Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-19T12:45:40.168Z Has data issue: false hasContentIssue false
  • English
  • Français

On the flow of a rotating mixture in a sectioned cylinder

Published online by Cambridge University Press:  21 April 2006

A. A. Dahlkild  and
H. P. Greenspan
A. A. Dahlkild
Affiliation:
Royal Institute of Technology, Department of Hydromechanics, 100 44 Stockholm, Sweden
H. P. Greenspan
Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA 02139, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the centrifugal separation of an initially homogeneous mixture in an asymmetric geometry. The mixture is shown to acquire a uniform and negative relative vorticity, manifested as a retrograde circulation, as the heavier phase is forced outwards by the centrifugal acceleration. The perturbation theory formulated accounts for inertial effects and endwall boundary layers as well as slight deviations of endwall shape from a level plane. The time-dependent separation process is described and the flow field, including kinematic shocks, is calculated in some cases of technological interest.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 198 , January 1989 , pp. 155 - 175
Copyright
1989 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

Amberg, G., Dahlkild, A. A., Bark, F. H. & Henningson, D. S., 1986 On time-dependent settling of a dilute suspension in a rotating conical channel. J. Fluid Mech. 166, 473–502Google Scholar
Amberg, G. & Greenspan, H. P., 1987 Boundary layers in a sectioned centrifuge. J. Fluid Mech. 181, 77–97.Google Scholar
Greenspan, H. P.: 1968 The Theory of Rotating Fluids. Cambridge University Press.
Greenspan, H. P.: 1983 On centrifugal separation of a mixture. J. Fluid Mech. 127, 91–101Google Scholar
Greenspan, H. P.: 1988 On the vorticity of a rotating mixture. J. Fluid Mech. 191, 517–528Google Scholar
Geenspan, H. P. & Ungarish, M., 1985a On the enhancement of centrifugal separation. J. Fluid Mech. 157, 359–373.Google Scholar
Greenspan, H. P. & Ungarish, M., 1985b On the centrifugal separation of a bulk mixture. Intl. J. Multiphase Flow 11, 825–836.Google Scholar
Ishii, M.: 1975 Thermo-Fluid Dynamic Theory of Two-Phase Flow.Paris: Eyrolles.
Kynch, G. J.: 1952 A theory of sedimentation. Trans. Faraday Soc. 48, 166–176.Google Scholar
Schaflinger, U., Köppl, A. & Filipczak, G.1986 Sedimentation in cylindrical centrifuges with compartments. Ing. Arch. 56, 321.Google Scholar
Schneider, W.: 1982 Kinematic-wave theory of sedimentation beneath inclined walls. J. Fluid Mech. 120, 323–346.Google Scholar
Ungarish, M.: 1986 Flow of a separating mixture in a rotating cylinder. Phys. Fluids 29, 640–646.Google Scholar
Ungarish, M.: 1988 Two-fluid analysis of centrifugal separation in a finite cylinder. Intl J. Multiphase Flow (to appear).Google Scholar