Swirl number based transposition of flow-induced mechanical stresses from reduced scale to full-size Francis turbine runners

At part load conditions, Francis turbines are subject to the emergence of a hydrodynamic instability in their draft tube, referred to as precessing vortex rope. It induces pressure pulsations in the water passages at the precession frequency of the vortex, leading to additional vibrations and dynamic loads on the runner blades. The prediction of both the dynamic behaviour of the vortex rope and the resulting dynamic loads over a wide operating range is of importance to improve the runner design and robustness on the one hand and to assess additional fatigue and related maintenance costs on the other hand. Such a prediction, either with numerical simulation or reduced scale physical model tests, remains however challenging. The present paper aims at introducing a methodology to assess the vortex behaviour, the related pressure fluctuations and the resulting dynamic strains on the runner over the complete part load operating range. It is based on reduced scale physical model tests of a Francis turbine, including the measurement of the pressure and the load on the runner with instrumented blades. It is shown that the influence of both the discharge factor and speed factor on the vortex dynamics behaviour and related pressure fluctuations can be represented by a single parameter, the swirl number. The correlation with the swirl number is further extended to the dynamic strains induced by the vortex rope on the runner blades. Similar mechanical load and pressure measurements are finally performed on the full-scale machine during a power ramp-up and the results are compared to the empirical correlations established on the reduced scale physical model.