Temporal-spatial and energy dissipation characteristics of vortex evolutions in Francis turbine during load reduction

This study numerically investigates the load reduction effects, on a model Francis turbine, combining cavitation model and structured dynamic grid technique. The results indicate that the vapor volume in the draft tube undergoes two rapid increases and decreases until cavitation ceases. The precessing vortex rope transitions from a strong helical structure to axial contraction as ellipticity increases, ultimately forming a discrete band before disappearing. Initially, vapor volume in the runner increases gradually and linearly, followed by continued growth with a consistent pulsation amplitude. The inter-blade vortex (IBV) first appears at the blade trailing edge and then develops into a complete structure extending from the runner crown to the blade trailing edge, driven by pulsating vapor volume growth. Axial force extracted by the runner changes significantly and correlates closely with variations in the vapor volume in the runner. Flow separation in the runner occurs near the runner crown, forming dual separation lines that enhance IBV formation, which highlights the significant influence of crown-proximal flow separation on IBV development. Regarding energy loss, initial decreases followed by increases are observed in both the draft tube and runner, with draft tube losses consistently exceeding 57.4% and runner losses exceeding 27.1%. Turbulent kinetic energy generation and Reynolds stress are the primary forms of energy dissipation, with high-value regions corresponding to vortex locations, underscoring the substantial role of vortices in energy dissipation. This study provides new insights into the evolution of vortices and energy dissipation characteristics during load reduction in Francis turbines.