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Computation of the flow between a rotating and a stationary disk

Published online by Cambridge University Press:  29 March 2006

S. M. Roberts
Affiliation:
IBM General Products Division, Palo Alto, California 94304
J. S. Shipman
Affiliation:
IBM Federal Systems Division, Gaithersburg, Maryland 20760

Abstract

A numerical exploration of multiple-cell solutions for the flow between a rotating and a stationary disk is carried out systematically by the continuation method. The paper confirms and extends the work of Mellor, Chapple & Stokes. The results include the discovery of one-, two-, three- and five-cell solution regions which have not been reported before.

Type
Research Article
Copyright
© 1976 Cambridge University Press

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References

Batchelor, G. K. 1951 Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow Quart. J. Mech. Appl. Math. 4, 29.Google Scholar
Bøudewadt, U. T. 1940 Die Drehströmung über festem Grunde Z. angew. Math. Mech. 20, 241.Google Scholar
Bulirsch, R. & Stoer, J. 1966 Numerical treatment of ordinary differential equations by extrapolation methods Numer. Math. 8, 1.Google Scholar
Kármán, T. Von 1921 Laminar und turbulente Reibung Z. angew. Math. Mech. 1, 233.Google Scholar
Lance, G. N. & Rogers, M. H. 1962 The axial symmetric flow of a viscous fluid between two infinite rotating disks. Proc. Roy. Soc. A 266, 109.Google Scholar
Mellor, G. L., Chapple, P. J. & Stokes, V. K. 1968 On the flow between a rotating and a stationary disk J. Fluid Mech. 31, 95.Google Scholar
Nguyen, N. D., Ribault, J. P. & Florent, P. 1975 Multiple solutions for flow between coaxial disks J. Fluid Mech. 68, 369.Google Scholar
Ockendon, H. 1972 An asymptotic solution for steady flow above an infinite rotating disc with suction Quart. J. Mech. Appl. Math. 25, 291.Google Scholar
Roberts, S. M. & Shipman, J. S. 1967 Continuation in shooting methods for two-point boundary value problems J. Math. Anal. Appl. 18, 45.Google Scholar
Roberts, S. M. & Shipman, J. S. 1968 Justification for the continuation method in two-point boundary value problems J. Math. Anal. Appl. 21, 23.Google Scholar
Roberts, S. M. & Shipman, J. S. 1972 Two-point Boundary Value Problems: Shooting Methods. Elsevier.
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Roberts and Shipman supplementary material

Supplementary Table S1-S5

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