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.
We investigate experimentally the effect of aspect ratio (AR) on the unsteady, threedimensional vortex structure of low-AR, flat-plate wings rotating from rest with a 45 angle of attack. This configuration is a simplified model of a flapping-wing hovering half-stroke. The objectives are to quantitatively characterize the evolution of the detailed, threedimensional vortex structure and its variation with AR. The experiments are conducted in a glass tank facility containing a mixture of glycerin and water. Plates of AR = 2 and 4 are tested, using a trapezoidal velocity program with a tip Reynolds number of 5,000 for each and a total rotation of 120°. The unsteady, three-dimensional, volumetric velocity data are reconstructed from phase-locked and phase-averaged stereoscopic digital particle image velocimetry measurements in multiple, closely-spaced chordwise planes. The threedimensional vortex formation is characterized using the Q-criterion and the helicity density. For each AR we find that the overall vortex structure is a loop consisting of a connection among the leading-edge, tip, and trailing-edge vortices. For both AR's the leading-edge vortex (LEV) is larger with increasing span, i.e. conical, which is more pronounced for AR = 4. The LEV for each AR is attached over the inboard portion of the plate up to about 50% span throughout the motion. However, after approximately 30° of rotation it detaches from the plate in the outboard region near the tip, forming an arch-like structure. The arch is anchored at the tip due to the influence of the tip vortex (TV). A second LEV then forms in front of the arch, close to the leading edge. For AR = 2 the overall LEV continues to move with the plate and does not exhibit shedding into the wake. In contrast, for AR = 4 the flow structure in the tip region breaks down significantly and the flow appears to be fullyseparated for the remainder of the run. The emergence of discrete vortices is observed in the separated shear layers at the tip and trailing edges for both AR's. The smaller vortices of the instability wrap around the primary trailing-edge vortex (TEV) and TV, forming a somewhat helical structure. For AR = 2 the helicity density is significant throughout the vortex loop, indicating a highly three-dimensional structure with flow velocity along the vortex. The AR = 4 case has substantially less helicity. The spanwise (root-to-tip) velocity is higher for AR = 2, in part due to the higher spanwise velocity gradient. The spanwise flow distribution within and near the LEV is complex, exhibiting both positive (outboard) and negative velocity. Significant positive spanwise velocity is distributed over portion of the plate aft of the LEV and within the TEV flow. Overall the AR = 2 and 4 flows are more similar with angular position than chord lengths traveled at the tip.
The use of flow field information to compute the fluid dynamic force on a body is investigated with specific application to experimental volumetric measurements. The calculation method used avoids the explicit evaluation of the pressure on the boundaries. It is shown that errors in the data introduce an artificial dependence of the calculations on the position origin, and also that these errors are amplified by the position vector. A statistical description of the calculation variation associated with origin dependence is presented. A method is developed that objectively determines an origin which reduces the effect of the amplified error. The method utilises mathematical identities which relate the measurements to the main sources of error in a physically meaningful way, and is also found to be effective for changes of the external and internal boundaries of the fluid.
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