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Axisymmetric vortex breakdown with and without temperature effects in a container with a rotating lid

Published online by Cambridge University Press:  21 April 2006

Hans J. Lugt  and
Michel Abboud
Hans J. Lugt
Affiliation:
David W. Taylor Naval Ship Research and Development Center, Bethesda, MD 20084, USA
Michel Abboud
Affiliation:
Institut für Strömungslehre und Strömungsmaschinen, Universität Karlsruhe, 7500 Karlsruhe, West Germany
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Abstract

A flow circulation in a closed circular-cylindrical container is produced by a rotating lid. After a transient phase from an initial state at rest a steady-flow situation is reached for a certain parameter range. In a subspace of this parameter range an undulating meridional flow occurs that may exhibit at the axis of rotation one or several separation bubbles which are interpreted as vortex breakdown. Numerical calculations on the basis of the Navier-Stokes equations for incompressible homogeneous and Boussinesq fluids enable the study of the influence of various flow parameters on the properties of these separation bubbles. The parameters varied are the Reynolds, Prandtl, Rayleigh, and Eckert numbers together with the ratio of height to radius of the container. The numerical results are in good agreement with experiments performed by Vogel, Ronnenberg, and Escudier. The stability of the fluid motions in these experiments with respect to non-axisymmetric disturbances strongly suggests that the corresponding axisymmetric solutions of the Navier-Stokes equations are stable configurations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 179 - 200
Copyright
© 1987 Cambridge University Press

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