Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T15:06:38.216Z Has data issue: false hasContentIssue false
  • English
  • Français

Capsular flow in pipelines

Published online by Cambridge University Press:  29 March 2006

A. E. Vardy ,
M. I. G. Bloor  and
J. A. Fox
A. E. Vardy
Affiliation:
Department of Civil Engineering, University of Leeds
M. I. G. Bloor
Affiliation:
Department of Applied Mathematics, University of Leeds
J. A. Fox
Affiliation:
Department of Civil Engineering, University of Leeds
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem considered is that of the steady motion of a series of neutrally buoyant, flat-faced, rigid, cylindrical capsules along the axis of a pipeline under the influence of a hydraulic pressure gradient. The Navier-Stokes equations are non-dimensionalized and expressed in central-difference form. Numerical solutions are found by the method of relaxation for Reynolds numbers up to 20 000 and a close agreement is obtained with readings from a laboratory apparatus for Reynolds numbers up to 2200.

The flow is examined in detail and the existence of toroidal vortices between successive capsules is demonstrated. Their shape is shown to be increasingly influenced by inertial forces as the Reynolds number increases, but the overall pressure gradient is not greatly dependent on the Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 1 , 14 November 1972 , pp. 49 - 59
Copyright
© 1972 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

Bloor, M. I. G. 1968 Phys. Med. Biol. 13, 443.
Brenner, H. 1970 J. Fluid Mech. 43, 641.
Bugliarello, G. & Hsiao, G. C. 1970 Biorheology, 7, 5.
Burggraf, O. R. 1966 J. Fluid Mech. 24, 113.
Bye, J. A. T. 1966 J. Fluid Mech. 26, 577.
Charles, M. E. 1963 Can. J. Chem. Eng. 41, 46.
Chen, T. C. & Skalak, R. 1970 Appl. Sci. Res. 22, 403.
Duda, J. L. & Vrentras, J. S. 1971a J. Fluid Mech. 45, 247.
Duda, J. L. & Vrentras, J. S. 1971 B J. Fluid Mech. 45, 261.
Fox, J. A. & Henson, D. A. 1969 The Engineer, 229, 53.
Hochmuch, R. M. & Sutera, S. P. 1970 Chem. Eng. Sci. 25, 593.
Kennedy, R. J. 1966 Can. J. Chem. Eng. 44, 354.
Lew, H. S. & Fung, Y. C. 1969 Biorheology, 6, 109.
Lighthill, M. J. 1968 J. Fluid Mech. 34, 113.
Moffatt, H. K. 1964 J. Fluid Mech. 18, 1.
Newton, R., Redberoer, P. J. & Round, G. F. 1964 Can. J. Chem. Eng. 42, 168.
Rayleigh, Lord 1920 Scientific Papers, vol. 6, p. 18. Cambridge University Press.
Runchal, A. K. & Wolfshtein, M. 1969 J. Mech. Eng. Sci. 11, 445.
Vardy, A. E. 1971 Ph.D. thesis, University of Leeds.
Wang, H. & Shalak, R. 1969 J. Fluid Mech. 38, 75.
Weiss, R. F. & Florsheim, B. H. 1965 Phys. Fluids, 8, 1631.