Experiments in Fluids

, 60:164 | Cite as

Influence of aspect ratio on wing–wake interaction for flapping wing in hover

  • Reynolds Addo-Akoto
  • Jong-Seob Han
  • Jae-Hung HanEmail author
Research Article


The interaction between an insect wing and its wake during hovering flight is inevitable. The effect of this wing–wake interaction (WWI) during stroke reversal is an intricate phenomenon that is difficult to forecast. Previous studies have mostly concentrated on the effect of aspect ratio (AR) on the leading-edge vortex (LEV) at the middle of stroke motion. However, the effect of AR on LEV during stroke reversal, which is where the intricate WWI phenomenon occurs, has not been fully exploited. This study aimed at revealing how AR affects WWI during stroke reversal at Re of ~ 104, and the role LEV plays. The experimental time-course measurement of force showed that the WWI at stroke reversal was strengthened by decreasing AR irrespective of pitching duration. A time-varying digital particle image velocimetry (DPIV) measurement revealed a jet-like flow induced by a pair of counter-rotating trailing edge vortex (TEV) as the primitive source of the interaction. This study found a WWI that appeared at the wing root contrary to the conventional type in literature, which appeared at the wing tip. The size of the LEV at the wing root played a key role by facilitating the effectiveness of the wing rotation. AR = 2 wing benefited much from this form of WWI by generating strong coherent shear layer at the end of stroke, and relatively weak LEV during stroke reversal. Thus, this type of WWI might be mostly beneficial for low AR wings (AR < 3).

Graphic abstract

List of symbols

Latin symbols


Advanced ratio


Aspect ratio


Drag coefficient


Flexural rigidity


Distance from the pivot to the wingtip


Lift coefficient


Non-dimensional radius of gyration




Reference length to the wing tip


Reference length to the location of the radius of gyration


Reference velocity


Reynolds number


Rossby number


Tip velocity ratio


Wing area


Wing chord length

\(\Delta R\)

Wing root offset distance


Wing span length


Young’s modulus

Greek symbols


Effective stiffness

\(\Delta \tau\)

Non-dimension duration

\(\Delta \tau_{\alpha }\)

Non-dimensional duration of the wing rotation

\(\Delta \tau_{\phi }\)

On-dimensional duration for acceleration and deceleration


Non-dimension time


Non-dimensional timing rotation

\(\hat{\omega }\)

Normalized vorticity


Pitch amplitude


Stroke amplitude



This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2017R1A2B4005676).


