A Triangle Based Finite Volume Method for the Integration of Lubrication’s Incompressible Bulk Flow Equations

Abstract

It is well known that for a reduced Reynolds number (Re*=ρVH/μ⋅H/L) greater than unity, inertia forces have a dominant effect in the transport equations, thus rendering the classical lubrication equation inapplicable. The so called “bulk flow” system of equations is then the appropriate mathematical model for describing the flow in bearing and seals operating at Re*≥1. The difficulty in integrating this system of equations is that one has to deal with coupled pressure and velocity fields. Analytic methods have a very narrow application range so a numerical method has been proposed by Launder and Leschziner in 1978. It represents a natural extrapolation of the successful SIMPLE algorithm applied to the bulk flow system of equations. The algorithm used rectangular, staggered control volumes and represented the state of the art at that moment. In the present work we introduced a method using triangular control volumes. The basic advantage of triangles versus rectangles is that non rectangular domains can be dealt without any a priori limitation. The present paper is focused on the description of the discretized equations and of the solution algorithm. Validations for bearings and seals operating in incompressible, laminar and turbulent flow regime are finally proving the accuracy of the method.