液桥中不同Prandtl数流体的热毛细对流

THE THERMOCAPILLARY CONVECTION IN THE LIQUID BRIDGE WITH DIFFERENT PRANDTL NUMBER

本文研究从上面加热的液桥中不同 pr 数流体的热表面张力驱动对流。在 Ma 数相同的条件下,不同 pr 数流体液桥中的温度分布和流场结构定性相似,但定量结果不同。小pr数(pr<<1)流体液桥中的粘性边界层远小于热边界层,最大流函数所在位置向冷端偏移,有较大的流动速度。结果表明,Ma 数是描述这种流动的敏感参数。

Due to the progresses of space technology, the manufacture of high quality materials such as the semi-conductors or metal (Pr<<1) in space is coming true. It is difficult to observe the flow structure and temperature distribution in the liquid bridge of opaque molten semi-conductor or metal. Therefore, in present time, the experiments of thermocapil-lary convection are mainly conducted in the liquid bridge with transparent medium (Pr>1) such as silicon oil. The purpose of this paper is to study whether the behavior of fluids with small Pr number can be described by these experimental results of transparent medium, and what is the effects of Pr number on thermocapillary convention.The two-dimensional, steady problem of thermocapillary convection in the liquid bridges with different Pr number, described by vorticity, stream function and energy equations, are numerically studied by Finite Eltment Method. The results show that the distributions of temperature and flow patterns are qualitatively similar in the liquid bridges with different Pr number, but the quantitative results are different according to certain Marangoni numbers. In the liquid bridge with smaller Pr number, the thickness of viscose boundard layer is much smaller than the thermal one. The place of the maximum stream function is shifted from the hot toward the cold rod of the liquid bridge, and the velocity is relatively larger for the case of smaller Pr number. Ma number is the sensitive parameter for describing thermocapillary convection. According to the experimental results of transparent medium the behavior of the-rmocapillary convection of opaque fluids can be qualitatively described.