  1. Bhat SS, Zhao J, Sheridan J, Hourigan K, Thompson MC (2019) Uncoupling the effects of aspect ratio, Reynolds number and Rossby number on a rotating insect-wing planform. J Fluid Mech 859:921–948MathSciNetzbMATHGoogle Scholar
  2. Birch JM, Dickinson MH (2003) The influence of wing–wake interactions on the production of aerodynamic forces in flapping flight. J Exp Biol 206:2257–2272Google Scholar
  3. Carr ZR, Chen C, Ringuette MJ (2013) Finite-span rotating wings: three-dimensional vortex formation and variations with aspect ratio. Exp Fluids 54:1–26Google Scholar
  4. Carr ZR, DeVoria AC, Ringuette MJ (2015) Aspect-ratio effects on rotating wings: circulation and forces. J Fluid Mech 767:497–525Google Scholar
  5. Cheng B, Roll R, Liu Y, Troolin DR, Deng X (2013) Three-dimensional vortex wake structure of flapping wings in hovering flight. J R Soc Interface 11:1111–1133Google Scholar
  6. Dickinson MH, Lehmann FO, Sane SP (1999) Wing rotation and the aerodynamic basis of insect flight. Science 284:1954–1960Google Scholar
  7. Ellington CP (1984a) The aerodynamics of hovering insect flight IV aerodynamic mechanisms. Philos Trans R Soc Lond B 305:79–113Google Scholar
  8. Ellington CP (1984b) The aerodynamics of hovering insect flight III kinematics. Philos Trans R Soc Lond B 305:41–78Google Scholar
  9. Ennos AR (1989) The kinematics and aerodynamics of the free flight of some diptera. J Exp Biol 142:49–85Google Scholar
  10. Fu J, Shyy W, Qui H (2017) Effects of aspect ratio on vortex dynamics of a rotating wing. AIAA J 55(12):4074–4082Google Scholar
  11. Fu J, Liu X, Shyy W, Qui H (2018) Effects of flexibility and aspect ratio on the aerodynamic performance of flapping wings. Bioinspir Biomim 13:036001Google Scholar
  12. Garmann DJ, Visbal MR (2014) Dynamics of revolving wings for various aspect ratios. J Fluid Mech 748:932–956Google Scholar
  13. Garmann DJ, Visbal MR, Orkwis PD (2013) Three-dimensional flow structure and aerodynamic loading on a revolving wing. Phys Fluids 25:034101Google Scholar
  14. Han JS, Chang JW, Kim ST (2014) Reynolds number dependency of an insect-based flapping wing. Bioinspir Biomim 9:046012Google Scholar
  15. Han JS, Chang JW, Cho HK (2015a) Vortices behavior depending on the aspect ratio of an insect-like flapping wing in hover. Exp Fluids 56:181–196Google Scholar
  16. Han JS, Chang JW, Kim JK, Han JH (2015b) Role of trailing edge vortices on the hawkmoth-like flapping wing. J Aircraft 52:1256–1266Google Scholar
  17. Han JS, Chang JW, Han JH (2016) The advance ratio effect on the lift augmentations of an insect-like flapping wing in forward flight. J Fluid Mech 808:485–510MathSciNetzbMATHGoogle Scholar
  18. Han JS, Chang JW, Han JH (2017) An aerodynamic model for insect flapping wings in forward flight. Bioinspir Biomim 12:036004Google Scholar
  19. 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 717:166–192zbMATHGoogle Scholar
  20. 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):20170933Google Scholar
  21. Keennon M, Klingebiel K, Won H, Andriukov A (2012) Development of the nano hummingbird: a tailless flapping wing micro air vehicle. AIAA paper No. AIAA 2012-0588Google Scholar
  22. Kim HY, Han JS, Han JH (2019) Aerodynamic effects of deviating motion of flapping wings in hovering flight. Bioinspi Biomim 14(2):026006Google 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 12:2015005Google Scholar
  24. Kweon JH, Choi H (2010) Sectional lift coefficient of a flapping wing in hovering motion. Phys Fluids 22:071703Google Scholar
  25. Kweon JH, Choi H (2012) Three-dimensional flows around a flapping wing in ground effect. Int Conf Comput Fluid Dyn (ICCFD) 7:4102Google Scholar
  26. Lee YJ, Lua KB (2018) Wing–wake interaction: comparison of 2D and 3D flapping wings in hover flight. Bioinspir Biomim 13(6):066003Google Scholar
  27. Lehmann FO, Sane SP, Dickinson MH (2005) The aerodynamic effects of wing–wing interaction in flapping insect wings. J Exp Biol 208:3075–3092Google Scholar
  28. Lentink D, Dickinson MH (2009a) Biofluiddynamic scaling of flapping spinning and translating finds and wings. J Exp Biol 212(16):2691–2704Google Scholar
  29. Lentink D, Dickinson MH (2009b) Rotational accelerations stabilize leading edge vortices on revolving fly wings. J Exp Biol 212:2705–2719Google Scholar
  30. Lu Y, Shen GX, Lai GJ (2006) Dual leading-edge vortices on flapping wings. J Exp Biol 209:5005–5016Google Scholar
  31. 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):1263–1291Google Scholar
  32. Lua KB, Lim TT, Yeo KS (2011) Effect of wing–wake interaction on aerodynamic force generation on a 2D flapping wing. Exp Fluids 51:177–195Google Scholar
  33. Lua KB, Lim TT, Yeo KS (2014) Scaling of aerodynamic forces of three-dimensional flapping wings. AIAA J 52:1095–1101Google Scholar
  34. Lua KB, Lim TT, Yeo KS (2017) Wing–wake interaction of three-dimensional flapping wings. AIAA J 55:729–738Google Scholar
  35. Luo G, Sun M (2005) The effects of corrugation and wing planform on the aerodynamic force production of sweeping model insect wings. Acta Mech Sin 21:531–541zbMATHGoogle Scholar
  36. Nabawy MR, Crowther WJ (2014) On the quasi-steady aerodynamics of normal hovering flight part I: the induced power factor. J R Soc Interface 11(93):20131196Google Scholar
  37. Nabawy MR, Crowther WJ (2015) A quasi-steady lifting line theory for insect-like hovering flight. PLoS One 10(8):e0134972Google Scholar
  38. Nabawy MR, Crowther WJ (2017) The role of the leading edge vortex in lift augmentation of steadily revolving wings: a change in perspective. J R Soc Interface 14(132):20170159Google Scholar
  39. Ozen CA, Rockwell D (2013) Flow structure on a rotating wing: effect of wing aspect ratio and shape. AIAA Paper No. AIAA 2013-0676Google Scholar
  40. Phillips N, Knowles K (2011) Effect of flapping kinematics on the mean lift of an insect-like flapping wing. Proc Inst Mech Eng Part G: J Aerosp Eng 225(7):723–736Google Scholar
  41. Phillips N, Knowles K, Bomphrey RJ (2015) The effect of aspect ratio on the leading-edge vortex over an insect-like flapping wing. Bioinspir Biomim 10:056020Google Scholar
  42. Phillips N, Knowles K, Bomphrey RJ (2017) Petiolate wings: effects on the leading-edge vortex in flapping flight. Interface focus 7(1):20160084Google Scholar
  43. Sane SP (2003) The aerodynamics of insect flight. J Exp Biol 206(23):4191–4208Google Scholar
  44. Sane SP, Dickinson MH (2001) The control of flight force by a flapping wing: lift and drag production. J Exp Biol 204:2607–2626Google Scholar
  45. Sane SP, Dickinson MH (2002) The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight. J Exp Biol 205:1087–1096Google Scholar
  46. Sun M, Tang J (2002a) Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. J Exp Biol 205(1):55–70Google Scholar
  47. Sun M, Tang J (2002b) Lift and power requirements of hovering flight in Drosophila virilis. J Exp Biol 205(1):2413–2427Google Scholar
  48. Thielicke W, Stamhuis EJ (2014) PIVlab–towards user-friendly affordable and accurate digital particle image velocimetry in MATLAB. J Open Res Softw 2(1):e30Google Scholar
  49. Wieneke B (2015) PIV uncertainty quantification from correlation statistics. Meas Sci Technol 26(7):074002Google Scholar
  50. Wu J, Sun M (2004) Unsteady aerodynamic forces of a flapping wing. J Exp Biol 207:1137–1150Google Scholar
  51. Wu J, Sun M (2005) The influence of the wake of a flapping wing on the production of aerodynamic forces. Acta Mech Sin 21(5):411–418zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Reynolds Addo-Akoto
    • 1
  • Jong-Seob Han
    • 1
  • Jae-Hung Han
    • 1
    Email author
  1. 1.Department of Aerospace EngineeringKorea Advanced Institute of Science and Technology (KAIST)DaejeonRepublic of Korea

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