Cavitation vortex evolution and alleviation in Francis turbines during load reduction: Numerical insights for grid stability-oriented blade optimization

In the context of flexible grid regulation, Francis turbines often operate under off-design conditions with frequent load transitions, during which cavitation vortices pose serious stability challenges. This study investigates the evolution of cavitating vortex structures during load reduction using dynamic mesh-based numerical simulations. Two distinct vortex types are identified: blade flow-separation cavitation vortices near the suction side leading edge, and inter-blade cavitation vortices extending from the runner crown to the trailing edge. As the load decreases, the former weakens and vanishes, while the latter intensifies and dominates the runner cavitation pattern. The reduced flow velocity aggravates blockage, and vortex cores are enveloped by high-speed regions. Hankel-Dynamic Mode Decomposition (DMD) analysis shows that Mode 0, reflecting the pressure trend, governs pressure fluctuations across all stages, alongside notable energy contributions from guide vane passing frequency and low-frequency modes. To suppress cavitation vortices, a blade optimization strategy targeting hydraulic efficiency and minimum pressure is proposed. The optimized blade, featuring a reverse C-shaped at the blade leading edge, reduces cavitation volume by 91.28 % and 83.15 %, and pressure amplitudes by 91.85 % and 80.73 % at two cavitation vortex conditions. These findings provide insights and solutions to enhance the operational stability of Francis turbines under transient conditions.