## 2 Materials and Methods
### Dynamic Characteristic Simulation of Temperature Control System  
To qualitatively analyze and verify the influencing factors of the temperature change at the outlet of the temperature control system valve, the temperature control valve is first modeled, and then the dynamic simulation is performed using Ansys. The movement in the cold path pipeline, as well as the temperature, rate, and flow of the gas of each pipeline of the temperature control valve, are observed. As shown in Figure 3, the CAD model of the temperature control valve system is drawn according to the actual pipe size (diameter: 100 mm). Ansys was used to simulate the situation. As shown in Figure 4, after the model was established, a CAD model of the established temperature control valve was meshed with the method of sweeping, which was convenient for the next calculation. Figure 3: Temperature control valve system CAD model. In the solution process, the initial condition parameters of each inlet fluid need to be set in Ansys simulation. In Ansys, we set the butterfly valve pipeline flow rate by finite element analysis method to predict the flow rate and temperature of hot-side and cold-side gas at different valve angles. A CFD model was built by importing CAD model in Ansys. The advantage of using tetrahedral mesh to segment the CAD model is that the mesh size is small, and the number is large. Tetrahedral mesh is suitable for complex surfaces and can be automatically generated. A Coupled Solver based on fluid density was used to solve the flow simulation of a high-speed compressible gas. The time scale factor of the solver was set to 1, and the number of experimental iterations was 150. The data for a specific working condition was taken as an example for simulation analysis, and the rotation axis and the speed of the butterfly valve were programmed and set. As shown in Figure 5, the pressure of the hot path of Pipeline 1 is \(P_{1}=1382\) kPa, the temperature is 756 K, the flow rate is 1412 kg/h, the known air density is 1.293 kg/m\({}^{3}\), and the pipe diameter is 100 mm. The flow rate can be obtained as 31 m/s. The pressure of the cold path of Pipeline 2 is \(P_{3}=62\) kPa, the temperature is 394 K, the flow rate is 2740 kg/h, the known air density is 1.293 kg/m\({}^{3}\), and the pipe diameter is 100 mm. The flow rate can be obtained as 62 m/s. Iterative calculations were performed. After the calculation was completed, the simulation results were analyzed, and the flow velocity distribution diagram and the temperature distribution diagram in the results were analyzed when the butterfly valve rotated at different angles. We describe the analysis of the temperature distribution and flow velocity distribution in three states: 0 degrees (cold path aisle is fully closed), 90 degrees (cold path aisle is fully open), and 30 degrees (cold path aisle is half open). Figure 4: Model mesh. The results show that, since the designed butterfly valve is in a state of constant rotation, when sampling the rotation angle of the butterfly valve at a certain moment, the flow at the cold path is affected by the previous state, so it can be seen from Figure 6 that when the butterfly valve only rotates to 0 degrees, although the cold path channel is closed at this moment, there is still flow through the channel. The gas at the cold path and the gas at the hot path exchange heat in the pre-cooler. It can be seen that the temperature at the outlet is also different when the valve rotation angle is different. The temperature at the outlet is affected by the gas flow at the cold path and the gas flow at the hot path. The cold gas flow can be changed by changing the valve angle. However, in the process of valve rotation from 0 degrees to 90 degrees, the flow rate of the cold path increases continuously, and the temperature at the outlet of the hot path decreases continuously. From the simulation results, it can be seen that there is a causal relationship between the temperature of the hot path and the valve rotation angle.