## 2 Materials and Methods  
### Research Model of Temperature Control System  
The principal experimental diagram of the temperature control system designed in this study is shown in the Figure 1.  
In the figure, \(P_{1}\), \(P_{2}\), \(P_{3}\), and \(P_{4}\) are pressure sensors; \(T_{h1}\), \(T_{h2}\), \(T_{c1}\), and \(T_{c2}\) are temperature sensors; and \(Gc\) and \(Gh\) are mass flow meters. Pipeline 1 passes the hot gas, the high-pressure bleed air control device is used to adjust the pressure of the hot gas at the inlet, and the pressure regulating valve is used to adjust the gas flow at the hot path. Pipeline 2 passes the cold gas and uses the butterfly valve to adjust the gas flow at the cold path. The cold and hot gas exchange heat through the heat exchanger without mixing. When the temperature at the outlet of the hot path is lower than the reference temperature, the temperature control valve is properly closed. At this time, the cold gas participates in the heat exchange. When the flow rate decreases, the temperature at the outlet of the hot path is higher outlet of the hot path increases. When the temperature at the outlet of the hot path is higher than the reference temperature, the butterfly valve is opened, the flow rate of the cold gas participating in the heat exchange increases, and the temperature at the outlet of the hot path decreases. After heat exchange occurs, the cold gas flows directly to the atmosphere, while the hot gas flows out from the outlet of the temperature control valve system to adjust the cabin temperature. At the same time, multiple temperature sensors, pressure sensors, and mass flow meters are used to monitor the gas temperature, pressure, and flow of each part of the temperature control system. To qualitatively analyze the system, a mathematical model of the temperature control value system was established. As shown in Figure 2, the cross-sectional area of the cold path passage is changed by adjusting the angle of the butterfly valve plate of Pipeline 2 (the inlet of the cold path), thereby changing the flow of the gas at the cold path. A torque motor controls the butterfly valve, and the working current of the torque motor is 0-250 mA. When the input current of the torque motor is 0 mA, the butterfly valve is in a fully open state. As the current increases, the cross-sectional area of the butterfly valve channel decreases when the valve plate rotates, and the flow at the cold path decreases. Therefore, the angle of the valve plate is controlled by the current, and the cross-sectional area of the valve pipeline is further changed to control the flow rate. Finally, the effect of adjusting the temperature at the outlet of Pipeline 1 is achieved. Figure 1: Schematic diagram of the experiment. With isentropic conditions, the Bernoulli equation of the butterfly valve is:  
\[\frac{P_{1}}{r}+\frac{V_{1}^{2}}{2g}=\frac{P_{2}}{r}+\frac{V_{2}^{2}}{2g} \tag{1}\]  
Solving these yields:  
\[V_{2}^{2}-V_{1}^{2}=2g\frac{P_{1}-P_{2}}{r} \tag{2}\]  
Additionally, \(V_{2}^{2}-V_{1}^{2}=\xi V^{2}\) Then, according to the continuous equation, \(Q=AV\) and the above formula can be solved:  
\[Q=AV=A\frac{1}{\sqrt{\xi}}\sqrt{V_{2}^{2}-V_{1}^{2}} \tag{3}\]  
\[Q=\frac{A}{\sqrt{\xi}}\sqrt{2g\frac{P_{1}-P_{2}}{r}} \tag{4}\]  
This is the flow equation of the butterfly valve. \(V_{1}\) (m/s) and \(V_{2}\) (m/s) are the speeds before and after throttling, \(V\) (m/s) is the average flow rate, \(P_{1}\) (kPa) and \(P_{2}\) (kPa) are the pressures before and after throttling, \(A\) (m\({}^{2}\)) is the throttling area, \(Q\) (kg/h) is the flow, and \(\xi\) is the resistance coefficient. In the derivation process, the average weight method is used to replace the butterfly valve with a pipeline of length \(L\) and section \(A\), and the medium is assumed to be an ideal fluid. When the medium flows stably through the pipeline, the compressible fluid flow equation is used:  
\[\frac{dp}{r}+d\frac{V^{2}}{2g}+dL_{f}=0 \tag{5}\]  
where \(L_{f}\) is the friction work.