Prediction of unstable full load conditions in a Francis turbine prototype

Francis turbines operating in full load conditions feature an axisymmetric vortex rotating in the opposite direction of the turbine runner. In low-pressure conditions, the resulting cavitation vortex may enter in an unstable self-exciting process, leading to large pressure pulsations and oscillations in the generating unit power output. In this research work, prototype on-site and reduced scale model test results are presented where the turbine changes from a stable to an unstable full load condition due to an increase in discharge. Measurements are compared in the frequency and time domain, where similarities are evidenced between model and prototype. Using the measurements on the reduced scale model and 1-D numerical models of both the reduced scale model and the turbine prototype, eigenvalue calculations are performed to predict the discharge value of transition from stable to unstable conditions. The transition point on the prototype is then predicted with a small deviation. Transient simulations in the time domain are performed replicating the self-exciting behavior of the unstable full load condition.