Reynolds' Model Suitability in Simulating Rayleigh Step Bearing Thermohydrodynamic Problems

A Reynolds-based numerical thermohydrodynamic analysis, performed on a discontinuous geometric domain, is unable to correctly predict the flow field in the close vicinity of the discontinuity. This limitation, due to the very hypotheses used to derive the Reynolds equation, explains the lack of studies treating such configurations. A Navier-Stokes–based model seems appropriate but its complexity and its requirements in terms of computing time are somewhat prohibitive. To compare the two models we have developed two independent, finite-volume-based numerical algorithms. They are applied to a simple two-dimensional geometric configuration (Rayleigh step bearing). This will allow us to prove that, for the configurations commonly encountered in hydrodynamic lubrication, the errors introduced by the Reynolds model are highly localized. The overall performance and running parameters are correctly determined with both models, rendering unnecessary the complex Navier-Stokes–based solution.