## 4 Results and Discussion
### Comparison between Pump Speed Adjustment and Joint Adjustment Schemes  
According to the mass flow and pressure requirements of the system, the operating state in all three stages was determined by continuously adjusting the pump speed and valve opening. The results of Scheme SYNC and Scheme JOINT are compared in Table 7, and the speed curve is shown in Figure 18. The system started from 1 s.  
Figure 17: Calculation process of pump speed and valve opening based on genetic algorithm. In Scheme SYNC, the pump speed in the first stage was 12,100 r/min, about one-third of the rated speed. When Scheme JOINT was adopted, the pump speed was 24,800 r/min, about two-thirds of the rated operating condition. Therefore, Scheme JOINT could significantly reduce the operating range of the pump and maintain the efficiency at a high level. In the second stage, the pump speed of Scheme SYNC was 19,600 r/min, about half of the rated operating condition. Under joint adjustment, the pump speed of Scheme JOINT was 29,700 r/min, about 5/6 of the rated operating condition. In the third stage, the pumps of both schemes worked under the rated operating conditions. The comparison between the pre-regulating pressure and pre-injection pressure of the two schemes is shown in Figure 19. In the start-up stage, there was an obvious pre-injection pressure peak in both schemes. The processes from the first stage to the second stage and from the second stage to the third stage were relatively stable. The pre-injection pressure of both schemes remained basically the same, because it was mainly determined by the thrust chamber. The pre-regulating pressure of Scheme JOINT was significantly higher than that of Scheme SYNC, especially in the first and second stages; thus, it could ensure that the regulating valve is in an obvious cavitation state. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Period**} & \multicolumn{2}{c}{**Scheme SYNC**} & \multicolumn{2}{c}{**Scheme JOINT**} \\ \cline{2-5}  & **Quantity of** & **Speed** & **Quantity of** & **Speed** \\  & **Working Pumps** & **(r/min)** & **Working Pumps** & **(r/min)** \\ \hline
1 st & 2 & 12,100 & 2 & 24,800 \\
2 nd & 2 & 19,600 & 2 & 29,700 \\
3 rd & 2 & 36,000 & 2 & 36,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Speed comparison between Scheme SYNC and Scheme JOINT. Figure 18: Pump speed between Scheme SYNC vs. Scheme JOINT. The mass flow and outlet pressure of the pump are shown in Figure 20. The steady-state flow of the two schemes could meet the design requirements. In terms of flow oscillations, the amplitude was larger in Scheme JOINT than that in Scheme SYNC; however, the time to reach a stable value was smaller in Scheme JOINT than in Scheme SYNC. In other words, the response time of the propulsion system was faster and the overshoot was larger in Scheme JOINT. The pressure of the pump outlet in Scheme JOINT was significantly higher than that in Scheme SYNC, mainly due to the decrease in valve opening and the increase in pump speed. In terms of pressure overshoot, the overshoot was smaller in Scheme JOINT than in Scheme SYNC when the maximum operating conditions were reached. Figure 19: Comparison of pre-regulating and pre-injection pressure in Scheme SYNC vs. Scheme JOINT. Figure 20: Comparison of flow and outlet pressure of pump in Scheme SYNC vs. Scheme JOINT. Overall, Scheme JOINT adopted the mode of joint adjustment of pump speed and valve opening, revealing multiple working points that could meet the requirements. The adjustable range was large, and the optimal scheme could be selected according to the calculation results. Compared with Scheme SYNC, Scheme JOINT could mainly improve the pump speed and the pressure of the pump outlet, enabling the regulating valve to work in a significant cavitation state. In this way, the pressure drop requirements of the catalytic bed, regulating valve, and injector could be met.