## 5 Structural Optimization of the Vortex Pump
### Optimization Scheme
The purpose of using the orthogonal design method is to further improve the head performance of the vortex pump while taking into account its efficiency. Combined with Tables 4 and 5, the parameter optimization analysis is as follows:  
Factor A (\(D_{2}\)): The impact of A on the head and efficiency of the vortex pump is relatively small. For the head, the A\({}_{1}\) value is the largest under the condition of 0.6\(Q_{\rm d}\)-1.0\(Q_{\rm d}\). For the efficiency, the A\({}_{1}\) value is close to the A\({}_{2}\) value. Considering the shape of the flow channel and radial clearance comprehensively, the optimal level of factor A is finally determined to be A\({}_{1}\). Factor B (\(r\)): B is a secondary factor affecting efficiency, yet it minimizes the effect on head. For the head, the values of B\({}_{1}\), B\({}_{2}\), and B\({}_{3}\) are similar. For the efficiency, the value of B\({}_{1}\) is greater than B\({}_{2}\) and B\({}_{3}\) under the condition of 0.6\(Q_{\rm d}\)-1.0\(Q_{\rm d}\). In order to take into account pump head and improve efficiency, the optimal level of factor B is finally determined to be B\({}_{1}\). Factor C (\(Z\)): C is the primary factor affecting pump head and efficiency. For the efficiency, the C\({}_{2}\) value is larger under the conditions of 0.6\(Q_{\rm d}\), 0.8\(Q_{\rm d}\), and 1.2\(Q_{\rm d}\). Under 1.0\(Q_{\rm d}\) and 1.4\(Q_{\rm d}\) conditions, the C\({}_{3}\) value is larger. For the head, the C\({}_{3}\) value is the largest under the condition of 0.6\(Q_{\rm d}\)-1.4\(Q_{\rm d}\). Considering the casting process of the blade comprehensively, the optimal level of factor C is finally determined to be C\({}_{3}\). Factor D (\(b\)): D is a secondary factor affecting the lift. For the head, the value of D\({}_{1}\) is the largest under the condition of 0.6\(Q_{\rm d}\)-1.0\(Q_{\rm d}\). For the efficiency, D\({}_{1}\), D\({}_{2}\), and D\({}_{3}\) values  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{4}{c}{**0.6\(Q_{\rm d}\)**} & \multicolumn{4}{c}{**0.8\(Q_{\rm d}\)**} & \multicolumn{4}{c}{**1.0\(Q_{\rm d}\)**} & \multicolumn{4}{c}{**1.2\(Q_{\rm d}\)**} & \multicolumn{4}{c}{**1.4\(Q_{\rm d}\)**} \\ \cline{2-19}  & **A** & **B** & **C** & **D** & **A** & **B** & **C** & **D** & **A** & **B** & **C** & **D** & **A** & **B** & **C** & **D** & **A** & **B** & **C** & **D** \\ \hline \(H\) & A\({}_{1}\) & B\({}_{3}\) & C\({}_{3}\) & D\({}_{1}\) & A\({}_{1}\) & B\({}_{3}\) & C\({}_{3}\) & D\({}_{1 are close. In order to ensure pump head and reduce pump volumetric efficiency loss, the optimal level of factor D is finally determined to be D\({}_{1}\). In order to ensure the performance and reliability of the vortex pump, it is necessary to analyze the primary and secondary order of various factors affecting the performance changes of the vortex pump, as shown in Figure 13. As shown in the figure, when the flow rate of the vortex pump varies between 0.6\(Q_{\rm d}\) and 1.4\(Q_{\rm d}\), the order of the influence of the four factors on the head of the vortex pump is C, D, A, and B. The factor with the greatest impact on the efficiency of the vortex pump among the four factors is C, followed by B. In addition, to meet the purpose of the vortex pump to achieve high head, the optimal combination of four factors is ultimately selected as A\({}_{1}\)B\({}_{1}\)C\({}_{3}\)D\({}_{1}\), which is \(D_{2}\) = 45.7 mm, \(r\) = 14.9 mm, \(Z\) = 32, and \(b\) = 5.15 mm.