Transposition of the mechanical behavior from model to prototype of Francis turbines

Hydropower is nowadays essential for balancing the electrical grid providing flexibility and fast response. The role of hydraulic turbines has changed from working at their Best Efficiency Point (BEP) to work in the whole operating range when demanded. Francis turbines working at off-design conditions suffer from dynamic problems that affect the useful life of their components, especially of the runner. Reduced scale physical models of Francis turbines are widely used to determine their hydraulic behavior. Most of the hydraulic parameters obtained in model tests are transposable to prototype by using the similarity theories as long as they meet similitude requirements. However, from the mechanical behavior point of view, both model and prototype structures are not always similar and the mechanical behavior of the model is often not considered for transposition. In this paper, a transposition method for the mechanical behavior of Francis turbines models is presented and the results are compared with the real size prototype. The modal behavior of the runner, its stress and fatigue life estimation for different operating conditions are experimentally compared for both model and prototype. Results present the possibilities and limitations of transposing the mechanical parameters from model to prototype.