# Parametric Analysis of Compliant End Face Gas Film Seals Considering Slip Flow Effects
## 1 Introduction  
As a new form of noncontact sealing, dry gas seals have been widely used in bioengineering, aerospace, and other fields [1, 2]. In recent years, with the experimental research and development of high-altitude hypersonic flight aero-engine and the development of supercritical carbon dioxide power generation technology [3, 4], the traditional rigid face dry gas seal is very easy to cause problems such as sealing vice deformation, wear, and abrasion, touching abrasion and so on, and even lead to instability and failure, which ultimately affects the normal work of the whole machine device in the rapid start-stop, abnormal perturbation, multi-variable rotational speeds, or skewed operation [5]. In response to the above problems, some scholars have proposed a new type of adaptive mechanical seal concept [6, 7, 8], which is more centrally designed as a compliant end face structure with wave foils and flat foils. The compliant end face deforms under the action of multiple loads, and the wedge-shaped gas film formed can greatly enhance the dynamic pressure effect and improve the opening force of the gas film. It can also spontaneously adjust the equilibrium relationship, effectively absorb vibration impact, and quickly adapt to the operating position so that the sealing system maintains a good sealing effect and stability. As early as the beginning of the twenty-first century, scholars such as [PERSON] and [PERSON] [9, 10] referred to the design concept of gas foil bearings, used elastic structureto replace the traditional rigid sealing end face and proposed a kind of compliant foil face gas seal structure. On this basis, [PERSON] et al. [11] explored the change rule of sealing performance of compliant foil face gas seals under different working conditions. The results show that the flexible end face can provide excellent deformation resistance. Under high temperature and high-speed working conditions, it can effectively cope with a change in the sealing gas film thickness and show good sealing performance. Subsequently, [PERSON] [12] introduced the compliant foil face gas seal into the aero-engine performance test. NASA Glenn Research Center [13] successfully completed the compliant foil face gas seal test at 25000 rpm and 70 psiD pressure. It was found that the surface coating had a large effect on the sealing performance. [PERSON] et al. [14; 15] conducted high-temperature tests on compliant foil face gas seal and the results showed that the noncontact compliant foil gas seal has excellent sealing performance. Then, [PERSON] et al. [16] used nonlinear coefficients to describe the turbulence effect and utilized the ultra-relaxation method to solve the coupled governing equations of flow pressure and film thickness to obtain the compressible fluid flow field under high-velocity conditions. In recent years, domestic scholars have gradually paid attention to compliant foil face gas seals and carried out related research. [PERSON] et al. [17; 18] analyzed the stable and dynamic performance of compliant foil face gas seals and studied the optimal design of the structure by establishing a theoretical model of gas-elastic coupling lubrication and solving the Reynolds equation by using the finite difference method. They analyzed the stability and dynamic performance of the compliant foil face gas seal and carried out research on the optimized design of the structure. The results of this study found that the compliant foil face gas seal has obvious advantages in terms of disturbance resistance compared with the traditional dry gas seal with a rigid end face. Subsequently, [PERSON] et al. [19] analyzed the influence of blocking flow and inertia effect on the pressure field of sealing velocity occasions and explored the influence of operating conditions on sealing performance. [PERSON] et al. [20] pointed out in their study that the comprehensive performance of the seal can be effectively improved by introducing a compliant end face structure under high-speed and low-pressure conditions. [PERSON] et al.