Finite element solution of the energy equation in lubricated contacts Application to mechanical face seals

In lubricated contacts, moving solids are separated by a strongly sheared thin fluid film. The resulting temperature rise due to viscous dissipation can greatly affect the behaviour of the contact. Therefore, it is essential to determine the temperature field in such contacts. Temperature is obtained by solving the energy equation (convection diffusion equation), which is modified to take into account the particular shape of the fluid film. Upwind schemes for the finite element method are presented for both the one- and two-dimensional steady configurations. They are then applied to simple lubrication problems and their results are compared. In some cases numerical oscillations occur. Modifications of the initial schemes are proposed to avoid those numerical problems. The influence of the boundary conditions and the effect of the orientation of the flow are analysed in more detail. Finally, the resolution of the three dimensional energy equation in a mechanical face seal is presented. There is a good correlation between the numerical results and the experimental data and this confirms the accuracy of the upwind scheme.