Study on the vortex dynamics and energy characteristics of the cone tip vortex under turbine operating conditions in low-head pumped storage systems

In low-head pumped storage systems operating in pump-as-turbine (PAT) mode, cone-tip vortices near the impeller guiding cone strongly influence safety and efficiency. This study investigates vortex evolution, vortex dynamics, and energy dissipation through numerical simulation and model testing, using the PAT unit of the South-to-North Water Diversion Project (Eastern Route) in China as a case study. The results indicate that under different flow conditions, the vortex structures in the outlet passage exhibit staged evolution. However, under off-design operation, the vortex frequently experiences a phase of breakdown followed by re-stabilization due to its reduced structural robustness. Vorticity stretching is identified as the dominant mechanism governing vorticity evolution. Under off-design conditions, steeper axial velocity gradients lead to intensified vortex tube stretching and twisting, whereas under design conditions, the smoother flow field at the impeller outlet effectively suppresses three-dimensional deformation of the vortex tubes. Entropy production analysis reveals that the impeller and outlet passage dominate energy loss, contributing over 95 % of total dissipation. During vortex initiation under off-design conditions, entropy production in the draft tube peaks and subsequently declines as the system stabilizes. In contrast, under design conditions, entropy production across flow passages shows minimal fluctuations, indicating optimal flow stability. Based on vortex dynamics and entropy production theory, a comprehensive unsteady vortex analysis framework is proposed, linking cone-tip vortex evolution to energy dissipation and offering design suggestions. The findings provide theoretical guidance for the performance optimization and engineering design of low-head pumped storage PAT systems.