# Numerical Simulation of Vacuum Leak Jet and Jet Noise
## 2 Numerical Simulation Setup  
The main pressure vessel of the space station cabin is a cylindrical shell structure with a thickness of 2.5 mm. As leak holes formed by the impact of tiny space debris are generally at the millimeter level, the computation model is simplified to an axisymmetric model with a leak hole of 2.5 mm in length and 2 mm, 1 mm, 0.5 mm in diameter, respectively. The pressure inlet, defined as the 1 atm atmospheric environment is in front of the leak hole, while the pressure outlet, defined as vacuum environment, is after the leak hole. The specific numerical region is depicted in Figure 1 and the commercial CFD software Fluent 19 Ansys Inc., which is located at Southpointe 2600 Ansys Drive Canonsburg, PA 15317, USA, is used in this paper for calculation. As the ambient pressure on the orbit of the space station is in the order of 10\({}^{-7}\)\(\sim\)10\({}^{-4}\) Pa, the pressure outlet should be set very low to mimic the actual working conditions. However, extremely low setting of outlet pressure imposes high requirements on computational convergence. Besides, the Navier-Stokes (N-S) equations are restricted to describe continuous flow, with limited descriptions of rarefied flow. To fully describe the vacuum jet flow, CFD-DSMC (Computational Fluid Dynamic-Direct Simulation of Monte Carlo) method is widely used. Roughly speaking, the CFD calculation is firstly proceeded to calculate the continuous region and capture the boundary surface between continuous and rarefied region through Knudsen number, denoted by \(Kn\). Then, the captured boundary surface is used to initiate the plume field calculation based on DSMC method. In the numerical calculation, this paper concentrates on the CFD calculation as the acoustic pressure perturbation is mostly related to the continuous fields. To get the convergence, two different configurations of output pressure with 1 Pa and 10 Pa are conducted, where the convergence of steady velocity, pressure, density and temperature is depicted in Figure 2. The results show the difference of aerodynamic properties in continuous region between the two configurations are so minor that they are almost negligible. In other words, under the condition that the back pressure is sufficiently small, the specific value of the back pressure has little effect on the computation accuracy in continuous region. As such, the pressure outlet is set to 10 Pa to improve the computational convergence while the pressure inlet is set to 1 atm to simulate actual pressure condition in the space station cabin. The temperature in the area in front of the leak hole is uniformly set to 300 K to simulate real thermal condition inside the spacecraft cabin. However, the temperature in orbit is greatly affected by solar radiation so that the temperature range outside the cabin is exceptionally large. In low earth orbit where most spacecrafts work, the temperature in the sun light area can reach above 120 degrees Celsius, while the temperature in the shadow area will quickly drop to below minus 100 degrees Celsius [23]. Therefore, the effect of temperature cannot be neglected. As such, the temperature in the area behind the leak hole is set to 173 K, 300 K and 393 K respectively. In order to explain the dynamic properties and aeroacoustic characteristics, jet in atmospheric environment under the same computational model  
Figure 1: Schematic diagram of the computational model. and pressure difference is also provided, where the pressure inlet and outlet is set to 2 atm and 1 atm respectively, meanwhile other setups remain unchanged. It is obvious in Figure 2 that the vacuum leak jet is a supersonic flow with a strong density gradient, thus the gas compressibility cannot be neglected.