环形液池内中等Pr数流体的浮力-热毛细对流

为了了解水平温度梯度作用时环形液池内的浮力-热毛细对流特性，利用有限差分法进行了非稳态三维数值模拟，环形液池外壁被加热，半径为40 mm，内壁被冷却，半径为20 mm，液池深度为3~17 mm，液池内流体为0.65cSt的硅油，其Pr数为6.7. 模拟结果表明，当水平温度梯度较小时，流动为轴对称稳态流动，随着温度梯度的增加，流动将会失去其稳定性，在浅的液池内(d=3mm)，转化成三维振荡流动，在深的液池内(d≥6mm)，转化成三维稳定流动；模拟计算的临界温差及表面温度分布图像与实验结果基本吻合.

Buoyant-thermocapillary convection of moderate prandtl number fluid

In order to understand the nature ofbuoyant-thermocapillary convection in an annular pool with the outer heatedcontainer of radius ro=40 mm and the inner cooled cylinder ofri=20 mm, and an adjustable depth d=3~17 mm, we conducted a series ofunsteady three-dimensional numerical simulations with the finite differencemethod. The pool was filled with the 0.65cSt silicone oil (Prandtl numberPr=6.7). Results show that a small temperature difference in the radialdirection generates steady roll-cell buoyant-thermocapillary flow. Withlarge temperature difference, the simulations can predict two types of flowinstability. In a shallow pool (d=3 mm), the hydrothermal wave characterizedby curved spokes traveling in the azimuthal direction is dominant while indeep pools (d≥6 mm), the three-dimensional stationary instabilityappears. The critical conditions for the onset of the instability flows andthe free surface temperature fluctuation are determined and compared withthe experimental results.