Radial–axial runner blade design using the coordinate slice technique

Abstract

Abstract There is a lack of information about the geometric description of radial–axial runner blades. The article aims to fill this gap using a method that exploits modern differential geometry for the description and shape modification of the runner blade. Three-dimensional Euclidean space with a curvilinear coordinate system serves as a basic manifold object, and the technique of coordinate slice gives the blade camber surface a submanifold. The camber surface definition given in the article is suitable for interactive design and optimization of the shape in a computer program optimization loop. Geometric entities and maps can be viewed as objects and methods of a computer object-oriented in-house program. The Francis runner blade serves as an example. Complete blade design contains the camber surface wrapped up with an airfoil surface, but this is not dealt with here. Basic knowledge of differential geometry and spline theory is expected.