The Influence of Variable Density and Viscosity on Flow Transition Between Two Concentric Rotating Cylinders

Abstract

In a journal bearing, the lubrication film can be analyzed by the laminar flow theory if the modified Reynolds number, R*, is small or by turbulent flow theories if R* is very high. R* of 41.17 has generally been quoted as the criterion below which simple laminar film is to be expected. This is a classical value obtained by assuming that the film is isothermal and that the journal and bearing are concentric. In high speed bearings, nonuniform oil film temperatures are generated due to viscous dissipation. This paper studies the influence of the temperature profiles on the onset of instability of the film between two concentric cylinders with small diametrical clearance. Linear and exponential temperature variations of density and viscosity, respectively, are considered. Direct integration coupled with Newton’s iteration is used to solve the eigenvalue problem. Results indicate that the critical modified Reynolds number for an oil film can be lowered significantly from its classical value of 41.17. For a lubricant with a Prandtl number of 200, a modified Reynolds number of about 21 is found to be the critical value for the onset of instability. Therefore, for this type of bearing, the nature of the flow deserves careful examination before laminar flow theory can be applied to the analysis of bearing performance.