Experiments in Fluids

, 60:122 | Cite as

Extended flexible trailing-edge on the flow structures of an airfoil at high angle of attack

  • Xi He
  • Qinfeng Guo
  • Jinjun WangEmail author
Research Article


A two-dimensional time-resolved particle image velocimetry experiment was carried out to investigate the effect of flexible trailing-edge on the flow structures of an airfoil at high angle of attack. The experimental model was composed of a rigid NACA0020 airfoil and a flexible extended trailing-edge plate. The Reynolds number ranged from 1.42 × 104 to 3.57 × 104 (based on the model length). The kinematic characteristics of the flexible trailing-edge plate were first analyzed. While interacting with the fluid, the flexible plate performed a strongly periodic vibration. The plate presented more complicated deformation and larger amplitude with the increase of Reynolds number. The flow field was also captured in this study. It was found that the vibration of the flexible plate caused the generation and shedding of the trailing-edge vortex. Furthermore, the disturbance of plate vibration could propagate upstream and influence the formation of the leading-edge vortex in the separated shear layer. In the wake region, the alternative shedding processes of the leading- and trailing-edge vortices were coupled with the vibration of the plate. Besides, this study further scaled the vibration frequencies with a Strouhal number based on the wake width. The scaled Strouhal numbers were in the range of 0.14–0.21 for all Reynolds number cases tested, which indicated that the fluid–structure coupling led the flow to form a bluff-body wake.

Graphic abstract

The vibration patterns of the flexible trailing-edge plate at various Reynolds numbers.



This work was supported by the National Natural Science Foundation of China (No. 11761131009 and 11721202). Besides, our deepest gratitude goes to the reviewers and editor for their careful works and thoughtful suggestions that have helped to improve this paper substantially.


