Hydrodynamics of Screw Propellers Based on a New Lifting Surface Theory (The 2nd Report)

Abstract

Recently, the auther has developed a new lifting surface theory for low aspect ratio wings, in which the bound vortices representing the wing are distributed not over the projected surface on the stream plane but over the wing surface itself, while the free vortices are trailed along the locus of the moving wing under the category of linearized theory.In the present paper, the application of this new lifting surface theory to screw propellers is discussed theoretically. The bound vortices representing the screw blade are distributed over the helical surface of the blade itself, while the free vortices are trailed along the helical locus of the moving blade. It is desirable to treat the problem three-dimensionally, in order to investigate the form of load distribution, not only in the radial direction but in the chord direction, in relation with the blade shapes and the working conditions. A two-dimensional integral equation that relate lift and downwash distributions on the screw blade is formulated. The numerical method of solution of the equation is obtained, considering the singularity of the kernel functions.Besides, some numerical calculations are made to examine the characteristics of the kernel functions.