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.

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.

Fused deposition modeling (FDM) technique is one of the most popular additive manufacturing techniques. Infill density is a critical factor influencing the mechanical properties of 3D-printed components using the FDM technique. For irregular components with variable cross-sections, to increase their overall mechanical properties while maintaining a lightweight, it is necessary to enhance the local infill density of the thin part while decreasing the infill density of the thick part. However, most current slicing software can only generate a uniform infill throughout one model to be printed and cannot adaptively create a filling structure with a varying infill density according to the dimensional variation of the cross-section. In the present study, to improve the mechanical properties of irregular components with variable cross-sections, an adaptive-density filling structure was proposed, in which Hilbert curve with the same order was used to fill each slice, i.e., the level of the Hilbert curves in each slice is the same, but the side length of the Hilbert curve decreases with the decreasing size of each slice; hence, the infill density of the smaller cross-section is greater than that of the larger cross-section. The ultimate bearing capacity of printed specimens with the adaptive-density filling structure was evaluated by quasi-static compression, three-point bending, and dynamic compression tests, and the printed specimens with uniform filling structure and the same overall infill density were tested for comparison. The results show that the maximum flexural load, the ultimate compression load, and the maximum impact resistance of the printed specimens with the adaptive-density filling structure were increased by 140%, 47%, and 82%, respectively, compared with their counterparts using the uniform filling structure.

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.

To realize a fault diagnosis of rolling bearings in a real R2R printing unit, a method based on Siamese Network is proposed in this work. First, vibration signals in rolling bearing were changed into a series of time–frequency spectra with Continuous Wavelet Transform, and thus the frequency components with time in various scales can be reflected as images. Siamese Networks with sub-nets composed of both Convolutional Neural Network (CNN) and Depth-wise Separable Convolution Network (DSCN) were proposed and established for fault diagnosis; meanwhile, fault samples were divided into sample twins to solve the problem of small samples. As to a database of rolling bearings, different kinds of faults with various degree, rotary speed and added noise were distinguished with both SN-CNN and SN-DSCN models successfully. Then an experiment for a R2R unit in printing press is also taken, there are all 7 classes of samples to be identified, and each group contains few numbers of samples. From this work, it can be seen that SN-CNN and SN-DSCN both can realize a fault diagnosis of rolling bearings in printing units based on 20 samples, which can be seen as a limited sample learning mission. Besides, SN-DSCN is proved to have a less time in training process compare to SN-CNN.