Investigation into unsteady inter-blade vortex in Francis turbines: Insight from unit speed effect and alleviation strategy

Inter-blade vortex is a special cavitation vortex within the Francis turbine runner, which can trigger high-amplitude pressure fluctuations, significantly limiting the flexible regulation capability. This paper numerically investigates the impact of attack angle variations on the evolution of inter-blade vortices by varying the unit speed. The cavitation volume, indicating vortex intensity, initially decreases sharply, then diminishes before rising swiftly with volume pulsations. Two types of inter-blade vortices emerge: type A is observed at low unit speed, attaching at the intersection of blade leading edge and runner crown, and type B, attaching at the mid-crown blade channel at high unit speed. The variational mode decomposition technology identifies vortex frequencies, type A at approximately 5.0fn and type B at around 1.0fn. Hydraulic instability, primarily driven by pressure fluctuations from inter-blade vortices, is more influenced by type B during transient simulations. Furthermore, an optimization approach including multi-objective and multi-condition was developed to reduces the vortex strength, improving hydraulic efficiency by 1.63% and 3.84%, decreasing cavitation volumes by 88.91% and 70.19%, with maximum pressure fluctuation amplitudes reduced by 57.7% and 82.6% for type A and type B inter-blade vortices, respectively. These findings enhance turbine stability across a wide operating range.