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Lift-induced drag of a cambered wing for Re ≤ 1 × 106

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Abstract

An investigation of the dependence of the lift-induced drag coefficient C Di of a square-tipped, cambered wing model on Reynolds number for Re ≤ 1 × 106 was conducted. Computed based on the vorticity distribution inferred from the near-field cross-flow velocity measurements of the tip vortex, different C Di prediction schemes were used. The effect of measurement plane size and grid resolution on the C Di calculations was also identified. The C Di estimated by the integral method was found to increase with increasing Re and was below the C Di = C 2l /πeAR prediction. Limits on the measurement plane size and grid resolution were determined to be at least 40% larger than the vortex outside diameter and no larger than 0.63% chord, respectively, in order to provide a good estimate of the induced drag.

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Abbreviations

AR:

aspect ratio, = b 2/S

b :

semi-wing span

c :

chord

C Di :

induced drag coefficient = D i/½ρu 2∞ S

C l :

lift coefficient

D i :

lift-induced drag

e :

span efficiency factor

M ∞ :

freestream Mach number

r :

radial position

r c :

vortex core radius

r o :

vortex outer radius

Re :

Reynolds number, = u ∞ c/ν

S :

wing area

t max :

maximum airfoil thickness

u, v, w :

axial, transverse and spanwise velocities

u ∞ :

free-stream velocity

v θ :

tangential velocity

x, y, z :

streamwise, transverse and spanwise directions

ζ:

streamwise vorticity

Γ:

circulation or vortex strength

Γb :

bound circulation

Γc :

core circulation

Γo :

total circulation

α :

angle of attack

ψ:

stream function

φ :

velocity potential

ρ :

fluid density

ν :

kinematic viscosity

σ :

a source term in Eq.  2

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Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. W., Montreal, QC, Canada, H3A 2K6

    P. Gerontakos & T. Lee

Authors
  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. Lift-induced drag of a cambered wing for Re ≤ 1 × 106 . Exp Fluids 42, 363–369 (2007). https://doi.org/10.1007/s00348-006-0242-6

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  • DOI: https://doi.org/10.1007/s00348-006-0242-6

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