1932

Abstract

The leading-edge vortex (LEV) is known to produce transient high lift in a wide variety of circumstances. The underlying physics of LEV formation, growth, and shedding are explored for a set of canonical wing motions including wing translation, rotation, and pitching. A review of the literature reveals that, while there are many similarities in the LEV physics of these motions, the resulting force histories can be dramatically different. In two-dimensional motions (translation and pitch), the LEV sheds soon after its formation; lift drops as the LEV moves away from the wing. Wing rotation, in contrast, incites a spanwise flow that, through Coriolis tilting, balances the streamwise vorticity fluxes to produce an LEV that remains attached to much of the wing and thus sustains high lift. The state of the art of vortex-based modeling to capture both the flow field and corresponding forces of these motions is reviewed, including closure conditions at the leading edge and approaches for data-driven strategies.

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2019-01-05
2024-06-14
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Literature Cited

  1. Acharya M, Metwally MH 1992. Unsteady pressure field and vorticity production over a pitching airfoil. AIAA J. 30:403–11
    [Google Scholar]
  2. Akkala JM, Panah AE, Buchholz JHJ 2015. Vortex dynamics and performance of flexible and rigid plunging airfoils. J. Fluid Struct. 54:103–21
    [Google Scholar]
  3. Ansari SA, Zbikowski R, Knowles K 2006. Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 2: implementation and validation. Proc. Inst. Mech. Eng. G 220:169–86
    [Google Scholar]
  4. Baik YS, Bernal LP, Granlund K, Ol MV 2012. Unsteady force generation and vortex dynamics of pitching and plunging aerofoils. J. Fluid Mech. 709:37–68
    [Google Scholar]
  5. Beckwith RMH, Babinsky H 2009. Impulsively started flat plate flow. J. Aircr. 46:2186–89
    [Google Scholar]
  6. Beem HR, Rival DE, Triantafyllou MS 2011. On the stabilization of leading-edge vortices with spanwise flow. Exp. Fluids 52:511–17
    [Google Scholar]
  7. Birch JM, Dickinson MH 2001. Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412:729–33
    [Google Scholar]
  8. Bomphrey R, Taylor G, Thomas A 2009. Smoke visualization of free-flying bumblebees indicates independent leading-edge vortices on each wing pair. Exp. Fluids 46:811–21
    [Google Scholar]
  9. Brown CE, Michael WH 1954. Effect of leading edge separation on the lift of a delta wing. J. Aeronaut. Sci. 21:690–94
    [Google Scholar]
  10. Brunton SL, Rowley CW, Williams DR 2013. Reduced-order unsteady aerodynamic models at low Reynolds numbers. J. Fluid Mech. 724:203–33
    [Google Scholar]
  11. Buchner AJ, Buchmann N, Kilany K, Atkinson C, Soria J 2012. Stereoscopic and tomographic PIV of a pitching plate. Exp. Fluids 52:299–314
    [Google Scholar]
  12. Calderon DE, Wang Z, Gursul I, Visbal M 2013. Volumetric measurements and simulations of the vortex structures generated by low aspect ratio plunging wings. Phys. Fluids 25:067102
    [Google Scholar]
  13. Carr Z, Chen C, Ringuette M 2013. Finite-span rotating wings: three-dimensional vortex formation and variations with aspect ratio. Exp. Fluids 54:1444
    [Google Scholar]
  14. Chen KK, Colonius T, Taira K 2010. The leading-edge vortex and quasisteady vortex shedding on an accelerating plate. Phys. Fluids 22:033601
    [Google Scholar]
  15. Choi J, Colonius T, Williams DR 2015. Surging and plunging oscillations of an airfoil at low Reynolds number. J. Fluid Mech. 763:237–53
    [Google Scholar]
