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Lift and the leading-edge vortex. (English) Zbl 1284.76059
Summary: Flapping wings often feature a leading-edge vortex (LEV) that is thought to enhance the lift generated by the wing. Here the lift on a wing featuring a leading-edge vortex is considered by performing experiments on a translating flat-plate aerofoil that is accelerated from rest in a water towing tank at a fixed angle of attack of 15\(^\circ\). The unsteady flow is investigated with dye flow visualization, particle image velocimetry (PIV) and force measurements. Leading- and trailing-edge vortex circulation and position are calculated directly from the velocity vectors obtained using PIV. In order to determine the most appropriate value of bound circulation, a two-dimensional potential flow model is employed and flow fields are calculated for a range of values of bound circulation. In this way, the value of bound circulation is selected to give the best fit between the experimental velocity field and the potential flow field. Early in the trajectory, the value of bound circulation calculated using this potential flow method is in accordance with Kelvin’s circulation theorem, but differs from the values predicted by Wagner’s growth of bound circulation and the Kutta condition. Later the Kutta condition is established but the bound circulation remains small; most of the circulation is contained instead in the LEVs. The growth of wake circulation can be approximated by Wagner’s circulation curve. Superimposing the non-circulatory lift, approximated from the potential flow model, and Wagner’s lift curve gives a first-order approximation of the measured lift. Lift is generated by inertial effects and the slow buildup of circulation, which is contained in shed vortices rather than bound circulation.

MSC:
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76B47 Vortex flows for incompressible inviscid fluids
76-05 Experimental work for problems pertaining to fluid mechanics
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