Turbulent Flow with the Inner Cylinder Rotating

Abstract

The dissipation theorem does a respectable job of describing turbulent mass transfer in the rotating-cylinder system, although parameters still need to be obtained by fitting against experimental data. Unfortunately the available experimental data show discrepancies that hamper theoretical development. This is part of a long-range program to compare the predictions of the dissipation theorem to systems ranging from pipe flow and rotating cylinders to developing flows on a rotating disk and on a flat plate at zero incidence, where extensive experimental data exist. One learns that values of the eddy viscosity should superpose after dividing by the stress parameter R⁺ in order to obtain coherent behavior at very large Reynolds numbers. One innovation here is to use the mass-transfer data as a proxy for the absence of torque data. One finds that the data of Eisenberg and of Mohr do not constitute a single coherent data set even though they were obtained on the same apparatus and with the same chemical system. New experimental data are needed to resolve these discrepancies. The dissipation theorem is supposed to enhance our understanding of turbulence and permit prediction of the behavior of turbulence in a variety of systems. The next step is to apply it to developing flows on a flat plate and a rotating disk.