We investigate experimentally the force generated by the unsteady vortex formation of low-aspect-ratio normal flat plates with one end free. The objective of this study is to determine the role of the free end, or tip, vortex. Understanding this simple case provides insight into flapping-wing propulsion, which involves the unsteady motion of low-aspect-ratio appendages. As a simple model of a propulsive half-stroke, we consider a rectangular normal flat plate undergoing a translating start-up motion in a towing tank. Digital particle image velocimetry is used to measure multiple perpendicular sections of the flow velocity and vorticity, in order to correlate vortex circulation with the measured plate force. The three-dimensional wake structure is captured using flow visualization. We show that the tip vortex produces a significant maximum in the plate force. Suppressing its formation results in a force minimum. Comparing plates of aspect ratio six and two, the flow is similar in terms of absolute distance from the tip, but evolves faster for aspect ratio two. The plate drag coefficient increases with decreasing aspect ratio. IntroductionWork on the flapping-wing propulsion of insects and birds has increased greatly in recent years, motivated by its potential application to the design of micro air vehicles. However, there is a corresponding lack of fundamental research on unsteady threedimensional vortex flows at the appropriate low to moderate Reynolds numbers. The present study focuses on understanding the effect of the wingtip vortex on the overall wing force of a hovering insect. This tip effect is dependent on the wing aspect ratio (AR).Flying insects have wing ARs between 2.75 and 6 (Ellington 1984; Dickinson, Lehmann & Sane 1999), while hummingbird wings have ARs of about 4 (Dhawan 1988). Aspect ratio is defined here as b 2 /S, where b is the span of a single wing and S is the single-wing planform (top-view) area. Hovering wing kinematics typically include a segment of downward, plunging motion which tilts the drag force upward so that it contributes to supporting the insect's weight; for dragonflies and hoverflies, drag is the primary wing force keeping the insect aloft (Wang 2004). Here, we focus on drag-based hovering. † Present address:
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