The positive slope on the pump performance curve of pump-turbines suggests potential operational instabilities in pump mode. Previous research has indicated that the increase of the hydraulic loss caused by sudden changes of flow patterns in pump-turbines is responsible for the positive slope, however its detailed flow mechanism is still unclear. A low specific speed model pump-turbine was numerically investigated against experiments in the present study, by applying unsteady RANS (Reynolds-Averaged Navier–Stokes equations) simulations with a v²-f turbulence model. The mechanism of occurrence of the positive slope on the pump performance curve was discussed regarding the energy balance, as this region appears when the value of $\frac{\partial P_u}{\partial Q}$ is larger than the critical value $\frac{P_u}{Q}$ . An unsteady local loss analysis, derived from the energy equation, was conducted to illustrate the contribution of local flow patterns to the loss in corresponding hydraulic components. The variation of the kinetic energy of the mean flow was taken into account for the first time so that this method can be applied to highly time dependent flow patterns, e.g., a rotating stall in the present study. The investigations on the flow patterns revealed that some guide vane channels stalled with a larger discharge coefficient than the positive slope region. Several guide vane channels near the stalled channels were stalling with minor decrease of the discharge coefficient, leading to sudden increases of the input power and the loss. When the discharge coefficient slightly decreased in further, the pump-turbine operated into the positive slope region, and the rotating stall with 3 stall cells appeared, proven by the FFT (Fast Fourier Transform) and cross-phase analysis on the pressure fluctuations.

When the Francis-type reversible pump-turbine runs under partial load, the pressure pulsation amplitude and frequency in vaneless space are high, posing a serious threat to the stability of unit operation. Water presents weak compressibility in a high-head pump-turbine, thereby affecting the amplitude–frequency characteristics of pressure pulsation. This study used numerical simulations in a model and prototype pump-turbine and particle image velocimetry (PIV) in a model pump-turbine to examine the internal flow field and pressure pulsation characteristics and determine the effect of the flow in the vaneless space on the amplitude–frequency characteristics of the pressure pulsation. The pressure pulsation amplitude–frequency characteristics were verified through prototype tests. The effects of the weak compressibility of the water on the propagation law of pressure pulsation throughout the flow passage of the prototype and model pump-turbine were roughly similar but exhibited certain differences. Considering the weak compressibility of water, the pressure pulsation fluctuations in each flow passage of the prototype and model pump-turbine exhibit varying degrees of improvement, which is more obvious at the prototype scale. Therefore, the pressure wave disturbance caused by the weak compressibility of the water has different effects on the prototype scale and model scale of the high-head Francis pump-turbine.

The clearance flow around the pump-turbine runner has significant influences on unit vibrations, which may cause accidents in transient processes. The dynamic hydraulic forces and flow patterns in the clearance flow channel (CFC) of a low specific-speed pump-turbine were analyzed based on 3D CFD simulations during the runaway oscillating process. It is shown that the axial force of the runner periodically fluctuates with large amplitudes, and its components in CFC and the main flow channel (MFC) demonstrate a similar significance level. The CFC component was formulated as a function of the clearance inlet pressure and rotational speed, while the MFC component as a function of the momentum changing rate and the runner outlet pressure force. The fluctuation of runner radial force is mainly caused by the flow evolution in MFC, however, the flow in CFC aggravates it. The pressure in CFC shows a few pulsating signals from MFC, and the radial pressure drop in CFC is proportional to the square of both radius and rotational speed. In CFC, strong rotating shear flow containing a velocity core region in the circumferential direction is formed, and rotational speed is the dominant factor.

The flow characteristics of the draft tube of a Francis turbine have a significant influence on turbine stability. Numerical simulations were performed for a Francis turbine under three different output conditions of 20%, 100%, and 120% at the rated and maximum heads. Laser Doppler velocimetry (LDV) tests were conducted to test the flow characteristics of the draft tube of the Francis turbine model. The flow characteristics in the draft tube, the mechanism of the flow characteristics change, and the effect of the opening on the vortex rope were analyzed. The results showed that the large and invisible vortex in the conical cross-section at the inlet of the draft tube gradually changed to a tangible vortex rope as the guide vane opening (GVO) increased. The pressure and velocity are significantly influenced by the GVO, and the flow characteristics in the draft tube improve as the GVO increases. Simultaneously, the influence range of the vortex rope increased as the head increased.

Hydropower units are usually operated in non-design conditions because of power grid requirements. In a partial-load condition, an inter-blade vortex phenomenon occurs between the runner blades of a Francis turbine, causing pressure pulsation and unit vibration, which hinder the safe and stable operation of power stations. However, the mechanism through which the inter-blade vortex generation occurs is not entirely clear. In this study, a specific model of the Francis turbine was used to investigate and visually observe the generation of the blade vortex in Francis turbines in both the initial inter-blade and vortex development zones. Particle image velocimetry was used for this purpose. In addition, we determined the variation law of the inter-blade vortex in the Francis turbine. We found that the size and strength of the inter-blade vortex depend on the unit speed of the turbine. The higher the unit speed is, the stronger the inter-blade vortex becomes. We concluded that the inter-blade vortex of such turbines originates from the pressure surface or secondary flow and stall of the blade at the inlet side of the runner at high unit speeds, and also from the backflow zone of the suction surface of the blade at low unit speeds.

For Francis pump turbines, the pressure pulsation characteristics of the draft tube are some of the key concerns during the operation of the units. The pressure pulsation characteristics of the draft tube are directly related to the draft tube spiral cavitating vortex rope. In this paper, the velocity distribution in the draft tube of a Francis pump turbine is tested by means of laser Doppler velocimetry. The velocity pulsation was found to be directly related to the pressure pulsation, while the velocity pulsation was also influenced by the cavitation coefficient. The main frequency of the velocity pulsation was close to the main frequency of the pressure pulsation and became larger as the cavitation factor increased.