Precessing vortex rope (PVR) plays a key role in inducing hydraulic resonance in Francis turbines operating at partial load, possibly degrading power plant stability and availability. Air injection into the runner cone is a suitable mitigating alternative; however, the influence mechanism of air injection on PVR remains unclear. The principal objective of this study was to establish response relationships between the characteristic parameters and air injection by the method of computational fluid dynamics (CFD) considering the fluid components of water, water vapour and air. The findings show that cavitation flow can be completely suppressed by slight air injection; however, the helical vortex structures are persisted at 1.0% and 2.0% air volume fractions, and the static pressure recovery is improved together with a slight increase in the hydraulic loss. At 3.0% air volume fraction, the vortex structure completely disappears, leaving an umbrella-shaped structure, with no pressure vibration arising in the turbine. Moreover, the physical mechanism of reducing the pressure amplitudes is clarified. This results clarify the influence mechanism of air injection on PVR, and contribute to steadily extending the flexibility of the operating range of the turbine during the engineering application.

Inter‐blade cavitation vortex at part load has raised significant concerns about operation stability for Francis turbines due to tremendous development and integration of renewable energy resources into power grid. The principal objective of this study is to investigate the flow characteristics of inter‐blade cavitation vortex and its influence on pressure fluctuations for a low‐head Francis model turbine. Unsteady numerical simulations are carried out using shear stress transport turbulence model and Zwart cavitation model. Numerical results yield to a good validation with the experimental data. The findings show that inter‐blade cavitation vortices highlighted by cavitation structure and vortex structure are extremely different at the points adjacent to the incipient line of inter‐blade cavitation vortex. The location of inter‐blade cavitation vortex development in the runner is more sensitive to rotating speed than that to guide vane opening. The formation mechanism of inter‐blade cavitation vortex is attributed to flow separation in the vicinity of the runner hub. Pressure fluctuations induced by inter‐blade cavitation vortex are directly associated with the evolution of vapour volume in the runner and feature wide‐band and low‐frequency characteristic, and the fluctuations on the suction side of the runner blade are significantly magnified because of the presence of inter‐blade cavitation vortex.

The presented paper numerically investigates the internal flow behaviors and energy dissipation during the no-load startup process toward a Francis turbine. Passive runner rotation is implemented through the angular momentum balance equation accompanied by dynamic mesh technology and user defined function. Three phases of rotational speed are identified: stationary, rapid increase, and slow increase. Head exhibits a monotonic decrease, rapid rise and fall, and eventual fluctuation. Flow rate shows quasi-linear increase. The pressure fluctuations in the vaneless region are primarily dominated by the frequencies induced by Rotor-Stator Interaction and a broad frequency range below 50 Hz, and below 30 Hz in the draft tube. Runner inlet experiences positive to negative incidence angles, causing intense flow separation and unstable structures. Draft tube exhibits large-scale recirculation and evolving vortex structures. Energy loss analysis based on the entropy production method highlights the runner and draft tube as primary contributors. The energy loss within the runner exhibits an initial increase, subsequent decrease, and then a rise again during the stationary and rapid speed increase phases. While the draft tube shows a rapid increase during the phase of rapid speed increase. Turbulent fluctuations significantly contribute to entropy production loss, with trends matching total entropy production. Maximum energy loss locations correspond to runner inlet and draft tube wall, emphasizing the importance of unstable flow and vortex generation. This study establishes foundational insights into unstable hydrodynamics and energy dissipation modes during hydraulic turbine no-load startup, paving the way for further research.

Sediment erosion poses a significant challenge for hydraulic turbines in sediment-laden rivers. This paper investigates the erosion patterns in high-head Francis turbines using numerical simulations. It analyzes how sediment concentration, particle size, and operating conditions affect wear on turbine components. The results identify the trailing edges of the guide vanes, the intersection of runner blade trailing edge, and runner band as primary erosion zones. Higher sediment concentrations increase erosion intensity and extend the erosion range upstream. Small particles uniformly affect both pressure and suction sides of the blades, while larger particles concentrate erosion near the runner band trailing edges. The flow rate has a greater impact on runner blade erosion than water head, with lower flow rates reducing pressure side erosion but initially increasing, then decreasing suction side erosion. Additionally, the study proposes a multi-objective, multi-condition optimization design method that balances erosion resistance and energy efficiency. The optimized runner reduces the maximum erosion rate by 23.91% while limiting the weighted efficiency loss to under 0.1%. The improved runner design reduces high erosion areas on both blade sides, particularly decreasing particle impact speeds near the trailing edges. Sensitivity analysis reveals a trade-off between minimizing erosion and maintaining hydraulic efficiency, highlighting the importance of span height at 75% for controlling erosion. Changes in blade circumference angle generally reduce erosion but may also lower efficiency. Overall, this research demonstrates a successful reduction in Francis turbine erosion while preserving hydraulic efficiency, offering valuable guidance for anti-erosion turbine design in sediment-heavy environments.

The Pelton turbine is an ideal choice for developing high-head hydropower resources. However, its cantilever-beam structure exposes the runner to intense alternating loads from high-velocity jets, causing localized high stresses, structural vibrations, and potential bucket fractures, all of which compromise safe operation. This study employs fluid–structure interaction analysis for the numerical investigation of a six-nozzle Pelton turbine to examine its unstable flow characteristics and hydrodynamic excitation under high-velocity jets. Our findings indicate that low-order frequencies primarily induce overall runner oscillations, while high-order frequencies result in oscillation, torsional displacement, and localized vibrations. Torsional displacement at the free end of the bucket induces stress concentrations at the root of the bucket and the splitter, the outflow edge, and the cut-out. The amplitudes of stress and displacement are correlated with the nozzle opening, with displacement typically in phase with torque, while stress fluctuations exhibit a phase lag. The stress and displacement values are higher on the bucket’s front, with maximum stress occurring at the bucket root and maximum displacement at the outflow edge, particularly in regions subjected to prolonged jet impact. The dominant frequency of the stress pulsations matches the number of nozzles. This study elucidates the dynamic response of Pelton turbines under high-velocity jets, correlating fluid load with runner dynamics, identifying maximum stress and deformation points, and providing technical support for performance evaluation.

Inter-blade vortex is a special cavitation vortex within the Francis turbine runner, which can trigger high-amplitude pressure fluctuations, significantly limiting the flexible regulation capability. This paper numerically investigates the impact of attack angle variations on the evolution of inter-blade vortices by varying the unit speed. The cavitation volume, indicating vortex intensity, initially decreases sharply, then diminishes before rising swiftly with volume pulsations. Two types of inter-blade vortices emerge: type A is observed at low unit speed, attaching at the intersection of blade leading edge and runner crown, and type B, attaching at the mid-crown blade channel at high unit speed. The variational mode decomposition technology identifies vortex frequencies, type A at approximately 5.0fn and type B at around 1.0fn. Hydraulic instability, primarily driven by pressure fluctuations from inter-blade vortices, is more influenced by type B during transient simulations. Furthermore, an optimization approach including multi-objective and multi-condition was developed to reduces the vortex strength, improving hydraulic efficiency by 1.63% and 3.84%, decreasing cavitation volumes by 88.91% and 70.19%, with maximum pressure fluctuation amplitudes reduced by 57.7% and 82.6% for type A and type B inter-blade vortices, respectively. These findings enhance turbine stability across a wide operating range.