Measurements of Cavitation Compliance in the Draft Tube Cone of a Reduced Scale Francis Turbine Operating at Part Load

Francis turbines operating at part load conditions typically experience a cavitation vortex rope immediately at the runner outlet. As the compliance of this cavitation flow is much higher than the one in cavitation-free conditions, a decrease in the value of the eigen frequencies of the hydraulic circuit is observed. One of the eigen frequencies can eventually match the frequency of the vortex precession, which acts as an excitation source for the hydraulic system, inducing strong pressure pulsations and output power swings. To predict such undesirable resonance conditions in hydropower plants, the cavitation compliance in the draft tube cone can be identified beforehand at the model scale. This paper presents the identification of the cavitation compliance on a reduced scale model of a Francis turbine over a wide range of part load operating conditions, for different Thoma and Froude numbers. The first eigen frequency of the test rig is firstly identified by modal analysis. The cavitation compliance is then defined by adjusting a 1-D numerical model of the test rig to match this first eigen frequency. These compliance results could then be transposed to the prototype scale, enabling the prediction of the first eigen frequency of the hydropower plant in any part load condition.