Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-29T13:31:57.397Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on a viscous fluid flow between concentric rotating spheres

Published online by Cambridge University Press:  11 April 2006

Manfred Wimmer
Manfred Wimmer
Affiliation:
Institut für Strömungslehre und Strömungsmaschinen, Universität Karlsruhe, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Some experimental results on incompressible viscous fluid flow in the gap between two concentric rotating spheres are discussed. The flow field in the spherical gap has been studied qualitatively by flow visualization (photographs) and quantitatively by measurements by the hot-wire technique. For a wide range of Reynolds numbers, the friction torque was measured for several gap widths and a relatively simple method of determining the torque theoretically is given. At higher Reynolds numbers instabilities appear. Their different behaviour for relatively small and large gap widths is demonstrated. For the larger gap widths, the different appearance of the Taylor–Görtler vortices, the reason for their generation, their regimes of existence as well as their influence on the friction torque are thoroughly treated. Detailed information is given on the new effect of the dependence of the wavelength of the vortices on the Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 2 , 23 November 1976 , pp. 317 - 335
Copyright
© 1976 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

Brailovskaya, I. Yu., Astafeva, N. M. & Yavorskaya, I. M. 1972 Nonstationary compressible viscous fluid motion in a spherical layer Fluid Dyn. 7, 370.Google Scholar
Bratukhin, Yu. K. 1961 An estimate of critical Reynolds number for fluid flow between two rotating spherical surfaces J. Appl. Math. Mech. 25, 1286.Google Scholar
Burkhalter, J. E. & Koschmieder, E. L. 1973 Steady supercritical Taylor vortex flow J. Fluid Mech. 58, 547.Google Scholar
Burkhalter, J. E. & Koschmieder, E. L. 1974 Steady supercritical Taylor vortices after sudden starts Phys. Fluids, 17, 1929.Google Scholar
Coles, D. 1965 Transition in circular Couette flow J. Fluid Mech. 21, 385.Google Scholar
Donnelly, R. J. 1965 Experiments on the stability of viscous flow between rotating cylinders. Proc. Roy. Soc. A283, 509.
Göbtler, H. 1940 Über seine dreidimensionale Instabilität laminarer Grenzschichten an konkaveri Wänden. Nachr. Oes. Wiss. Göttingen Math. Phys. Kl. Neue Folge I, vol. 2, 1.
Khlebutin, G. N. 1968 Stability of fluid motion between a rotating and stationary concentric sphere. Fluid Dyn. 3 (6), 31.
Kirchgässner, K. 1961 Die Stabilität der Strömung zwischen zwei rotierenden Zylindern gegenüber Taylor-wirbeln für beliebige Spaltweiten Z. angew. Math. Phys. 12, 14.Google Scholar
Kotschin, N. J., Kibel, I. A. & Rose, N. W. 1955 Theoretische Hydrodynamik, vol. 2. Berlin: Akademie-Verlag.
Munson, B. R. & Joseph, D. D. 1971 Viscous incompressible flow between concentric rotating spheres. Parts 1 and 2. J Fluid Mech. 49, 289.Google Scholar
Munson, B. R. & Menguturk, M. 1975 Viscous incompressible flow between concentric rotating spheres. Part 3. J Fluid Mech. 69, 705.Google Scholar
Ovseenko, J. G. 1963 Über die Bewegung einer viskosen Flüssigkeit zwischen zwei rotierenden Kugelflächen Isv. Vuz, Math. 4, 129.
Ritter, C. F. 1973 Berechnung der zahen, inkompressiblen Strömung im Spalt zwischen zwei konzentrischen rotierenden Kugelflachen. Dissertation, Universität (TH) Karlsruhe.
Sawatzki, O. 1970 Das Strömungsfeld urn eine rotierende Kugel Acta Mechanica, 9, 159.Google Scholar
Sawatzki, O. & Ziebep, J. 1970 Das Stromfeld im Spalt zwischen zwei konzentrischen Kugelflächen, von denen die innere rotiert Acta Mechanica, 9, 13.Google Scholar
Snyder, M. A. 1969 Wave-number selection at finite amplitude in rotating Couette flow J. Fluid Mech. 35, 273.Google Scholar
Taylor, G. J. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. A 223, 289.
Wimmeb, M. 1974 Experimented Untersuchungen der Strömung im Spalt zwischen zwei konzentrischen Kugeln, die beide um einen gemeinsamen Durchmesser rotieren. Dissertation, Universität (TH) Karlsruhe.
Yakushin, V. J. 1968a Steady motion of a viscous fluid in a spherical layer. Fluid Dyn. 3 (2), 94.
Yakushin, V. J. 1968b Motion of a fluid between two rotating concentric spheres. Fluid Dyn. 3 (6), 35.
Yakushin, V. J. 1969 Stability of fluid motion in a thin spherical layer. Fluid Dyn. 4 (1), 83.
Yakushin, V. J. 1970 Stability of the motion of a liquid between two rotating concentric spheres Fluid Dyn. 5, 660.Google Scholar
Ziebep, J. & Sawatzki, O. 1970 Three-dimensional instabilities and vortices between two rotating spheres. 8th Symp. Naval Hydrodyn. (cf. Sawatzki & Zierep, 1970).Google Scholar