The Influence of Fluid Inertia in Unsteady Lubrication Films

Abstract

The influence of the inertial forces in steady and unsteady lubrication films has been analyzed by means of an accurate computational model of the complete set of Navier Stokes equations for incompressible flows. A coordinate transformation accounts for the geometrical shape of the film boundary and its variation in time, reducing the numerical integration to a rectangular constant domain in the transformed plane. A dimensional analysis of the equations, both in steady and unsteady conditions, is performed to deduce the most significant nondimensional variables and parameters to be considered for a proper evaluation of the inertial effects. The applications are restricted to two-dimensional fields and simple boundary conditions to test the simulation capabilities of the computational model, by comparison with analytical solutions available in literature. Several geometrical and kinematic conditions are discussed and the effect of the convective and time dependent inertial terms is quantitatively evaluated.