This article presents a methodology for optimizing the operation of parallel pumping stations in an open-channel water transfer system. A mathematical model was established for the minimum power with constraints on water level, flow rate and pump unit performance, and related factors. In the objective function, energy consumption of relevant equipment or facilities, such as main pump units, power transmission and transformation equipment, and auxiliary equipment, was considered comprehensively. The model was decomposed to two layers for solving. In the first layer, by using discharge distribution ratio as a variable, the flow rate and water level of the two water channels could be determined by employing the dichotomy approach (DA), and were calculated according to the principle of energy conservation, considering energy loss caused by hydraulic leakage and evaporation losses. In the second layer, the number of running pumps and the flow rate of a single pump were obtained by simulated annealing–particle swarm optimization (SA–PSO). The hybrid of the two algorithms is called the dichotomy approach–simulated annealing–particle swarm optimization (DA–SA–PSO). To verify the efficiency and validity of DA–SA–PSO, SA–PSO is also applied to determine discharge distribution ratio. The results indicate that the computation time using DA–SA–PSO is 1/30 of that using double-layer SA–PSO (dSA–PSO). Compared with the original plan, the optimal solution could result in power savings of 14–35%. Thus, the DA–SA–PSO is highly efficient for optimizing system operation in real time.

To investigate the effect of inlet elbow geometry on the performance of a large low-head pumping system and improve its comprehensive performance, this paper calculated and analyzed the internal flow fields, external characteristics, and entropy production distribution of the pumping system with different parametric combinations of the inlet elbow via numerical simulations with a Reynolds averaged Navier Stokes-volume of fluids fixed net head method. The energy characteristics were further studied using a newly introduced method of local internal energy change to visualize energy consumption. An automatic multi-software optimization design method was developed based on MATLAB, a feed-forward neural network, and a differential evolution algorithm to optimize the geometrical parameters of the inlet elbow. The research results indicate that appropriate heights of the throat and truncated cone improve velocity distribution, decrease the hydraulic loss in the inlet conduit, and foster a favorable flow condition at the pump inlet and outlet. Well-distributed axial velocity at the impeller inlet improves the pump efficiency. Well-distributed axial velocity and circulation at the pump outlet could reduce and eliminate flow separation, reflow, and vortices in the outlet conduit, thereby reducing energy consumption. Compared with the original design, the optimized geometry of the inlet elbow significantly improves the pumping system efficiency by 8.4 percentage points. The findings reveal the effect of the inlet elbow geometry on the performance of large low-head pumping systems and provide an easy, efficient, and economical method for the design and modification of low-head pumping systems.

In large low-lift pump stations, the pump assembly comprises an inlet conduit, a pump, and an outlet conduit. A short conical frustum section that connects the elbow section with the impeller inlet directly affects the impeller inflow state, thereby influencing the overall performance. Therefore, investigating the conical frustum section contributes to studying the effect of inflow states on the performances of pump assemblies and similar pumping systems. To improve the pump assembly efficiency, three parameters of the conical frustum section, i.e., the contraction angle, height, and centerline inclination angle, are investigated and optimized via univariate and multivariate analyses. The flow field and external characteristics of the pump assembly are investigated via computational fluid dynamics simulation with a constant head. Furthermore, a comprehensive analysis and discussion of the performance improvement mechanisms are presented. The results indicate that the axial velocity distribution at the impeller inlet conforming to the cascade high-efficiency characteristics will achieve a better pump performance compared with a uniform distribution. The pump efficiency distribution can be predicted and visualized based on the cascade efficiency characteristics and the flow state at the impeller inlet using a machine learning method. In addition, the directions and distribution of the lateral and axial components of the inflow velocities have great impacts on the circulation distribution. A sensible circulation distribution at the guide vane outlet can suppress the entropy production and reduce hydraulic loss of the outlet conduit. In this case, a significant increase in the pump assembly efficiency is obtained.

This study aims to investigate the critical state of the saddle-shaped unstable region of the axial-flow pump and propose a suitable criterion for identifying this state. The bifurcation SST $k–\omega$ model considered the rotation effect is used in the present work and verified in the numerical calculation of a water jet pump. Then, it is used to simulate the critical state of the axial-flow pump. Results show that the leading-edge separation vortex generates at 0.6Q_d, while the head declines only at 0.55Q_d. Therefore, using the inflection point of the head-flow curve as the critical state criterion is unsuitable. In addition, the fixed monitoring point is unsuitable for identifying the critical state due to the insensitivity to the amplitude, main frequency, and periodicity changes at the critical state. Finally, to identify the critical state, it is essential to arrange a monitoring point at the leading edge of the blade suction near the shroud, which should rotate with the impeller. The critical state criterion is that the main frequency position of the pressure fluctuation signal is offset at the monitoring point, and the amplitude is increased by 10 times.

A water diversion system (WDS) with cascade pumping stations (CPSs) plays an important role in the application of water resources. However, high energy consumption is reported due to unreasonable scheduling schemes and long decision times. Herein, this paper presents a new method to achieve optimal scheduling schemes effectively, including the head allocation of CPSs, the number of running pumps, and pump blade angles. A double-layer mathematical model for a WDS was established with the goal of achieving minimal energy consumption, considering the constraints of flow rate, water level, and the characteristics of pump units. The inner-layer model was used to obtain scheduling schemes of single-stage pumping stations, as well as the water levels and flow rates of water channels, while the outer-layer model was used to optimize inter-stage head allocation. An improved wolf-pack algorithm (IWPA) was proposed to solve the model, using a Halton sequence to obtain the uniform initial population distribution and introducing simulated annealing (SA) to improve the global searchability. Moreover, an idea for a pre-established scheme library was suggested for inner-layer models to obtain the solutions in real time with less calculation workload. Taking an actual project as a case, in contrast with the actual schemes, the optimal scheduling method could result in energy savings of 14.37–20.39%, a CO₂ emission reduction of 13–32 tons per day, and water savings of 0.14–18.34%. Moreover, the time complexity decreased to square order, and the CPU time of the optimal method was about 1% that of the traditional method. This study provides an efficient method for the high-value utilization of energy and water resources for a WDS.