LAMINAR-TURBULENT VELOCITY PROFILE TRANSI-TION FOR FLOWS IN CONCENTRIC ANNULI, PARALLEL PLATES AND PIPES

Abstract

A method to predict the time-smoothed velocity profiles in the laminar-turbulent transitional region for incompressible fluid flows in smooth concentric annuli and pipes and between parallel plates is presented.
Under the assumption that the apparent viscosity is affected only by the surrounding solid wall and is expressed as a function of the n-th power of the distance between wall and noticed point and the apparent wall length, the velocity profiles are calculated numerically for various values of exponent, n, and are expressed in values relative to the cross-sectional average velocity. For each conduit flow, the relationships between exponent, n, and Reynolds number, Re, are determined by comparing the numerically calculated profiles with the experimental results.
By making use of these relationships between Re and n, the relative distribution of apparent viscosity and the relative time-smoothed velocity profile for an arbitrary Reynolds number can be predicted.