Static and dynamic calculation of a Francis turbine runner with some remarks on accuracy

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The work presented in this paper describes both the static deformation under centrifugal forces and water pressure, and the natural vibrations of a hydraulic runner of the Francis type. First, the method of calculation is described; it uses finite elements and considers only one sector of the structure with appropriate boundary conditions. Second, preliminary test calculations with two simple bodies are shown; these tests were performed in order that we might familiarise ourselves with the method, in particular with the plane and curved shell elements used, and they had to provide information about the accuracy that could be expected from the results. Finally, several calculations of the Francis runner are presented and their main features are discussed.