Axisymmetric turbulent mass transfer in a circular tube

1969 ◽  
Vol 38 (3) ◽  
pp. 433-455 ◽  
Author(s):  
Alan Quarmby ◽  
R. K. Anand
Keyword(s):  
Mass Transfer ◽  
Velocity Profile ◽  
Circular Tube ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Eddy Diffusivities ◽  
Direct Measurements ◽  
Fluid Properties ◽  
Fully Developed Turbulent Flow ◽  
Good Agreement

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.

Non-axisymmetric turbulent mass transfer in a circular tube

1969 ◽  
Vol 38 (3) ◽  
pp. 457-472 ◽  
Author(s):  
Alan Quarmby ◽  
R. K. Anand
Keyword(s):  
Mass Transfer ◽  
Circular Tube ◽  
Eddy Diffusivity ◽  
Concentration Profiles ◽  
Tracer Gas ◽  
Direct Evaluation ◽  
Measured Concentration ◽  
Eddy Diffusivities ◽  
Fluid Properties ◽  
Fully Developed Turbulent Flow

Theory and experiment are presented for mass transfer into a fully developed turbulent flow in a plain circular tube in two non-axisymmetric cases. The cases studied are a diametral line source and a discontinuous ring source, in which there is a uniform mass flux over rectangular areas of the tube wall. A comparison is made between the concentration profiles predicted by the solutions of the diffusion equation and experiments using nitrous oxide, Schmidt number S = 0·77, as a tracer gas in air. The range of experiments covers Reynolds numbers R from 20,000 to 120,000.In the analysis, the assumption is made that the tangential and radial eddy diffusivities of mass are equal at a point. The radial diffusivity of mass, which is a function of radial position, is related to the radial eddy diffusivity of momentum by a ratio, which takes account of fluid properties and the value of the radial eddy diffusivity of momentum. The satisfactory agreement between analysis and experiment establishes the correctness of this assumption. Further confirmation was obtained by direct evaluation of the tangential eddy diffusivity of mass from the measured concentration profiles.

A Heat-Mass Transfer Analogy Applied to Fully Developed Turbulent Flow in an Annulus

1971 ◽  
Vol 13 (4) ◽  
pp. 286-292 ◽  
Author(s):  
J. S. Lewis
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Friction Factor ◽  
Heat Mass Transfer ◽  
Eddy Diffusivity ◽  
Round Tube ◽  
Fully Developed Turbulent Flow ◽  
The Difference

A heat-mass transfer analogy based on the ‘universal’ velocity profile applied to an annulus is compared with analogy values based on similar but more sophisticated expressions for the eddy diffusivity and hence velocity profile. The difference between these analogy values and those of Chilton and Colburn (I)† are noted to be appreciable and to increase with increasing Reynolds number. Heat transfer predictions from mass transfer measurements using ‘universal’ velocity profile type analogies are compared with established results. Friction factor measurements were made and found to be up to 10 per cent higher than the values for flow in a round tube at the corresponding Reynolds number.

The effects of surface topography on momentum and mass transfer in a turbulent boundary layer

1981 ◽  
Vol 108 ◽  
pp. 423-442 ◽  
Author(s):  
R. A. Dawkins ◽  
D. R. Davies
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Turbulent Boundary Layer ◽  
Theoretical Calculations ◽  
Eddy Diffusivity ◽  
Open Circuit ◽  
Applied Theory ◽  
Mean Velocity ◽  
Method Of Calculation ◽  
Good Agreement

An approximate, conveniently applied theory with corresponding experimental data is presented concerning the changes in momentum and mass transfer produced by a ridge of small slopes in a flat-surface quasi-stationary turbulent boundary layer. A first-order mean velocity perturbation solution is found to be in good agreement with measured velocities on the up-slope side of a two-dimensional ridge, of length 20 cm and height 1 cm, fixed on the floor of the working section of an open-circuit wind tunnel. A vapour-transfer eddy-diffusivity distribution is then calculated for the inner boundary-layer region and solutions of the consequent vapour-transfer equation give the variation of rate of evaporation from surfaces of varying lengths placed at different positions on the up-slope region of the ridge. Corresponding measurements are found to be in good agreement with the theoretical calculations, and show that, even over small slopes (of 1 in 10), the evaporation rate varied with position by 25% from maximum to minimum. This method of calculation is extended to examine the effect of surface curvature on diffusion of gas from an upstream line source in a turbulent boundary layer over the ridge; experimental and theoretical concentration profiles compare extremely well over the leading slope.