  16. Darakananda D, Eldredge JD, Colonius T, Williams DR 2016. A vortex sheet/point vortex dynamical model for unsteady separated flows Paper presented at AIAA Aerospace Science Meeting, 54th, San Diego, CA, AIAA Pap. 2016-2072
    [Google Scholar]
  17. Darakananda D, Eldredge JD, da Silva A, Colonius T, Williams D 2018. EnKF-based dynamic estimation of separated flows with a low-order vortex model Paper presented at AIAA Aerospace Science Meeting, 56th, Kissimmee, FL, AIAA Pap. 2018-0811
    [Google Scholar]
  18. DeVoria AC, Ringuette MJ 2012. Vortex formation and saturation for low-aspect-ratio rotating flat-plate fins. Exp. Fluids 52:441–62
    [Google Scholar]
  19. Dickinson MH, Lehmann FO, Sane SP 1999. Wing rotation and the aerodynamic basis of insect flight. Science 284:1954–60
    [Google Scholar]
  20. Edwards RH 1954. Leading edge separation from delta wings. J. Aerosp. Sci. 21:134–35
    [Google Scholar]
  21. Eldredge JD, Wang C 2010. High-fidelity simulations and low-order modeling of a rapidly pitching plate Paper presented at Fluid Dynamics Conference and Exhibit, 40th, Chicago, IL, AIAA Pap. 2010-4281
    [Google Scholar]
  22. Eldredge JD, Wang C, Ol MV 2009. A computational study of a canonical pitch-up, pitch-down wing maneuver Paper presented at AIAA Fluid Dynamics Conference, 39th, San Antonio, TX, AIAA Pap. 2009-3687
    [Google Scholar]
  23. Ellington CP 1984. The aerodynamics of hovering insect flight. VI. Lift and power requirements. Philos. Trans. R. Soc. B 305:145–81
    [Google Scholar]
  24. Ellington CP, van den Berg C, Willmott AP, Thomas ALR 1996. Leading-edge vortices in insect flight. Nature 384:626–30
    [Google Scholar]
  25. Evensen G 2009. Data Assimilation: The Ensemble Kalman Filter Berlin: Springer-Verlag
    [Google Scholar]
  26. Fenercioglu I, Cetiner O 2012. Categorization of flow structures around a pitching and plunging airfoil. J. Fluid Struct. 31:92–102
    [Google Scholar]
  27. Freymuth P, Finaish F, Bank W 1987. Further visualization of combined wing tip and starting vortex systems. AIAA J. 25:1153–59
    [Google Scholar]
  28. Garmann D, Visbal M 2014. Dynamics of revolving wings for various aspect ratios. J. Fluid Mech. 748:932–56
    [Google Scholar]
  29. Graftieaux L, Michard M, Grosjean N 2001. Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows. Meas. Sci. Technol. 12:1422–29
    [Google Scholar]
  30. Granlund K, Monnier B, Ol M, Williams DR 2014. Airfoil longitudinal gust response in separated versus attached flows. Phys. Fluids 26:027103
    [Google Scholar]
  31. Granlund K, Ol MV, Bernal LP 2013. Unsteady pitching flat plates. J. Fluid Mech. 733:R5
    [Google Scholar]
  32. Granlund K, Ol MV, Jones AR 2016. Streamwise oscillation of airfoils into reverse flow. AIAA J. 54:1628–36
    [Google Scholar]
  33. Haller G 2001. Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Phys. Fluids 13:3365–85
    [Google Scholar]
  34. Harbig R, Sheridan J, Thompson M 2013. Reynolds number and aspect ratio effects on the leading-edge vortex for rotating insect wing planforms. J. Fluid Mech. 717:166–92
    [Google Scholar]
  35. Hemati MS, Eldredge JD, Speyer JL 2014. Improving vortex models via optimal control theory. J. Fluid Struct. 49:91–111
    [Google Scholar]
  36. Huang Y, Green MA 2015. Detection and tracking of vortex phenomena using Lagrangian coherent structures. Exp. Fluids 56:147
    [Google Scholar]
  37. Hubel TY, Tropea C 2010. The importance of leading edge vortices under simplified flapping flight conditions at the size scale of birds. J. Exp. Biol. 213:1930–39
    [Google Scholar]
