Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T13:05:25.997Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymmetric flow between parallel rotating disks

Published online by Cambridge University Press:  20 April 2006

C.-Y. Lai ,
K. R. Rajagopal  and
A. Z. Szeri
C.-Y. Lai
Affiliation:
Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261
K. R. Rajagopal
Affiliation:
Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261
A. Z. Szeri
Affiliation:
Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261
Get access Rights & Permissions [Opens in a new window]

Abstract

Flows occurring between parallel rotating disks have recently been generalized by Parter & Rajagopal (1984) to include solutions that are not axisymmetric. They prove existence, whereas in the present paper we report, for the first time, numerical results for two cases: (i) rotation about a common axis, and (ii) rotation about distinct axes. Calculations were performed for two values of the Ekman number E = v/d2ω at the relative disk rotations of s = 0·8, s = 0 and s = −0·25, where s = ω2/ω1.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 146 , September 1984 , pp. 203 - 225
Copyright
© 1984 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

Abbot, T. N. & Walters, K. 1970 Rheometrical flow systems. Part 2. Theory of the orthogonal rheometer, including an exact solution of the Navier-Stokes equations. J. Fluid Mech. 40, 205–213.Google Scholar
Adams, M. L. & Szeri, A. Z. 1982 Incompressible flow between finite disks. Trans. ASME E: J. Appl. Mech. 49, 1–14.Google Scholar
Batchelor, G. K. 1951 Note on a class of solutions of the Navier-Stokes equations representing rotationally symmetric flow. Q. J. Appl. Maths 4, 29–41.Google Scholar
Berker, R. 1936 Sur Quelques cas d'Integration des Equations du Mouvement d'un Fluide Visqueux Incompressible. Lille, Paris.
Berker, R. 1979 A new solution of the Navier-Stokes equation for the motion of a fluid contained between two parallel planes rotating about the same axis. Arch. Mech. Stosowanej 31, 265–280.Google Scholar
de Boor, C. 1978 A Practical Guide to Splines. Springer.
Dijkstra, D. & van Heijst, G. J. F. 1983 The flow between finite rotating disks enclosed by a cylinder. J. Fluid Mech. 128, 123–154.Google Scholar
Greenspan, D. 1972 Numerical studies of flow between rotating coaxial disks. J. Inst. Maths Applies 9, 370–377.Google Scholar
Holodniok, M., Kubíček, M. & Hlav´ček, V. 1977 Computation of the flow between two rotating coaxial disks. J. Fluid Mech. 81, 680–699.Google Scholar
Holodniok, M., Kubíček, M. & Hlav´ček, V. 1981 Computation of the flow between two rotating coaxial disks: multiplicity of steady-state solutions. J. Fluid Mech. 108, 227–240.Google Scholar
K´rm´n, T. von 1921 Über laminare und turbulente Reibung. Z. angew. Math. Mech. 1, 233.Google Scholar
Keller, H. B. & Szeto, R. K.-H. 1983 Calculation of flows between rotating disks. Unpublished.
Lance, G. N. & Rogers, M. H. 1961 The axially symmetric flow of viscous fluid between two infinite rotating disks. Proc. R. Soc. Lond. A 266, 109–121.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, 95–112.Google Scholar
Nguyen, N. D., Ribault, J. P. & Florent, P. 1975 Multiple solutions for flow between coaxial disks. J. Fluid Mech. 68, 369–388.Google Scholar
Parter, S. V. 1982 On the swirling flow between coaxial disks: A survey. In Theory and Applications of Singular Perturbations. Lecture Notes in Mathematics, vol. 942. Springer.
Parter, S. V. & Rajagopal, K. R. 1984 Swirling flow between rotating plates. Arch. Rat. Mech. Anal. (in press).Google Scholar
Pearson, C. E. 1965 Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks. J. Fluid Mech. 21, 623–633.Google Scholar
Rajagopal, K. R. 1981 Flow of a second order fluid between rotating parallel plates. J. Non-Newt. Fluid Mech. 9, 185–190.Google Scholar
Rajagopal, K. R. 1982 On the flow of a simple fluid in an orthogonal rheometer. Arch. Rat. Mech. Anal. 79, 29–47.Google Scholar
Rajagopal, K. R. 1984 A class of exact solutions to the Navier-Stokes equations. Intl J. Engng Sci. 22, 451–458.Google Scholar
Rajagopal, K. R. & Gupta, A. S. 1981 Flow and stability of a second grade fluid between two rotating parallel plates. Arch. Mech. Stosowanej 33, 663–674.Google Scholar
Roberts, S. M. & Shipman, J. S. 1976 Computation of the flow between a rotating and a stationary disk. J. Fluid Mech. 73, 53–63.Google Scholar
Szeri, A. Z. & Giron, A. 1984 Stability of flow over an infinite rotating disk. Numer. Meth. Fluids (in press).Google Scholar
Szeri, A. Z., Giron, A., Schneider, S. J. & Kaufman, H. N. 1983a Flow between rotating disks. Part 2. Stability. J. Fluid Mech. 134, 133–154.Google Scholar
Szeri, A. Z., Giron, A., Schneider, S. J. & Kaufman, H. N. 1983b Flow between rotating disks. Part 1. Basic flow. J. Fluid Mech. 134, 103–131.Google Scholar
Wilson, L. O. & Schryer, N. L. 1978 Flow between a stationary and a rotating disk with suction. J. Fluid Mech. 85, 579–496.Google Scholar