## 4 Results and Discussion  
### Comparison of Pump Speed Adjustment Schemes  
While adjusting the pump speed, the regulating valve in front of the thrust chamber was kept under the maximum opening state. The flow into the thrust chamber could be adjusted only by the pump speed. The flow in the first stage and the second stage was small; hence, a single pump could be started in the first stage and the second stage. In the third stage, the two pumps worked at the same time. This was determined as Scheme ASYNC. Since the states of the two pumps were consistent, the two pumps could be kept in an operating state in all three stages considering the symmetry. This was determined as Scheme SYNC. These two schemes are studied below. According to the mass flow requirements of the system, the speed of the pump in all three stages was determined by continuously adjusting the speed, as shown in Table 6. The speed regulation curve is shown in Figure 8, and the system started from 1 s.  
In Scheme ASYNC, the pump speed in the first stage was 13,300 r/min, which was about 37% of the rated speed, and the mass flow was 50% of the rated mass flow. In Scheme SYNC, the speed of the two pumps in the first stage was 12,100 r/min, about one-third of the rated speed. Under low operating conditions, the efficiency of the pump would be low. In the second stage, the pump speed was about 62% of the rated \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Scheme ASYNC**} & \multicolumn{2}{c}{**Scheme SYNC**} \\ \cline{2-5}
**Period** & \begin{tabular}{c} **Quantity of** \\ **Working Pumps** \\ \end{tabular} & \begin{tabular}{c} **Speed** \\ **(r/min)** \\ \end{tabular} & \
\begin{tabular}{c} **Quantity of** \\ **Working Pumps** \\ \end{tabular} &
\begin{tabular}{c} **Speed** \\ **(r/min)** \\ \end{tabular} \\ \hline
1 st & 1 & 13,300 & 2 & 12,100 \\
2 nd & 1 & 22,300 & 2 & 19,600 \\
3 rd & 2 & 36,000 & 2 & 36,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Speed comparison between Scheme ASYNC and Scheme SYNC. Figure 8: Pump speed comparison in Scheme ASYNC vs. Scheme SYNC. and the pump speed was about 54% of the rated speed in Scheme SYNC. In the third stage, both pumps operated under the rated operating conditions. The comparison between the pre-regulating pressure and pre-injection pressure of the two schemes is shown in Figure 9. In the start-up stage, there was an obvious pressure peak of the pre-injection pressure in Scheme SYNC. The processes from the first stage to the second stage and from the second stage to the third stage were relatively stable in the two schemes. In terms of response time, the pressure building time of Scheme SYNC was shorter than that of Scheme ASYNC in terms of pre-regulating pressure and pre-injection pressure. This was mainly due to the simultaneous operation of two pumps, and the regulation range of each pump was lower than that of Scheme ASYNC. The mass flow curve of the system is shown in Figure 10, and the pressure of the pump outlet is shown in Figure 11. The steady-state flow of the two schemes conformed to the state value of the design point. In Scheme ASYNC, there was a large peak in the flow of the continuously operating pump from the second stage to the third stage. Meanwhile, there was also a pressure peak from the second stage to the third stage for the other pump, which was mainly caused by starting up at this time. That is, the pump going from non-operating to maximum operating conditions would result in a larger water hammer affecting the other pump. This is mainly due to the instantaneous flow increase in the regulating valve inlet causing a pressure increase in the pump outlet. Furthermore, the start-up time of the pump had an obvious impact on this peak. Figure 9: Comparison of pre-regulating and pre-injection pressure in Scheme ASYNC vs. Scheme SYNC. Figure 11: Comparison of pump outlet pressure in Scheme ASYNC vs. Scheme SYNC. Figure 10: Comparison of flow in Scheme ASYNC vs. Scheme SYNC. cavitation pressure of the pump.