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Calculating the shut-off head for centrifugal pumps poses significant challenges due to inaccuracies in existing empirical methods. This paper presents a predictive model based on extensive experimental data, employing a back propagation (BP) neural network optimized via grey theory and genetic algorithms (GAs). Data were collected from 141 single-stage volute centrifugal pumps, and grey theory was used to analyze nine critical parameters of the impeller and volute, yielding five optimal input schemes with correlation coefficients exceeding 0.6. The GA was utilized to optimize the weights and thresholds of the BP model. The training involved 121 samples, while 20 additional samples were used to evaluate the models against three established methods (throne, modified throne, and regression fitting). The results indicate that the optimal input scheme consists of four parameters (impeller diameter, blade wrap angle, inlet diameter, and rotational speed) with correlation coefficients greater than 0.7. Both the BP and GA-BP models achieved training regression coefficients approaching 0.999. Within the specific speed range of 22–215, the GA-BP model demonstrated superior performance to the BP model and the three established methods, with maximum testing errors of 10.0%, 20.6%, 20.7%, 19.9%, and 23.3%, and average relative errors of 3.9%, 5.0%, 8.4%, 8.1%, and 5.8%, respectively. This paper introduces a novel prediction model for the shut-off head with an accuracy of 96%, providing a valuable reference for hydraulic design and performance prediction in centrifugal pumps.

Energy recovery turbines (ERTs) play an important role in reducing the energy consumption of seawater reverse osmosis (SWRO). The internal flow loss mechanisms and hydraulic vibration characteristics of a centrifugal ERT model used in SWRO were studied under multiple conditions. The results show that the high-efficiency range of the ERT tends toward high-flow conditions. The energy loss is mainly concentrated at the tongue in the volute, which is due to the generation of flow separation vortices. There is a flow separation phenomenon on the suction surface side of the blade, trailing under the 0.8Qd condition. The energy loss of the ERT is the lowest under the 1.0Qd condition, because the interaction between the fluid and the blades is the weakest. There are vortices formed by flow impact on the blade pressure surface under the 1.2Qd condition. There are vortices on the blade suction face, which are generated by fluid separation. The closer the relative liquid flow angle is to the blade settle angle, the smaller the energy loss is in the impeller. Therefore, the ERT should first reduce rated flow appropriately before hydraulic design, as this is beneficial for efficient operation under multiple conditions.

Pump as turbine plays an important role in modern industrial process. One of the major goals of turbine design and optimization is to maximize its efficiency. Therefore, it is of great importance to connect force with work in the analysis process. In the present study, the three-dimensional flow field of the pump as a hydraulic turbine has been investigated in the steady-state mode. The load distribution along three captured streamlines (i.e., the shroud, hub and middle streamline) on both the pressure and the suction surface is observed, and the relationship between the load distribution and the working capability is systematically analyzed. The results show that the load distribution on the pressure surface of the hydraulic turbine blade gradually transitions from the reverse “S” shape to the “S” shape in the process of increasing flow rate, while the load distribution on the suction surface keeps increasing with a concave trend. The main work area of the fluid medium on the hydraulic turbine impeller is in the middle section of the blade. As the flow rate increases, the loads on the blade depict a linear decreasing trend from the inlet to the outlet. The net load acting on the blade is distributed in a concave parabola profile along the radial position of the blade. Focusing on the inlet and middle section of the blade profile in the design or optimization process of the hydraulic turbines will be more useful. This study provides a new analysis method for the design or optimization of hydraulic turbine impellers.

In view of the poor performance of pumps as turbines (PAT) operation, and the problem that the structural parameters cannot be optimized in the whole domain, the hybrid model of support vector machine (SVM) model and high-dimensional model representation (HDMR) method is applied to the optimization of PAT blade. Specifically, a PAT was selected, and the surrogate model for PAT blade optimization was constructed with MATLAB, Creo, and ANSYS software. The particle swarm optimization (PSO) algorithm was used to predict the performance data by global optimization. Finally, numerical prediction and experimental methods were used to verify the predicted data. These proved the applicability of the hybrid model in the optimization of fluid machinery. The numerical simulation results show that at the optimal operating point, the numerical simulation efficiency of the optimized PAT is 5.49% higher than that of the prototype PAT, and the output power is 7.2% higher. The test results show that the external characteristic curve of the numerical simulation PAT is basically consistent with the test results. At the optimal operating point, the test efficiency of the optimized PAT is 5.1% higher than that of the prototype PAT, and the output power is 6.9% higher.

Vortex pumps have good non-clogging performance and are widely used in the fluid transportation of food, sewage treatment, and mineral and coal slurry transportation. In order to design and manufacture a vortex pump with good performance and establish a method of optimum design, we must master the internal flow rules of the pump. Based on the self-design vortex pump (32WB8-12) experiment, the discharge-pump head (qv-H), discharge-pump shaft power (qv-P), discharge-pump efficiency (qv-η), and discharge-critical net positive suction head (qv-NPSHc) curves are obtained, and the qv-NPSHc curve shows an opposite tendency compared with the centrifugal pump. With the mathematical model selected with respect to the optimal condition, the three-dimensional internal flow within the vortex pump has been numerically simulated by a renormalization group k-ε (RNG k-ε) turbulence model. The static pressure (ps) and velocity distribution of the impeller and the middle section of the volute at 0°, 90°, 180°, and 270° are obtained, and the performance curves have been fitted using a CFX-calculated energy parameter. It was illustrated that the velocity field is relatively disordered and the flow in the impeller region is of a forced vortex character. The flow in the volute is similar to that of the combined vortex with backflow, which is a non-axisymmetric unsteady flow with quite high turbulence intensity. These factors are the main reasons for the relatively low efficiency of the vortex pump. The measurement of flow field in volute with a five-hole probe was conducted, and it is demonstrated that the numerical results are in good agreement with the flow field measurement data. An upward pressure gradient forms in the portal area of the impeller, and it is confirmed that the lowest pressure point is located in the upper position of the impeller hub. It is revealed that for the vortex pump to have advanced suction and anti-cavitation performance, the lowest pressure in the pump should be −4 × 104 Pa and it should be located at the center of the vortex chamber cavity.

This study focuses on a DN50 pipeline-type Savonius hydraulic turbine. The torque variation of the turbine in a rotation cycle is analyzed theoretically in the framework of the plane potential flow theory. Related numerical simulations show that the change in turbine torque is consistent with the theoretical analysis, with the main power zone and the secondary power zone exhibiting a positive torque. In contrast, the primary resistance zone and the secondary resistance zone are characterized by a negative torque. Analytical relationships between the turbine's internal flow angle θ, the deflector's inclination angle α0, and the coverage angle α of the power zone are introduced, and a method for calculating the optimal number of blades is proposed to maximize the power zone. Results are presented about performance tests conducted on five groups of hydraulic turbines with the blade number ranging from 3 to 7. Such results indicate that both the turbine's recovery power and efficiency attain the highest values when the blade number is 4, which is in agreement with the number of blades calculated by the proposed method. Additionally, the study examines the effects of the flow rate on turbine parameters and the projected energy generation and cost savings for a specific pipeline configuration. [ABSTRACT FROM AUTHOR]