# Performance of the Compliant Foil Gas Seal with Surface Micro-Textured Top Foil+
## 4 Results
### Analysis of the Static Characteristics  
As can be seen from Figure 8a,b, with the linear increase in rotational speed, the gas dynamic pressure effect is enhanced and the gas film force increases significantly. However, the accelerated Couette flow does not have a significant effect on the flow in the axial direction. Hence, the mass leakage rate does not change with the change of rotational speed: the mass leakage rate of the elliptical texture is the largest and its value is maintained close to 9.87 \(\times\) 10\({}^{-4}\) kg\(\cdot\)s\({}^{-1}\). Figure 8c graphically shows the relationship between attitude angle and rotational speed. The attitude angles of the six texture types all show a decreasing trend as the rotational speed increases. A smaller attitude angle can make the operation of the sealing system more stable; thus, the higher the rotational speed, the better the stability of the compliant foil gas seal. Furthermore, it is found that when the rotational speed is 60,000 r\(\cdot\)min\({}^{-1}\), the minimum attitude angle of the triangular textures is 12.45\({}^{\circ}\). In addition, as can be seen from the data in Figure 8d, when the rotational speed increases linearly, the viscous friction force also increases close to linearly because the speed gradient in the thickness direction of the gas film increases with the increase in rotational speed and the frequency of friction between the fluid layers. As shown in Figure 9a,b, as texture depth increases, the gas film forces of the six textures all show a decreasing trend, and the mass leakages present a linear increasing trend. The gas film force and mass leakage rate of the elliptical texture change with the fastest speed, followed by the square texture. When \(h_{\rm c}\) < 5 \(\upmu\)m, the gas film force and mass leakage of the circular texture exceed those of the diamond-shaped texture, whereas when \(h_{\rm c}\) \(\geq\) 5 \(\upmu\)m, the situation is reversed, which implies that when the depth of the textures increases, the diversion effect is disadvantageous because the effect of the increasing gas film thickness is more obvious in a low-pressure environment. When the texture depth  
Figure 8: (**a**) Description of force with rotational speed. (**b**) Description of leakage with rotational speed. (**c**) Description of attitude angle with rotational speed. (**d**) Description of friction with rotational speed. varies from 1 to 11 \(\upmu\)m, the gas film force of the inverted triangle and triangle are close and show the best ranking of the gas film force. However, the leakage rate of the triangle is not as good as that of the inverted triangle, and the difference is more obvious with the greater texture depth. This implies that the mass leakage rate is more sensitive to the divergence and convergence of the texture, and the fully divergent texture type is not conducive to reducing the mass leakage rate. It can be seen from Figure 9c that as the texture depth increases, the attitude angle increases for different types of texture. The attitude angle of the elliptical texture is always larger than that of others, and the value of the inverted triangle is the smallest. The greater the texture depth, the more obvious the attitude angle difference of different textures is. When \(h_{\text{c}}\geq 9\) \(\upmu\)m, the attitude angle of the diamond-shaped texture exceeds that of the square texture, while the fluctuation of the inverted triangular texture tends to be gentle. It can be seen from Figure 9d that as texture depth increases, the viscous friction force of air film decreases. Compared with the other texture types, the elliptical texture has the largest cross-section and increasing the texture depth can rapidly increase the volume of the micro-pits, thereby considerably increasing the thickness of the gas film in the overall range. Thus, the viscous friction force of the elliptical texture is the most affected by the texture depth, i.e., it is reduced by 38.31%.