Experiments in Fluids

, 60:12 | Cite as

Volumetric measurement and vorticity dynamics of leading-edge vortex formation on a revolving wing

  • Long Chen
  • Jianghao Wu
  • Bo ChengEmail author
Research Article



Leading-edge vortex (LEV) is a hallmark of insect flight that forms and remains stably attached on high angle-of-attack (AoA), low aspect ratio (AR) wings undergoing revolving or flapping motion. Despite the efforts on explaining the stability of LEV when it reaches steady state in revolving wings, its formation process remains largely underexplored. Here, we investigate the LEV formation on a revolving wing (AoA = 45°, AR = 4 and Re = 1500), starting with a constant acceleration in the first chord (c) length of travel and then rotating at a constant velocity. The ‘Shake-the-box’ (STB) Lagrangian particle tracking velocimetry (PTV) system together with a volumetric patching process were performed to reconstruct the entire time-resolved flow field. Results show that LEV reaches steady state after approximately 4c of travel, within which its formation can be separated into three stages. In the first stage, a conical LEV structure begins to form with a tangential downstream convection of (negative) radial shear vorticity. In the second stage, the radial vorticity within the LEV is further convected downwards by the developed downwash, which limits its growth, whereas vorticity stretching increases the LEV strength. In the third stage, vorticity tilting and spanwise convection reduce the LEV strength at its rear end next to the trailing edge and, therefore, preventing it from growing. Our results suggest that insect wings with AR ~ 4, Re ~ 103 and flapping amplitude between 2c and 4c may barely or even not reach the steady state of LEV, indicating an indispensable role of transient LEV dynamics in understanding insect flight.

Graphical abstract



This research was supported by National Science Foundation (NSF CMMI 1554429), Army Research Office DURIP Grant (No. W911NF-16-1-0272), National Natural Science Foundation of China (NSFC, Grant No. 11672022), China Scholarship Council (joint Ph.D. program for Long Chen) and the Academic Excellence Foundation of BUAA for Ph.D. Students. We thank Dr. Steve Anderson at LaVision Inc. for his assistance with the ‘Shake-The-Box’ system, and Shih-Jung Hsu for the design of robotic wing mechanism.

Supplementary material

Supplementary material 1 (MP4 7273 KB)


