A New Model for Transition Flow of Thin Films in Long Journal Bearings

Abstract

This paper investigates the flow of a viscous fluid in the narrow gap (C/R = 0.002 to 0.01) between two cylinders with low eccentricity ratios (ϵ ≤ 0.2), where the shaft radius is 25.4 mm (1.0 in.). The computational engine is provided by CFD-ACE+, a commercial multi-task software. Calculations show that during the Taylor vortex regime velocity profiles in the radial direction are sinusoidal, and that pressure does vary in the axial direction even for the case of the “long journal bearing” (L/D > 2). Both velocity and pressure profiles are axisymmetric and time-independent during the Taylor vortex regime for the concentric case (ϵ = 0). During the wavy vortex regime the velocities maintain their sinusoidal profiles, while pressure varies in both axial and circumferential directions. Both velocity and pressure profiles are non-axisymmetric and time-dependent. An order of magnitude analysis for the Navier-Stokes equation shows that the inertia, viscous terms, pressure, and the Reynolds stress terms are equally significant. Based on these findings, a new model for predicting the flow behavior in long journal bearing films in the transition regime (Taylor and wavy vortex regimes) is proposed and justified. The new model indicates that the velocity profiles are sinusoidal and depend on the local Reynolds number and the position in the axial direction. Unlike the modified turbulent viscosity of the most accepted models (Constantinescu, Ng-Pan, Hirs, and Gross et al.), the value of the dynamic viscosity used in the new model is kept at its laminar original value. Finally, a modified form for the Reynolds equation is proposed for the transition regime; a comparison is made between the results of this model and the four most accepted turbulence models mentioned above.