# Parametric Analysis of Compliant End Face Gas Film Seals Considering Slip Flow Effects
## 1 Introduction
[21; 22] designed a T-slot compliant foil gas film seal structure based on the existing floating plunger seal in order to meet the dynamic stability of an aero-engine and analyzed the effects of operating parameters on the rotor dynamic coefficient. [PERSON] [23] and others proposed a new compliant seal structure. Based on the fluid-structure coupling analysis method, their three-dimensional flow field was simulated, and the effects of operating parameters and structural parameters on the steady-state characteristics were investigated. Since the scale of the fluid lubrication gas film between the friction parts of the dry gas seal is micrometer scale, some scholars have carried out research on the thinning effect of the gas film seal. [PERSON] [24] utilized the generalized gas film lubrication equation at an arbitrary Knudsen number derived using Fukui and Kaneko to analyze the flow field of a classical spiral groove dry gas seal. By studying the characteristic curves of the gas film pressure and gas film thickness, the results showed that the slip flow is most significant when the Knudsen number is greater than 0.05. On the basis of previous research, [PERSON] [25] fitted the equation for the flow coefficient of Poiseuille flow based on the movement of fluid in a wider flow channel, combined with the F-K (Fukui-Kaneko) model and the linear Boltzmann equation set. [PERSON] et al. [26; 27] modified the generalized Reynolds equation and applied the PH linearization method to iteratively solve the key seal performance parameters under second-order nonlinear slip boundary conditions. [PERSON] et al. [28; 29] used the effective viscosity to characterize the slip flow and analyzed the degree of influence on the performance of the dry gas seal of the spiral groove under different working conditions by taking into account the real gas effect and the slip flow effect. [PERSON] et al. [30; 31] established a slip flow model considering the roughness of the seal end face and analyzed the interactive relationship between surface roughness and slip flow on the seal performance. [PERSON] [32; 33] compared the effects of the first-order velocity slip model, the second-order velocity slip model, and the F-K model on the new floating cylindrical microgroove gas film seal, respectively. It was found that the F-K model was more stable for calculations at high rotational speeds. [PERSON] [34] et al. numerically solved the pressure distribution of a spiral groove dry gas seal using the finite difference method by integrating the slip flow effect and the real gas effect. The influence laws of the two effects on the startup characteristics of S-DGS under different structural parameters were discussed. The results show that the slip flow effect inhibits the opening ability of CO\({}_{2}\) S-DGS, while the real gas effect enhances its opening ability. [PERSON] [35] et al. used a high-precision eight-node finite difference method to calculate the gas film buoyancy by taking into account the coupling between the slip flow effect, surface microgrooves, and eccentricity. The influence of the slip flow effect on the gas sealing performance of spiral groove cylinders was discussed. So far, although there have been studies describing the results on the flow field characteristics of cylindrical compliant foil gas film seals and the slip flow effect of rigid end-face dry gas seals, there are fewer studies on the slip flow effect of compliant foil face gas seals. In this paper, the linear Boltzmann equation is introduced into the process of seal performance analysis by taking the compliant foil face gas seal as the research object. Based on the Fukui-Kaneko slip flow model, a generalized Reynolds equation suitable for the solution of compliant foil face gas seal is established, which is coupled with the sealing gap control equation considering the deformation of wave and flat foils. The above equations are solved by coupling the center difference method and Newton-Raphson iteration method.