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Numerical simulation of cellular convection in air

Published online by Cambridge University Press:  29 March 2006

N. F. Veltishchev  and
A. A. Zelnin
N. F. Veltishchev
Affiliation:
Hydrometeorological Centre of the U.S.S.R., Moscow
A. A. Zelnin
Affiliation:
Hydrometeorological Centre of the U.S.S.R., Moscow
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Abstract

Three-dimensional convection in a Boussinesq fluid confined between horizontal rigid boundaries is studied in a series of numerical experiments. Convection in air, whose Prandtl number Pr = 0·71, is systematically investigated, together with another model for Pr = 1. Convection with a steadily changing mean temperature is also considered. Two-dimensional rolls over the Rayleigh number range 4500 [les ] Ra [les ] 24000 and three-dimensional flow patterns over the range 26000 [les ] Ra ≤ 32000 are shown to be stable in air when the mean temperature of the layer is constant ($\partial \overline{T}/\partial t = \eta = 0$). Discrete changes in the slope of the heat-flux curve are shown to exist in the ranges \[ 7000\leqslant Ra\leqslant 8000,\quad 12000\leqslant Ra\leqslant 14000\quad{\rm and}\quad 24000\leqslant Ra\leqslant 26000 \] in air. Only the last discrete transition in the heat flux is asSociated with a significant transition in the flow pattern. Two-dimensional rolls with a horizontally asymmetric distribution of upward and downward motions over the range 4500 [les ] Ra [les ] 8000, and three-dimensional flow patterns over the range 10 000 [les ] Ra [les ] 20 000 are shown to be stable when the mean temperature varies with time. The circulation in a three-dimensional cell depends on the sign of the mean temperature change: downward motions occupy the centre of the cell when $\partial\overline{T}/\partial t > 0$, and upward motions when $\partial\overline{T}/\partial t < 0 $. Motions start to be time dependent for Ra > 20000. Transitions in the planform are asSociated with discrete changes in the slope of the heat-flux curve. Transitions in both the heat flux and flow pattern depend quantitatively on the Prandtl number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 2 , 25 March 1975 , pp. 353 - 368
Copyright
© 1975 Cambridge University Press

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