:Potential Flow Field around a Lifting Wing by Use of the Surface Velocity Components

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An integral equation of the second kind for the surface velocity components of the incompressible three-dimensional potential flow around a body is obtained by extending the procedure explored by W. PRAGER, F. VANDREY and E. MARTENSEN in two-dimensional situations. The formulation is based on the representation of the velocity potential by a doublet distribution over the body surface, and is realized by replacing the original body-surface boundary condition of vanishing normal velocity component with the equivalent condition of a quiescent flow in the region inside the body. The equation is then generalized to cases where the prescribed normal velocity component to the body surface does not necessarily vanish identically.<BR>As a prerequisite of dealing with the flow around a lifting wing, the implication of the KUTTA condition within the present formulation is studied by examining the behaviour of the derived integral equation at the sharp trailing edge of a wing. It is found that the geometry of the trailing vortex sheet and the direction of vortex-shedding in the immediate neighbourhood of the trailing edge bear an essential relation to the fulfilment of the condition. In this context, the present formulation needs a more elaborate representation of the trailing vortex sheet than envisaged by the classical PRANDTL's model.
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