Representation of Potential Flow about Axisymmetric Bodies with Discrete Singularities

A rational methodology has been developed whereby three-dimensional sources and sinks may be placed along the major axis of a class of ovary ellipsoids so as to minimize normal velocity and to calculate as exactly as possible the tangential velocity, pressure distribution, and the body shape. For this purpose the strength and position of the singularities and the position and number of the control points were optimized through the use of the method of least squares and the Automated Design Synthesis optimization technique. The results have shown that the previous methods are far from satisfactory and the use of two types of optimization in the determination of the strength and position of the singularities yields and the desired body shape and flow characteristics with excellent accuracy. A comprehensive computer code has been developed to enable one to calculate most of the practically significant body shapes.