The advance ratio effect on the lift augmentations of an insect-like flapping wing in forward flight

Abstract

Time-varying force/moment measurements and digital particle image velocimetry (DPIV) were conducted to reveal the influence of an advance ratio $J$ on an insect-like flapping wing. A scaled-up robotic model and a servo-driven towing tank were employed to investigate nine individual $J$ cases – $J=0$ (hovering), 0.0625, 0.1250, 0.1875, 0.25, 0.50, 0.75, 1.0 and $\infty$ (gliding motion) – at a high Reynolds number ($Re\sim 10^{4}$). At $J\leqslant 0.25$, the aerodynamic forces slightly increased from those in hover ($J=0$). The centres of pressure in these cases were concentrated in the outboard section, and the leading-edge vortices (LEVs) grew more conically than those in hover. Spanwise cross-sectional DPIV indicated that the wings generated more balanced downwashes, which effectively supported the slight lift increments in this range. At $J>0.25$, a drastic force drop appeared as $J$ increased. The DPIV results in the $J=0.5$ case clearly showed a strong trailing-edge vortex on the outboard trailing edges encroaching into the upper surface, which had been occupied by the LEV for lower $J$. The LEV vorticity was noticeably weakened, and coherent substructures with substantial turbulence accompanied this vorticity. In the $J=1.0$ case, such encroachment was extended to 50 % of the section, and the LEV outboard became significantly irregular. The near-wake structures also showed that the $J=1.0$ case had the narrowest downwash area, with unstable root and tip vortices, which reflected considerable attenuation in the lift enhancements. It was of note that all of these vortical behaviours were clearly distinguishable from aspect ratio ($AR$) effects. The $J$ even played a similar role to that of the $AR$ in the Navier–Stokes equation. These findings clearly indicated that the $J$ could be an independent quantity governing the overall vortical system and lift enhancing mechanism on a flapping wing of a flapping-wing micro air vehicle.