###### Abstract
[12] found through numerical simulation and experiment verification that reducing the blade wrap angle of the cylindrical vane vortex pump can improve head and efficiency and increase the shaft power. At the same time, it is also found that increasing the blade wrap angle can extend the length of the rotary reflux, which affects the liquid flow. Therefore, when designing the vortex pump, it can be considered to choose a smaller blade wrap angle to optimize the pump performance. [PERSON] et al. [13] studied the internal flow field characteristics of the vortex pump with different inlet positions and blade pitch changes through numerical simulation and found that the performance of the vortex pump can reach the optimum under specific parameter combinations. [PERSON] et al. [14; 15; 16] proposed several strategies to enhance the performance of vortex pumps through research. First, it is found that the head and flow of the vortex pump can be significantly increased by increasing the induction wheel, which is crucial to enhance the stability of the solid-liquid two-phase flow pump. Second, the numerical simulation shows that the significant influence of blade structure on pump performance, especially the forward-curved blade design, performs well in reducing axial vortex and circulating flow. In addition, orthogonal experimental design and numerical simulation are used to optimize the impeller structure and determine the best impeller parameter combination, which greatly improves the design efficiency. These research results not only provide a scientific basis for the design of the vortex pump but also provide a practical method for performance optimization. [PERSON] et al. [17] optimized the cylinder head structure of the high-head pump turbine and analyzed the strength and axial stiffness of the cylinder head before and after optimization by using the finite element method. The results showed that the optimized cylinder head significantly improved in terms of axial stiffness. [PERSON] et al. [18] proposed a new algorithm based on twisted rotor blades in order to improve the performance prediction accuracy and to meet the new design requirements of high-speed turbo molecular pumps, which provides a new design concept and performance prediction method for the structural optimization of high-speed turbo molecular pumps. [PERSON] et al. [19] discussed the effect of axial clearance on the performance of the vortex pump through numerical simulation and experimental verification and analyzed the influence of axial clearance on the internal flow field and external characteristics of the pump from multiple flow field perspectives by establishing four different clearance schemes. [PERSON] et al. [20] studied the matching relationship between impeller diameter and height to improve the hydraulic performance of regenerative flow pumps (RFPs) in response to the low efficiency problem. They compared the effects of the various impeller diameters and heights on the performance of RFP through the experimental design under two different operating conditions. [PERSON] et al. [21] studied the influence of impeller structural parameters on the hydraulic performance and casting formation of the double-vane spiral pump. The Plackett-Burman experiment design method is used to select blade thickness and impeller outlet width as the key influencing factors, which provided important guidance for the optimal design of spiral centrifugal pumps. [PERSON] et al. [22] studied the sealing performance of the multistage liquid-sealed impeller of the turbo pump and optimized the structural parameters of the impeller through the response surface method to improve the pressurization coefficient and reduce the leakage flow, so as to improve the sealing performance of the pump. [PERSON] [23] studied the modal characteristics of the mechanical structure of the vane pump through finite element simulation and impact modal experimentation in order to ensure the stability and reliability of the vane pump.