## 3 Models and Methods
### Electric Pump  
According to the law of energy conservation, the power generated by the impeller of a centrifugal pump is consumed in the energy growth of liquid flow [33; 34]. The pressure head of the pump is mainly determined by four factors: the speed of the pump, the change rate of the pump speed, the mass flow through the pump, and the change rate of the mass flow through the pump. The effect of speed and mass flow on the actual working process is usually considered. The pressure head function of the centrifugal pump is obtained by the curve fitting method, as shown in Equation (1). The form of the dynamic equation of centrifugal pump torque is the same as that of pressure head. \[\left\{ \begin{array}{c}\Delta p=f(Q,N)\\ T=f(Q,N)\end{array} \right., \tag{1}\]  
where, \(Q\) is the volume flow, and \(N\) is the pump speed. According to the definition of \(\theta\) and specific speed (\(N_{S}\)) in Equation (2), the head function (\(WH\)) and torque function (\(WT\)) are defined in Equation (3) [8]. \[\left\{ \begin{array}{c}\theta=\pi+\text{atan2}(\frac{v}{A})\\ N_{S}=\frac{N_{\text{R}}\cdot\sqrt{Q_{\text{R}}}}{H_{\text{R}}^{2}S}\end{array}  \right., \tag{2}\]  
\[\left\{ \begin{array}{c}WH(N_{S},\theta)=\frac{h}{\delta^{2}}/(1+\frac{v^{2}} {\alpha^{2}})\\ WT(N_{S},\theta)=\frac{h}{\delta^{2}}/(1+\frac{v}{\alpha^{2}})\end{array}  \right., \tag{3}\]  
where the subscript R represents the rated operating condition, \(H\) refers to the pressure head, and \(h\),\(\
u\),\(\alpha\), and \(\beta\) are the dimensionless pressure head, volume flow, pump speed, and torque, respectively. When two pumps are operating simultaneously under maximum operating conditions, they need to meet the requirements of the maximum pressure and flow rate of the system. The maximum flow rate of the system was 10.6 kg/s. Therefore, the flow rate of a single pump at the design point was 5.3 kg/s and the pressure head was 597.7 m. According to the current operating conditions of most centrifugal pumps, the pump speed under  
Figure 4: Working sequence of joint adjustment (Scheme JOINT). maximum operating conditions is 36,000 r/min. The structural parameters of the electric pump are shown in Table 3.  
The electric pump structure is shown in Figure 5, and it is driven by a canned motor. The impeller and the rotor are all in the propellant. This avoids the dynamic seal structure; thus, no propellant leakage occurs. A reliable dynamic seal in a high-speed rotating part is very difficult [35]. Furthermore, a small portion of propellant in the pump backflows through the shaft into the pump inlet. This takes heat away through the propellant from the stator coil. In order to achieve stable operation under different operating conditions, the pump characteristic curves at different speeds were calculated in this study. The pump characteristics are described by the curve of the pump head with the flow rate and the curve of the pump efficiency with the flow rate. The pump characteristic curves are shown in Figures 6 and 7. The speed ranged from 15,000 r/min to 36,000 r/min, thus covering the regulating range in this study. Several characteristic curves obtained from 3D numerical simulation and their interpolations were used to describe the pump characteristics, instead of using 3D numerical simulations of real-time interactive data for the whole system. This is because the real-time interaction data would lead to a large amount of computation for the whole system. Using the characteristic curves and their interpolations reduces the accuracy to some extent; however, this method is acceptable in the whole-system simulation. Figure 5: Electric pump structure.