Numerical Solution of Lubrication’s Compressible Bulk Flow Equations: Applications to Annular Gas Seals Analysis

The appropriate theoretical model for lubrication flows characterized by reduced Reynolds numbers greater than unity (Re^*=ρVH/μ·H/L≥l) is the so-called “bulk flow” system of equations. Its solution is more difficult than for the simple Reynolds equation because one has to deal with coupled pressure and velocity fields and the equations are of mixed elliptic-hyperbolic type. Adapting some methods borrowed from CFD can develop a suitable numerical approach. In the present work we introduce a pressure-based method belonging to the family of SIMPLE algorithms where compressibility is taken into account by coupling density corrections with pressure corrections. The method is capable of handling all compressible flows and doesn’t require any specific treatment of the incompressible flow regime. It is an adaptation for the bulk flow equations of Karki and Patankar’s (1989) work and is developed in conjunction with a triangular finite volume formulation. The present paper is focused on the description of the discretized equations, of the accompanying boundary conditions and of the solution algorithm. Comparisons with analytic solutions for subsonic and supersonic channel flows prove the ability of the method to handle all compressible flow regimes. Published results for gas (air) annular seals are further used to evaluate the proposed numerical model.