Aspect-ratio effects on rotating wings: circulation and forces

Abstract

We employ experiments to study aspect ratio (A) 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 A = 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 A = 4 volumetric data set matching the span-based Reynolds number (Re) of A = 2. For A = 1-4 and Re span of O(10 3 -10 4 ), we directly measure the lift force. The total leading-edge-region circulation for A = 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 A = 2. After the startup, the total circulation for each A has a similar slope and a slow growth. The first leading-edge vortex (LEV) and the tip vortex (TV) for A = 4 move past the trailing edge, followed by substantial breakdown. For A = 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 A = 2 and the growth slows for A = 4. Aft LEV tilting reduces the spanwise LEV circulation for each A. Both positive and negative axial flow are found in the first LEV for A = 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 A from 1 to 4 during the slow growth phase, although the large-time behaviour shows a slight decrease in lift coefficient with increasing A. 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 A = 2 and 4, due to similar trailing-edge vortex interactions, LEV saturation behaviour and total circulation slopes. However, for A = 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.

Closed-form solution for the edge vortex of a revolving plate

“…As t becomes large, the r 4/3 power law becomes dominant. Similar trends were found in the experiments by Carr et al (2015).…”

“…In PIV experiments as well as in numerical simulations, the circulation is usually calculated by summing up the spanwise vorticity contained in flat rectangular windows, cf. Carr et al (2015). Therefore, in this example, we also use flat windows of hight c and width 0.5r, shown as gray shaded areas in figure 3(a).…”

“…The solution derived in §2.2 is steady. However, the wing rotation starts from rest in our numerical simulations, as in many practical situations (such as the experiments by Carr et al 2015, using rectangular wings operating at 45 • angle of attack and Re of order several thousand). In addition to that, the flow may become unsteady due to hydrodynamic instabilities.…”

Coriolis effect and the attachment of the leading edge vortex

“…Moreover, the extent of this stable region is not significantly reduced with respect to its extent at φ = 60 • . As such, the flow seems to have reached a limit cycle at φ = 120 • , which is consistent with previous experimental and numerical studies (Carr et al 2015;Percin & van Oudheusden 2015;Jardin & David 2017). The flow fields at φ = 120 • , 150 • and 180 • exhibit roughly similar patterns with (i) an unsteady outboard region and (ii) a quasi-steady inboard region.…”

Quantification and Analysis of Propulsive Wake Topologies in Finite Aspect-Ratio Pitching-Rolling Plates

“…They observed that the higher aspect-ratio wing showed a steeper growth in lift coefficient with increasing angle of attack. In another experimental study, Carr et al [8] investigated the rotating rectangular wings with AR=2 and 4 at AoA= 45 . An arch-shaped LEV was observed and found detaching from the wing surface outboard in both cases.…”