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

Abstract

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.

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References

  • Abernathy FH (1962) Flow over an inclined plate. ASME J Basic Eng 84:380–388

    Article  Google Scholar 

  • Adrian RJ, Christensen KT, Liu ZC (2000) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29(3):275–290

    Article  Google Scholar 

  • Allen JJ, Smits AJ (2001) Energy harvesting eel. J Fluid Struct 15:629–640

    Article  Google Scholar 

  • Anderson JM, Streitlien K, Barrett DS, Triantafyllou MS (1998) Oscillating foils of high propulsive efficiency. J Fluid Mech 360:41–72

    Article  MathSciNet  MATH  Google Scholar 

  • Blake R (1983) Fish locomotion. Cambridge Univ. Press, Cambridge

    Google Scholar 

  • 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 70:214–234

    Article  Google Scholar 

  • Cantwell B, Coels D (1983) An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder. J Fluid Mech 136:321–374

    Article  Google Scholar 

  • 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):1169–1182

    Article  Google Scholar 

  • Connell B, Yue D (2007) Flapping dynamics of a flag in a uniform stream. J Fluid Mech 581:33–68

    Article  MathSciNet  MATH  Google Scholar 

  • David MJ, Govardhan RN, Arakeri JH (2017) Thrust generation from pitching foils with flexible trailing edge flaps. J Fluid Mech 828:70–103

    Article  MATH  Google Scholar 

  • 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):981–991

    Article  Google Scholar 

  • Dewey PA, Boschitsch BM, Moored KW, Stone HA, Smits AJ (2013) Scaling laws for the thrust production of flexible pitching panels. J Fluid Mech 732:29–46

    Article  MATH  Google Scholar 

  • Eloy C, Souilliez C, Schouveiler L (2007) Flutter of a rectangular plate. J Fluid Struct 23:904–919

    Article  Google Scholar 

  • Eloy C, Lagrange R, Souilliez C, Schouveiler L (2008) Aeroelastic instability of cantilevered flexible plates in uniform flow. J Fluid Mech 611:97–106

    Article  MathSciNet  MATH  Google Scholar 

  • Giacomell A, Porfiri M (2011) Underwater energy harvesting from a heavy flag hosting ionic polymer metal composites. J Appl Phys 109(8):084903

    Article  Google Scholar 

  • 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):591–606

    Article  Google Scholar 

  • Heathcote S, Gursul I (2007) Flexible flapping airfoil propulsion at low Reynolds numbers. AIAA J 45(5):1066–1079

    Article  Google Scholar 

  • Katz J, Weihs D (1978) Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility. J Fluid Mech 88(3):485–497

    Article  MATH  Google Scholar 

  • Kim W, Yoo JY, Sung J (2006) Dynamics of vortex lock-on in a perturbed cylinder wake. Phys Fluids 18(7):1–22

    Google Scholar 

  • Lighthill MJ (1970) Aquatic animal propulsion of high hydromechanical efficiency. J Fluid Mech 44(2):265–301

    Article  MATH  Google Scholar 

  • Lindsey CC (1978) Form, function and locomotory habits in fish. Fish Physiol 7:1–100

    Article  Google Scholar 

  • Liu TS, Montefort J, Liou W, Pantula SR, Shams QA (2007) Lift enhancement by static extended trailing edge. J Aircraft 44(6):1939–1947

    Article  Google Scholar 

  • 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, Florida

  • Liu TS, Montefort J, Pantula SR (2010) Effects of flexible fin on low-frequency oscillation in poststall Flows. AIAA J 48(6):1235–1247

    Article  Google Scholar 

  • Ma LQ, Feng LH, Pan C, Gao Q, Wang JJ (2015) Fourier mode decomposition of PIV data. Sci China Technol Sc 58:1935–1948

    Article  Google Scholar 

  • Mackowski AW, Williamson CHK (2015) Direct measurement of thrust and efficiency of an airfoil undergoing pure pitching. J Fluid Mech 765:524–543

