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Ground effect on the aerodynamics of a two-dimensional oscillating airfoil

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Abstract

This paper reports results of an experimental investigation into ground effect on the aerodynamics of a two-dimensional elliptic airfoil undergoing simple harmonic translation and rotational motion. Ground clearance (D) ranging from 1c to 5c (where c is the airfoil chord length) was investigated for three rotational amplitudes (α m) of 30°, 45° and 60° (which respectively translate to mid-stroke angle of attack of 60°, 45° and 30°). For the lowest rotational amplitude of 30°, results show that an airfoil approaching a ground plane experiences a gradual decrease in cycle-averaged lift and drag coefficients until it reaches D ≈ 2.0c, below which they increase rapidly. Corresponding DPIV measurement indicates that the initial force reduction is associated with the formation of a weaker leading edge vortex and the subsequent force increase below D ≈ 2.0c may be attributed to stronger wake capture effect. Furthermore, an airfoil oscillating at higher amplitude lessens the initial force reduction when approaching the ground and this subsequently leads to lift distribution that bears striking resemblance to the ground effect on a conventional fixed wing in steady translation.

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Abbreviations

A :

Instantaneous translation position

A m :

Translation amplitude

c :

Chord length

C l :

Lift coefficient = F L/(0.5ρ f U 2rms S)

\(\bar{C}_{\text{l}}\) :

Cycle-averaged lift coefficient over several cycles in the periodic state

\(\bar{C}_{\text{l}} /\bar{C}_{\text{d}}\) :

Lift-to-drag ratio

C d :

Drag coefficient = F D/(0.5ρ f U 2rms S)

\(\bar{C}_{\text{d}}\) :

Cycle-averaged drag coefficient over several cycles in the periodic state

D :

Ground clearance

f :

Flapping frequency

F L :

Lift force

F D :

Drag force

L :

Airfoil span

LEV:

Leading edge vortex

Re :

Reynolds number = U rms c/υ

S :

Airfoil planform area = Lc

t :

Dimensional time

t*:

Nondimensional time = ft

TEV:

Trailing edge vortex

U rms :

Root mean square velocity = \(\sqrt 2 \pi fA_{\text{m}}\)

α :

Instantaneous geometric angle of attack

α m :

Rotational amplitude

ϕ :

Phase angle

υ :

Kinematic viscosity

ρ f :

Fluid density

References

  • Ahmed MR, Takasaki T, Kohama T (2007) Aerodynamics of a NACA4412 airfoil in ground effect. AIAA J 45(1):37–47

    Article  Google Scholar 

  • An S, Maeing J, Han C (2009) Thickness effect on the thrust generation of heaving elliptic airfoils. AIAA J 46(1):216–222

    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  MATH  MathSciNet  Google Scholar 

  • Aono H, Liu H (2008) A numerical study of hovering aerodynamics in flapping insect flight. Bio-Mech Swim Fly Fluid Dyn Biomim Robots Sports Sci 179–191

  • Aono H, Shyy W, Liu H (2009) Near wake vortex dynamics of a hovering hawkmoth. Acta Mech Sin 25(1):23–36

    Article  MATH  Google Scholar 

  • Birch JM, Dickinson MH (2003) The influence of wing–wake interaction on the production of aerodynamic forces in flapping flight. J Exp Biol 206:2257–2272

    Article  Google Scholar 

  • Dickinson MH, Lehmann FO, Sane SP (1999) Wing rotation and the aerodynamic basis of insect flight. Science 284(5422):1954–1960

    Article  Google Scholar 

  • Dudley R (2002) The biomechanics of insect flight: form, function, evolution. Princeton University Press, New Jersey

    Google Scholar 

  • Ellington CP (1984a) The aerodynamics of hovering insect flight. 1. The quasi-steady analysis. Philos Trans R Soc B 305(1122):1–15

    Article  Google Scholar 

  • Ellington CP (1984b) The aerodynamics of hovering insect flight. 4. Aerodynamic mechanisms. Philos Trans R Soc B 305(1122):79–113

    Article  Google Scholar 

  • Ellington CP, Van den Berg C, Willmott AP, Thomas ALR (1996) Leading-edge vortices in insect flight. Nature 384(6610):626–630

    Article  Google Scholar 

  • Freymuth P (1990) Thrust generation by an airfoil in hover modes. Exp Fluids 9(1–2):17–24

    Article  Google Scholar 

  • Gao T, Lu XY (2008) Insect normal hovering flight in ground effect. Phys Fluids 20:087101

    Article  Google Scholar 

  • Jung KH, Chun HH, Kim HJ (2008) Experimental investigation of wing-in-ground effect with a NACA6409 section. J Mar Sci Technol 13:317–327

    Article  Google Scholar 

  • Lehmann FO, Pick S (2007) The aerodynamic benefit of wing–wing interaction depends on stroke trajectory in flapping insect wings. J Exp Biol 210:1362–1377

    Article  Google Scholar 

  • Lehmann FO, Sane SP, Dickinson M (2005) The aerodynamic effects of wing–wing interaction in flapping insect wings. J Exp Biol 208:3075–3092

    Article  Google Scholar 

  • 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):461–477

    Google Scholar 

  • Lua KB, Lim TT, Yeo KS, Oo GY (2007) Wake-structure formation of a heaving two-dimensional elliptic airfoil. AIAA J 45(7):1571–1583

