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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.

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.