## 2 Numerical Simulation
### Solving for Control and Monitoring Points  
Figure 4 shows the setting of the monitoring points of the computational model. In the figure, four monitoring surfaces were set, which were located at the inlet of the front guide vane, the inlet, and outlet of the runner chamber, and the outlet of the movable guide vane. A total of 16 monitoring points were set that can monitor the changes in the pressure pulsation on different interfaces in more detail. On different monitoring surfaces, the monitoring points were distributed along the radial direction, and the angle between the two groups of monitoring points was 90\({}^{\circ}\). Among them, the monitoring points a2 and b3 were located at the outer edge positions of each monitoring surface, which was consistent with the monitoring positions of the test arrangement. \begin{table}
\begin{tabular}{c c c c} \hline
**Pump** & **1700 ZWSQ10-2.5** & **Blade Placement Angle** & \(-6^{\circ}\)\(\rightarrow\)\(4^{\circ}\) \\ \hline Diameter of impeller & 1.7 m & Impeller center elevation & 1 m \\ Number of impeller blades & 4 & Design discharge & 10 m\({}^{3}\)/s \\ Design head & 2.5 m & Number of front guide vanes & 5 \\ Number of guide vanes & 7 & Design speed & 250 r/min \\ \hline \end{tabular}
\end{table} 
Table 1: Relevant design parameters of the pump. Figure 2: Grid independence verification. Figure 3: Meshing of the axial-flow pump fluid domain. (**i**) Front guide vane area. (**ii**) Turbine blade region. (**iii**) Active guide vane region. In this paper, FLUENT software was used for numerical simulation. The three-dimensional Reynolds time-averaged N-S equation was chosen as the basic governing equation to describe the turbulence in the pump. Using the RNG k-\(\varepsilon\) turbulence model can effectively improve the computational efficiency. We used the automatic wall function to set the wall as a no-slip wall. The numerical calculation precision was set to \(10^{-4}\). The inlet boundary conditionwas set as mass inlet and the outlet boundary condition was set as free outflow boundary conditions, respectively. When calculating the working conditions of the turbine in reverse, we chose the total pressure inlet at the inlet and the static pressure outlet at the outlet. In Table 2, some turbulence models are listed. In order to obtain accurate numerical simulation results, a suitable turbulence model must be selected according to different research conditions [25; 26; 27]. After referring to the literature, it was found that the RNG k-\(\varepsilon\) turbulence model had a good effect on the calculation of the pressure pulsation and internal flow in the axial flow pump and could achieve accurate results. In the simulation, the RNG k-\(\varepsilon\) turbulence model was selected for the numerical simulation based on the comprehensive consideration of computational resources, main research directions, and previous research results. The calculated results were consistent with the test. The stable state computation was performed on the model first, and then the non-stable state computation was performed on the stable state computation results. In the unsteady calculation, the sliding mesh technology was used in the area of the runner body. The rotating speed of the runner was 250 r/min, and one cycle was T = \(1/n\) = 0.24 s. For ensuring the stability of setting analysis and to facilitate calculation and analysis, the time step of unsteady calculation was set to 0.005 s. For ensuring the stability of the unsteady calculation results, the sampling time of the unsteady calculation in this paper was 10 cycles.