Three-dimensional Design. Francis Runner

A Ful1 three-dimensional design method has been applied to thedesign of Francis runner. By this method the interaction of thedifferent parts can be taken into account. On the assumption ofinviscid and imcompressible flow, the runner with thickness takeninto account is replaced by the superposition of vortices and sourceson the blade mean surface. The three-dimensiona1 rotational flow isdivided into a circumferentia11y averaged mean flow and a periodicflow according to the flow characteristic. After Fourier seriesexpansion, the three-dimensional problem is converted to manytwo-dimensional problems which can be easily solved. The equationsof the mean flow and the periodic flow as we11 as the mean blade surfaceequation are set up. The flow equations are so1ved using finitedifference technique. The boundary conditions is treated by usingbody-fitted curvi1inear coordinate system. By iteratiYe1y so1vingthe flow governing equation and the b1ade equation, the design ofFrancis runner in the three-dimensiona1 rotat iona1 f1ow can beperformed according to the V_θr distribution,flow channel and theb1ade thickness given. Using modularizational theory, computerprogram including two-dimensiona1 and quasi-three-dimensiona1 aswell as full three-dimensiona1 method is designed. The inf1uences ofthe rotation in coming flow and the runner itself on the meridionalflow field are described in this paper.