Heat Transfer in Turbulent Pipe Flow With Optically Thin Radiation

1969 ◽  
Vol 91 (3) ◽  
pp. 330-335 ◽  
Author(s):  
C. S. Landram ◽  
R. Greif ◽  
I. S. Habib
Keyword(s):  
Heat Transfer ◽  
Circular Tube ◽  
Constant Heat Flux ◽  
Turbulent Pipe Flow ◽  
Radiation Problem ◽  
Constant Heat ◽  
Nusselt Numbers ◽  
Fully Developed Turbulent Flow ◽  
Good Agreement

The problem considered is the determination of the heat transfer in fully developed turbulent flow of a radiating optically thin gas in a circular tube. The radiation problem is formulated in terms of the Planck mean and the modified Planck mean coefficients and the temperature profiles and Nusselt numbers have been determined. It is shown that the simple constant shear, constant heat flux formulation yields results that are in very good agreement with more complex calculations.

Heat Transfer in Two-Dimensional Turbulent Confined Flows

1972 ◽  
Vol 186 (1) ◽  
pp. 625-633
Author(s):  
A. P. Hatton ◽  
N. H. Woolley
Keyword(s):  
Prediction Method ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Turbulence Energy ◽  
Two Dimensional ◽  
Narrow Angle ◽  
Before And After ◽  
Dimensional Equation ◽  
Confined Flows ◽  
Good Agreement

Measurements of displacement and momentum thickness, friction factor and Stanton number were made in a narrow angle diverging duct consisting of two plane walls, width 0·82 m. The height of the duct varied from 0·051 to 0·152 m over a length of 3·94 m. Reynolds numbers ranged from 8·7 × 104 to 20·7 × 104. The results are compared with a prediction method using a numerical solution of the two-dimensional equation of motion and energy. An eddy diffusivity hypothesis was used, based on the turbulence energy equation and an empirical length scale distribution. Good agreement was obtained between the theoretical and experimental results, both before and after the boundary layers interfered, and with previously reported experiments in a parallel duct. It was necessary to change the value of one of the constants in the analysis for each geometry.

Turbulent Heat Transfer at Low Reynolds Numbers

1969 ◽  
Vol 91 (4) ◽  
pp. 532-536 ◽  
Author(s):  
C. J. Lawn
Keyword(s):  
Heat Transfer ◽  
Gas Flow ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Low Reynolds Numbers ◽  
Eddy Diffusivities ◽  
Uniform Wall ◽  
Uniform Wall Heat Flux

A realistic velocity profile and semiempirical values for the ratio of the eddy diffusivities of momentum and heat are used to solve the heat-balance equation for the situation of fully developed gas flow in a pipe with uniform wall heat flux. The predicted heat transfer is higher than the experimental at Reynolds numbers below 104 and this is shown to be due to the inadequacy of the simple eddy-diffusivity hypothesis.

