Origin of unsteady pressure and force oscillations in the S-region: Insights from vortex dynamics of a high-head pump turbine

As a flexible regulating power source, pumped storage units play a crucial role in enabling the large-scale integration of renewable energy into power grids. Through interregional regulation, they balance the generation and consumption of renewable energy across different regions, thereby enhancing overall utilization efficiency. However, during this process, units frequently traverse or directly operate within the S-shaped characteristic region (S region), which may induce operational instability. When a high-head pump turbine enters the S region, large-scale flow separation and complex vortex inevitably develop within the flow components. The dynamic evolution of these unsteady structures induces high-amplitude pressure fluctuations and force pulsations, posing significant threats to the safe and stable operation of the unit. To elucidate the mechanisms of pressure fluctuation and force evolution in the S region, this study investigates a high-head model pump turbine through unsteady numerical simulations at representative operating points with a 12° guide vane opening. The analysis focuses on internal flow characteristics, pressure fluctuations, and runner force pulsations. The results show that unstable vortex structures, including circumferential and cross flows, develop near the runner inlet, leading to pronounced pressure fluctuations. Time-frequency analysis reveals that cross flow within the runner generates low-frequency components at 0.3 fn and 0.4 fn, while rotating stall in the vaneless space causes low-frequency fluctuations at 0.6 fn and 0.7 fn. In contrast, rotor–stator interaction produces high-frequency components at 9.0 fn. Further analysis confirms that rotating stall and cross flow are the primary sources of flow instability in the S region of pump turbines. Moreover, the runner force results demonstrate that vortex structures induced by cross flow significantly affect the radial force distribution, whereas the axial force is predominantly governed by rotor–stator interaction. These findings provide a theoretical basis for optimizing the hydraulic design and enhancing the operational stability of pumped storage units.