## 3 The Results and Discussion
### Effects of Different Initial Pressures on the Field Strength Characteristics of the Leaked R290
gas inside the cloud could be jetted to a farther position, so a more intense shock wave (Mach disk) appeared farther away from the leak hole. The curves of the R290 concentration changes over time at the measurement points in the external space under different pressures is shown in Figure 13, and the change in the flammable area formed by the leaked R290 in the external space under different leakage pressures is shown in Figure 14. It can be seen from Figure 13 that as the initial leakage pressure increased from 0.5 to 2 Mpa, the response times of the concentration change at the different locations in the space shortened, and the concentration values increased. After the local flow area concentration field stabilized, the concentrations of point 4 were maintained at 0.84, 1.12, 1.41 and 1.65 vol% under different pressures, the concentrations of point 7 were maintained at 0.42, 0.57, 0.71 and 0.83 vol% and the concentrations of point 11 were maintained at 0.28, 0.38, 0.47 and 0.56 vol%. The concentration response times of points 7 and 11 were shortened from 0.18 to 0.05 s and from 0.5 to 0.2 s, respectively. With the increase in the distance from the measuring point to the leak hole on the jet axis, the influence of the initial leakage pressure on the leakage R290 concentration decreased. It can be seen from Figure 14 that the flammable area formed by the leaked R290 was mainly concentrated in the local area below the leakage hole. As the initial leakage pressure increased from 0.5 to 2 Mpa, the ranges of the flammable area in the horizontal direction changed little, whereas the ranges of the flammable areas in the vertical direction increased significantly: 0.2, 0.27, 0.34 and 0.4 m. The reason for this was mainly that with the increase in the initial pressure, more R290 leaked into the external space and diffused to different positions at a higher velocity, which made the response time of the concentration change  
Figure 12: Variations in the Mach disk distance and circumferential diameter in the near-field flow area under different leakage pressures: (**a**) 2; (**b**) 1.5; (**c**) 1; (**d**) 0.5 MPa. multiple fields were discussed when R290 leaked from the refrigeration system into the external space, and the influence of different initial leakage pressures on the field strength of the leaked R290 was analyzed. The conclusions are as follows:  
1. An improved gas leakage model suitable for describing refrigerant leakage in the refrigeration system was proposed, and the calculation results obtained by the improved model were compared with the experimental data from the published literature. The results found that the theoretical values of the position and circumferential diameter of the Mach disk and the concentration of the leaked gas were in good agreement with the experimental values, and the reliability of the improved gas leakage model was verified;
2. Based on the improved leakage model, the leakage and diffusion characteristics of R290 were analyzed. When the initial pressure was 2 MPa, the temperature was 360 K, the R290 gas continued to expand after it leaked into the external space, and its temperature and pressure decreased rapidly, reaching the minimum of 199.8 K and 0.013 MPa, respectively; its velocity increased rapidly, and the maximum reached 680.3 m/s. A Mach disk was formed in the flow area below the leakage hole, and the R290's thermo-physical parameters changed abruptly through the Mach disk. After two consecutive expansion and compression processes, the temperature, pressure and the velocity of the R290 gas gradually decreased along the jet direction and, finally, the R290 gas returned to room temperature and normal pressure. In addition, the expansion and compression process of the leaked R290 gas in the local flow area caused the gas diffusion position to deviate away from the leakage hole, and the high concentration area formed by R290 increased. The formation of the Mach disk was not conducive to the diffusion of the leakage gas;
3.