Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-27T17:45:22.168Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical study of the time-dependent viscous flow between two rotating spheres

Published online by Cambridge University Press:  28 March 2006

Carl E. Pearson
Carl E. Pearson
Affiliation:
The Boeing Company, Renton, Washington
Get access Rights & Permissions [Opens in a new window]

Abstract

An extension of numerical methods described in previous papers is used to analyse the time-dependent rotationally-symmetric motion of an incompressible viscous fluid contained between two concentric spheres having a common axis of rotation. The motion is governed by a pair of coupled non-linear partial differential equations in three independent variables, with singular end conditions. The computational process is described, and numerical solutions are presented for cases in which one (or both) of the spheres is given an impulsive change in angular velocity-starting from a state of either rest or uniform rotation. Reynolds numbers lie in the range 10-1500.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 2 , 8 May 1967 , pp. 323 - 336
Copyright
© 1967 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

Carrier, G. F. 1966 J. Fluid Mech. 24, 641.
Du Fort, E. C. & Frankel, S. P. 1953 M.T.A.C. 7, 135.
Fox, J. 1964 NASA TN D-2491.
Greenspan, H. P. 1964 J. Fluid Mech. 21, 673.
Howarth, L. 1951 Phil. Mag. Ser. 7, 42, 1308.
Lord, R. G. & Bowden, F. P. 1963 Proc. Roy. Soc. A, 271, 143.
Peaceman, D. W. & Rachford, H. H. 1955 J. Soc. Ind. App. Math. 3, 28.
Pearson, C. E. 1965a J. Fluid Mech. 21, 611.
Pearson, C. E. 1965b J. Fluid Mech. 21, 623.
Pearson, C. E. 1965c Math. of Computation, 19, 570.
Pearson, C. E. 1966 Proc. SIAM Symp. Num. Anal. (to appear).
Proudman, I. 1956 J. Fluid Mech. 1, 505.
Rosenhead, L. 1963 Laminar Boundary Layers. Oxford University Press.