Procedure for predicting part load resonance in Francis turbine hydropower units based on swirl number and local cavitation coefficient similitude

Francis turbines operating at part load conditions develop a cavitation precessing vortex known as a vortex rope in the draft tube cone below the runner outlet. At part load conditions, this vortex precession acts as an excitation source inducing pressure pulsations in the whole hydraulic system at the vortex precession frequency. Simultaneously, the lower pressure levels in the vortex core can lead to cavitation development, increasing the local flow compliance and reducing drastically the pressure wave speed. As a result, the eigenfrequencies of the hydraulic circuit are lowered and may match the vortex rope excitation frequency, leading to undesired resonance conditions. This paper presents a procedure to predict this type of resonance phenomenon in turbine prototypes by performing reduced scale physical turbine model measurements and eigenvalue calculations with linearized system matrices. This new procedure requires the transposition of hydroacoustic parameters from the reduced scale physical model to the prototype scale based on the swirl number and the local cavitation coefficient similarity. The procedure is validated by measurements performed on a turbine prototype featuring a peak of power swings and pressure pulsations in the predicted operating conditions.