## 3 Models and Methods
### Valve, Pipeline, and Tank
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Value** & **Unit** \\ \hline Throat diameter of regulating valve & 10.47 & mm \\ Maximum regulating valve flow & 10.6 & kg/s \\ Flow coefficient of regulating valve & 0.8 & / \\ Nominal diameter of gas valve & 10 & mm \\ Nominal diameter of valve before and & 25 & mm \\ after pump & 10 & mm \\ Nominal diameter of gas pipeline & 40 & mm \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main parameters of the regulating valve and the pipelines. the gravitational potential energy, \(\dot{m}_{out}\) represents the mass flow out of the control body, \(\dot{m}_{in}\) represents the mass flow into the control body, and \(p_{i}\) represents the internal work done per unit time. The mass equation in the gas tank is  
\[\frac{\mathrm{d}m}{\mathrm{d}\tau}=V[(\frac{\partial\rho}{\partial p})_{t}\cdot \frac{\mathrm{d}p}{\mathrm{d}\tau}+(\frac{\partial\rho}{\partial t})_{p}\cdot \frac{\mathrm{d}t}{\mathrm{d}\tau}], \tag{8}\]  
where \(m\) represents the gas mass in the tank, \(\rho\) represents the gas density, \(V\) represents the gas volume, \(p\) represents the gas pressure, and \(t\) represents the gas temperature. The energy equation in the gas tank is  
\[\mathrm{d}U=\sum\dot{m}_{i}h_{Si}+\delta q-p\frac{\mathrm{d}V}{\mathrm{d}\tau}, \tag{9}\]  
where \(U\) refers to the internal energy of the gas in the tank, \(h_{Si}\) is the specific enthalpy of the gas, \(p\) represents the pressure of the gas, \(V\) is the volume of the gas, and \(q\) refers to the heat exchange between the gas and the wall. The propellant tank is ellipsoidal, and it is mainly used to store hydrogen peroxide. The volume of the propellant tank is 500 L and that of the pneumatic cushion is 75 L. The pneumatic cushion pressurizes the propellant to prevent the cavitation phenomenon of the pump. The gas tank is spherical, and it is mainly used to store the high-pressure nitrogen. The volume of the gas tank is 30 L, and the initial pressure is 15 MPa. The main parameters of propellant tank and gas tank are shown in Table 5.  
The valves and tanks were modeled using the centralized parameter method, and the pipelines were modeled using the distributed parameter method. The centralized parameter method treats the component as a point and ignores the internal dynamic process of the component. The components of the system were modeled in AMESim software, and the calculations were performed through this platform. In particular, the characteristic curves of the pump were obtained via a numerical simulation and imported into AMESim. After the parameters of each component were determined, the system was completed. The high-pressure gas supplied by the gas tank enters the oxidant tank, and the oxidant enters the two pumps from the tank. The two pumps are connected in parallel, and the oxidant finally enters the thrust chamber. The integration of the propulsion system components was performed on the AMESim platform. The liquid medium was modeled using a two-phase flow model because the pump and regulating valve may experience a cavitation state during operation. The pumps were modeled using pressure head curves and efficiency curves and imported into the platform. A permanent magnet synchronous motor model and control signals were used to regulate the pump speed. The AMESim platform has an intelligent and robust integral solver that adjusts the algorithm to the characteristics of the model itself in real time. The accuracy of the computational solution in the propulsion system was set to \(1\times 10^{-6}\). This platform has been successfully applied in a variety of different fields, covering multidomain modeling and dynamic simulations of complex systems including mechanical, fluid, thermal analysis, electromagnetic, and control systems.