\textit {Re}$ decreases from 1000 to 10. Moreover, the primary mechanisms contributing to LEV stability can vary at different $\textit {Re}$ levels. At $\textit {Re} <200$, the LEV stability is mainly driven by viscous diffusion. At $200<\textit {Re} <1000$, the LEV is maintained by two distinct vortex-tilting-based mechanisms, i.e. the planetary vorticity tilting and the radial–tangential vorticity balance. At $\textit {Re}>1000$, the radial–tangential vorticity balance becomes the primary contributor to LEV stability, in addition to secondary contributions from tip-ward vorticity convection, vortex compression and planetary vorticity tilting. It is further shown that the regions of tip-ward vorticity convection and tip-ward pressure gradient almost overlap at high $\textit {Re}$. In addition, the contribution of planetary vorticity tilting in LEV stability is $\textit {Re}$-independent. This work provides novel insights into the various mechanisms, in particular those of vortex tilting, in driving the LEV formation and stability on low-$\textit {Re}$ revolving wings.

JFM classification

Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , A13
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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