Vortex structure variation with flapping-wing stroke-reversal kinematics
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The behavior of three-dimensional (3D) vortex structures formed during the pitching stroke-reversal of a two degree-of-freedom (2DOF) flapping wing in hover is investigated. Dye flow visualization is conducted using a scaled wing model with an internal dye manifold executing periodic flapping during dye injection, facilitating the identification of unsteady vortices. A vortex skeleton model is developed to represent the vortex loop topology, and used for description of the 3D flow structure evolutions generated with varying kinematics. Qualitative conclusions are drawn from varying the pitching reduced frequency for an advanced and symmetric pitch timing with respect to the rotational turn-around. Advanced pitch timing typically promoted the growth of pitching structures at the trailing edge, while a symmetric pitch timing promoted the growth of vortex structures at the leading edge. Large pitching reduced frequency produces stronger pitching vortices at the leading edge which remain near the wing longer and interfere with subsequent vortex formations in the following half-stroke. These dye visualization results motivate the study of the quantitative behavior via an experiment using stereo digital particle imagine velocimetry (S-DPIV). The instantaneous, phase-averaged out-of-plane vorticity, span-wise velocity, vorticity flux, and circulation at five planes along the span of the wing are measured at the end of stroke reversal for varied pitching reduced frequency with advanced pitch timing. Vortex structures formed at the leading and trailing edges from pitching have significant span-wise variation due to the rotating DOF, with the outboard structures, typically, having stronger vorticity and circulation. The circulation is normalized by the sum of a local velocity characteristic of the spanwise position and the pitching edge speed to capture the contributions of both rotating and pitching motions to the formation of the circulating structures. This scaling both collapses and flattens the circulation plots of the pitching structures formed for different pitching reduced frequency at the trailing edge.