  38. Jantzen RT, Taira K, Granlund K, Ol MV 2014. Vortex dynamics around pitching plates. Phys. Fluids 26:053606
    [Google Scholar]
  39. Jardin T 2017. Coriolis effect and the attachment of the leading edge vortex. J. Fluid Mech. 820:312–40
    [Google Scholar]
  40. Jardin T, David L 2014. Spanwise gradients in flow speed help stabilize leading-edge vortices on revolving wings. Phys. Rev. E 90:013011
    [Google Scholar]
  41. Jardin T, Farcy A, David L 2012. Three-dimensional effects in hovering flapping flight. J. Fluid Mech. 702:102–25
    [Google Scholar]
  42. Jeong J, Hussain F 1995. On the identification of a vortex. J. Fluid Mech. 285:69–94
    [Google Scholar]
  43. Jones AR, Babinsky H 2010. Unsteady lift generation on rotating wings at low Reynolds numbers. J. Aircr. 47:1013–21
    [Google Scholar]
  44. Jones AR, Manar FH, Phillips N, Nakata T, Bomphrey R et al. 2016. Leading-edge vortex evolution and lift production on rotating wings (invited) Paper presented at AIAA Aerospace Sciences Meeting, 54th, San Diego, CA, AIAA Pap. 2016-0288
    [Google Scholar]
  45. Jones MA 2003. The separated flow of an inviscid fluid around a moving flat plate. J. Fluid Mech. 496:405–41
    [Google Scholar]
  46. Jumper E, Schreck S, Dimmick R 1987. Lift-curve characteristics for an airfoil pitching at constant rate. J. Aircr. 24:680–87
    [Google Scholar]
  47. Kaden H 1931. Aufwicklung einer unstabilen Unstetigkeitsfläche. Ing.-Arch. 2:140–68
    [Google Scholar]
  48. Katz J 1981. A discrete vortex method for the nonsteady separated flow over an airfoil. J. Fluid Mech. 102:315–28
    [Google Scholar]
  49. Kim D, Gharib M 2010. Experimental study of three-dimensional vortex structures in translating and rotating plates. Exp. Fluids 49:329–39
    [Google Scholar]
  50. Kolluru Venkata S, Jones AR 2013. Leading-edge vortex structure over multiple revolutions of a rotating wing. J. Aircr. 50:1312–16
    [Google Scholar]
  51. Krishna S, Green MA, Mulleners K 2018. Flowfield and force evolution for a symmetric hovering flat-plate wing. AIAA J. 56:41360–71
    [Google Scholar]
  52. Lentink D, Dickinson MH 2009. Rotational accelerations stabilize leading edge vortices on revolving fly wings. J. Exp. Biol. 212:2705–19
    [Google Scholar]
  53. Li J, Wu ZN 2016. A vortex force study for a flat plate at high angle of attack. J. Fluid Mech. 801:222–49
    [Google Scholar]
  54. Lind AH, Jones AR 2016. Unsteady aerodynamics of reverse flow dynamic stall on an oscillating blade section. Phys. Fluids 28:077102
    [Google Scholar]
  55. Liska S, Colonius T 2017. A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions. J. Comput. Phys. 331:257–79
    [Google Scholar]
  56. Lu Y, Shen GX 2008. Three-dimensional flow structures and evolution of the leading-edge vortices on a flapping wing. J. Exp. Biol. 211:1221–30
    [Google Scholar]
  57. Lu Y, Shen GX, Lai GJ 2006. Dual leading-edge vortices on flapping wings. J. Exp. Biol. 209:5005–16
    [Google Scholar]
  58. Manar F, Mancini P, Mayo D, Jones AR 2016. Comparison of rotating and translating wings: force production and vortex characteristics. AIAA J. 54:519–30
    [Google Scholar]
  59. Mancini P, Manar F, Granlund K, Ol MV, Jones AR 2015. Unsteady aerodynamic characteristics of a translating rigid wing at low Reynolds number. Phys. Fluids 27:123102
    [Google Scholar]
  60. Mangler KW, Smith JHB 1959. A theory of the flow past a slender delta wing with leading edge separation. Proc. R. Soc. A 251:200–17
    [Google Scholar]
  61. Medina A, Jones AR 2016. Leading-edge vortex burst on a low-aspect-ratio rotating flat plate. Phys. Rev. Fluids 1:044501
    [Google Scholar]
