# Performance of the Compliant Foil Gas Seal with Surface Micro-Textured Top Foil+
## 4 Results
### Analysis of the Dynamic Characteristics  
Figure 10a,c show the variation of the direct dynamic coefficients with different rotational speeds. Specifically, \(k_{xx}\) of the six texture types is positive and decreases as rotational speed increases, whereas \(k_{yy}\) is negative and increases gradually. When the speed varies 10,000 and 20,000 r\(\cdot\)min\({}^{-1}\), the range of change of direct stiffness coefficient is large, however, it becomes smaller once the speed exceeds 30,000 r\(\cdot\)min\({}^{-1}\), which indicates that the  
Figure 9: (**a**) Description of force with depth; (**b**) Description of leakage with depth; (**c**) Description of attitude angle with depth; (**d**) Description of friction with depth. direct stiffness coefficient is easily affected by the speed variation in the low-speed range and prone to instability. The changes in the direct damping coefficients have an approximate trend; as the speed increases, \(c_{xx}\) and \(c_{yy}\) monotonically increases from a negative value to a positive value. Regardless of the texture type, when the speed is less than 30,000 r\(\cdot\)min\({}^{-1}\), the rate of increase of \(c_{xx}\) and \(c_{yy}\) is higher. Once this speed is exceeded, the fluctuation of the direct damping gradually becomes smaller; it eventually remains flat, and the magnitude decreases to zero. As can be seen from Figure 10b,d, the distributions of the cross dynamic characteristic coefficients are mutually symmetrical. As the speed increases, the sum of cross damping of the different texture types has different degrees of convergence, and the value keeps approaching zero, indicating that the cross damping does not need to dissipate more energy; thus, the speed increases to make the sealing system stable. As increasing the rotational speed in the low-speed range significantly improves the dynamic pressure effect, when the rotational speed exceeds a certain value, the dynamic pressure effect decreases, resulting in a larger difference in the cross-damping coefficients when the rotational speed is less than 30,000 r\(\cdot\)min\({}^{-1}\). Figure 11 shows the influence of the texture depth on the dynamic characteristics. Owing to the change in the texture depth, the Couette flow and Poiseuille flows of the gas between the sealing interfaces are changed. The change in the fluid pressure distribution causes the changes in foil deformation; the thickness of the gas film changes accordingly, and the complexity of the flow field is enhanced. Therefore, when the texture depth changes, the dynamic characteristics fluctuate considerably. Figure 11a,b show the relationship between the stiffness coefficient and the texture depth for different texture types; \(k_{yy}\) gradually increases with the increase of texture depth, and elliptical, triangular, and inverted triangular textures have the maximum positive \(k_{xx}\) at \(h_{\rm C}=9\)\(\mu\)m, after which the value drops sharply. The distributions of \(k_{xy}\) and \(k_{yx}\) are still symmetrical. Except for the triangular texture, the sum of the cross stiffnesses of the others is basically stable. Figure 10: (**a**) Description of \(k_{xx}\) and \(k_{yy}\) with rotational speed; (**b**) Description of \(k_{xy}\) and \(k_{yx}\) with rotational speed; (**c**) Description of \(c_{xx}\) and \(c_{yy}\) with rotational speed; (**d**) Description of \(c_{xy}\) and \(c_{yx}\) with rotational speed. From Figure 11b,c, when the texture depth increases, \(c_{xx}\) of all textures decreases continuously. It is found by calculation that when the texture depth increases from 1 to 9 \(\upmu\)m, the sum of direct damping shows an initially decreasing and subsequently increasing trend.