Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T07:29:11.818Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow between rotating disks. Part 1. Basic flow

Published online by Cambridge University Press:  20 April 2006

A. Z. Szeri ,
S. J. Schneider ,
F. Labbe  and
H. N. Kaufman
A. Z. Szeri
Affiliation:
Department of Mechanical Engineering, The University of Pittsburgh, Pittsburgh, PA 15261
S. J. Schneider
Affiliation:
Department of Mechanical Engineering, The University of Pittsburgh, Pittsburgh, PA 15261
F. Labbe
Affiliation:
Department of Mechanical Engineering, The University of Pittsburgh, Pittsburgh, PA 15261
H. N. Kaufman
Affiliation:
Department of Mechanical Engineering, The University of Pittsburgh, Pittsburgh, PA 15261 Research and Development Center, Westinghouse Electric Co., Beulah Rd, Pittsburgh PA 15235
Get access Rights & Permissions [Opens in a new window]

Abstract

Laser-Doppler velocity measurements were obtained in water between finite rotating disks, with and without throughflow, in four cases: ω1 = ω2 = 0; ω2/ω1 = −1; ω2/ω1 = 0; ω2/ω1 = 1. The equilibrium flows are unique, and at mid-radius they show a high degree of independence from boundary conditions in r. With one disk rotating and the other stationary, this mid-radius ‘limiting flow’ is recognized as the Batchelor profile of infinite-disk theory. Other profiles, predicted by this theory to coexist with the Batchelor profile, were neither observed experimentally nor were they calculated numerically by the finite-disk solutions, obtained here via a Galerkin, B-spline formulation. Agreement on velocity between numerical results and experimental data is good at large values of the ratio RQ/Re, where RQ = Q/2πνs is the throughflow Reynolds number and Re = R22ω/ν is the rotational Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 134 , September 1983 , pp. 103 - 131
Copyright
© 1983 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

Adams, M. L. & Szeri, A. Z. 1982 Incompressible flow between finite disks. Trans. ASME E: J. Appl. Mech. 49, 1–14.
Batchelor, G. K. 1951 Note on a class of solutions of the Navier-Stokes equations representing rotationally symmetric flow Q. J. Mech. Appl. Maths 4, 29.Google Scholar
Deboor, C. 1978 A Practical Guide to Splines. Springer.
Dijkstra, D. 1980 On the relation between adjacent inviscid cell type solutions to the rotating-disk equations J. Engng Maths 14, 133–154.Google Scholar
Gregory, N., Stuart, J. T. & Walker, W. S. 1955 On the stability of three dimensional boundary layers with application to the flow due to a rotating disk Phil. Trans. R. Soc. Lond. A248, 155.Google Scholar
Hall, C. A. 1968 On error bounds for spline interpolation J. Approx. Theory 1, 209–218.Google Scholar
Holodniok, M., Kubicek, M. & Hlavacek, V. 1977 Computation of the flow between two rotating coaxial disks J. Fluid Mech. 81, 680–699.Google Scholar
Holodniok, M., Kubicek, M. & Hlavacek, V. 1981 Computation of the flow between two rotating coaxial disks: multiplicity of steady-state solutions. J. Fluid Mech. 108, 227–240.Google Scholar
Kármán, T. VON 1921 Laminar und turbulente Reibung Z. angew. Math. Mech. 1, 233.Google Scholar
Kreith, F. 1965 Reverse transition in radial source flow between two parallel plates Phys. Fluids 8, 1189–1190.Google Scholar
Labbe, F. 1981 Computation of stationary laminar solutions of flow between finite rotating disks. Ph.D. thesis, University of Pittsburgh.
Lance, G. N. & Rogers, M. H. 1961 The axially symmetric flow of viscous fluid between two infinite rotating disks Proc. R. Soc. Lond. A266, 109–121.Google Scholar
Lentini, M. & Keller, H. B. 1980 The von Kármán swirling flows SIAM J. Appl. Maths 38, 52–63.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
Rogers, M. H. & Lance, G. N. 1960 The rotationally symmetric flow of a viscous fluid in the presence of an infinite disk J. Fluid Mech. 7, 617–631.Google Scholar
Rudd, M. J. 1969 A new theoretical model for the laser Doppler-meter. J. Phys. E: Sci. Instr. 2, 55–63.Google Scholar
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Schneider, S. J. 1982 Flow between finite rotating disks: an experimental study of the basic motion and stability. Ph.D. thesis, University of Pittsburgh.
Stewartson, K. 1953 On the flow between two rotating co-axial disks Proc. Camb. Phil. Soc. 3, 333–341.Google Scholar
Szeri, A. Z. & Adams, M. L. 1978 Laminar throughflow between closely spaced rotating disks J. Fluid Mech. 86, 1–14.Google Scholar
Szeri, A. Z., Giron, A., Schneider, S. J. & Kaufman, H. N. 1983 Flow between rotating disks. Part 2. Stability J. Fluid Mech. 134, 133–154.Google Scholar
Weidman, P. D. & Redekopp, L. G. 1975 On the motion of a rotating fluid in the presence of an infinite rotating disk. In Proc. 12th Biennial Fluid Dyn. Symp., Bialowicza, Poland.Google Scholar
Wilson, L. O. & Schryer, N. L. 1978 Flow between a stationary and a rotating disk with suction J. Fluid Mech. 85, 479–496.Google Scholar
Yeh, Y. & Cummins, H. Z. 1964 Localized fluid flow measurements with an He-Ne laser spectometer Appl. Phys. Lett. 4, 176–184.Google Scholar
Zandbergen, P. J. & Dijkstra, D. 1977 Non-unique solutions of the Navier-Stokes equations for the Kármán swirling flow J. Engng Maths 11, 167–188.Google Scholar