The effect of aspect ratio on the three-dimensional vortex formation of rotating flat-plate wings

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.