In the context of constructing high-head hydro-power stations, the Pelton turbine assumes a critical role as the primary energy converter. This study employs the Eulerian–Lagrangian method to simulate the multi-phase flow occurring within the Pelton turbine bucket. Furthermore, it introduces a novel aspect by investigating and comparing the effects of cavitation on erosion within the bucket region under varying conditions of sediment-water, involving different particle sizes and concentrations. The research findings unveiled several key insights. Primarily, cavitation predominantly influences the flow characteristics of particles at the air–liquid interface, while particles with larger sizes tend to concentrate in the center of the jet. Consequently, cavitation's impact on erosion is more pronounced in the case of smaller-sized particles. Moreover, the study revealed that cavitation can either exacerbate erosion under high particle concentration conditions or mitigate it when particle concentration is low. Furthermore, the investigation highlighted variations in the degree of erosion and the affected area of the bucket based on different position angles. Particularly, at a position angle of 65°, the presence of water vapor induced by cavitation alters particle trajectories, thereby modifying the overall erosion pattern of the bucket. These findings collectively contribute to a deeper understanding of the complex interplay between cavitation and erosion within the Pelton turbine bucket.

Pelton turbines are widely used in hydropower stations located in mountainous regions, especially with water head drop of more than 2000 m. Due to the complex structure and working principle of the turbine, the flow is more complicated than reaction turbines, making the numerical simulation more difficult. The impulse action causes the occurrence of erosion phenomena in Pelton turbines, which will directly decrease the hydraulic efficiency and reduce the turbine's life. For investigating the erosion characteristics, computational fluid dynamics is widely used on variegated platforms according to their unique advantage. Thus, different platforms are introduced and compared in solving the multi-phase flow using a discrete element method or the other meshless methods. In addition, the erosion mechanism is studied and classified in different aspects such as impact angle and impact velocity. However, unlike the feasibility of numerical simulations, experimental work on the erosion mechanism is still challenging to reproduce. Furthermore, the state of experimental research is discussed by listing the various major facilities in operation and comparing their methods of experimental analysis. Case studies all over the world provide a very rich database of erosion patterns which would be highly useful in validation and verification of simulation and experimental results. Studies have shown that particle parameters, such as size, concentration, shape, velocity, and the interaction between particles and material surfaces, significantly impact the erosion of Pelton turbines. In response to this erosion, upgrading materials and implementing geometric optimization have proven to be effective strategies.

The present work combines experiments, computational fluid dynamics, and hydraulic models to explain the recirculation length variations downstream of sudden lateral expansions of an open-channel flow. This situation can be compared to the classical turbulent backward facing step situation, but the flow shallowness brings substantial differences. Experiments show that the recirculating zone length relative to the expansion width, L/d, varies in a quite wide range from 2 to 14. The expansion ratio R_b and mostly the bed friction number S influence these variations. Three dimensional numerical simulations confirm these results but also detail the role of a third parameter, the relative water depth h/d. A one dimensional hydraulic model reveals the mechanisms leading to so huge L/d variations. Finally, two dimensional depth-averaged flow equations reveal the prevailing role of bed friction for high S values. Thanks to all these results, the present paper explains the evolution of the recirculation zone length with the different parameters. The shortening of this length is caused by two different mechanisms, corresponding to two asymptotical regimes. For low bed friction numbers S and high relative water depth h/d, large-scale vortices shed from the expansion corner drive the momentum exchanges from the freestream to the recirculation. For high bed friction numbers, their role is negligible: the recirculation zone is accelerated by a velocity leveling due to bed friction, leading to L/d ∝ S^−0.7.

The Pelton turbine will play a massive role in China's water conservancy and power generation development process. In practical engineering applications, sediment will erode the components of the Pelton turbine when they come into contact, threatening the safe and stable operation of the unit. Therefore, based on the Eulerian–Lagrangian method, this study analyzes the effects of particle size, concentration, and position angle on the degree and distribution of erosion of each component without considering the cavitation effect of the flow. The results show that the larger the particle size, the more concentrated the distribution, and the more severe the abrasion caused on the spray needle and water bucket. However, the degree of nozzle erosion weakens, and the erosion area increases. It was also found that the higher the concentration, the more severe the abrasion caused to each component. When the jet completely hits the position on the bucket, due to the low impact speed, the impact angle remains almost unchanged, resulting in less erosion. Finally, the classic Finnie model was refined by adjusting the average erosion rate, particle size, concentration, and rotation angle. This modification yielded an enhanced model, mainly showcasing improved performance for moderate particle sizes.

The bad-behaved flow in Pelton turbine, particularly in the runner region influences the efficiency performance of the system, sometimes brings out problems such as cavitation and efficiency loss. This paper will focus the physics of negative flow which are interaction of the cutting edge, two jets flow into the same bucket and flow towards the back side of bucket. Dynamic rotating process is numerically investigated in the runner region using CFX commercial code under one operating condition. These unsteady numerical simulations were conducted by RNG k-ǫ turbulence model combined with two-phase homogeneous model. Through the whole working process of the water jet on the bucket, the torque of the bucket and the whole runner is analyzed in detail. Four parts are divided as bucket head, pressure surface, suction surface and cutting edge region. This study deeply recognized the influences of two bad-behaved flows and proves that they are the main reasons of the torque decrease characteristic.

This study investigates the influence of key operating parameters of fill factor, rotor speed, and rotor wear on the power consumption of an isothermal intermeshing internal mixer. A three-dimensional computational fluid dynamics (CFD) model incorporating dynamic remeshing was developed using the finite volume method to solve the continuity and momentum equations for non-Newtonian rubber flow. The dynamic remeshing approach enabled accurate tracking of the moving rotor geometry and maintained mesh quality under varying operating conditions. The model integrates the actual mixer geometry and rheological properties of the rubber, and was validated against plant-scale power consumption data, showing good agreement. Simulations were performed across a range of operating conditions to quantify the effects of each parameter. Results indicate that increasing the fill factor from 50% to 82% raises normalized power from 14–19 kW/% to 17–22 kW/%, with higher levels producing extensive shear stress coverage to the rotor barrels but at the cost of potential clogging and reduced energy efficiency. Increasing rotor speed from 35 to 60 rpm increases normalized power from 20–22 kW/rpm to 22–23 kW/rpm, as higher rotor speeds intensify the local shear stress and strain rate fields near the rotor tips, thereby increasing power consumption. Rotor wear was found to significantly influence power consumption, with increasing wear leading to a progressive reduction in energy demand. The results indicate that worn rotor conditions reduce mechanical energy transfer due to diminished rotor–material interaction and increased clearances, resulting in lower shear stress generation within the mixing chamber. These findings identify operational windows that minimize energy costs while maintaining effective wall shear stress, offering practical guidance for optimizing mixer performance.