Skip to main content
×
Home
    • Aa
    • Aa

Computation of the flow between two rotating coaxial disks

  • M. Holodniok (a1) (a2), M. Kubicek (a1) and V. Hlavácek (a1)
Abstract

A numerical investigation of the problem of rotating disks is made using the Newton–Raphson method. It is shown that the governing equations may exhibit one, three or five solutions. A physical interpretation of the calculated profiles will be presented. The results computed reveal that both Batchelor and Stewartson analysis yields for high Reynolds numbers results which are in agreement with our observations, i.e. the fluid may rotate as a rigid body or the main body of the fluid may be almost at rest, respectively. Occurrence of a two-cell situation at particular branches will be discussed.

Copyright
References
Hide All
Batchelor, G. K. 1951 Note on a class of solution of the Navier — Stokes equations representing rotationally symmetric flow. Quart. J. Mech. Appl. Math. 4, 29.
Bellman, R. E. & Kalaba, R. E. 1965 Quasilinearization and boundary value problems. Rep. Rand. Corp., Santa Monica, California no. R-438-PR.
Greenspan, D. 1972 Numerical studies of flow between rotating coaxial disks. J. Inst. Math. Appl. 9, 370.
Kármán, T. Von 1921 Laminar und turbulente Reibung. Z. angew. Math. Mech. 1, 233.
KubÍČEk, M. 1973 Algorithm 470. Linear systems with almost tridiagonal matrix. Comm. A.C.M. 16, 760.
KubÍČEk, M. & Hlaváček, V. 1975 Evaluation of branching points based on the differentiation with respect to boundary conditions. Chem. Engng Sci. 30, 1439.
KubÍČEk, M., Holodniok, M. & Hlaváček, V. 1976 Calculation of flow between two rotating coaxial disks by differentiation with respect to an actual parameter. Comp. Fluids 4, 59.
KubÍČEk, M., Holodniok, M. & Hlaváček, V. 1977 Problem of a flow of an incompressible viscous fluid between two rotating disks solved by one-parameter imbedding techniques. J. Comp. Phys. (to appear).
Lance, G. N. & Rogers, M. H. 1962 The axially 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.
Osborne, M. R. 1969 On shooting methods for boundary value problems. J. Math. Anal. Appl. 27, 417.
Pearson, C. E. 1965 Numerical solutions of the time-dependent viscous flow between rotating coaxial disks. J. Fluid Mech. 21, 623.
Roberts, S. M. & Shipman, J. S. 1976 Computation of the flow between a rotating and a stationary disk. J. Fluid Mech. 73, 53.
Stewartson, K. 1953 On the flow between two rotating coaxial disks. Proc. Camb. Phil. Soc. 49, 333.
Well, K. H. 1972 Note on a problem by Lance and a problem by Bellman. J. Math. Anal. Appl. 40, 258.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 31 *
Loading metrics...

Abstract views

Total abstract views: 97 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th October 2017. This data will be updated every 24 hours.