  62. Milne-Thomson LM 1996. Theoretical Hydrodynamics New York: Dover. 5th ed.
    [Google Scholar]
  63. Mulleners K, Raffel M 2012. The onset of dynamic stall revisited. Exp. Fluids 52:779–93
    [Google Scholar]
  64. Ohmi K, Coutanceau M, Daube O, Loc TP 1991. Further experiments on vortex formation around an oscillating and translating airfoil at large incidences. J. Fluid Mech. 225:607–30
    [Google Scholar]
  65. Ohmi K, Coutanceau M, Loc TP, Dulieu A 1990. Vortex formation around an oscillating and translating airfoil at large incidences. J. Fluid Mech. 211:37–60
    [Google Scholar]
  66. Ol MV, Altman A, Eldredge JD, Garmann DJ, Lian Y 2010. Résumé of the AIAA FDTC Low Reynolds Number Discussion Group's canonical cases Paper presented at AIAA Aerospace Sciences Meeting, 48th, Orlando, FL, AIAA Pap. 2010-1085
    [Google Scholar]
  67. Ol MV, Babinsky H 2016. Unsteady flat plates: a cursory review of AVT-202 research Paper presented at AIAA Aerospace Sciences Meeting, 54th, San Diego, CA, AIAA Pap. 2016-0285
    [Google Scholar]
  68. Ol MV, Bernal LP, Kang CK, Shyy W 2009. Shallow and deep dynamic stall for flapping low Reynolds number airfoils. Exp. Fluids 46:883–901
    [Google Scholar]
  69. Ozen CA, Rockwell D 2010. Vortical structures on a flapping wing. Exp. Fluids 50:23–34
    [Google Scholar]
  70. Ozen CA, Rockwell D 2012. Flow structure on a rotating plate. Exp. Fluids 52:207–23
    [Google Scholar]
  71. Panah AE, Akkala JM, Buchholz JHJ 2015. Vorticity transport and the leading-edge vortex of a plunging airfoil. Exp. Fluids 56:160
    [Google Scholar]
  72. Percin M, van Oudheusden BW 2015. Three-dimensional flow structures and unsteady forces on pitching and surging revolving flat plates. Exp. Fluids 56:47
    [Google Scholar]
  73. Phillips N, Knowles K, Bomphrey R 2015. The effect of aspect ratio on the leading-edge vortex over an insect-like flapping wing. Bioinspir. Biomim. 10:056020
    [Google Scholar]
  74. Pitt Ford CW, Babinsky H 2013. Lift and the leading-edge vortex. J. Fluid Mech. 720:280–313
    [Google Scholar]
  75. Pitt Ford CW, Babinsky H 2014. Impulsively started flat plate circulation. AIAA J. 52:1800–2
    [Google Scholar]
  76. Polhamus EC 1966. A concept of the vortex lift of sharp-edge delta wings based on a leading-edge-suction analogy Tech. Note D-3767, NASA, Washington, DC
    [Google Scholar]
  77. Pullin DI 1978. The large-scale structure of unsteady self-similar rolled-up vortex sheets. J. Fluid Mech. 88:401–30
    [Google Scholar]
  78. Pullin DI, Wang ZJ 2004. Unsteady forces on an accelerating plate and application to hovering insect flight. J. Fluid Mech. 509:1–21
    [Google Scholar]
  79. Ramesh K, Gopalarathnam A, Granlund K, Ol MV, Edwards JR 2014. Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding. J. Fluid Mech. 751:500–48
    [Google Scholar]
  80. 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 55:1660
    [Google Scholar]
  81. Rival DE, Tropea C 2010. Characteristics of pitching and plunging airfoils under dynamic-stall conditions. J. Aircr. 47:80–86
    [Google Scholar]
  82. Sarpkaya T 1975. An inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined plate. J. Fluid Mech. 68:109–28
    [Google Scholar]
  83. Schlueter KL, Jones AR, Granlund K, Ol M 2014. Effect of root cutout on force coefficients of rotating wings. AIAA J. 52:1322–25
    [Google Scholar]
  84. Schreck S, Faller W, Robinson M 2002. Unsteady separation processes and leading edge vortex precursors: pitch rate and Reynolds number influences. J. Aircr. 39:868–75
    [Google Scholar]
  85. Shih C, Lourenco L, Van Dommelen L, Krothapalli A 1992. Unsteady flow past an airfoil pitching at a constant rate. AIAA J. 30:1153–61
    [Google Scholar]
