## 4 Results and Discussion
### Multivariable Design of Joint Adjustment Scheme  
Under the condition of pump speed adjustment only, the regulating valve in front of the thrust chamber was kept under the maximum opening state. The flow could be adjusted only by the pump speed. Under the condition of joint adjustment, the pump speed and the regulating valve opening were adjusted at the same time to meet the requirements. Since there are two independent variables, many combinations of pump speed and valve opening could meet the same requirements. In the case of joint adjustment, \(A\) represents the area of the regulating valve, while \(A/A_{\max}\) represents the opening of the regulating valve, with a value ranging from 0 to 1. Under the maximum operating conditions, the pump speed was 36,000 r/min and the valve opening was 1. In the second stage, i.e., in the medium state, the pump speed ranged from 24,000 to 33,000 r/min, and the valve opening ranged from 0.5 to 0.7. Multiple combinations of pump speed and valve opening were calculated. The results are shown in Figures 13 and 14, where \(p_{0}\) represents the pressure of the pump outlet, and \(q_{\mathrm{m}}\) represents the mass flow of the pump. At a certain valve opening, the outlet pressure and mass flow of the pump increased with the increase in speed. At a certain speed, the pressure of the pump outlet remained basically unchanged with the change in valve opening, whereas the mass flow of the pump increased almost linearly with the increase in valve opening. Figure 12: Comparison of pump inlet pressure in scheme ASYNC vs. scheme SYNC. The available combinations of pump speed and valve opening can be found in Figures 13 and 14. In Figure 14, the mass flow required was 5.3 kg/s, and the mass curve intersecting with this straight line indicates the available combination. For example, under 33,000 r/min and 0.52, the pressure of the pump outlet reached about 7.8 MPa. This high pressure caused a large pressure loss in the regulating valve. For example, under 25,500 r/min and 0.67, the pressure of the pump outlet was about 4.7 MPa. This low pressure resulted in incomplete cavitation at the regulating valve. In the first stage, that is, the low operating conditions, the pump speed ranged from 20,000 r/min to 29,000 r/min, and the valve opening ranged from 0.2 to 0.4. Multiple combinations of pump speed and valve opening were calculated. The results are shown in Figures 15 and 16. In the case of a certain opening, the outlet pressure and mass flow  
Figure 14: Mass flow vs. speed and valve opening under medium operating conditions. Figure 13: Pressure of pump outlet vs. speed and valve opening under medium operating conditions. of the pump increased with the increase in speed. At a certain speed, the pressure of the pump outlet decreased slightly with the increase in valve opening. The mass flow increased almost linearly with the increase in valve opening. A greater pump speed led to a more obvious increase in mass flow. Similarly, the combination of pump speed and valve opening available under low operating conditions can be found in Figures 15 and 16, and the curve intersecting with the aim line indicates the available combination. It can be clearly seen that the intersection range of the curve and aim line under low operating conditions was smaller than that under medium operating conditions. The range of available combination points under low operating conditions was smaller than that under medium operating conditions. Figure 16: Mass flow vs. speed and valve opening under low operating conditions. Figure 15: Pressure of pump outlet vs. speed and valve opening under low operating conditions. In order to obtain the optimal combination of pump speed and valve opening in the electric pump feed system, this study used a genetic algorithm to perform the calculation process, as shown in Figure 17. First, the target flow rate for this engine was determined. For this study, the target flow rate in the first stage was 2.6 kg/s and that in the second stage was 5.3 kg/s.