Axisymmetric turbulent mass transfer in a circular tube

Abstract

Solutions of the diffusion equation are obtained for mass transfer in a fully developed turbulent flow in a plain circular tube in two axisymmetric situations. The cases studied are a point source positioned at the centre of the tube and a ring source in the tube wall in which there is a uniform mass flux along a short length of the tube. The purpose of the work is to establish the correctness of the descriptions of the velocity profile and radial eddy diffusivities of mass and momentum in order to provide a firm base from which consideration of the non-axisymmetric situation could proceed.The turbulent velocity profile is deduced from a two-part model based on a sublayer profile and the Von Kármán similarity hypothesis. The radial eddy diffusivity of momentum is described by an expression due to Reichardt and Van Driest and from this the radial eddy diffusivity of mass as a function of radius is obtained by use of a ratio which takes account of fluid properties and the value of the radial eddy diffusivity.The analysis is substantiated by experiments carried out with nitrous oxide, Schmidt number = 0·77, for Reynolds numbers from 20,000 to 130,000. The concentration profiles measured at several axial positions downstream from the source are in good agreement with the analytical solutions in both cases. Direct measurements of the eddy diffusivity of mass and momentum were obtained as added confirmation and also gave good agreement with the theory.

Experimental Determination of the Turbulent Prandtl Number in a Developing Temperature Boundary Layer

“…Quarmby and Amand [161,162] and Goldman and Marchello [163] have recently published some experimental results for the turbulent Schmidt number.…”

Mixing Characterization of Transient Puffs in a Rotary Kiln Incinerator

“…Kerstein (1992aKerstein ( , 1989 derived that in homogeneous turbulence the diffusivity due to block inversions is higher by a factor of (27/12); in inhomogeneous turbulence, there may not be a constant factor. (3) In the wall region, the experiments of Durbin and Frost (1981) suggest a higher turbulent diffusivity than those of Quarmby and Anand (1969). The reason for this is unclear.…”

“…The group at Louisiana State University (Lester et al, 1990) called for "more understanding of the large mixing phenomena in the kiln", suggesting that .lImixing of relatively cooler gases from the bottom half of the kiln may have an inhibiting effect on waste destruction et al (1990), in evaluating their model said that lIultimately, mixing in the gas phase in the kiln environment must also be considered (Sherwood and Woertz, 1939), nitrous oxide (Quarmby and Anand, 1969;Sheriff and O'Kane, 1971), and other contaminants. (2) Temperature can be used as a scalar (provided the temperature differences are not so large that they interact with the fluid dynamics) and can be measured with thermo-couples (Bremhorst and Bullock, 1973;Hishida and Nagano, 1979;Durbin and Frost, 1981).…”

“…Average heat and mass transfer in fully developed turbulent pipe flow (and channel flow) have been researched extensively, both experimentally and theoretically, e.g. Sherwood and Woertz (1939), Quarmby and Anand (1969), Hughmark (1971), Sheriff and O'Kane (1971), Sandall et al (1980). The general approach in all these studies is to use a turbulent diffusivity, or an effective heat or mass transfer coefficient, to calculate the average scalar profile.…”

“…Even though more accurate models are available (Quarmby and Anand, 1969;Sandall et a/., 1980), this model was chosen because of its simplicity, facilitating derivation of the eddy frequency in the linear eddy model.…”