Abstract: Based on the concept of two types of relative flow surfaces, the present work established a mathematical model for the inverse problem solution of three-dimensional blade design by the characteristic method. A calculation procedure was developed according to this model to generate blade shapes that conform to the stream function (orthogonal), the continuity function and also the equations of motion. This is a blade design method from given meridional flow conditions, and it forms the basis of iteration between direct and inverse solutions which will make it very useful in designing three-dimensional blade systems for Francis type turbines.

Key words: 反问题特征线解法, 混流式水轮机, 三元设计, 优迭法