# Parametric Analysis of Compliant End Face Gas Film Seals Considering Slip Flow Effects
## 4 Results and Discussion
### Influence Law of Inlet and Outlet Pressure Ratio  
Select the range of the inlet and outlet pressure ratio as 1.50-3.30, keep other parameters unchanged, and obtain the sealing characteristic parameters with the change rule of the inlet and outlet pressure ratio considering the slip flow effect and not considering the slip flow effect, as shown in Figure 8.  
Figure 8 shows the change rule of compliant end face gas film sealing characteristics under two velocity slip step cases. From Figure 8a, it can be seen that with an increase in the inlet and outlet pressure ratio, the gas film opening force increases significantly, showing a linear increasing trend. An increase in the inlet and outlet pressure ratio means that the pressure of the flow field between the end faces rises as a whole, so the effect on the opening force of the gas film is more significant. The minimum gas film thickness value of 1.25 \(\upmu\)m is selected for analysis, and when the inlet/outlet pressure ratio is 3.30, the opening force of the gas film considering the slip flow effect and not considering the slip flow effect are 2342.66 N and 2351.61 N, respectively, with a relative error of 0.38%; when the inlet/outlet pressure ratio is 1.50, the opening force of the gas film considering the slip flow effect and not considering the slip flow effect are 1113.17 N and 1117.69 N, with a relative error of 0.41%. The calculation results show that the role of the slip flow effect will gradually appear with a reduction in the ambient  
Figure 8: Influence law of the inlet and outlet pressure ratio. (**a**) Gas film opening force and mass leakage rate; (**b**) Viscous friction power consumption and Stiffness Leakage Ratio. pressure, so when the compliant end face gas film seal is used in lower pressure conditions, the slip flow effect can not be ignored. The inlet/outlet pressure ratio of 1.5 is selected for the analysis, and when the minimum gas film thickness is 1.25 \(\upmu\)m, the opening force of the gas film considering the slip flow effect decreases by 4.53 N compared with that without the slip flow effect; when the minimum gas film thickness is 2.5 \(\upmu\)m, the opening force of the gas film considering the slip flow effect decreases by 0.75 N compared with that without the slip flow effect. It is learned that the slip flow effect will gradually weaken with an increase in the gas film thickness, which is because the smaller the thickness of the gas film, the easier it is to gather the Knudsen layer at the sealing interface of the medium gas movement, resulting in the more obvious slip flow effect. Observation of Figure 8a in the mass leakage rate with the law of change of the inlet and outlet pressure ratio can be seen; the mass leakage with an increase in the inlet and outlet pressure ratio shows an accelerated upward trend. As the mass leakage amount is expressed as the inner radius end surface medium in the outlet of the flow rate of the integral when the inlet and outlet pressure ratio increases, fluid under pressure from the outer radius to the inner radius of the direction of the accelerated flow, and thus the mass leakage rate increases. The presence of the slip flow effect increases the velocity distribution of the lubricating gas along the radial direction compared with the case where the slip flow effect is not considered. By solving the integral of the radial velocity distribution, it can be seen that the mass leakage rate considering the slip flow effect is slightly larger than the mass leakage rate without considering the slip flow effect, which is consistent with the results of reference [44]. According to the relationship curve between the inlet and outlet pressure ratio and viscous friction power consumption in Figure 8b, it can be seen that the slip flow effect can reduce the viscous friction power consumption. The smaller the ratio of the gas film thickness and inlet/outlet pressure, the larger the difference.