Aspect-ratio effects on rotating wings: Circulation and forces

We employ experiments to study aspect ratio (AR) effects on the vortex structure, circulation and lift force for flat-plate wings rotating from rest at 45° angle of attack, which represents a simplified hovering-wing half-stroke. We use the time-varying, volumetric AR =2 data of Carr et al. (Exp. Fluids, vol. 54, 2013, pp. 1-26), reconstructed from phase-locked, phase-averaged stereoscopic digital particle image velocimetry (S-DPIV), and an AR =4 volumetric data set matching the span-based Reynolds number (Re) of AR =2. For AR =1-4 and Re_span of O(10³- 10^-4), we directly measure the lift force. The total leading-edge-region circulation for AR =2 and 4 compares best overall using a span-based normalization and for matching rotation angles. The total circulation increases across the span to the tip region, and is larger for AR =2. After the startup, the total circulation for each AR has a similar slope and a slow growth. The first leading-edge vortex (LEV) and the tip vortex (TV) for AR =4 move past the trailing edge, followed by substantial breakdown. For AR =2 the outboard, aft-tilted LEV merges with the TV and resides over the tip, although breakdown also occurs. Where the LEV is 'stable' inboard, its circulation saturates for AR =2 and the growth slows for AR =4. Aft LEV tilting reduces the spanwise LEV circulation for each AR. Both positive and negative axial flow are found in the first LEV for AR =2 and 4, with the positive component being somewhat larger. This yields a generally positive (outboard) average vorticity flux. The average lift coefficient is essentially constant with AR from 1 to 4 during the slow growth phase, although the large-time behaviour shows a slight decrease in lift coefficient with increasing AR. The S-DPIV data are used to obtain the lift impulse and the spanwise and streamwise components contributing to the lift coefficient. The spanwise contribution is similar for AR =2 and 4, due to similar trailing-edge vortex interactions, LEV saturation behaviour and total circulation slopes. However, for AR =2 the streamwise contribution is much larger, because of the stronger, coherent TV and aft-tilted LEV, which will create a relatively lower-pressure region over the tip.