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Three-dimensional numerical simulation of buoyancy-driven convection in vertical cylinders heated from below

Published online by Cambridge University Press:  26 April 2006

G. Neumann
G. Neumann
Affiliation:
Institut für Werkstoffwissenschaften VI, Universität Erlangen-Nürnberg, Martensstraße 7, D-8520 Erlangen, FRG Present address: Fraunhofer-Institut für Angenwandte Festkörperphysik, Eckerstraße 4, D-7800 Freiburg, FRG
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Abstract

Steady and oscillatory convection in rigid vertical cylinders heated from below studied by means of a numerical solution of the three-dimensional, time-dependent Boussinesq equations. Both adiabatic and ideal conducting sidewalls are considered. The effect of the geometry of the container on the onset of convective instability and the structure and symmetry of the flow are analysed and compared with the results of linear stability theories. The nonlinear evolution and stability of convective flows at Rayleigh numbers beyond the critical number for the onset of convective motion are investigated for Prandtl numbers of 0.02 to 6.7. The limits of stable axisymmetric solutions are an important finding of this study. The onset and the frequency of oscillatory instability are calculated for the small Prandtl number 0.02 and compared with experimental data. Calculated stream patterns and velocity profiles illustrate the three-dimensional structure of steady convection and the time-dependent behaviour of oscillatory flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 559 - 578
Copyright
© 1990 Cambridge University Press

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