The Spatiotemporal Correlation Between Hydraulic Loss and Liutex-Based Vortex Dynamics Across Four Stall Regimes in a Pump-Turbine
Pumped-storage hydropower requires pump-turbines to operate safely and efficiently under off-design conditions, where stall-induced unsteady flows can redistribute hydraulic losses and reduce operational stability. Unlike previous analyses focused mainly on spatial correlations, this study develops a spatiotemporal framework to clarify how hydraulic loss (HL) and vortex evolution (VE) co-vary under different stall states at the valley point of the pump-mode hump region in a low-specific-speed, ultra-high-head pump-turbine. Detached eddy simulations (DESs) were performed for an original-runner scheme (ORI) and an optimized-runner scheme (OPT), with identical stationary components, boundary conditions, and numerical settings. The comparative cases cover four representative flow states: non-stall, fixed stall, rotating stall, and mixed stall. The local hydraulic-loss rate (LHLR) was decomposed into dissipation (DIS) and transport (TRANS) terms, and Liutex-based vorticity decomposition was used to distinguish shear- and rigid-rotation-related vortex quantities. Pearson correlation analysis was then applied in both space and time. The results show that DIS is consistently associated with shear enstrophy ΩS, whereas the spatiotemporal correlation associated with TRANS and VE parameters exhibits stronger regional and stall-state dependence. These findings provide a quantitative basis for identifying loss-sensitive vortex features and support flow-control and runner-optimization strategies for improving pump-turbine efficiency and stability.