物体表面に沿う流速を未知関数とする積分方程式による

三次元非圧縮ポテンシャル流れの新しい定式化

抄録

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.
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.