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Computation of the flow between a rotating and a stationary disk

  • S. M. Roberts (a1) and J. S. Shipman (a2)

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.

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References

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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.
Bøudewadt, U. T. 1940 Die Drehströmung über festem Grunde Z. angew. Math. Mech. 20, 241.
Bulirsch, R. & Stoer, J. 1966 Numerical treatment of ordinary differential equations by extrapolation methods Numer. Math. 8, 1.
Kármán, T. Von 1921 Laminar und turbulente Reibung Z. angew. Math. Mech. 1, 233.
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.
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.
Nguyen, N. D., Ribault, J. P. & Florent, P. 1975 Multiple solutions for flow between coaxial disks J. Fluid Mech. 68, 369.
Ockendon, H. 1972 An asymptotic solution for steady flow above an infinite rotating disc with suction Quart. J. Mech. Appl. Math. 25, 291.
Roberts, S. M. & Shipman, J. S. 1967 Continuation in shooting methods for two-point boundary value problems J. Math. Anal. Appl. 18, 45.
Roberts, S. M. & Shipman, J. S. 1968 Justification for the continuation method in two-point boundary value problems J. Math. Anal. Appl. 21, 23.
Roberts, S. M. & Shipman, J. S. 1972 Two-point Boundary Value Problems: Shooting Methods. Elsevier.
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Supplementary materials

Roberts and Shipman supplementary material
Supplementary Table S1-S5

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Computation of the flow between a rotating and a stationary disk

  • S. M. Roberts (a1) and J. S. Shipman (a2)

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