Hostname: page-component-cb9f654ff-65tv2 Total loading time: 0 Render date: 2025-08-05T20:00:56.881Z Has data issue: false hasContentIssue false
  • English
  • Français

Dual-stage radial–tangential vortex tilting reverses radial vorticity and contributes to leading-edge vortex stability on revolving wings

Published online by Cambridge University Press:  19 May 2023

Long Chen Open the ORCID record for Long Chen [Opens in a new window] ,
Chao Zhou ,
Nathaniel H. Werner Open the ORCID record for Nathaniel H. Werner [Opens in a new window] ,
Bo Cheng Open the ORCID record for Bo Cheng [Opens in a new window]  and
Jianghao Wu Open the ORCID record for Jianghao Wu [Opens in a new window]
Long Chen
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China
Chao Zhou
Affiliation:
School of Transportation Science and Engineering, Beihang University, Beijing 100191, PR China
Nathaniel H. Werner
Affiliation:
Department of Mechanical Engineering, Liberty University, Lynchburg, VA 24515, USA
Bo Cheng
Affiliation:
Department of Mechanical Engineering, Pennsylvania State University, University Park, PA 16802, USA
Jianghao Wu*
Affiliation:
School of Transportation Science and Engineering, Beihang University, Beijing 100191, PR China
*
†Email address for correspondence: buaawjh@buaa.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The physics of leading-edge vortex (LEV) stability on flapping wings and autorotating seeds is still underexplored due to its complex dependency on Reynolds number ($\textit {Re}$), aspect ratio (AR) and Rossby number (Ro). Our previous study observed an interesting dual-stage vortex tilting between radial and tangential components in a stable LEV. Here, the establishment of this novel mechanism, i.e. dual-stage radial–tangential vortex tilting (DS-VT$_{r-t}$), is investigated and explained in detail using numerical methods. The contributions of other tangential vorticity transport terms are also considered. It is shown that the stable LEV region coincides mostly with a constant ratio of tangential and radial vorticity components. The DS-VT$_{r-t}$ mechanism functions as a negative feedback loop for radial vorticity, thereby contributing to the LEV stability at $\textit {Re} > 500$. Specifically, this mechanism involves a dual-stage vortex tilting starting from negative radial component to positive tangential component, and then back to positive radial component, thereby leading to a $180^{\circ }$ reversal of radial vorticity. The radial Coriolis acceleration can also assist the DS-VT$_{r-t}$ by enhancing the tangential vorticity component and the reduction of radial vorticity inside the LEV via the second stage of DS-VT$_{r-t}$. The effects of $\textit {Re}$, AR and Ro on the constant radial–tangential vorticity ratio and DS-VT$_{r-t}$ are then analysed. The coupled effects of AR and Ro are separated into rotational effects and those of tip and root vortices. Our results establish an evident relationship among the LEV stability, the constant radial–tangential vorticity ratio, and the DS-VT$_{r-t}$, thereby deepening the understanding in the vorticity transport of LEV formation and stability.

JFM classification

Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex dynamics

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , A29
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Åström, K.J. & Murray, R.M. 2021 Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press.Google Scholar
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
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, K.K., Colonius, T. & Taira, K. 2010 The leading-edge vortex and quasisteady vortex shedding on an accelerating plate. Phys. Fluids 22 (3), 033601.CrossRefGoogle Scholar
Chen, L., Wang, L., Zhou, C., Wu, J. & Cheng, B. 2022 Effects of Reynolds number on leading-edge vortex formation dynamics and stability in revolving wings. J. Fluid Mech. 931, A13.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
Chin, D.D. & Lentink, D. 2016 Flapping wing aerodynamics: from insects to vertebrates. J. Expl Biol. 219 (7), 920–932.CrossRefGoogle ScholarPubMed
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
Dudley, R. 2002 The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton University Press.Google Scholar
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
Kruyt, J.W., Van Heijst, G.F., Altshuler, D.L. & Lentink, D. 2015 Power reduction and the radial limit of stall delay in revolving wings of different aspect ratio. J. R. Soc. Interface 12 (105), 20150051.CrossRefGoogle ScholarPubMed
Lee, Y.J., Lua, K.-B. & Lim, T.T. 2016 Aspect ratio effects on revolving wings with Rossby number consideration. Bioinspir. Biomim. 11 (5), 056013.CrossRefGoogle ScholarPubMed
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
Minotti, F.O. & Speranza, E. 2005 Leading-edge vortex stability in insect wings. Phys. Rev. E 71 (5), 051908.CrossRefGoogle ScholarPubMed
Poelma, C., Dickson, W.B. & Dickinson, M.H. 2006 Time-resolved reconstruction of the full velocity field around a dynamically-scaled flapping wing. Exp. Fluids 41 (2), 213–225.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
Smith, D.T., Rockwell, D., Sheridan, J. & Thompson, M. 2017 Effect of radius of gyration on a wing rotating at low Reynolds number: a computational study. Phys. Rev. Fluids 2 (6), 064701.CrossRefGoogle Scholar
Sun, M. 2014 Insect flight dynamics: stability and control. Rev. Mod. Phys. 86 (2), 615–646.CrossRefGoogle Scholar
Van Den Berg, C. & Ellington, C.P. 1997 The three-dimensional leading-edge vortex of a ‘hovering’ model hawkmoth. Phil. Trans. R. Soc. Lond. B 352 (1351), 329–340.CrossRefGoogle Scholar
Visbal, M.R. & Garmann, D.J. 2019 Dynamic stall of a finite-aspect-ratio wing. AIAA J. 57 (3), 962–977.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
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
Zhao, T., Yan, K., Li, H. & Wang, X. 2022 Study on theoretical modeling and vibration performance of an assembled cylindrical shell-plate structure with whirl motion. Appl. Math. Model. 110, 618–632.CrossRefGoogle Scholar