Turbulent Flow in an Annulus

1967 ◽  
Vol 89 (1) ◽  
pp. 25-31 ◽  
Author(s):  
S. Levy
Keyword(s):  
Turbulent Flow ◽  
Tube Wall ◽  
Eddy Diffusivity ◽  
Test Results ◽  
Core Tube ◽  
The Core ◽  
Roughened Surface ◽  
Shear Mixing ◽  
Fully Developed Turbulent Flow ◽  
Good Agreement

Equations describing fully developed turbulent flow in an annulus are derived. They are based upon Reichardt’s expression for the eddy diffusivity of momentum, and they assume that the velocity profiles starting from the core tube wall and the outer tube wall have the same velocity and eddy diffusivity at the plane of zero shear. The predicted location of the plane of zero shear, mixing length, eddy diffusivity, velocity distribution, and friction factor are compared to available data and are found to give good agreement with the test results. Potential extension of the proposed method to more complex geometries is illustrated by considering the case of flow in an annulus with one artificially roughened surface.

The decay of a turbulent swirl in a pipe

1965 ◽  
Vol 22 (2) ◽  
pp. 257-271 ◽  
Author(s):  
Frank Kreith ◽  
O. K. Sonju
Keyword(s):  
Experimental Data ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Experimental Measurements ◽  
Number Range ◽  
Swirl Velocity ◽  
Linearized Theory ◽  
Flow Through ◽  
Initial Intensity ◽  
Good Agreement

This paper presents a linearized theory for the average decay of a tape-induced fully developed turbulent swirl in flow through a pipe. In the Reynolds number range between 104 and 105 the theoretical analysis was found to be in good agreement with experimental data obtained with water in a 1 in. pipe, provided the eddy diffusivity was chosen appropriately.It was observed that a turbulent swirl decays to about 10–20% of its initial intensity in a distance of about 50 pipe diameters, the decay being more rapid at smaller than at larger Reynolds numbers. The theoretical swirl velocity distribution agreed qualitatively with experimental measurements at distances less than 20 diameters downstream from the outlet of the swirl inducer, but deviated from the experimental results further downstream.

Mixing efficiency in controlled exchange flows

2008 ◽  
Vol 600 ◽  
pp. 235-244 ◽  
Author(s):  
TJIPTO PRASTOWO ◽  
ROSS W. GRIFFITHS ◽  
GRAHAM O. HUGHES ◽  
ANDREW McC. HOGG
Keyword(s):  
Turbulent Mixing ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Scaling Analysis ◽  
Stratified Turbulence ◽  
Exchange Flows ◽  
Maximum Value ◽  
Direct Measurements ◽  
Overall Efficiency ◽  
Good Agreement

Turbulence and mixing are generated by the shear between two counter-flowing layers in hydraulically controlled buoyancy-driven exchange flows through a constriction. From direct measurements of the density distribution and the amount of turbulent mixing in steady laboratory exchange flows we determine the overall efficiency of the mixing. For sufficiently large Reynolds numbers the mixing efficiency is 0.11(±0.01), independent of the aspect ratio and other details of constriction geometry, in good agreement with a scaling analysis. We conclude that the mixing in shear flows of this type has an overall efficiency significantly less than the maximum value widely proposed for stratified turbulence.

Friction Factors for Fully Developed Turbulent Flow in Ducts With and Without Heat Transfer

1964 ◽  
Vol 86 (3) ◽  
pp. 627-636 ◽  
Author(s):  
G. W. Maurer ◽  
B. W. LeTourneau
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Circular Tube ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Inlet Temperature ◽  
Equivalent Diameter ◽  
Friction Factors ◽  
Rectangular Channels ◽  
Fully Developed Turbulent Flow

Tests were performed with water flowing vertically upward through a 0.087-in. × 1-in. × 27-in. long rectangular channel to determine friction factors with and without heat transfer. The following range of variables was covered: Mass velocities: 0.60 × 106 to 4.0 × 106 lbm/hr-ft2; Heat flux: 0 to 1.6 × 106 Btu/hr-ft2; Inlet temperature: 59 to 510 deg F; Pressures: 300 to 2000 psia. The isothermal data confirmed the use of the hydraulic equivalent diameter with the conventional circular tube friction factors for narrow rectangular channels at Reynolds numbers from 4 × 103 to 5 × 105. Using the results of the heated tests and the data existing in the literature, a general correlation was formulated which correlated the data for both water and air.

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