# Numerical Simulation of Vacuum Leak Jet and Jet Noise
## 3 Discussion
### Comparison of Vacuum and Atmospheric Environment
#### 3.1.1 Dynamic Properties  
Figure 4 shows the velocity contour of steady leak jet under vacuum environment and atmospheric environment respectively, where the leak hole diameter is 2 mm. For vacuum environment, the gas will expand rapidly through the leak hole into vacuum environment outside and form a supersonic region with Mach 2 to 3. Furthermore, the diameter of the jet potential core is about 25 times the diameter of the leak hole. For atmospheric environment, the jet is a subsonic jet and no obvious expansion is observed. The jet's diameter is roughly consistent with the diameter of the leak hole.  
In a normal atmospheric environment, a supersonic jet will form a series of expansion fans at the exit of the nozzle, which will be reflected when reaching the jet boundary. Then a series of compression waves is formed and constitutes a Mach disk. When the compression waves travel downstream to the jet boundary, the occurrence of reflection induces new expansion fans. Repeated circulation forms a quasi-periodic shock cell structure, as shown in Figure 5. On a micro level, the generation, propagation and reflection of wave systems are essentially due to the collisions of a large number of molecules. When a certain point in the flow field is disturbed, the energy state of surrounding molecules and the probability of collision between molecules will be changed. Energy transfer will occur between molecules once the collision happens. As the disturbance propagates to the surrounding environment, series of directional wave systems are formed.  
However, in vacuum environment, the extremely low molecular number density makes the jet quickly transform from a continuous flow to a rarefied flow once the gas enters the vacuum environment. When the expansion fan reaches the jet boundary, it cannot reflect or generate compression wave  
Figure 4: Velocity contour of different external environment. (**a**) vacuum environment; (**b**) atmospheric environment.  
Figure 5: Shock cell structure and mixing layer in a supersonic jet.  
system because the local molecular number density is far lower than that in the normal atmospheric environment. Therefore, there is no shock cell structure generated in the vacuum environment.  
Figure 6 shows the density and pressure distribution of steady leak jet under vacuum environment and atmospheric environment, respectively. It can be seen that the density in vacuum environment shows a shape of droplets, which is in high agreement with the approximate analytical solution of [PERSON] and [PERSON] [10]. Besides, there is a large density gradient in a small area near the leak hole exit, which satisfies the tendency that the closer to the exit center, the larger the density gradient. The density drops rapidly from 0.59 kg/m\({}^{3}\) to 0.33 kg/m\({}^{3}\) at a distance of 1 mm downstream from the leak hole exit center. As a contract, the change of the density in conventional atmospheric environment is relatively gentle and no strong gradient is observed. The density only decreases from 1.45 kg/m\({}^{3}\) to 1.44 kg/m\({}^{3}\) at a distance of 1 mm downstream from the leak hole exit center. The pressure in vacuum environment is similar to the density contour, showing a regular droplet shape. A large pressure gradient is also observed in a small area near the leak hole exit with a rapid drop of about 38,000 Pa as the expansion fan travels 5 mm downstream. Nevertheless, the pressure change in conventional environment is relatively smooth.