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Analytical and experimental studies of wing tip vortices Duan, Shizhong


Wing tip vortices, and their relationship to wing tip geometry and wing total drag, are investigated here both analytically and experimentally. The purpose of the analysis is to answer the basic question — what are the effects of wing drag on tip vortex structure? The purpose of the experiments is to determine the effect of wing tip geometry on wing tip vortices (tip vortex cavitation) and wing drag (vortex induced drag). In the analytical work, a new method has been developed for wing tip vortices. This approach is referred to as the “quasi-similarity” method. This new method combines a polynomial solution with a similarity variable technique. A non-linear analytical tip vortex model is achieved for the first time. The first order (linear) velocity components and pressure of the polynomial solution for the new model can be expressed in complete function form. Higher order (non-linear) velocity components and pressure can be obtained analytically or numerically. The most important feature of this new tip vortex model is that the predicted wing drag due to such a single vortex is finite. To the author’s knowledge, no other vortex model has this property. At distances fairly far downstream of the wing, tip vortex structure is found to be an explicit function of wing total drag, vortex circulation, freestream velocity, downstream distance and fluid properties. It is verified that the first order tangential velocity component and pressure of the tip vortex model are exactly the same as that of the linear wing tip vortex model proposed by Batchelor (1964). The decay of the axial and tangential velocity components predicted by this theory compare well with experimental measurements. In the experimental work, a novel ducted tip device was tested in a wind tunnel and a water tunnel. The ducted tip consists of a hollowed duct attached to the tip of a rectangular untwisted wing. This novel tip device was found to improve the Lift/Drag ratio by up to 6% at elevated angles of attack compared with a conventional round tip configuration with the same span. The wing tip vortex cavitation was substantially delayed by the ducted tip device. In view of its superior cavitation characteristics and aerodynamic performance, the ducted tip has potential application to marine propellers. The ducted tip is effective because it redistributes the shed vorticity in the transverse plane (Trefftz plane) behind the wing. The shed vorticity is distributed along the wing and duct trailing edge for the ducted tip configuration, rather than solely along the wing trailing edge, which would be the case for a conventional wing tip configuration.

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