Analysis of hydraulic characteristics during low head start-up transition of pumped storage units based on entropy production theory

To investigate the hydraulic characteristics during the start-up process of a full-flow pumped-storage unit (PSU) under low head conditions, numerical simulations and prototype tests were conducted to study the dynamic characteristics during the process. Based on the torque balance equation to control the real-time rotational speed of the runner, an incremental Proportional-Integral-Derivative (PID) algorithm was used to control the guide vanes in real time. Using dynamic mesh technology and computational fluid dynamics (CFD) methods, a numerical simulation of the pump-turbine start-up process was carried out under low-head conditions with PID control. These established the correlation mechanism between the internal flow evolution and external characteristic changes of the pump-turbine. Additionally, the entropy generation theory quantified the energy losses in different regions, including EPDD, EPTD, and EPWS. The results indicated that EPDD and EPTD dominated the entropy generation and were the main causes of hydraulic losses, were basically consistent with the TKE distribution. During the entire start-up process, the combined energy loss ratio of EPDD and EPTD exceeds 80 %, while the maximum proportion of EPWS was only 17 % at 17 s. The distribution characteristics and the generation mode of hydraulic losses were further clarified by combining the transport equation of enstrophy and the flow field distribution. The analysis showed that G_ω is the dominant factor leading to vortex formation during the start-up process and is consistent with the spatial distribution of EPR. The region with higher vortex is also the region with higher energy losses. This paper provides a valuable research direction on the start-up process and energy loss change during low-head conditions and lays the foundation for future research to improve the stability and safety of PSUs during the start-up process under low-head conditions.