    Article  Google Scholar 

  • Lua KB, Lim TT, Yeo KS (2008) Aerodynamic forces and flow fields of a two-dimensional hovering wing. Exp Fluids 45(6):1047–1065

    Article  Google Scholar 

  • Lua KB, Lim TT, Yeo KS (2010) On the aerodynamic characteristics of hovering rigid and flexible hawkmoth-like wings. Exp Fluids 49(6):1263–1291

    Article  Google Scholar 

  • Lua KB, Lim TT, Yeo KS (2011) Effect of wing–wake interaction on aerodynamic force generation on a 2D flapping wing. Exp Fluids 51(1):177–195

    Article  Google Scholar 

  • Luo SC, Chen YS (2012) Ground effect on flow past a wing with a NACA0015 cross-section. Exp Therm Fluid Sci 40:18–28

    Article  Google Scholar 

  • Molina J, Zhang X, Angland D (2011) On the unsteady motion and stability of a heaving airfoil in ground effect. Acta Mech Sin 27(2):164–178

    Article  MATH  Google Scholar 

  • Perry AE, Chong MS, Lim TT (1982) The vortex-shedding process behind two-dimensional bluff-bodies. J Fluid Mech 116:77–90

    Article  Google Scholar 

  • Platzer MF, Jones KD, Young J, Lai JCS (2008) Flapping-wing aerodynamics: progress and challenges. AIAA J 46(9):2136–2149

    Article  Google Scholar 

  • Rayner JMV (1991) On the aerodynamics of animal flight in ground effect. Phil Trans R Soc Lond B 334(1269):119–128

    Article  Google Scholar 

  • Rozhdestvensky KV (2006) Wing-in-ground effect vehicles. Prog Aerosp Sci 42(3):211–283

    Article  Google Scholar 

  • Sane SP (2003) The aerodynamics of insect flight. J Exp Biol 206(23):4191–4208

    Article  Google Scholar 

  • Sane SP, Dickinson MH (2002) The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight. J Exp Biol 205(8):1087–1096

    Google Scholar 

  • Shyy W, Lian YS, Tang J, Viieru D, Liu H (2008) Aerodynamics of low Reynolds number flyers. Cambridge University Press, Cambridge, Cambridge aerospace series

    Google Scholar 

  • Shyy W, Trizilia P, Kang C, Aono H (2009) Can tip vortices enhance lift of a flapping wing? AIAA J 47(2):289–293

    Article  Google Scholar 

  • Shyy W, Aono H, Chimakurthi SK, Trizila P, Kang CK, Cesnik CES, Liu H (2010) Recent progress in flapping wing aerodynamics and aeroelasticity. Prog Aerosp Sci 46(7):284–327

    Article  Google Scholar 

  • Su JY, Tang JH, Wang CH, Yang JT (2013) A numerical investigation on the ground effect of a flapping-flying bird. Phys Fluids 25:093101

    Article  Google Scholar 

  • Sun M, Tang H (2002) Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. J Exp Biol 205(1):55–70

    Google Scholar 

  • Tang J, Viieru D, Shyy W (2008) Effects of Reynolds number and flapping kinematics on hovering aerodynamics. AIAA J 46(4):967–976

    Article  Google Scholar 

  • Tang JH, Su JY, Wang CH, Yang JT (2013) Numerical investigation of the ground effect for a small bird. J Mech 29(03):433–441

    Article  Google Scholar 

  • Van den Berg C, Ellington CP (1997) The three dimensional leading-edge vortex of a “hovering” model hawkmoth. Phil Trans B 352(1351):329–340

    Article  Google Scholar 

  • Wang ZJ (2005) Dissecting insect flight. Annu Rev Fluid Mech 2005(37):183–210

    Article  Google Scholar 

  • 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):449–460

    Article  Google Scholar 

  • Weis-Fogh T (1973) Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J Exp Biol 59(1):169–230

    Google Scholar 

  • Withers PC, Timko PL (1977) The significance of ground effect to the aerodynamic cost of flight and energetic of the black skimmer (Rhyncopsnigra). J Exp Biol 70:13–26

    Google Scholar 

  • Zerihan J, Zhang X (2000) Aerodynamics of a single element wing in ground effect. J Aircr 37(6):1058–1064

    Article  Google Scholar 

  • Zhang XH, Lua KB, Lim TT, Yeo KS (2013) Experimental study of two-dimensional flapping wings in tandem configuration. In: 43rd AIAA fluid dynamics conference and exhibit, San Diego, USA

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Acknowledgments

The authors wish to thank the anonymous reviewers for their thoughtful and constructive comments in reviewing the manuscript. The first author (H. Lu) gratefully acknowledges the National University of Singapore for providing research scholarship for this work.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Block EA 07-08, Singapore, 117576, Singapore

    H. Lu, K. B. Lua, T. T. Lim & K. S. Yeo

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  1. H. Lu
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  2. K. B. Lua
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  3. T. T. Lim
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  4. K. S. Yeo
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Correspondence to K. B. Lua.

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Lu, H., Lua, K.B., Lim, T.T. et al. Ground effect on the aerodynamics of a two-dimensional oscillating airfoil. Exp Fluids 55, 1787 (2014). https://doi.org/10.1007/s00348-014-1787-4

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  • DOI: https://doi.org/10.1007/s00348-014-1787-4

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