  86. Shukla RK, Eldredge JD 2007. An inviscid model for vortex shedding from a deforming body. Theor. Comput. Fluid Dyn. 21:343–68
    [Google Scholar]
  87. Shyy W, Liu H 2007. Flapping wings and aerodynamic lift: the role of leading-edge vortices. AIAA J. 45:2817–19
    [Google Scholar]
  88. Spedding GR, Hedenström A 2008. PIV-based investigations of animal flight. Exp. Fluids 46:749–63
    [Google Scholar]
  89. Stevens PRRJ, Babinsky H 2016. Experiments to investigate lift production mechanisms on pitching flat plates. Exp. Fluids 58:7
    [Google Scholar]
  90. Strickland J, Graham G 1987. Force coefficients for a NACA-0015 airfoil undergoing constant pitchrate motions. AIAA J. 25:622–24
    [Google Scholar]
  91. Taira K, Colonius T 2009. Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers. J. Fluid Mech. 623:187–207
    [Google Scholar]
  92. Usherwood JR 2008. The aerodynamic forces and pressure distribution of a revolving pigeon wing. Exp. Fluids 46:991–1003
    [Google Scholar]
  93. Usherwood JR, Ellington CP 2002. The aerodynamics of revolving wings I. Model hawkmoth wings. J. Exp. Biol. 205:1547–64
    [Google Scholar]
  94. Visbal MR 2011. Numerical investigation of deep dynamic stall of a plunging airfoil. AIAA J. 49:2152–70
    [Google Scholar]
  95. Visbal MR 2017. Unsteady flow structure and loading of a pitching low-aspect-ratio wing. Phys. Rev. Fluids 2:024703
    [Google Scholar]
  96. Visbal MR, Shang JS 1989. Investigation of the flow structure around a rapidly pitching airfoil. AIAA J. 27:1044–51
    [Google Scholar]
  97. Wagner H 1925. Über die Entstehung des dynamischen Auftriebes von Tragflügeln. Z. Angew. Math. Mech. 5:17–35
    [Google Scholar]
  98. Walker JM, Chou DC 1987. Forced unsteady vortex flows driven by pitching airfoils Paper presented at AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference, 19th, Honolulu, HI, AIAA Pap. 1987-1331
    [Google Scholar]
  99. Wang C, Eldredge JD 2013. Low-order phenomenological modeling of leading-edge vortex formation. Theor. Comput. Fluid Dyn. 27:577–98
    [Google Scholar]
  100. Widmann A, Tropea C 2015. Parameters influencing vortex growth and detachment on unsteady aerodynamic profiles. J. Fluid Mech. 773:432–59
    [Google Scholar]
  101. Willmott A, Ellington CP 1997. The mechanics of flight in the hawkmoth Manduca sexta. II. Aerodynamic consequences of kinematic and morphological variation. J. Exp. Biol. 200:2723–45
    [Google Scholar]
  102. Willmott AP, Ellington CP, Thomas ALR 1997. Flow visualization and unsteady aerodynamics in the flight of the hawkmoth, Manduca sexta. Philos. Trans. R. Soc. B 352:303–16
    [Google Scholar]
  103. Wojcik CJ, Buchholz JHJ 2014.a Parameter variation and the leading-edge vortex of a rotating flat plate. AIAA J. 52:348–57
    [Google Scholar]
  104. Wojcik CJ, Buchholz JHJ 2014.b Vorticity transport in the leading-edge vortex on a rotating blade. J. Fluid Mech. 743:249–61
    [Google Scholar]
  105. Wolfinger M, Rockwell D 2014. Flow structure on a rotating wing: effect of radius of gyration. J. Fluid Mech. 755:83–110
    [Google Scholar]
  106. Xia X, Mohseni K 2013. Lift evaluation of a two-dimensional pitching flat plate. Phys. Fluids 25:091901
    [Google Scholar]
  107. Xu L, Nitsche M 2014. Scaling behavior in impulsively started viscous flow past a finite flat plate. J. Fluid Mech. 756:689–715
    [Google Scholar]
  108. Yilmaz T, Rockwell D 2012. Flow structure on finite-span wings due to pitch-up motion. J. Fluid Mech. 691:518–45
    [Google Scholar]
  109. Yu HT, Bernal LP 2016. Effects of pivot location and reduced pitch rate on pitching rectangular flat plates. AIAA J. 55:702–18
    [Google Scholar]
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