# Parametric Analysis of Compliant End Face Gas Film Seals Considering Slip Flow Effects
## 4 Results and Discussion
### Influence Law of Structural Parameters  
#### 4.3.1 Influence Law of Wave Foil Thickness  
The thickness of wave foil was chosen as 0.20-0.38 mm, the other parameters remained changed, and the change rule of sealing characteristic parameter with the thickness of wave foil considering the slip flow effect and not considering the slip flow effect was obtained, as shown in Figure 9.  
According to the change rule of gas film opening force and mass leakage rate with the wave foil thickness in Figure 9a, it can be seen that the gas film opening force decreases gradually with an increase in the wave foil thickness. In the minimum gas film thickness of 2.25 um for analysis, when the wave foil thickness increases from 0.20 mm to 0.38 mm, the gas film opening force without slip flow effect decreases from 1844.00 N to 1723.19 N. This is due to an increase in the wave foil thickness, which strengthens the structure's own support ability in the axial direction so that the compliant end face does not easily generate displacement in the axial direction, weakening the wedge-shaped effect, so the opening force of the gas film decreases. This change in its own properties caused by an increase in the thickness of the wave foil also implies a reduction in the sealing gap and a reduction in the leakage channels, and thus, it can be seen that the mass leakage rate decreases with an increase in the thickness of the wave foil, but the trend of this decrease is not infinite, but rather slowing down. It is shown that as the wave foil thickness tends to some larger value, the effect on the end face stiffness diminishes or does not even occur, i.e., the end face stiffening is approached.  
The changing law of viscous friction power consumption and stiffness leakage ratio with the wave foil thickness is shown in Figure 9b. When the wave foil thickness increases, the end face stiffness increases, the deformation of the compliant end face decreases, and the end face distance decreases; thus, under the condition of the same gas film thickness, the velocity gradient of the gas film in the axial direction increases, and the relative motion  
Figure 9: Influence law of wave foil thickness. (**a**) Gas film opening force and mass leakage rate; (**b**) Viscous friction power consumption and Stiffness Leakage Ratio.  
between the fluid layer and the fluid layer is enhanced, and the viscous friction power consumption increases. Meanwhile, it can be observed that compared with the effect of the wave foil thickness on the viscous friction power consumption and the stiff leakage ratio, the effect of the gas film thickness on the stiff leakage ratio is more obvious. When the thickness of the gas film is smaller, the change in the stiffness leakage ratio is more obvious with an increase in the wave foil thickness. Therefore, the proper design of the wave foil thickness is crucial; the choice of the wave foil thickness not only depends on the impact of sealing performance but also on the processing method. A thinner or thicker wave foil is not easy to process, and molding is likely to rebound, so the structure of the dimensional accuracy is not enough.