Finite Element Solution of Inertia-Influenced Flow in Thin Fluid Films

The aim of this paper is to present a numerical model to compute laminar, turbulent, and transitional incompressible fluid flows in thin lubricant films where inertia effects cannot be neglected. For this purpose, an averaged inertia method is used. A numerical scheme based on the finite element method is presented to solve simultaneously the momentum and continuity equations. The numerical model is then validated by confronting it with previously published analytical, experimental, and numerical results. Particular attention is devoted to analyzing the numerical conservation of mass and momentum. The influence of mesh size on numerical precision is also analyzed. Finally, the model is applied to a misaligned hydrostatic seal. These seals operate with a substantial leakage flow, where nonlaminar phenomena occur. The influence of inertia and misalignment of the faces on the seal behavior is analyzed through a comparison with an inertialess solution. Significant differences are observed for high values of the tilt angle when the flow is nonlaminar. Inertia effects increase when the flow is laminar.