  1. Abernathy FH (1962) Flow over an inclined plate. ASME J Basic Eng 84:380–388CrossRefGoogle Scholar
  2. Adrian RJ, Christensen KT, Liu ZC (2000) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29(3):275–290CrossRefGoogle Scholar
  3. Allen JJ, Smits AJ (2001) Energy harvesting eel. J Fluid Struct 15:629–640CrossRefGoogle Scholar
  4. Anderson JM, Streitlien K, Barrett DS, Triantafyllou MS (1998) Oscillating foils of high propulsive efficiency. J Fluid Mech 360:41–72MathSciNetCrossRefzbMATHGoogle Scholar
  5. Blake R (1983) Fish locomotion. Cambridge Univ. Press, CambridgeGoogle Scholar
  6. Bleischwitz R, De Kat R, Ganapathisubramani B (2017) On the fluid-structure interaction of flexible membrane wings for MAVs in and out of ground-effect. J Fluid Struct 70:214–234CrossRefGoogle Scholar
  7. Cantwell B, Coels D (1983) An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder. J Fluid Mech 136:321–374CrossRefGoogle Scholar
  8. Champagnat F, Plyer A, Le BG, Leclaire B, Davoust S, Le Saut Y (2011) Fast and accurate PIV computation using highly parallel iterative correlation maximization. Exp Fluids 50(4):1169–1182CrossRefGoogle Scholar
  9. Connell B, Yue D (2007) Flapping dynamics of a flag in a uniform stream. J Fluid Mech 581:33–68MathSciNetCrossRefzbMATHGoogle Scholar
  10. David MJ, Govardhan RN, Arakeri JH (2017) Thrust generation from pitching foils with flexible trailing edge flaps. J Fluid Mech 828:70–103CrossRefzbMATHGoogle Scholar
  11. Deng SC, Pan C, Wang JJ, Rinoshika A (2017) POD analysis of the instability mode of a low-speed streak in a laminar boundary layer. Acta Mech Sin 33(6):981–991CrossRefGoogle Scholar
  12. Dewey PA, Boschitsch BM, Moored KW, Stone HA, Smits AJ (2013) Scaling laws for the thrust production of flexible pitching panels. J Fluid Mech 732:29–46CrossRefzbMATHGoogle Scholar
  13. Eloy C, Souilliez C, Schouveiler L (2007) Flutter of a rectangular plate. J Fluid Struct 23:904–919CrossRefGoogle Scholar
  14. Eloy C, Lagrange R, Souilliez C, Schouveiler L (2008) Aeroelastic instability of cantilevered flexible plates in uniform flow. J Fluid Mech 611:97–106MathSciNetCrossRefzbMATHGoogle Scholar
  15. Giacomell A, Porfiri M (2011) Underwater energy harvesting from a heavy flag hosting ionic polymer metal composites. J Appl Phys 109(8):084903CrossRefGoogle Scholar
  16. Griffin OM (1978) An universal Strouhal number for the “locking-on” of vortex shedding to the vibrations of bluff cylinders. J Fluid Mech 85(3):591–606CrossRefGoogle Scholar
  17. Heathcote S, Gursul I (2007) Flexible flapping airfoil propulsion at low Reynolds numbers. AIAA J 45(5):1066–1079CrossRefGoogle Scholar
  18. Katz J, Weihs D (1978) Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility. J Fluid Mech 88(3):485–497CrossRefzbMATHGoogle Scholar
  19. Kim W, Yoo JY, Sung J (2006) Dynamics of vortex lock-on in a perturbed cylinder wake. Phys Fluids 18(7):1–22Google Scholar
  20. Lighthill MJ (1970) Aquatic animal propulsion of high hydromechanical efficiency. J Fluid Mech 44(2):265–301CrossRefzbMATHGoogle Scholar
  21. Lindsey CC (1978) Form, function and locomotory habits in fish. Fish Physiol 7:1–100CrossRefGoogle Scholar
  22. Liu TS, Montefort J, Liou W, Pantula SR, Shams QA (2007) Lift enhancement by static extended trailing edge. J Aircraft 44(6):1939–1947CrossRefGoogle Scholar
  23. Liu TS, Montefort J, Liou W, Pantula SR, Yang Y and Shams QA (2009) Post-stall flow control using a flexible fin on airfoil. In: 47th Asia Aerospace Sciences Meeting. 5–8 Jan 2009, Orlando, FloridaGoogle Scholar
  24. Liu TS, Montefort J, Pantula SR (2010) Effects of flexible fin on low-frequency oscillation in poststall Flows. AIAA J 48(6):1235–1247CrossRefGoogle Scholar
  25. Ma LQ, Feng LH, Pan C, Gao Q, Wang JJ (2015) Fourier mode decomposition of PIV data. Sci China Technol Sc 58:1935–1948CrossRefGoogle Scholar
  26. Mackowski AW, Williamson CHK (2015) Direct measurement of thrust and efficiency of an airfoil undergoing pure pitching. J Fluid Mech 765:524–543CrossRefGoogle Scholar
