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

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Abstract

Numerical simulations for flow past a finite rectangular wing with a NACA 0012 section at $Re=1000$ for various semi-aspect ratios ( $0.25\le sAR \le 7.5$) over a range of angles of attack ( $0^{\circ }\le \alpha \le 14^{\circ }$) reveal streamwise vortices, which increase in strength and number to occupy an increasing spanwise extent with increase in $\alpha$. They result in non-monotonic spanwise variation of local force coefficients and increased strength of wing-tip vortex for $\alpha >8^{\circ }$. 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 $\alpha =14^{\circ }$ 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 $\alpha$ and $sAR$. Dislocations for $\alpha =14^{\circ }$ appear at the same spanwise location for $sAR=3$ and at different spanwise locations for $sAR\ge 4$. Vortex shedding for $\alpha =12^{\circ }$ 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 $sAR\ge 1$. Additional linkages between shed- and wing-tip vortices are observed for lower $sAR$. At each $\alpha$, 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.