  1. Batchelor GK (2000) An introduction to fluid dynamics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  2. Birch JM, Dickinson MH (2001) Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412(6848):729CrossRefGoogle Scholar
  3. Birch JM, Dickson WB, Dickinson MH (2004) Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers. J Exp Biol 207(7):1063–1072CrossRefGoogle Scholar
  4. Bomphrey RJ, Nakata T, Phillips N, Walker SM (2017) Smart wing rotation and trailing-edge vortices enable high frequency mosquito flight. Nature 544(7648):92–95CrossRefGoogle Scholar
  5. Carr ZR, Chen C, Ringuette MJ (2013) Finite-span rotating wings: three-dimensional vortex formation and variations with aspect ratio. Exp Fluids 54(2):1444–1470CrossRefGoogle Scholar
  6. Carr ZR, DeVoria AC, Ringuette MJ (2015) Aspect-ratio effects on rotating wings: circulation and forces. J Fluid Mech 767:497–525CrossRefGoogle Scholar
  7. Chen KK, Colonius T, Taira K (2010) The leading-edge vortex and quasisteady vortex shedding on an accelerating plate. Phys Fluids 22(3):033601CrossRefGoogle Scholar
  8. Chen L, Wu JH, 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):051903CrossRefGoogle Scholar
  9. Cheng B, Sane SP, Barbera G, Troolin DR, Strand T, Deng XY (2013) Three-dimensional flow visualization and vorticity dynamics in revolving wings. Exp Fluids 54(1):1423–1435CrossRefGoogle Scholar
  10. Cheng B, Roll J, Liu Y, Troolin DR, Deng XY (2014) Three-dimensional vortex wake structure of flapping wings in hovering flight. J R Soc Interface 11(91):20130984CrossRefGoogle Scholar
  11. Chin DD, Lentink D (2016) Flapping wing aerodynamics: from insects to vertebrates. J Exp Biol 219(7):920–932CrossRefGoogle Scholar
  12. Dickinson MH, Gotz KG (1993) Unsteady aerodynamic performance of model wings at low Reynolds numbers. J Exp Biol 174(1):45–64Google Scholar
  13. Ellington CP (1984a) The aerodynamics of hovering insect flight. III. Kinematics. Phil Trans R Soc Lond B 305(1122):41–78CrossRefGoogle Scholar
  14. Ellington CP (1984b) The aerodynamics of insect flight. II. Morphological parameters. Phil Trans R Soc Lond B 305(1122):17–40CrossRefGoogle Scholar
  15. Ellington CP, Van Den Berg C, Willmott AP, Thomas AL (1996) Leading-edge vortices in insect flight. Nature 384(6610):626CrossRefGoogle Scholar
  16. Garmann DJ, Visbal MR (2014) Dynamics of revolving wings for various aspect ratios. J Fluid Mech 748:932–956CrossRefGoogle Scholar
  17. Harbig RR, Sheridan J, Thompson MC (2013) Reynolds number and aspect ratio effects on the leading-edge vortex for rotating insect wing planforms. J Fluid Mech 717:166–192CrossRefGoogle Scholar
  18. Harbig RR, Sheridan J, Thompson MC (2014) The role of advance ratio and aspect ratio in determining leading-edge vortex stability for flapping flight. J Fluid Mech 751:71–105MathSciNetCrossRefGoogle Scholar
  19. Jain MV, Wong JG, Rival DE (2015) Investigation of vortex development on accelerating spanwise-flexible wings. J Fluids Struct 54:466–478CrossRefGoogle Scholar
  20. Jardin T (2017) Coriolis effect and the attachment of the leading edge vortex. J Fluid Mech 820:312–340MathSciNetCrossRefGoogle Scholar
  21. Jardin T, David L (2015) Coriolis effects enhance lift on revolving wings. Phys Rev E 91(3):031001CrossRefGoogle Scholar
  22. Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94MathSciNetCrossRefGoogle Scholar
  23. Kruyt JW, van Heijst GF, Altshuler DL, 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):20150051CrossRefGoogle Scholar
  24. Lee YJ, Lua KB, Lim TT (2016) Aspect ratio effects on revolving wings with Rossby number consideration. Bioinspir Biomim 11(5):056013CrossRefGoogle Scholar
  25. Lentink D (2013) Flying like a fly. Nature 498:306–308CrossRefGoogle Scholar
  26. Lentink D, Dickinson MH (2009) Rotational accelerations stabilize leading edge vortices on revolving fly wings. J Exp Biol 212(16):2705–2719CrossRefGoogle Scholar
  27. Lim TT, Teo CJ, Lua KB, Yeo KS (2009) On the prolong attachment of leading edge vortex on a flapping wing. Mod Phys Lett B 23(03):357–360CrossRefGoogle Scholar
  28. Liu H, Ellington CP, Kawachi K, Van Den Berg C, Willmott AP (1998) A computational fluid dynamic study of hawkmoth hovering. J Exp Biol 201(4):461–477Google Scholar
  29. Lua KB, Lai KC, Lim TT, Yeo KS (2010) On the aerodynamic characteristics of hovering rigid and flexible hawkmoth-like wings. Exp Fluids 49(6):1263–1291CrossRefGoogle Scholar
