Characteristics of high-amplitude pressure fluctuation induced by inter-blade cavitation vortex in Francis turbine

Abstract: Hydraulic turbines can accommodate the variable electricity demand and frequently operate at part load conditions, thereby keeping the dynamic balance of grid parameters, particularly under the tremendous development and integration of renewable resources. In the case of part-load operation, a particular cavitation flowing (called inter-blade cavitation vortex) can be developed adjacent to runner blades in a Francis turbine. It has been a great threat to the service life of the machine, such as the rapid degradation of performance, and fatigue damage. Therefore, the hydraulic instability induced by the inter-blade cavitation vortex has been an urgent technical issue, particularly for the extending operating range of the hydraulic turbine. In the presented study, an unsteady numerical investigation was carried out to simulate the evolution of the inter-blade cavitation vortex using the combined SST k-ω turbulence model and the Zwart-Gerber-Belamri cavitation model. The pressure fluctuation characteristics were also determined in a low-head Francis turbine operating at 40% of the rated output. Furthermore, an experimental test was conducted to visualize the external characteristics, including the head and hydraulic efficiency, as well as the vortex appearance. The vapor volume in the time and frequency domains was also calculated to clarify the evolution of the inter-blade cavitation vortex in the turbine. The results show that a periodical oscillation of the vapor volume was captured under the inter-blade cavitation vortex, where the dominant frequency of vapor volume was 1.1 times the rotational frequency. Simultaneously, the high-amplitude pressure fluctuations were also captured with the same frequency of inter-blade cavitation vortex in the runner. More importantly, a dynamic cycle in the evolution of inter-blade cavitation was associated with the cavitation vortex incipient, development, local collapse, and disappearance, as well as the cavitation vortex re-formation in the blade channels. Specifically, the vortex structure was attached up to the runner hub all the time, where the most pronounced collapse of cavitation was observed at the intersection of the trailing edge and the runner shroud on the suction sides. There was a global influence on the distribution of pressure fluctuation, thereby locally amplifying the amplitude of pressure fluctuation in the suction side of the runner blade. A relationship was also established between the transient characteristics of the high-amplitude pressure fluctuation signals and the spatial-temporal evolution of the vortex structure, using the combined one-dimensional theory of cavitation and the three-dimensional turbulence numerical calculation. It confirmed that the difference in flow rate between the runner inlet and the outlet was proportional to the change rate of vapor volume. Furthermore, the instantaneous pressure fluctuation was proportional to the acceleration of the vapor volume, indicating that the inter-blade cavitation mainly dominated the high-amplitude pressure fluctuation. The presented investigation can further clarify the evolution of inter-blade cavitation vortex at the part load, thereby revealing the internal physical mechanism of high-amplitude pressure fluctuation induced by inter-blade cavitation vortex in the Francis turbine.