Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T10:15:14.371Z Has data issue: false hasContentIssue false
  • English
  • Français

The axial flow of a Bingham plastic in a narrow eccentric annulus

Published online by Cambridge University Press:  26 April 2006

I. C. Walton  and
S. H. Bittleston
I. C. Walton
Affiliation:
Schlumberger Cambridge Research, Madingley Road, Cambridge CB3 OEL, UK
S. H. Bittleston
Affiliation:
Schlumberger Cambridge Research, Madingley Road, Cambridge CB3 OEL, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper describes analytical and numerical solutions for the flow of a Bingham plastic in an eccentric annulus. Analytical solutions are obtained by expanding in powers of δ, the ratio of the difference in radii of the bounding cylinders to their mean. The solution over most of the annulus is similar to that in a slot of uniform width, containing a central plug-like region over which the velocity is independent of the radial variable. However, unlike the uniform-slot solution, the velocity in the plug varies around the annulus and the stress exceeds the yield stress. This simple structure is supplemented by true plugs (over which the velocity is constant and the stress is below the yield stress) at the widest and, in some cases, the narrowest parts of the annulus. A simple criterion is given for conditions under which the fluid ceases to flow on the narrow side and bounds are obtained for the extent of the motionless region and for the true plugs.

The predictions of the theory have been compared to numerical results over a wide range of eccentricities, radius ratios, fluid properties and flow parameters. Good quantitative agreement has been reached for radius ratios in excess of about 0.7. In particular the extent and location of pseudo-plugs and true plugs are confirmed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 39 - 60
Copyright
© 1991 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

Bercovier, M. & Englbman, M., 1980 A finite element method for incompressible non-Newtonian flows. J. Comput. Phys. 36, 313–326.Google Scholar
Beris, A. N., Tsamopoulos, J. A., Armstrong, R. C. & Brown, R. A., 1985 Creeping motion of a sphere through a Bingham plastic. J. Fluid Mech. 158, 219–244.Google Scholar
Bird, R. B., Dai, G. C. & Yarusso, B. J., 1983 The rheology and flow of viscoplastio materials. Rev. Chem. Engng 1, 36–69.Google Scholar
Crochet, M. J., Davies, A. R. & Walters, K., 1984 Numerical Simulation of Non-Newtonian Flow. Elsevier.
Gartling, D. K. & Phan-Thien, N. 1984 A numerical simulation of a plastic fluid in a parallelplate plastometer. J. Non-Newtonian Fluid Mech. 14, 347–360.Google Scholar
Guckes, T. L.: 1975 Laminar flow of non-Newtonian fluid in an eccentric annulus. Trans. ASME B: J. Engng Indust. 97, 498–506.Google Scholar
Hill, R.: 1950 The Mathematical Theory of Plasticity. Oxford University Press.
Iyoho, A. W. & Azar, J. J., 1980 An accurate slot flow model for non-Newtonian fluid flow through eccentric annuli. Paper SPE 9447 Presented at the 55th Annual Technical Conf., Dallas.Google Scholar
Lipscombe, G. G. & Denn, M. M., 1984 Flow of Bingham fluids in complex geometries. J. Non-Newtonian Fluid Mech. 14, 337–346.Google Scholar
Mitsuishi, N. & Aoyagi, Y., 1973 Non-Newtonian fluid flow in an eccentric annulus. J. Chem. Engng Japan 6, 402–408.Google Scholar
O'Donovan, E. J. & Tanner, R. I. 1984 Numerical study of the Bingham squeeze film problem. J. Non-Newtonian Fluid Mech. 15, 75–83.Google Scholar
Snyder, W. T. & Goldstein, G. A., 1965 An analysis of fully developed flow in an eccentric annulus. AIChEJ. 11, 462–467.Google Scholar