## 5 Analysis of Results
### Pressure Pulsation Analysis  
Figure 14 shows the pressure pulsation characteristics at the Y1 monitoring point set at the secondary impeller inlet for the three models before and after optimization. Figure 14a shows the time domain distribution of the pressure pulsation at point Y1. Due to the strong dynamic and static interference effects, five wave peaks appear in one cycle, which are equal to the number of guide vanes. The peaks and troughs of the time domain characteristics of the pressure pulsation for the three models before and after optimization correspond to each other, which indicates that the optimization has not affected the phase values of the pressure pulsation. Figure 14b shows the frequency domain distribution of pressure pulsation at the Y1 monitoring point. The dominant frequency of pressure pulsation before and after optimization is around the doubled guide vane frequency, so the dynamic interference effect is dominant. After optimization, the magnitude of pressure pulsation at the inlet of the secondary impeller is significantly lower for the individual with the better head and the individual with the better efficiency. The pressure pulsation of the individual with the  
Figure 14: Pressure fluctuation characteristic diagram of the Y1 monitoring point before and after optimization. **(a)** Time domain; **(b)** frequency domain. Figure 13: Unfold diagram of the velocity streamline in the middle section of the secondary impeller and secondary space guide vane before and after optimization. **(a)** Initial model; **(b)** individuals with better heads; **(c)** more efficient individuals. better head was reduced by 46.7% compared to the initial individual, and the pressure pulsation of the individual with the better efficiency was reduced by 59.9% compared to the initial individual. Figure 15 shows the pressure pulsation characteristics at the Y2 monitoring point at the outlet of the secondary impeller for the initial individual model before optimization, the individual model with the better head after optimization, and the individual model with the better efficiency after optimization. Compared with Figure 14a, there are still five peaks in the individual models before and after optimization. The difference is that the fluctuation of the pressure pulsation coefficient in Figure 15a is significantly larger, which is the result of the work performed by the impeller rotation. The peak position of the more efficient individual corresponds to the trough position of the initial individual, while the phase of the higher-head individual is in between, which indicates that the phase value of the pressure pulsation at the outlet of the secondary impeller has changed after optimization. As can be seen from the frequency domain characteristics plot in Figure 15b, the dominant frequency of pressure pulsation before and after optimization is still around the doubled guide vane frequency, which indicates that dynamic interference is still the dominant influencing factor. After optimization, the pressure pulsation amplitude of the individual with the better head is reduced by 21.3% compared to the initial individual, and the pressure pulsation amplitude of the individual with the better efficiency is reduced by 29% compared to the initial individual. Figure 16 shows the pressure pulsation characteristics at monitoring point Y3 at the inlet of the secondary space guide vane for the initial individual model before optimization, the individual model with the better head after optimization, and the individual model with the better efficiency after optimization. As can be seen in Figure 16a, the number of pressure fluctuations at this point becomes six before and after optimization, the same as the number of impeller blades, again due to strong dynamic interference effects. The peak and trough positions of the more efficient individual correspond essentially to those of the initial individual, with the phase of the higher-head individual remaining in between.