# Numerical Evaluation of Rotordynamic Coefficients for Compliant Foil Gas Seal
## 1 Introduction  
The deformation generated by heat and vibration in the small seal gaps may lead to seal system instability and failure [1; 2]. To resolve the challenges and increase the control efficiency of the power system response, the cylindrical structure of the gas seal was designed to avoid seal system failure and improve efficiency with its compliant structure [3; 4]. Compliant foil gas seal was one of the advanced cylindrical gas seals and first introduced by [PERSON] and [PERSON] [5]. It can be used to reduce leakage in extremely small gaps of the secondary flow system of the aero-engine, including in compressors, turbine, and even other turbomachinery [6; 7]. The compliant foil gas seal can increase the seal efficiency and reliability of the aero-engine, and its main role is flexible ability in dynamic deformation [6]. Therefore, the numerical evaluation of the compliant foil gas seal is analyzed in this paper, and it is beneficial to predict the performance of the compliant foil gas seal in a complex environment by meeting the steady requirements of the gas seal. At the same time, the numerical evaluation also acquires the optimization values of operating parameters and reduces the costs of the test rig [8]. To investigate the numerical performance of the gas seal, the Reynolds lubrication equation and Hirs lubricate equation was commonly used to solve the flow model in the related researches [9]. [PERSON] and [PERSON] [10] derived a finite difference procedure to solve the dynamic coefficients of the seal at an eccentric positionwith a turbulent model. [PERSON] [11; 12] evaluated the leakage of different seals to acquire the prediction using commercial computational fluid dynamics (CFD) software. [PERSON] [13] analyzed the numerical performance of a cylinder gas seal on the T-shaped groove using CFD software. With the uncertainty of CFD software analyses in the field of gas seal, [PERSON] [14; 15] developed the finite element method (FEM) to analyze the quasi-dynamic characteristics of a cylindrical gas seal based on high dynamic performance of the fluid lubrication bearing and numerical evaluation of rotordynamic coefficients of the spiral groove. [PERSON] [16] used the finite difference method (FDM) to acquire the numerical performance of the cylindrical gas seal on the slot and spiral groove. Because of high accuracy and short computation time, this study used the FDM to extend the analysis of the cylindrical gas seal presented by [PERSON] [16] and determine the rotordynamic coefficients of the compliant foil gas seal on the T-shaped groove. In this paper, the steady performance of the compressible flow field of the compliant foil gas seal was calculated using the different operating parameters, and pressure distribution was obtained to verify the credibility of the numerical analysis. The rotordynamic coefficients were integrated by the gas force in the seal area in this study, including stiffness and damping coefficients. The stiffness \(K\) and damping \(D\) are important rotordynamic coefficients that provide the stability and instability of the seal system [17; 18].