Evolution of Inter-Blade Vortex and Hydraulic Excitation in a Francis Turbine Under Partial-Load Conditions

Hydropower, as an important part of clean energy, can effectively optimize the energy structure. However, units frequently operate under partial-load conditions due to environmental and grid demands, where hydraulic excitations threaten stability. This study investigates six partial-load conditions (25–60% rated load) using the SST k–ω turbulence model to systematically analyze the runner internal flow (the vorticity, pressure, and velocity distributions), blade load distribution, and pressure fluctuation characteristics. The results reveal a load-dependent transition of the dominant hydraulic excitation source: under low-load conditions, the draft tube vortex rope frequency 0.33fn is modulated by the rotational frequency, generating dominant 0.67fn pulsations propagating upstream. Under extremely low-load conditions, fully developed inter-blade vortices block the flow passages, suppress vortex-rope propagation, and induce high-frequency disturbances. This transition occurs at approximately 35% rated load. These findings clarify the evolution mechanism of inter-blade vortices from development to dominant hydraulic excitation.