The pressure fluctuations and runner loads on a pump-turbine runner during runaway process are very violent and the corresponding flow evolution is complicated. To study these phenomena and their correlations in depth, the runaway processes of a model pump-turbine at four guide vane openings (GVOs) were simulated by three-dimensional computational fluid dynamics (3D-CFD). The results show that the flow structures around runner inlet have regular development and transition patterns—the reverse flow occurs when the trajectory moves to the turbine-brake region and the main reverse velocity shifts locations among the hub side, the shroud side and the midspan as the trajectory comes forward and backward in the S-shape region. The locally distributed reverse flow vortex structures (RFVS) enhance the local rotor–stator interaction (RSI) and make the pressure fluctuations in vaneless space at the corresponding section stronger than at the rest sections along the spanwise direction. The transitions of RFVS, turning from the hub side to midspan, facilitate the inception and development of rotating stall, which propagates at approximately 45–72% of the runner rotation frequency. The evolving rotating stall induces asymmetrical pressure distribution on the runner blade, resulting in intensive fluctuations of runner torque and radial force. During the runaway process, the changing characteristics of the reactive axial force are dominated by the change rate of flow discharge, and the amplitude of low frequency component of axial force is in proportion to the amplitude of discharge change rate.

Understanding the formation mechanism of the S-shaped characteristics (SSCs) and the relationship between flow structures and the runaway instability (RI) is the prerequisite for optimizing runner design to promote operational reliability and flexibility. In this study, a new turbine equation is derived to reveal the prime cause of the SSCs, and the influence of geometric parameters on the SSCs is analyzed. Moreover, the flow patterns in three model turbines of different specific-speeds are simulated by unsteady Computational fluid dynamics (CFD), and the correlation between inverse flow vortex structures (IFVSs) and the RI in the SSCs region is identified. Theoretical analysis shows that the turbine equation can theoretically predict the change trend of the first quadrant SSCs curves of the pump-turbines; the flow losses caused by small blade inlet angle, instead of the diameter ratio, are the primary cause of the SSCs. The numerical simulation results reveal that the IFVSs at the hub side of the runner inlet are the origin of the RI; when operating points are far away from the best efficiency point (BEP), the IFVS locations change regularly. For large guide vane openings (GVOs), the IFVSs first incept at the shroud side, and then translate to the hub side, and further back to the midspan, when the discharge decreases. The inception points (IPs) of the SSCs correspond to the onset of the IFVSs at the hub side, which are in advance of the zero-torque operating points (ZTOPs); therefore, the ZTOPs are located in the positive slope region, leading to RI. For small GVOs, however, the IFVSs only locate at the midspan; the IPs of the SSCs, having no definite correlation with the IFVSs, are coincided with or are below the ZTOPs, because the ZTOPs are in the negative slope region and RI disappears. It is also found that the IPs of SSCs are the turning points of the predominant states between the turbine effect and pump effect. These results are valuable for design and optimization of pump-turbine runners.

During transients, hydroturbines may demonstrate some dynamic characteristics that differ from the corresponding static characteristics in steady operating conditions. To study the dynamic characteristics of a pump-turbine, we simulated the runaway transients in a model pumped-storage plant by coupling one-dimensional (1D) water conveyance system and three-dimensional (3D) pump-turbine. The results show that the runaway dynamic trajectories form loops in the S-shaped region in the unit discharge and unit torque charts of the pump-turbine, not following the corresponding static characteristics. Theoretical analysis and flow patterns comparisons illustrate that the looping trajectories are mainly caused by the successive features of transient flow patterns, namely, the transient flows in the pump-turbine are influenced by their previous status. These features induce different performances between similar dynamic operating points in different moving directions. Furthermore, through comparing the transient parameters calculated by the dynamic and static characteristics separately, we found that both methods are available to capture the unstable behaviors of the pump-turbine, but the dynamic method displays more accurate results when simulating the critical transient parameters. Therefore, in practical engineering applications, we suggest to use the static characteristics method for stability analysis while dynamic characteristics method for transient parameters, which is important for optimizing the layout of water conveyance systems.

To fully understand the evolution of flow structures and pressure fluctuations in the S-shaped region of pump-turbines, three dimensional (3D) numerical simulations were carried out for a model pump-turbine at four different guide-vane openings (GVOs). We found that special backflow vortex structures (BFVSs) form around the runner inlet. The backflow location shifts from the hub side to the shroud side and then to the midspan, as the operating point moves from the best efficiency point to the zero discharge point along the S-shaped characteristic curve. At large GVO, if the discharge is relatively large, the flow separations at the runner inlet are primarily driven by the local adverse pressure gradient, resulting in hub and shroud side backflows. At small GVO or small discharge, the separations are mainly dominated by the centrifugal force, resulting in backflow at the guide-vane midspan section. The locally distributed BFVSs enhance the local rotor-stator interaction (RSI) in the vaneless space, leading to different pressure fluctuating intensities along the spanwise direction for high frequency components. On the other hand, the rotating stall is the main cause of the uneven distributions of low frequency pressure fluctuations along the vaneless space between runner and guide-vanes.

Frequent working condition conversions in pumped-storage power stations often induce stability problems, especially when the operating point enters the S-shaped region, during which flow transitions and pressure fluctuations are serious. The pump-turbines with different specific speed values show different characteristics, but their differences in stability features are still not clear. In this study, four different pump-turbines were selected to simulate the runaway processes from turbine modes. The similarities and differences of flow patterns and pressure fluctuations were analyzed. For the similarities, pressure pulsations increase gradually and fluctuate suddenly once the backflows occur at the runner inlets. For the differences, the evolutions of backflows and pressure pulsations are related to specific speeds and runner shapes. Firstly, it is easier for the lower specific speed turbines to enter the reverse pump mode. Secondly, the blade lean angle influences the position where backflows occur, because it determines the pressure gradient at the runner inlets. Thirdly, the runner inlet height influences pressure pulsations in the vaneless space, because the relative range of backflow transitions will be enlarged with the decrease of specific speed. Overall, investigating the mechanisms of flow pattern transitions and pressure variations is important for runner design and transient process control.

The runaway oscillation process of the pump-turbine in a high head pumped-storage power plant is usually unstable. The root cause of its instability is still unclear. In this paper, its internal mechanism and the improvement method were studied in depth. First, the flow characteristics in a model pump-turbine during the runaway process at four guide-vane openings (GVOs) were investigated by 3D transient numerical simulations. Then, the energy dissipation characteristics of different types of backflow vortex structures (BFVSs) occurring at the runner inlet and their impacts on the runaway stability were investigated by the entropy production theory. The results show that the location change of BFVSs between the hub side and the mid-span of the runner inlet around the no-load point leads to the sharp change in the energy dissipation rate, which makes the slope of dynamic trajectory positive and the runaway oscillation self-excited. If the occurrence of BFVSs at the hub side is suspended, the runaway process will be damped. Finally, the pump-turbine runner was improved to obtain a wider stable operating range.