An energy loss evaluation of vortex evolution mechanisms and entropy production coupling in a low-head mixed-flow PAT system based on a time-lagged lasso regression model

Pump-as-Turbine (PAT), as an economical and efficient solution for renewable energy recovery in small- and medium-scale power generation, has its efficient and stable operation significantly affected by guide-vane shedding vortices (GSV) inside the impeller. However, the coupled interaction mechanism between GSV evolution and energy dissipation remains unclear. This study investigates the evolution of GSV and its stage-dependent influence on turbulent dissipation loss rate (TDLR) through combined experimental and numerical approaches. A spatiotemporal correlation between vorticity transport terms and TDLR is established, revealing that the spatiotemporal evolution of GSV precedes and drives the generation of TDLR. The intrinsic time lag between GSV evolution and TDLR variation is primarily concentrated in the range of 0.38–22.73 ms. Furthermore, lagged response characteristics are incorporated to develop a time-lagged least absolute shrinkage and selection operator (LASSO) regression model, which elucidates the dynamic contributions of vorticity transport components to TDLR along the GSV evolution pathway. The results indicate that the influence of the vorticity transport term on energy dissipation dynamically alternates between dissipation enhancement and suppression during the evolution of the GSV. Along the evolutionary pathway of the GSV from inception to breakdown, the dominant generation mechanisms of TDLR exhibit clear stage-dependent transitions. Coriolis deflection dominates in the inception region, followed by centrifugal stretching in the downstream development region. As the vortices enter the rotating impeller domain, the coupled blade-induced rotational shear and Coriolis effects become the primary drivers, while rotational shear ultimately dominates within the impeller passage.