  30. Lua KB, Lim TT, Yeo KS (2014) Scaling of aerodynamic forces of three-dimensional flapping wings. AIAA J 52(5):1095–1101CrossRefGoogle Scholar
  31. Lua KB, Lee YJ, Lim TT, Yeo KS (2016) Aerodynamic effects of elevating motion on hovering rigid hawkmothlike wings. AIAA J 54(8):2247–2264CrossRefGoogle Scholar
  32. Percin M, Van Oudheusden BW (2015) Three-dimensional flow structures and unsteady forces on pitching and surging revolving flat plates. Exp Fluids 56(2):47CrossRefGoogle Scholar
  33. Poelma C, Dickson WB, Dickinson MH (2006) Time-resolved reconstruction of the full velocity field around a dynamically-scaled flapping wing. Exp Fluids 41(2):213–225CrossRefGoogle Scholar
  34. Rival DE, Kriegseis J, Schaub P, Widmann A, Tropea C (2014) Characteristic length scales for vortex detachment on plunging profiles with varying leading-edge geometry. Exp Fluids 55(1):1660–1668CrossRefGoogle Scholar
  35. Sane SP (2003) The aerodynamics of insect flight. J Exp Biol 2006(23):4191–4208CrossRefGoogle Scholar
  36. Schanz D, Schröder A, Gesemann S (2014) Shake the box—a 4D PTV algorithm: accurate and ghostless reconstruction of Lagrangian tracks in densely seeded flows. In: 17th international symposium on applications of laser techniques to fluid mechanics, LisbonGoogle Scholar
  37. Schanz D, Gesemann S, Schröder A (2016) Shake-the-box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57(5):70–97CrossRefGoogle Scholar
  38. Schröder A, Schanz D, Michaelis D, Cierpka C, Scharnowski S, Kähler CJ (2015) Advances of PIV and 4D-PTV” Shake-The-Box” for turbulent flow analysis—the flow over periodic hills. Flow Turbul Combust 95(2–3):193–209CrossRefGoogle Scholar
  39. Shyy W, Liu H (2007) Flapping wings and aerodynamic lift: the role of leading-edge vortices. AIAA J 45(12):2817–2819CrossRefGoogle Scholar
  40. Shyy W, Lian YS, Tang J, Viieru D, Liu H (2008) Aerodynamics of low Reynolds number flyers. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  41. Smith DT, 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):064701CrossRefGoogle Scholar
  42. Sun M (2005) High-lift generation and power requirements of insect flight. Fluid Dyn Res 37(1–2):21–39CrossRefGoogle Scholar
  43. Usherwood JR, Ellington CP (2002) The aerodynamics of revolving wings I. Model hawkmoth wings. J Exp Biol 205(11):1547–1564Google Scholar
  44. Vogel S (1967) Flight in Drosophila. III. Aerodynamic characteristics of fly wings and wing models. J Exp Biol 46(3):431–443Google Scholar
  45. Wang ZJ (2004) The role of drag in insect hovering. J Exp Biol 207(23):4147–4155CrossRefGoogle Scholar
  46. Wang ZJ (2005) Dissecting insect flight. Annu Rev Fluid Mech 37(37):183–210MathSciNetCrossRefGoogle Scholar
  47. Wang ZJ, Birch JM, Dickinson MH (2004) Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments. J Exp Biol 207(3):449–460CrossRefGoogle Scholar
  48. Weis-Fogh T (1973) Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J Exp Biol 59(1):169–230Google Scholar
  49. Widmann A, Tropea C (2015) Parameters influencing vortex growth and detachment on unsteady aerodynamic profiles. J Fluid Mech 773:432–459MathSciNetCrossRefGoogle Scholar
  50. Wojcik CJ, Buchholz JH (2014) Vorticity transport in the leading-edge vortex on a rotating blade. J Fluid Mech 743:249–261CrossRefGoogle Scholar
  51. Wong JG, Rival DE (2015) Determining the relative stability of leading-edge vortices on nominally two-dimensional flapping profiles. J Fluid Mech 766:611–625MathSciNetCrossRefGoogle Scholar
  52. Wong JG, Jochen K, David ER (2013) An investigation into vortex growth and stabilization for two-dimensional plunging and flapping plates with varying sweep. J Fluids Struct 43:231–243CrossRefGoogle Scholar
  53. Wu JH, Sun M (2004) Unsteady aerodynamic forces of a flapping wing. J Exp Biol 207(7):1137–1150CrossRefGoogle Scholar
  54. Wu JH, Chen L, Zhou C, Hsu S-J, Cheng B (2018) Aerodynamics of a flapping-perturbed revolving wing. AIAA J. CrossRefGoogle Scholar
  55. Zhu HJ, Sun M (2017) Unsteady aerodynamic force mechanisms of a hoverfly hovering with a short stroke-amplitude. Phys Fluids 29(8):081901CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Transportation Science and EngineeringBeihang UniversityBeijingPeople’s Republic of China
  2. 2.Department of Mechanical EngineeringPennsylvania State UniversityUniversity ParkUSA

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