  27. Miyanawala TP, Jaiman RK (2019) Decomposition of wake dynamics in fluid-structure interaction via low-dimensional models. J Fluid Mech 867:723–764MathSciNetCrossRefzbMATHGoogle Scholar
  28. Morse DR, Liburdy JA (2009) Vortex dynamics and shedding of a low aspect ratio, flat wing at low Reynolds numbers and high angles of attack. J Fluid Eng T ASME 131(5):051202CrossRefGoogle Scholar
  29. Pan C, Xue D, Xu Y, Wang JJ, Wei RJ (2015) Evaluating the accuracy performance of Lucas–Kanade algorithm in the circumstance of PIV application. Sci China Phys Mech 58(10):1–16CrossRefGoogle Scholar
  30. Pantula SR (2008) Modeling fluid structure interaction over a flexible fin attached to a NACA0012 airfoil. Ph.D. Thesis, Department of Mechanical and Aeronautical Engineering, Western Michigan University, Kalamazoo, MI, 2008Google Scholar
  31. Roshko A (1954) On the drag and shedding frequency of two dimensional bluff bodies. NACA Technical Note 3169Google Scholar
  32. Sfakiotakis M, Lane DM, Davies JBC (1999) Review of fish swimming modes for aquatic locomotion. IEEE J Ocean Eng 24(2):237–252CrossRefGoogle Scholar
  33. Shelley MJ, Zhang J (2011) Flapping and bending bodies interacting with fluid flows. Annu Rev Fluid Mech 43(1):449–465MathSciNetCrossRefzbMATHGoogle Scholar
  34. Shelley MJ, Vandenberghe N, Zhang J (2005) Heavy flags undergo spontaneous oscillations in flowing water. Phys Rev Lett 94(9):094302CrossRefGoogle Scholar
  35. Timpe A, Zhang Z, Hubner J, Ukeliey L (2013) Passive flow control by membrane wings for aerodynamic benefit. Exp Fluids 54(3):1471CrossRefGoogle Scholar
  36. Triantafyllou MS, Triantafyllou GS, Gopalkrishnan R (1991) Wake mechanics for thrust generation in oscillating foils. Phys Fluids 3(12):2835–2837CrossRefGoogle Scholar
  37. Triantafyllou MS, Triantafyllou GS, Yue DKP (2000) Hydrodynamics of fishlike swimming. Annu Rev Fluid Mech 32(1):33–53MathSciNetCrossRefzbMATHGoogle Scholar
  38. Triantafyllou MS, Techet AH, Hover FS (2004) Review of experimental work in biomimetic foils. IEEE J Oceanic Eng 29(3):585–594CrossRefGoogle Scholar
  39. Wang JS, Feng LH, Wang JJ, Li T (2018) Görtler vortices in low-Reynolds-number flow over multi-element airfoil. J Fluid Mech 835:898–935CrossRefGoogle Scholar
  40. Watanabe Y, Suzuki S, Sugihara M, Sueoka Y (2002) An experimental study of paper flutter. J Fluid Struct 16:529–542CrossRefGoogle Scholar
  41. Wolfgang M, Anderson JM, Grosenbaugh MA, Yue DKP, Triantafyllou MS (1999) Nearbody flow dynamics in swimming fish. J Exp Biol 202(17):2303–2327Google Scholar
  42. Wu T (1971) Hydromechanics of swimming propulsion. Part 1. Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid. J Fluid Mech 46(2):337–355MathSciNetCrossRefzbMATHGoogle Scholar
  43. Yarusevych S, Sullivan PE, Kawall JG (2006) Coherent structures in an airfoil boundary layer and wake at low Reynolds numbers. Phys Fluids 18:044101CrossRefGoogle Scholar
  44. Yarusevych S, Sullivan PE, Kawall JG (2009) On vortex shedding from an airfoil in low-Reynolds-number flows. J Fluid Mech 632:245–271CrossRefzbMATHGoogle Scholar
  45. Zhang J, Childress S, Libchaber A, Shelley M (2000) Flexible filament in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408:835–839CrossRefGoogle Scholar
  46. Zhou Y, Yiu MW (2006) Flow structure, momentum and heat transport in a two-tandem-cylinder wake. J Fluid Mech 548:17–48CrossRefGoogle Scholar
  47. Zhou J, Adrian RJ, Balachandar S, Kendall TM (1999) Mechanisms for generating coherent packets of hairpin vortices in channel flow. J Fluid Mech 387:353–396MathSciNetCrossRefzbMATHGoogle Scholar
  48. Zhou Y, Zhang HJ, Yiu MW (2002) The turbulent wake of two side-by-side circular cylinders. J Fluid Mech 458:303–332CrossRefzbMATHGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Key Laboratory of Fluid Mechanics (Ministry of Education)Beijing University of Aeronautics and AstronauticsBeijingChina

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