    Article  Google Scholar 

  • Miyanawala TP, Jaiman RK (2019) Decomposition of wake dynamics in fluid-structure interaction via low-dimensional models. J Fluid Mech 867:723–764

    Article  MathSciNet  MATH  Google Scholar 

  • 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):051202

    Article  Google Scholar 

  • 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):1–16

    Article  Google Scholar 

  • 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, 2008

  • Roshko A (1954) On the drag and shedding frequency of two dimensional bluff bodies. NACA Technical Note 3169

  • Sfakiotakis M, Lane DM, Davies JBC (1999) Review of fish swimming modes for aquatic locomotion. IEEE J Ocean Eng 24(2):237–252

    Article  Google Scholar 

  • Shelley MJ, Zhang J (2011) Flapping and bending bodies interacting with fluid flows. Annu Rev Fluid Mech 43(1):449–465

    Article  MathSciNet  MATH  Google Scholar 

  • Shelley MJ, Vandenberghe N, Zhang J (2005) Heavy flags undergo spontaneous oscillations in flowing water. Phys Rev Lett 94(9):094302

    Article  Google Scholar 

  • Timpe A, Zhang Z, Hubner J, Ukeliey L (2013) Passive flow control by membrane wings for aerodynamic benefit. Exp Fluids 54(3):1471

    Article  Google Scholar 

  • Triantafyllou MS, Triantafyllou GS, Gopalkrishnan R (1991) Wake mechanics for thrust generation in oscillating foils. Phys Fluids 3(12):2835–2837

    Article  Google Scholar 

  • Triantafyllou MS, Triantafyllou GS, Yue DKP (2000) Hydrodynamics of fishlike swimming. Annu Rev Fluid Mech 32(1):33–53

    Article  MathSciNet  MATH  Google Scholar 

  • Triantafyllou MS, Techet AH, Hover FS (2004) Review of experimental work in biomimetic foils. IEEE J Oceanic Eng 29(3):585–594

    Article  Google Scholar 

  • Wang JS, Feng LH, Wang JJ, Li T (2018) Görtler vortices in low-Reynolds-number flow over multi-element airfoil. J Fluid Mech 835:898–935

    Article  Google Scholar 

  • Watanabe Y, Suzuki S, Sugihara M, Sueoka Y (2002) An experimental study of paper flutter. J Fluid Struct 16:529–542

    Article  Google Scholar 

  • Wolfgang M, Anderson JM, Grosenbaugh MA, Yue DKP, Triantafyllou MS (1999) Nearbody flow dynamics in swimming fish. J Exp Biol 202(17):2303–2327

    Google Scholar 

  • 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):337–355

    Article  MathSciNet  MATH  Google Scholar 

  • Yarusevych S, Sullivan PE, Kawall JG (2006) Coherent structures in an airfoil boundary layer and wake at low Reynolds numbers. Phys Fluids 18:044101

    Article  Google Scholar 

  • Yarusevych S, Sullivan PE, Kawall JG (2009) On vortex shedding from an airfoil in low-Reynolds-number flows. J Fluid Mech 632:245–271

    Article  MATH  Google Scholar 

  • 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 408:835–839

    Article  Google Scholar 

  • Zhou Y, Yiu MW (2006) Flow structure, momentum and heat transport in a two-tandem-cylinder wake. J Fluid Mech 548:17–48

    Article  Google Scholar 

  • Zhou J, Adrian RJ, Balachandar S, Kendall TM (1999) Mechanisms for generating coherent packets of hairpin vortices in channel flow. J Fluid Mech 387:353–396

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou Y, Zhang HJ, Yiu MW (2002) The turbulent wake of two side-by-side circular cylinders. J Fluid Mech 458:303–332

    Article  MATH  Google Scholar 

Download references

Acknowledgements

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.

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Correspondence to Jinjun Wang.

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He, X., Guo, Q. & Wang, J. Extended flexible trailing-edge on the flow structures of an airfoil at high angle of attack. Exp Fluids 60, 122 (2019). https://doi.org/10.1007/s00348-019-2767-5

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  • DOI: https://doi.org/10.1007/s00348-019-2767-5