# Analysis of an Elasto-Hydrodynamic Seal by Using the Reynolds Equation
## 1 Introduction
The proposed EHD seal is superior to the existing sealing technologies, including labyrinth, brush, finger, and compliant foil seals in the sense that (i) a non-contact EHD seal provides a long operating life; (ii) low friction is realized by the non-contacting nature of the seal at the operating conditions; (iii) the relatively simple structure results in low initial cost and long operating life, saving maintenance costs; (iv) the innovative seal design eliminates any sharp angles and, thus, stress concentration risks that would otherwise reduce the product life; (v) the EHD seal is a clearance type seal, and the benefit of low leakage comes from the dynamic throttling, which will potentially increase fuel efficiency, and (vi) the secondary seal will provide a smoother startup when the system is ramping up. This paper aims to prove the proposed concept by using a sound scientific methodology. To achieve this, we will use the Reynolds equation, which has been widely applied in the EHD lubrication theory, to model the flow physics in the seal clearance, while we will use the governing equations of solid mechanics to model the deformation of the seal due to the imparted pressures from the flow field. There have been countless studies based on the Reynolds equation [17; 18; 19; 20; 21; 22]. Generally speaking, in the majority of these studies, the Reynolds equation and the related Fluid-Solid Interaction (FSI) problems were solved by using in-house codes that were written by researchers themselves [23; 24; 25; 26; 27; 28; 29; 30; 31]. Commercial Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) codes have made significant advancements in recent years in terms of both solution algorithms and efficiencies. As such, researchers began making increasing use of commercial software packages in their scientific quests. Among others, [PERSON] et al. used their in-house Reynolds equation solver together with ABAQUS Finite Element software to model a strongly coupled Fluid-Solid-Interaction (FSI) EHD lubrication problem. Their results showed excellent agreement with previously publisheddata [32]. [PERSON] et al. employed an OpenFOAM open-source CFD package to propose a reduced-order FSI model to be used in EHD lubrication problems [33]. [PERSON] et al. provided an engineering software solution for EHD lubrication theory by using COMSOL and MATLAB [34]. Their goal was to show that complex EHD problems could be solved with the help of readily available commercial software, enabling researchers to shift their focus from the numerical modeling to the physical modeling. Similarly, [PERSON] et al., a large group of researchers from General Electric and Southwest Research Institute, employed ANSYS CFX software to simulate their proposed seal design for sCO2 turboexpanders [16]. [PERSON] et al. used OpenFOAM for proposing a CFD-based frequency method for determining the dynamic coefficients of the hydrodynamic linear slider and journal bearings. The authors did not consider cavitation as the high ambient pressure bearings do not experience the cavitation scenario [35]. [PERSON] at el. developed a numerical model for soft Elasto-Hydrodynamic lubrication and compared the numerical results of the hard EHL with that of the soft EHL. Their work is a coupling of the Reynolds equation, the elasticity equation, and the load balance equation, which they solved in COMSOL Multiphysics [36]. [PERSON] et al. showed how the thin film flow past occlusions can be modeled in COMSOL Multiphysics by the lubrication approach, which is similar to the previous literature on the finite element simulations of the coating flows [37]. An Elasto-Hydrodynamic lubrication model for the slip influence in the mechanical components has recently been proposed using Computational Fluid Dynamics (CFD) and FSI based on the Finite Element Analysis that was performed by [PERSON] et al., 2022 [38].