Streamwise vortices, cellular shedding and force coefficients on finite wing at low Reynolds number

Abstract

Numerical simulations for flow past a finite rectangular wing with a NACA 0012 section at Re = 1000 for various semi-aspect ratios (0.25 ≤ sAR ≤ 7.5) over a range of angles of attack (0◦ ≤ α ≤ 14◦) reveal streamwise vortices, which increase in strength and number to occupy an increasing spanwise extent with increase in α. They result in non-monotonic spanwise variation of local force coefficients and increased strength of wing-tip vortex for α > 8◦. Viscous and pressure drag dominate for low and high sAR, respectively. The time-averaged drag coefficient first decreases and then increases with increase in sAR. Vortex shedding for α = 14◦ is single cell and parallel for sAR < 3. Shedding is in two cells with an oblique angle that varies with time, leading to large spanwise variation in the root mean square of local force coefficients for higher sAR. Various types of dislocations, reported earlier in wakes of bluff bodies, are seen for different α and sAR. Dislocations for α = 14◦ appear at the same spanwise location for sAR = 3 and at different spanwise locations for sAR ≥ 4. Vortex shedding for α = 12◦ and sAR = 5 exhibits one cell structure in the near wake and two cells in the far wake due to splitting and reconnection of vortices near the mid-span in the moderate wake. Linkages form between counter-rotating spanwise vortices for sAR ≥ 1. Additional linkages between shed- and wing-tip vortices are observed for lower sAR. At each α, the strength of the wing-tip vortex and radius of its core, estimated using Rankine and Lamb–Oseen models, increases up to a certain sAR beyond which it is approximately constant.