## 5 Structural Optimization of the Vortex Pump
### Optimization Scheme  
The impeller is the core component of the vortex pump, and the geometric design of its blade plays a decisive role in the hydraulic performance and the flow characteristics of the vortex pump. In the orthogonal experimental design, four structural parameters of impeller diameter \(D_{2}\), blade groove radius \(r\), blade number \(Z\), and impeller width \(b\) are selected as experimental factors. The specific reasons for selection and parameters are determined as follows:  
1. Impeller diameter \(D_{2}\): The recommended design range of impeller diameter \(D_{2}\) is usually 40-50 mm. For closed vortex pumps, it is necessary to consider that the value range of the clearance \(\delta_{2}\) between the impeller and the baffle tongue is usually 0.1-0.3 mm. Based on the basic parameter \(D_{2}\), which is 45.9 mm of the impeller diameter of the original model in Table 1, the corresponding value of \(\delta_{2}\) is 0.1. Compared with the original model, the values of the slightly smaller 45.7 and 45.8, the final \(D_{2}\) is selected as 45.7, 45.8, and 45.9 as the three levels for \(D_{2}\). 2. Blade groove radius \(r\): The blade groove is the hub structure connecting the blade, and its radius plays a decisive role in the overall performance of the pump. If the radius of the blade groove is small, the tip of the groove can be sharp, which inhibits the formation of vortices and reduces the effective transfer of energy. In contrast, if the radius of the blade groove is large, the flow of fluid between the vanes is restricted, which prevents the smooth flow of fluid and leads to the decline in the overall performance of the pump. Therefore, based on the basic parameter \(r\) of the blade groove radius of 15 of the vortex pump for the original model in Table 1, the final \(r\) is 14.9, 15, and 15.1 as the three levels. 3. Blade number \(Z\): Through preliminary screening through single-factor simulation calculation, the overall performance of the vortex pump is poor when the number of blades is less than 27. When the number of blades is 27-33, the pump head can be increased. When the number of blades is greater than 33, the increase in head and efficiency growth slows down or even decreases in order to reduce the load per unit area of the blade and enhance the constraint of the fluid between the blades. Therefore, based on the basic parameter \(Z\) of the blade number, which is 30 of the vortex pump blades for the original model in Table 1, the final \(Z\) is selected as 28, 30, and 32 as three levels. 4. Impeller width \(b\): The axial clearance \(\delta_{1}\) formed between the impeller and the shell is the key parameter that affects the flow rate and high head, and the value of \(\delta_{1}\) is usually 0.04\(-\)0.25 mm. In order to reduce the volume loss of the vortex pump and meet the performance of the pump, the \(\delta_{1}\) value corresponding to 5.15 of the impeller width \(b\) of the original model in Table 1 is 0.22. Considering that it is convenient to compare the performance differences between the two larger impeller widths and the original model impeller width, we selected the value 5.37, which lies midway between 5.15 and 5.51. Therefore, the value 5.37, which is larger than both 5.15 and 5.51, was chosen. Finally, 5.15, 5.37, and 5.51 are selected as the three levels for \(b\). In order to explore the optimal matching relationship between the performance of the vortex pump and the four structural parameters of the impeller, the orthogonal experiment is developed based on the four factors, three levels, and their corresponding values determined above, and the experimental factors and levels are shown in Table 2, in which the four factors \(D_{2}\), \(r\), \(Z\), and \(b\) are represented by A, B, C, and D, respectively.