Buoyancy-driven convection in cylindrical geometries
Buoyancy-driven convection in cylindrical geometries
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DOI：
10.1017/s0022112069001637
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发表时间：
1969-04
影响因子：
3.7
通讯作者：
S. Liang;A. Vidal;A. Acrivos
中科院分区：
文献类型：
--
作者：
S. Liang;A. Vidal;A. Acrivos
对于轴对称浮力驱动的圆柱室内对流流动，给出了含有温度相关粘性的Boussinesq方程的数值解。对于所考虑的每组边界条件，找到了两种解，一种是在单元中心有上行流动，另一种是下行流动。对于具有刚性绝缘横向边界和等温顶底面的圆柱形单元，这两个稳态Régime的存在得到了实验验证。利用摄动展开法，还证明了这些解中只有一个在亚临界区域内是稳定的。然而，这似乎局限在非常窄的瑞利数范围内，超过这个范围，根据目前所有的证据，对于发生轴对称运动的瑞利数和普朗特数值，这两种解都是同样稳定的。最后，简要地讨论了本文所考虑的问题与无限大水平范围内的热对流问题之间的某些根本区别。
Numerical solutions to the Boussinesq equations containing a temperature-dependent viscosity are presented for the case of axisymmetric buoyancy-driven convective flow in a cylindrical cell. Two solutions, one with upflow and the other with downflow at the centre of the cell, were found for each set of boundary conditions that were considered. The existence of these two steady-state régimes was verified experimentally for the case of a cylindrical cell having rigid insulating lateral boundaries and isothermal top and bottom planes. Using a perturbation expansion it is also shown that only one of these solutions remains stable in the subcritical régime. This, however, seems to be confined to a very narrow range of Rayleigh numbers, beyond which, according to all the evidence presently at hand, both solutions are equally stable for those values of the Rayleigh and Prandtl numbers for which axisymmetric motions occur. Finally, certain fundamental differences between the problem considered here and that of thermal convection in a layer of infinite horizontal extent are briefly discussed.