Three-dimensional numerical simulation of buoyancy-driven convection in vertical cylinders heated from below
Three-dimensional numerical simulation of buoyancy-driven convection in vertical cylinders heated from below
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DOI：
10.1017/s002211209000026x
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发表时间：
1990-05
影响因子：
3.7
通讯作者：
G. Neumann
中科院分区：
文献类型：
--
作者：
G. Neumann
用三维含时Boussinesq方程的数值解研究了从下面加热的刚性垂直圆柱体中的定常和振荡对流。绝热和理想的导电侧壁被认为是。对流不稳定的发病和流动的结构和对称性的容器的几何形状的效果进行了分析和比较与线性稳定性理论的结果。本文研究了普朗特数为0.02 ~ 6.7时，瑞利数超过临界数时对流运动的非线性演化和稳定性。稳定轴对称解的极限是本研究的一个重要发现。计算了小普朗特数为0.02时振荡不稳定性的起始点和频率，并与实验数据进行了比较。计算的流型和速度剖面说明了稳定对流的三维结构和振荡流的时间依赖性行为。
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.