## 2 Numerical Simulation Method
### Grid Scheme and Boundary Conditions  
#### 2.2.1 Grid Scheme and Interface Setting  
The structural grid of each flow passage component of the vertical axial-flow pump device is divided, and the grid quality of the impeller and the guide vane have an important influence on the accuracy of the numerical simulation of the internal flow of the pump device; the H/J-L-Grid topology structure is adopted for the impeller and the H-Grid topology structure is adopted for the guide vane. The grid is densified around the blade, and the wall grid of the impeller and the guide vane is shown in Figure 4. The impeller grid orthogonality angle is between 21-161\({}^{\circ}\), and the guide vane grid orthogonality angle  
Figure 3: Single line diagram of the inlet and straight outlet conduit. Figure 2: Three-dimensional model of the axial-flow pump device. 1. Elbow inlet conduit, 2. impeller, 3. guide vane, 4. 90\({}^{\circ}\) elbow, 5. straight outlet conduit. is 37\(\sim\)158\({}^{\circ}\), meeting the requirement of a grid orthogonality angle between 15-165\({}^{\circ}\)[27]. The determinant 2 \(\times\) 2 \(\times\) 2 values of the straight outlet conduit and the 90\({}^{\circ}\) elbow of the axial-flow pump device are all above 0.7, which meets the requirements of a value greater than 0.4; furthermore, the angle values are all greater than 40\({}^{\circ}\) and the grid quality is good, which meets the calculation requirements, and the grid \(y^{+}\) value of each flow component of the axial-flow pump device is shown in Table 1, which meets the requirement of 30 \(<\)\(y^{+}\)\(<\) 500 [27]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Overcurrent Parts** & **Elbow Inlet Conduit** & **Impeller** & **Guide Vane** & **90\({}^{\circ}\) Elbow** & **Straight Outlet Conduit** \\ \hline \(y^{+}\) & 268.083 & 90.244 & 71.627 & 249.616 & 193.776 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Grid \(y^{+}\) value of each flow component of the axial-flow pump device. Figure 4: Grid diagram of the flow components of the axial-flow pump device. The physical quantities between the rotating area and the static area are transferred through the interface, the dynamic and static interfaces between the elbow inlet conduit and the impeller, and the impeller and the guide vane are of the Stage type. The interfaces between the guide vane and the 90\({}^{\circ}\) elbow, the 90\({}^{\circ}\) elbow and the straight outlet conduit are of the None type. The straight outlet conduit of the axial-flow pump device was analyzed for the independence of the number of grids, and the influence curve of the number of grids on the efficiency of the axial-flow pump device under the optimal working conditions was drawn as shown in Figure 5. It can be clearly seen that the efficiency of the axial-flow pump device in the straight outlet conduit increases with the increase in the number of grids. When the number of grids increases from 3.9 million to 5.1 million, the efficiency of the axial-flow pump device changes to be significantly less than 1%, and the efficiency of the pump device tends to stabilize after the number of grids reaches 5.1 million; therefore, a value of 5.4 million grids for the axial-flow pump device model under grid combing is selected as the final numerical calculation model. At the speed of 2200 r/min, as shown in Figure 6, the results of the model test and numerical calculation of the pump device and straight outlet conduit are compared and analyzed. Under the condition of a low flow rate, the \(Q\)-\(H\) curve of the numerical calculation is slightly higher than that of the model test; near the optimal operating point, the \(Q\)-\(H\) curve of the numerical calculation coincides with that of the model test. The results show that the \(Q\)-\(\eta\) curve of the numerical calculation is higher than that of the model test, the absolute error of efficiency between the numerical calculation and model test is 2.6% and the absolute error of each point is less than 3%.