# Parametric Analysis of Compliant End Face Gas Film Seals Considering Slip Flow Effects
## 4 Results and Discussion
### Influence Law of Structural Parameters
#### 4.3.2 Influence Law of Wave Foil Chord Length  
The value range of the chord length was selected as 3.00-4.80 mm, the other parameters remained unchanged, and the change rule of the sealing characteristic parameters with the chord length considering the slip flow effect and not considering the slip flow effect was obtained, as shown in Figure 10.  
Both the gas film opening force and mass leakage rate increase with an increase in the wave foil chord length, and the viscous friction power consumption and stiff leakage ratio decrease with an increase in the wave foil chord length. The increasing and decreasing  
Figure 10: Influence law of wave foil chord length. (**a**) Gas film opening force and mass leakage rate; (**b**) Viscous friction power consumption and Stiffness Leakage Ratio.  
t trends of the four sealing parameters are basically similar at different gas film thicknesses, regardless of whether the slip flow effect is considered or not. The effect of the wave foil chord length on the increase in the mass leakage rate is more pronounced than the effect of the wave foil chord length on the increase in gas film opening force, i.e., the mass leakage rate increases faster with an increase in the gas film thickness, a change that is not conducive for the seal structure to meet the performance requirements. Specifically, when the gas film thickness takes the maximum value of 2.5 \(\upmu\)m, the mass leakage rate considering the slip flow effect grows by a factor of 0.91 compared with ignoring the slip flow effect.  
Observing Figure 10b, it can be seen that the viscous friction power dissipation decreases with an increase in the chord length of the wave foil, and the smaller the minimum gas film thickness is, the more pronounced the decreasing trend of the viscous friction power dissipation. This is due to the fact that an increase in chord length leads to an increase in the end face spacing, which largely reduces the viscous drag force before the fluid layer, thus decreasing the viscous friction power dissipation. Without considering the slip flow effect, the viscous friction power consumption decreases by 44.48% for a minimum gas film thickness of 1.25 \(\upmu\)m and 30.42% for a minimum gas film thickness of 2.50 \(\upmu\)m when the chord length is increased from 3.00 mm to 4.80 mm. It can be seen that the smaller the gas film thickness, the more obvious the reduction in the viscous friction power consumption. In fact, compared with the stiff end face dry gas seal structure, the end face gas film seal with compliant foil structure plays an active role in reducing the viscous friction power consumption, reduces the friction heat generation between the end faces, and is more suitable for high-temperature environment service. Further observation reveals that the stiffness leakage ratio shows an exponentially distributed decreasing trend with increasing wave foil chord length, i.e., the decreasing magnitude of the stiffness leakage ratio gradually decreases. Under different gas film thicknesses, the stiffness leakage ratio tends to be a stable value with the chord length of the wave foil.