## 3 The Results and Discussion
### Effects of Different Initial Pressures on the Field Strength Characteristics of the Leaked R290  
Figure 11 shows the pressure, temperature and velocity distributions of the leaked gas on the jet axis of the local flow area under different initial leakage pressures. It can be seen from Figure 11 that with the increase in the initial leakage pressure, the gas pressure at the outlet plane of the leakage section increased. When the initial pressures were 0.5, 1, 1.5 and 2 MPa, respectively, the pressures of the gas at the outlet of the leakage section reached 0.23, 0.46, 0.7 and 0.95 MPa. The leakage mass flow rates also increased, which were 0.84, 1.7, 2.6 and 3.6 g/s, respectively. The leaked R290 at a higher initial leakage pressure could expand to a lower pressure and temperature in the external space. When the initial pressures were 0.5 and 2 MPa, the minimum pressure and temperature of the gas in the annular cloud below the leak hole reached 0.046 MPa and 281.4 K and 0.013 MPa and 199.8 K, respectively; the temperature and pressure of the leaked gas at a high initial leakage pressure were higher after through the Mach disk. The reason for this was mainly that with the increase in the initial leakage pressure, the intensity of the shock wave generated by the leaked gas inside the near-field flow area increased, and a stronger driving force was generated during the gas expansion and compression process. At the same time, under high-pressure conditions, a higher velocity could be obtained during the expansion of the leaked gas. When the initial leakage pressures were 0.5 and 2 MPa, the maximum velocities of the leaked gas were 513.2 and 680.3 m/s, respectively. Moreover, after the gas expansion  
Figure 10: Flow field distribution of the leaked R290 gas in external space. Figure 9: Changes in the R290 concentration at different locations in space over time. and compression process disappeared, the leaked gas at a higher initial leakage pressure had a higher temperature and velocity on the jet axis. There is a complex shock wave (Mach disk) structure inside the annular cloud formed by the leaked gas in the local flow area, which has a great impact on the concentration distribution of the leaked R290 gas. Therefore, it is very important to understand the position and circumferential diameter of the Mach disk under different initial pressures. As shown in Figure 12, it can be seen that as the initial leakage pressures increased from 0.5 to 2 MPa, the distances from the Mach disk to the leak hole were about 1.7, 2.3, 2.9 and 3.5 mm, respectively, and the circumferential diameters of the Mach disk increased accordingly, but the number of the Mach disks did not change significantly. The reason for the above phenomenon was mainly that with the increase of the initial leakage pressure, the potential energy and kinetic energy of the leaked gas increased, but more gas accumulated under the leak hole during the same leakage time, and the jet boundary area increased. The energy loss of the gas during the expansion and compression process increased. After the leaked gas underwent two expansion and compression processes, the pressure was very close to the atmospheric pressure, so the number of Mach disks formed in the flow area did not change with the increase in the initial pressure. The increase in the distance from the Mach disk to the leak hole and the circumferential diameter of the Mach disk can be explained that the intensity of the expansion wave generated inside the annular cloud increased, which made the gas in expansion process reach a lower temperature and pressure, the expansion duration prolonged. At the same time, due to the increase of the flow area, it took longer time for the expansion wave to reach the jet boundary, and the low-pressure  
Figure 11: Field strength distribution of R290 on the jet axis under different initial leakage pressures: (**a**) pressure distribution; (**b**) temperature distribution; (**c**) velocity distribution.