Negative eddy diffusivities for asymmetric turbulent velocity profiles?

Abstract

Abstract-It appears from the experimental results obtained by quite a number of authors that for asymmetrie turbulent velocity profiles the locations of maximum velocity and zero shear stress are not identical. This report deals with the importance of this effect for the calculation of momentum, heat, and mass transfer in non-circular channels as well as for the discussion on universal velocity profiles. The report is providing a survey of the works referring to this effect. These informations are supplemented by unpublished results derived from the critical interpretation of measurements carried out by several authors.An empirical relation is indicated which allows to estimate the magnitude of the effect studied.

Simple method of predicting friction factors of turbulent flow in non-circular channels

“…Quarmby concludes that the results by Brighton and Jones are wrong. However, we believe the results by Brighton and Jones have been misinterpreted because of the assumption that the line of maximum velocity was identical with the line of zero shear stress [14], which results in a dependence on wall curvature of the velocity profile in the results of Brighton and Jones.…”

Heat transfer and friction coefficients for turbulent flow of air in smooth annuli at high temperatures

“…Kjellström and Hedberg showed that these two lines were not coincident in turbulent regime and in presence of central rough rods [24J, i.e, in presence of a strongly not-symmetrical velocity profile, possible also with smooth annuli with small DdD 2 ratios. This discrepancy has been investigated in more detail and confirmed by many experimental results in arecent paper of Maubach and Rehme [25]. We apply here a method suggested by K. Maubach [26J which satisfies the experiments of Kjellström and Hedberg.…”

“…To do so, it is necessary to evaluate the mean gas temperatures Tl and Tz of the two regions. We assume with Gowen and Smith [28, 29J that the temperature profiles in the two regions are x J(I;) J(;:) (from equations (25) and (26)) and q is a correction factor which will be determined by the heat balance, how explained below.…”

Turbulent flow in channels in terms of turbulent shear and normal stresses

“…The mixing length concept is subject to similar anomalies. Maubach and Rehme (1972) apparently first noted such discrepancies in the eddy viscosity in connection with flow between one rough and one smooth parallel plate. These shortcomings were, however, not recognized by earlier experimenters who determined the eddy viscosity or mixing length for annuli, or by analysts who utilized such quantities.…”

“…Although Wilke et al (1967) did not determine the location of the zero in the shear stress in their experiments with one smooth and one rough plate, they concluded retrospectively that the failure to do so was the source of the obvious discrepancies in their correlations for such data. Determinations of separate locations for the zero in the shear stress and the maximum in the velocity were accomplished for one rough and one smooth plate by Maubach and Rehme (1972) experimentally and by HanjaliC and Launder (1972a) computationally. Maubach and Rehme attempted, without great success, to construct a general correlation for the location of the zero in the shear stress as a function of the location of the maximum in the velocity for both parallel plates and annuli with both smooth and nonidentical surfaces.…”