Axisymmetric Turbulent Boundary Layers in Zero Pressure-Gradient Flows

Abstract

An experimental and theoretical study of the axisymmetric turbulent boundary layer on circular cylinders over a range of radius Reynolds numbers Ra from 425 to 2 × 105, suggests the existence of a law of the wall in the form u* = A log Y* + B, where Y* = (uτa/ν) log (r/a). The constant A depends only on Ra while B has been found to depend on Ra as well as auτ/ν. It was observed that from the beginning of transition to turbulent flow in the boundary layer, there was a “negative wake” region in the outer part of the boundary layer which progressively disappeared as the flow was swept downstream, giving, at some station, a velocity profile (called here the “marginal profile”), which had no wake component. Further downstream, there was progressively increasing positive wake component. In these regions, it is surmized that the penetration of the viscous effect from the wall to larger distances across the boundary layer (as indicated by the absence of a constant stress layer), as well as the probable effect of viscosity in the wake portion (as in a purely axisymmetric wake), yielded similarlity of the defect (U − u)/uτ, only in terms of the quantity (ruτ/ν) for a given Ra. From a study of the rate of decrease of Cf with Rx in laminar and turbulent flows, there is reason to believe that an initially turbulent boundary layer will undergo relaminarization if Ra is less than about 15,000 which may be compared with the stability limit of 11,000 found by Rao [6].