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Near-field tip vortex behind a swept wing model

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Abstract

The near-field flow structure of a tip vortex behind a sweptback and tapered NACA 0015 wing was investigated and compared with a rectangular wing at the same lift force and Re=1.81×105. The tangential velocity decreased with the downstream distance while increased with the airfoil incidence. The core radius was about 3% of the root chord c r, regardless of the downstream distance and α for α<8°. The core axial velocity was always wake-like. The core Γc and total Γo circulation of the tip vortex remained nearly constant up to x/c r=3.5 and had a Γc/Γo ratio of 0.63. The total circulation of the tip vortex accounted for only about 40% of the bound root circulation Γb. For a rectangular wing, the axial flow exhibited islands of wake- and jet-like velocity distributions with Γc/Γo=0.75 and Γo/Γb=0.70. For the sweptback and tapered wing tested, the inner region of the tip vortex flow exhibited a self-similar behavior for x/c r≥1.0. The lift force computed from the spanwise circulation distributions agreed well with the force-balance data. A large difference in the lift-induced drag was, however, observed between the wake integral method and the inviscid lifting-line theory.

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Abbreviations

AR:

Aspect ratio (b 2/S)

b :

(Semi-)wing span

c :

Chord of rectangular wing

c r :

Root chord

c t :

Tip chord

C D :

Drag coefficient without wing tip effects

C Di :

Lift-induced drag coefficient (D i /0.5ρu 2∞ S)

C D,3-D :

Drag coefficient of a 3-D wing configuration

C L :

Lift coefficient without wing tip effects (L/0.5ρu 2∞ S)

C L,3-D :

Lift coefficient of a 3-D wing configuration

D :

Drag without wing tip effects

D 3-D :

Drag of a 3-D wing configuration

D i :

Lift-induced drag

L :

Lift

p :

Local static pressure

p ∞ :

Free-stream static pressure

r :

Radial position

r o :

Vortex outer radius

r c :

Vortex core radius

Re :

Reynolds number (u ∞ c r/ν or u ∞ c/ν)

S :

Wing area

u :

Axial mean velocity

u c :

Core axial velocity

u ∞ :

Free-stream velocity

v :

Transverse mean velocity

v θ :

Tangential velocity

w :

Spanwise mean velocity

x :

Streamwise or axial direction

y :

Normal direction

z :

Spanwise direction

ρ:

Fluid density

ν:

Fluid kinematic viscosity

ζ:

Streamwise vorticity (∂w/∂y - ∂v/∂z)

Γ:

Circulation or vortex strength

Γb :

Bound root circulation

Γc :

Core circulation

Γo :

Total circulation

α:

Angle of attack

αss :

Static-stall angle

λ:

Taper ratio (c t/c r)

ψ:

Stream function

φ:

Velocity potential

σ:

A source term in Eq. 6 (∂v/∂y + ∂w/∂z)

References

  • Batchelor GK (1964) Axial flow in trailing line vortices. J Fluid Mech 20:645–658

    Article  MATH  MathSciNet  Google Scholar 

  • Birch D, Lee T (2004) Structure and induced drag of a tip vortex. J Aircr 41(5):1138–1145

    Google Scholar 

  • Brune GW (1994) Quantitative low-speed wake surveys. J Aircr 31(2):249–255

    Google Scholar 

  • Chow JS, Zilliac GG, Bradshaw P (1997) Mean and turbulence measurements in the near field of a wingtip vortex. AIAA J 35(10):1561–1567

    Google Scholar 

  • Devenport WJ, Rife MC, Liapis SI, Follin GJ (1996) The structure and development of a wing-tip vortex. J Fluid Mech 312:67–106

    Article  MathSciNet  Google Scholar 

  • El-Ramly Z, Rainbird WJ, Earl DG (1976) Wind tunnel measurement of rolling moment in a swept-wing vortex wake. J Aircr 13(12):962–967

    Google Scholar 

  • Francis MS, Kennedy DA (1979) Formation of a trailing vortex. J Aircr 16(3):148–154

    Google Scholar 

  • Francis TB, Katz J (1988) Observations on the development of a tip vortex on a rectangular hydrofoil. J Fluids Eng 110:208–215

    Article  Google Scholar 

  • Glauert TH (1926) The elements of airfoil and airscrew theory. Cambridge University Press, London

    Google Scholar 

  • Green SI, Acosta AJ (1991) Unsteady flow in trailing vortices. J Fluid Mech 227:107–134

    Article  Google Scholar 

  • Hoffmann ER, Joubert PN (1963) Turbulent line vortices. J Fluid Mech 16:395–411

    Article  Google Scholar 

  • Kusunose K (1997) Development of a universal wake survey data analysis code. AIAA 2294

  • Lamb H (1945) Hydrodynamics, 6th edn. Dover, New York, p 592

    Google Scholar 

  • Maskell E (1973) Progress towards a method for the measurement of the components of the drag of a wing of finite span. RAE Technical Report 72232

  • McAlister KW, Takahashi RK (1991) NACA 0015 wing pressure and trailing vortex measurements. NASA TP-3151

  • Moore DW, Saffman PG (1973) Axial flow in laminar vortices. Proc R Soc Lond A 333:491–508

    Article  MATH  Google Scholar 

  • Naik DA, Ostowari C (1990) Effects of nonplanar wing forms on a wing. J Aircr 27(2):117–122

    Google Scholar 

  • Orloff KL, Ciffone DL (1974) Vortex measurements behind a swept wing transport model. J Aircr 11(6):362–364

    Google Scholar 

  • Ozger E, Schell I, Jacob D (2001) On the structure and attenuation of an aircraft wake. J Aircr 38(5):878–887

    Google Scholar 

  • Phillips WRC (1981) The turbulent trailing vortex during roll-up. J Fluid Mech 105:451–467

    Article  MATH  Google Scholar 

  • Ramaprian BR, Zheng Y (1997) Measurements in rollup region of the tip vortex from a rectangular wing. AIAA J 35(12):1837–1843

    Google Scholar 

  • Shekarriz A, Fu TC, Katz J, Huang TT (1993) Near-field behavior of a tip vortex. AIAA J 31(1):112–118

    Google Scholar 

  • Spalart PR (1998) Airplane trailing vortices. Ann Rev Fluid Mech 30:107–138

    Article  MathSciNet  Google Scholar 

  • Wenger CW, Devenport WJ (1999) Seven-hole pressure probe calibration utilizing look-up error tables. AIAA J 37(6):675–679

    Google Scholar 

  • Williams GM (1974) Viscous modeling of wing-generated trailing vortices. Aeronaut Q 25:143–154

    Google Scholar 

  • Zeman O (1995) The persistence of trailing vortices: a modeling study. Phys Fluids 7(1):135–143

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

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  1. Department of Mechanical Engineering, McGill University, Quebec, Canada

    P. Gerontakos & T. Lee

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  1. P. Gerontakos
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  2. T. Lee
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Correspondence to T. Lee.

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Gerontakos, P., Lee, T. Near-field tip vortex behind a swept wing model. Exp Fluids 40, 141–155 (2006). https://doi.org/10.1007/s00348-005-0056-y

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