Vortex Formation and Saturation for Low-Aspect-Ratio Rotating Flat Plates at Low Reynolds Number

Abstract

We investigate experimentally the unsteady, three-dimensional vortex formation of lowaspect-ratio flat plates undergoing rotation from rest at fixed angles of attack and low Reynolds number (order 10 3 ). Two configurations are investigated: a trapezoidal plate at 90° angle of attack that is a simplified model of a fish-fin starting flow, and rectangular plates at 45° angle of attack that are very simplified models of a hovering-wing half-stroke. The objectives are to characterize the time-varying, three-dimensional vortex structure for various velocity profiles and geometries, to understand the effect of the significant root-to-tip flow on the vortex formation, and to investigate whether vortex saturation (“formation number”) effects are present. The experiments are performed in a water tank facility, and the diagnostic tools are dye flow visualization and digital particle image velocimetry (DPIV). For the fin-like starting configuration, the flow is dominated by the tip vortex and the overall flow structure is a symmetrical ring-like vortex. At high rotational amplitudes and speeds this vortex sheds while the plate is still in motion, indicating that it has saturated (achieved maximum circulation). The time-varying vortex circulation calculation, obtained from DPIV measurements in the symmetry plane, also shows evidence of saturation effects for some cases. For the majority of the velocity profiles and amplitudes tested, the behavior of the circulation with time is complex, making an objective determination of the saturation time difficult. This complexity is directly related to flow phenomena such as the strong rootto-tip velocity induced by the tip and side-edge vortices, and a Kelvin-Helmholtz-like instability inherent in the separated shear layers at this Reynolds number. For the wing-like starting case, rectangular wings of aspect ratio (AR) 2 and 4 are compared. Dye flow visualization reveals a strong spanwise (root-to-tip) flow over the entire wing and an attached helical leading-edge vortex (LEV) early in the motion, consistent with prior research. We observe LEV bursting for both AR’s, however for the AR = 2 wing the bursting occurs relatively later. For the AR = 2 case the flow consists of an overall, three-dimensional vortex loop made up of a connection among the LEV, the tip vortex (TV), and the trailingedge vortex (TEV), similar to previous studies. For the AR = 4 wing the flow is less coherent and exhibits massive separation near the tip late in the motion. For this flow the KelvinHelmoltz-like instability is also observed in the separated shear layers, and is relatively larger with distance toward the tip. This instability most likely contributes to the breakdown of the LEV structure, which has been found previously.