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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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References

REFERENCES

Bhat, S.S., Zhao, J., Sheridan, J., Hourigan, K. & Thompson, M.C. 2019 a Aspect ratio studies on insect wings. Phys. Fluids 31 (12), 121301.CrossRefGoogle Scholar
Bhat, S.S., Zhao, J., Sheridan, J., Hourigan, K. & Thompson, M.C. 2019 b Uncoupling the effects of aspect ratio, Reynolds number and Rossby number on a rotating insect-wing planform. J. Fluid Mech. 859, 921–948.CrossRefGoogle Scholar
Birch, J.M. & Dickinson, M.H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412 (6848), 729–733.CrossRefGoogle Scholar
Birch, J.M., Dickson, W.B. & Dickinson, M.H. 2004 Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers. J. Expl Biol. 207 (7), 1063–1072.CrossRefGoogle Scholar
Carr, Z.R., DeVoria, A.C. & Ringuette, M.J. 2015 Aspect-ratio effects on rotating wings: circulation and forces. J. Fluid Mech. 767, 497–525.CrossRefGoogle Scholar
Chen, L., Wu, J. & Cheng, B. 2019 Volumetric measurement and vorticity dynamics of leading-edge vortex formation on a revolving wing. Exp. Fluids 60 (1), 12.CrossRefGoogle Scholar
Chen, L., Wu, J. & Cheng, B. 2020 Leading-edge vortex formation and transient lift generation on a revolving wing at low Reynolds number. Aerosp. Sci. Technol. 97, 105589.CrossRefGoogle Scholar
Chen, L., Wu, J., Zhou, C., Hsu, S.-J. & Cheng, B. 2018 Unsteady aerodynamics of a pitching-flapping-perturbed revolving wing at low Reynolds number. Phys. Fluids 30 (5), 051903.CrossRefGoogle Scholar
Cheng, B., Sane, S.P., Barbera, G., Troolin, D.R., Strand, T. & Deng, X. 2013 Three-dimensional flow visualization and vorticity dynamics in revolving wings. Exp. Fluids 54 (1), 1423.CrossRefGoogle Scholar
Cheng, X. & Sun, M. 2016 Wing-kinematics measurement and aerodynamics in a small insect in hovering flight. Sci. Rep. 6, 25706.CrossRefGoogle Scholar
Dickinson, M.H. & Gotz, K.G. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Expl Biol. 174 (1), 45–64.CrossRefGoogle Scholar
Dickinson, M.H., Lehmann, F.-O. & Sane, S.P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284 (5422), 1954–1960.CrossRefGoogle ScholarPubMed
Ellington, C.P., Van Den Berg, C., Willmott, A.P. & Thomas, A.L.R. 1996 Leading-edge vortices in insect flight. Nature 384 (6610), 626–630.CrossRefGoogle Scholar
Garmann, D.J. & Visbal, M.R. 2014 Dynamics of revolving wings for various aspect ratios. J. Fluid Mech. 748, 932–956.CrossRefGoogle Scholar
Garmann, D.J., Visbal, M.R. & Orkwis, P.D. 2013 Three-dimensional flow structure and aerodynamic loading on a revolving wing. Phys. Fluids 25 (3), 034101.CrossRefGoogle Scholar
Harbig, R.R., Sheridan, J. & Thompson, M.C. 2013 Reynolds number and aspect ratio effects on the leading-edge vortex for rotating insect wing planforms. J. Fluid Mech. 717, 166–192.CrossRefGoogle Scholar
Jardin, T. 2017 Coriolis effect and the attachment of the leading edge vortex. J. Fluid Mech. 820, 312–340.CrossRefGoogle Scholar
Jardin, T. & Colonius, T. 2018 On the lift-optimal aspect ratio of a revolving wing at low Reynolds number. J. R. Soc. Interface 15 (143), 20170933.CrossRefGoogle ScholarPubMed
Jardin, T. & David, L. 2014 Spanwise gradients in flow speed help stabilize leading-edge vortices on revolving wings. Phys. Rev. E 90 (1), 013011.CrossRefGoogle ScholarPubMed
Jardin, T. & David, L. 2015 Coriolis effects enhance lift on revolving wings. Phys. Rev. E 91 (3), 031001.CrossRefGoogle ScholarPubMed
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Kim, D. & Gharib, M. 2010 Experimental study of three-dimensional vortex structures in translating and rotating plates. Exp. Fluids 49 (1), 329–339.CrossRefGoogle Scholar
Lentink, D. & Dickinson, M.H. 2009 Rotational accelerations stabilize leading edge vortices on revolving fly wings. J. Expl Biol. 212 (16), 2705–2719.CrossRefGoogle ScholarPubMed
Mou, X., Liu, Y. & Sun, M. 2011 Wing motion measurement and aerodynamics of hovering true hoverflies. J. Expl Biol. 214 (17), 2832–2844.CrossRefGoogle ScholarPubMed
Ozen, C.A. & Rockwell, D.O. 2012 Three-dimensional vortex structure on a rotating wing. J. Fluid Mech. 707, 541–550.CrossRefGoogle Scholar
Sane, S.P. 2003 The aerodynamics of insect flight. J. Expl Biol. 206 (23), 4191–4208.CrossRefGoogle ScholarPubMed
Shyy, W. & Liu, H. 2007 Flapping wings and aerodynamic lift: the role of leading-edge vortices. AIAA J. 45 (12), 2817–2819.CrossRefGoogle Scholar
Sun, M. 2014 Insect flight dynamics: stability and control. Rev. Mod. Phys. 86 (2), 615–646.CrossRefGoogle Scholar
Sun, M. & Wu, J. 2004 Large aerodynamic forces on a sweeping wing at low Reynolds number. Acta Mechanica Sin. 20 (1), 24–31.Google Scholar
Weis-Fogh, T. 1973 Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Expl Biol. 59 (1), 169–230.CrossRefGoogle Scholar
Werner, N.H., Chung, H., Wang, J., Liu, G., Cimbala, J.M., Dong, H. & Cheng, B. 2019 Radial planetary vorticity tilting in the leading-edge vortex of revolving wings. Phys. Fluids 31 (4), 041902.CrossRefGoogle Scholar
Werner, N.H., Wang, J., Dong, H., Panah, A.E. & Cheng, B. 2020 Scaling the vorticity dynamics in the leading-edge vortices of revolving wings with two directional length scales. Phys. Fluids 32 (12), 121903.CrossRefGoogle Scholar
Wojcik, C.J. & Buchholz, J.H.J. 2014 Vorticity transport in the leading-edge vortex on a rotating blade. J. Fluid Mech. 743, 249–261.CrossRefGoogle Scholar
Wolfinger, M. & Rockwell, D.O. 2014 Flow structure on a rotating wing: effect of radius of gyration. J. Fluid Mech. 755, 83–110.CrossRefGoogle Scholar
Wu, J., Chen, L., Zhou, C., Hsu, S.-J. & Cheng, B. 2019 Aerodynamics of a flapping-perturbed revolving wing. AIAA J. 57 (9), 3728–3743.CrossRefGoogle Scholar
Wu, J. & Sun, M. 2004 Unsteady aerodynamic forces of a flapping wing. J. Expl Biol. 207 (7), 1137–1150.CrossRefGoogle ScholarPubMed
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