After long-term operation, the material loss due to slurry erosion often leads to significant changes in the impeller geometry. This change can, in turn, affect the flow characteristics and the erosion mechanism in a centrifugal pump. To investigate this matter, we consider two geometric models based on a prototype stainless steel impeller, which failed due to huge erosion problems from the pulp slurry. These two models are different in the degree of wear, with one model at the pre-erosion stage and the other with worn blades. For both models, the flow characteristics have been obtained in the Eulerian reference frame by means of the SST k-ω model. Then, in order to determine the erosion patterns, the particles have been tracked in the Lagrangian reference frame. In this way, the influence of the flow characteristics on the erosion patterns has been analyzed. Results show that the geometric variations greatly affect the flow characteristics, and consequently the erosion patterns. Particularly, it has been found that the clearance flow plays a significant role in defining erosion characteristics, such as erosion distribution, areas, and rates. Interestingly, the simulation results for current study show that the erosion rates after long-term operation greatly decrease near both the outlet edge and the blade bottom. It follows also that for accurate erosion predictions, these geometric variations have to be considered in the numerical model. This paper provides a better understanding of the complex erosion mechanism in centrifugal pumps, which can help to reduce the wear in future designs.

Francis turbines are widely used due to their large capacity and broad head adaptability, placing higher demands on the internal flow characteristics and runner performance of the units. In this paper, numerical simulations of a Francis turbine model were conducted using ANSYS CFX 2022 R1. The SST turbulence model, ZGB cavitation model, and VOF multiphase flow model were selected for the calculations. The internal flow characteristics and pressure pulsations in the runner and draft tube under different operating conditions were analyzed, and the variations in normal and tangential forces acting on the runner blades during operation were investigated. The results indicate significant differences in the internal flow within the runner and draft tube under various guide vane opening conditions. The pressure pulsation in the unit is influenced by both the internal flow in the draft tube and the rotation of the runner. The mechanical load on the runner blades is affected by multiple factors, including the wake from upstream fixed guide vanes, rotor–stator interaction, and downstream vortex ropes. Under low-flow conditions, the variation in forces acting on the runner blades is relatively small, whereas under high-flow conditions, the runner blades are prone to abrupt force fluctuations at 0.6–0.8 times the rotational frequency. This is manifested as periodic abrupt force changes in both the X and Y directions of the runner blades under high-flow conditions. The normal force in the Z-direction of the runner blades increases instantaneously and then decreases immediately, while the tangential force decreases instantaneously and then increases promptly.

Pump-turbines are critical for maintaining power grid stability, but they frequently suffer from flow instabilities induced by cavitation due to frequent operating condition changes. This study employs numerical simulations to systematically analyze the internal flow characteristics and changes in runner forces within a model pump-turbine under varying guide vane openings and cavitation coefficients. Results indicate that, under low opening conditions, a spiral vortex rope forms within the draft tube, inducing significant low-frequency pressure fluctuations. As cavitation intensifies, the vortex rope undergoes substantial expansion. At guide vane openings of 30.6 degrees and 37.3 degrees, the draft tube vortex rope exhibits a straight conical shape, with its dimensions increasing as flow rate rises. Additionally, the radial force on the runner is dominated by low-frequency fluctuations generated by the draft tube at low opening conditions, shifting to high-frequency characteristics caused by rotor–stator interaction at high opening conditions. Meanwhile, the expansion and contraction of the cavity volume induce low-frequency fluctuations in the axial force on the runner. These findings reveal the mechanism of vortex rope evolution on runner forces, emphasizing the impact of cavitation on the flow characteristics and force characteristics of the unit.

During frequent peak-regulation operation, pumped storage units inevitably operate under off-design conditions. Variations in draft tube flow structures under different load conditions may alter the hydraulic loading acting on the runner and shaft system. In this study, a model pump-turbine was investigated using unsteady numerical simulations combined with finite element structural analysis. Analyses were conducted under 70%, 100%, and 105% load conditions, representing typical part-load, rated, and overload operating states. The results show that under 70% load, the draft tube flow exhibits an eccentric structure with strong circumferential pressure non-uniformity. At the rated condition (100% load), the flow field is closest to axisymmetric with the most uniform pressure distribution. Under 105% load, a concentrated central vortex forms, and the degree of non-uniformity is intermediate. The hydraulic loads under different conditions lead to significant differences in the stress and deformation characteristics of the shaft system. The maximum equivalent stress increases from 1.84 MPa at the rated condition to 3.33 MPa under overload conditions, while more pronounced flow asymmetry and pressure non-uniformity occur at part-load operation. These findings clarify the relationship between load variation, draft tube flow structures, and the mechanical response of the shaft system.

To investigate the dynamic transmission of unsteady hydraulic excitation within pumped-storage units, this study presents a numerical investigation on the three-dimensional shafting vibrations of a pump-turbine based on a one-way transient fluid-structure interaction approach. To resolve the flow field, we adopt the shear stress transport (SST) k-ω turbulence model in conjunction with the Zwart-Gerber-Belamri (ZGB) cavitation model, and the combined numerical approach is first calibrated against experimental measurements. The results indicate that under the 70% partial load, an eccentric helical vortex rope develops inside the draft tube, generating intense low-frequency pressure pulsations that induce chaotic shaft orbits and distinct orbital drift at the turbine guide bearing. Conversely, near the optimal efficiency point (90% load), the vortex rope transitions into a slender, straight conical core, yielding minimum vibration magnitude and exceptional operational stability. At the 100% rated load, the vortex rope expands into a robust straight conical structure extending continuously into the elbow section. Stress analysis reveals that while equivalent stress concentrations consistently occur at the blade root regions, a reduction in the cavitation number at both 90% and 100% loads leads to a counterintuitive decline in blade surface peak stress values. Additionally, stiffness sensitivity analysis demonstrates that the relative change rates of the shaft runout are highly sensitive to the stiffness variations of the turbine guide bearing, where a stiffness reduction triggers a substantial runout growth of approximately 100% along the X- and Y-directions, whereas the variations in the upper and lower guide bearings exert extremely weak impacts.