Analysis of Transitional and Fully Turbulent Plane Couette Flow

Abstract

The two-dimensional, incompressible, fully-developed, turbulent plane Couette flow is a limiting case of circular Couette flow. As such, plane Couette flow analyses have been used in lubrication theory to analyze the lubrication flow in an unloaded journal bearings. A weakness of existing analyses, other than the turbulent burst analysis, is that they are not capable of characterizing the transitional turbulent regime. The objective of the proposed paper is to develop a model of the turbulent burst phenomenon for momentum in transitional turbulent and fully turbulent plane Couette flow. Model closure is obtained by specification of the mean turbulent burst frequency and, for moderate to high Reynolds numbers, by interfacing with classical eddy diffusivity models for the turbulent core. The analysis is shown to produce predictions for the mean velocity profile and friction factor that are in good agreement with published experimental data for transitional turbulent and fully turbulent flow. This approach to modeling the wall region involves a minimum level of empiricism and provides a fundamental basis for generalization. The use of the present analysis extends the applicability of plane Couette flow analysis in lubrication problems to the transitional turbulent regime.