When considering the interaction between the impeller and diffuser, it is necessary to provide logical and systematic guidance for their matching optimization. In this study, the goal was to develop a comprehensive matching optimization strategy to optimize the impeller and diffuser of a mixed flow pump. Some useful tools and methods, such as the inverse design method, computational fluid dynamics (CFD), design of experiment, surrogate model, and optimization algorithm, were used. The matching optimization process was divided into two steps. In the first step, only the impeller was optimized. Thereafter, CFD analysis was performed on the optimized impeller to get the circulation and flow field distribution at the outlet of the impeller. In the second step of optimization, the flow field and circulation distribution at the inlet of the diffuser were set to be the same as the optimized impeller outlet. The results show that the matching optimization strategy proposed in this study is effective and can overcome the shortcomings of single-component optimization, thereby further improving the overall optimization effect. Compared with the baseline model, the pump efficiency of the optimized model at 1.2Q_des, 1.0Q_des, and 0.8Q_des is increased by 6.47%, 3.68%, and 0.82%, respectively.

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 spanwise distribution of impeller exit circulation (SDIEC) has an important influence on the performance of the impeller. To quantitatively study the influence of SDIEC on optimization results, a comprehensive optimization system composed of the computational fluid dynamics, inverse design method, design of experiment, surrogate model, and optimization algorithm was used to optimize a mixed flow pump impeller in two different cases. In the first case, the influence of SDIEC was ignored, while in the second case, the influence of SDIEC was considered. The result shows that the optimization upper limit can be further improved when the influence of SDIEC is considered in the optimization process. The pump efficiency of the preferred optimized impeller F1 obtained in the first case at 1.2Q_des, 1.0Q_des, and 0.8Q_des are increased by 6.48%, 2.41%, and 0.06%, respectively, over the baseline model. Moreover, the pump efficiency of the preferred optimized impeller S2 obtained in the second case further increased by 0.76%, 1.24%, and 1.21%, respectively, over impeller F1. Furthermore, the influence of SDIEC on the performance of the mixed flow pump is clarified by a comparative analysis of the internal flow field.

Most pumping machineries have a problem of obtaining a higher efficiency over a wide range of operating conditions. To solve that problem, an optimization strategy has been designed to widen the high-efficiency range of the double-suction centrifugal pump at design (Q_d) and nondesign flow conditions. An orthogonal experimental scheme is therefore designed with the impeller hub and shroud angles as the decision variables. Then, the “efficiency-house” theory is introduced to convert the multiple objectives into a single optimization target. A two-layer feedforward artificial neural network (ANN) and the Kriging model were combine based on a hybrid approximate model and solved with swarm intelligence for global best parameters that would maximize the pump efficiency. The pump performance is predicted using three-dimensional Reynolds-averaged Navier–Stokes equations which is validated by the experimental test. With ANN, Kriging, and a hybrid approximate model, an optimization strategy is built to widen the high-efficiency range of the double-suction centrifugal pump at overload conditions by 1.63%, 1.95%, and 4.94% for flow conditions 0.8Q_d, 1.0Q_d, and 1.2Q_d, respectively. A higher fitting accuracy is achieved for the hybrid approximation model compared with the single approximation model. A complete optimization platform based on efficiency-house and the hybrid approximation model is built to optimize the model double-suction centrifugal pump, and the results are satisfactory.

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.