The Effect of Inertia in Lubrication Flow Including Entrance and Initial Conditions

Abstract

This study is concerned with the influence of fluid inertia in thin film steady or transient laminar flows, emphasizing the role of initial conditions and inlet boundary conditions. Most existing studies implicitly omit these effects due to the method of formulation or the type of problem studied. In the present study, linearization for the convective inertia terms is used to transform the problem to a coordinate system which results in a simple diffusion equation. Closed-form solutions are obtained, considering initial or entrance conditions in the classical manner. Predictions are tested against cases for which solutions exist in the literature and against a numerical solution and excellent agreement is found. For simple squeeze films, large discrepancies from lubrication theory are found at short times following the start-up, or at moderate Reynolds numbers. In the steady flow case, fluid is assumed to enter the bearing with a slug flow profile. The inlet pressure is determined by coupling the bearing flow with the upstream inviscid flow. Large discrepancies from lubrication theory are found at Reynolds numbers where the lubrication theory was previously thought to be satisfactory. The load may increase or decrease, depending on the upstream conditions.