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Hartmann flow in annular channels. Part 2. Numerical solutions for low to moderate Hartmann numbers

Published online by Cambridge University Press:  29 March 2006

C. J. Apelt
C. J. Apelt
Affiliation:
University of Queensland, Brisbane, Australia
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Abstract

Flow of a conducting fluid along the annular channel between two non-conducting circular cylinders is examined by a numerical method for concentric and eccentric cases. Solutions have been obtained for Hartmann numbers ranging from 0·1 to 40 and, for some of these, details of velocity distribution and of induced current are given. The results obtained enable the development of the patterns of velocity and of current flow to be traced as the Hartmann number increases. The details of the development of the current flow patterns for eccentric cylinders are particularly interesting and are discussed in detail. At the higher values of Hartmann number studied the solutions are in excellent agreement with the results of Todd's (1967) high Hartmann number analysis and it is possible to determine at what value of Hartmann number Todd's analysis becomes applicable within a specified accuracy. The effect of eccentricity of the cylinders on the flow rate at a fixed pressure gradient is shown to diminish rapidly with increasing Hartmann number. The net flow of current around the annulus, which occurs when the cylinders are eccentric, has a maximum value for each case studied at a Hartmann number of 3, approximately.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 2 , 23 June 1969 , pp. 209 - 229
Copyright
© 1969 Cambridge University Press

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References

Benjamin, T. B. 1959 J. Fluid Mech. 6, 161.
Blackman, R. B. & Tukey, J. W. 1958 Measurements of Power Spectra from the Point of View of Communications Engineering. New York: Dover.
Bradshaw, P. 1967 J. Fluid Mech. 27, 209.
Clauser, F. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4. New York: Academic Press.
Cohen, L. S. & Hanratty, T. J. 1965 A.I.Ch.E. J. 11, 138.
Drake, R. 1967 The generation of wind waves on open channel flows. Unpublished Ph.D. dissertation, Colorado State University, Department of Civil Engineering, Fort Collins, Colorado.
Drake, R. & Plate, E. J. 1968 The generation of wind waves on open channel flows. Proc. 10th Midwestern Mechanics Conference.
Feldman, S. 1957 J. Fluid Mech. 2, 343.
Gaster, M. 1962 J. Fluid Mech. 14, 222.
Hess, G. D. 1968 Turbulent air now over small water wave. Unpublished Ph.D. dissertation, University of Washington, Seattle, Washington.
Hidy, G. M. & Plate, E. J. 1965 Phys. Fluids, 8, 1387.
Hidy, G. M. & Plate, E. J. 1966 J. Fluid Mech. 26, 651.
Hinze, J. O. 1959 Turbulence. New York: McGraw-Hill.
Keulegan, G. H. 1951 J. Natl Bur. of Standards, 46, 358.
Klebanoff, P. S. 1954 NACA T.N. 3133.
Laufer, J. 1954 NACA T.R. 1174.
Longuet-Higgins, M. S. 1952 J. Marine Res. 11, 245.
Miles, J. W. 1960 J. Fluid Mech. 8, 593.
Miles, J. W. 1962a J. Fluid Mech. 13, 433.
Miles, J. W. 1962b J. Fluid Mech. 13, 427.
Phillips, O. M. 1957 J. Fluid. Mech. 2, 417.
Phillips, O. M. 1958 J. Fluid Mech. 4, 426.
Plate, E. J. & Hidy, G. M. 1967 J. Geophys. Res. 72, 4627.
Pond, S., Stewart, R. W. & Burling, R. W. 1963 J. Atmos. Sci. 20, 319.
Sandborn, V. A. & Marshall, R. D. 1965 Local Isotropy in Wind Turbulence. TR CER-65VAS-RDM71, Civil Engineering Department, Colorado State University, Fort Collins, Colorado.
Sutherland, A. 1967 Spectral Measurements and Growth of Wind-generated Water Waves. TR 84, Department of Civil Engineering, Stanford University, Stanford, California.
Tominaga, M. 1964 Bull. Soc. Franco-Japonaise d'Oceanographie, 2, 22.
Willmarth, W. & Wooldridge, C. 1962 J. Fluid Mech. 14, 187.