微重力环境下Marangoni对流的有限元数值模拟

NUMERICAL SIMULATION OF MARANGONI CONVECTION IN THE FLOATING ZONE UNDER MICROGRAVITY BY FEM

本文以悬浮区为背景研究液桥中气液交界面上由表面张力所驱动的流体对流。我们采用有限元方法对轴对称、定常运动方程,能量方程,自由面切向、法向应力平衡条件迭代求解,首次考虑了边界形状的影响,得到了自洽的流区位形和流场、温度场、表面压强分布。一般说来,流区自由面呈弯月形。结果表明,只要表面张力数 C_a<1,静态平衡的流区位形就是动态情况的良好近似。本文还分析了C_a数及G_r 数对流区位形的影响,得到了不同 M_a 数及散热条件下的温度场和流函数分布。

The convection of melt in a floating zone driven by surface tension due to temperature gradient is studied in this paper. Axisymmetric steady momentum and energy equations along with kinetic and dynamic boundary conditions are numerically solved by FEM. The effects of free surface of the liquid bridge have been firstly taken into account. We finally yield the solutions for the configuration, flow field, temperature distribution and pressure on the interface. It is shown that the dynamic crescent-shaped liquid-gas interface are wellappro-ximated by the static one if capillary number Ca<1. The influences of Ca and Gr on the configuration of floating zone are analysed. Also, the temperature distribution and flow pattern corresponding to several pairs of Ma and Bi numbers are provided in the article.