Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-07-08T03:45:18.407Z Has data issue: false hasContentIssue false
  • English
  • Français

Axisymmetric turbulent mass transfer in a circular tube

Published online by Cambridge University Press:  29 March 2006

Alan Quarmby  and
R. K. Anand
Alan Quarmby
Affiliation:
The University of Manchester Institute of Science and Technology
R. K. Anand
Affiliation:
Indian Institute of Technology, Delhi
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 3 , 18 September 1969 , pp. 433 - 455
Copyright
© 1969 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Azer, N. Z. & Chao, B. T. 1960 Int. J. Heat Mass Transfer, 1, 121.
Bakke, P. & Leach, S. K. 1965 Appl. Sci. Res. A, 15, 97.
Corcoran, W. H. & Page, F. 1952 Ind. Engng Chem. 44, 410.
Deissler, R. G. 1955 NACA TM 1210.
Elrod, H. G. 1957 J. Aero. Sci. 24, 468.
Fage, A. & Falkner, V. M. 1932 Proc. Roy. Soc. A, 135, 685.
Isakoff, S. E. & Drew, T. B. 1951 General Discussion on Heat Transfer. I. Mech. E.
Jenkins, R. 1951 Proc. Heat Transfer and Fluid Mechanics Inst. Stanford, California.
Lanczos, C. 1957 Applied Analysis. London: Pitman.
Leung, E. Y., Kays, W. M. & Reynolds, W. C. 1963 Int. J. Heat Mass Transfer, 6, 445.
Prandtl, L. 1933 Z. Ver. dt. Ing. 77, 105.
Quarmby, A. 1969 J. mech. Engng Sci. 2, 45.
Quarmby, A. & Anand, R. K. 1969 Chem. Engng Sci. 24, 171.
Reichardt, H. 1951 ZAMM, 31, 208.
Schlinger, W. G. & Sage, B. H. 1953 Ind. Engng Chem. 45, 659.
Sherwood, T. K. & Woertz, B. B. 1939 Am. Inst. Chem. Eng. 35, 519.
Sleicher, C. A. 1958 Trans. Am. Soc. mech. Engrs, 80, 693.
Sparrow, E. M., Hallman, J. M. & Seigel, R. 1957 Appl. Sci. Res. A, 7, 37.
Stokes, G. G. 1851 Trans. Camb. Phil. Soc. 9, 73.
Taylor, G. I. 1954 Proc. Roy. Soc. A, 223, 446.
Towle, W. L. & Sherwood, T. K. 1939 Ind. Engng Chem. 31, 457.
Van Driest, E. R. 1956 J. Aero. Sci. 23, 1007.
Von Kármán, T. 1930 Proc. 3rd Int. Congr. Appl. Mech. 1, 85.