相场法模拟悬浮熔融硅液滴内部对流及自由界面变形现象

Phase Field Modeling of Internal Convection and Free Interface Deformation of Levitated Droplet of Molten Silicon

为了模拟具有高密度比的两相流,提出采用牛顿迭代求解半隐式格式离散Cahn-Hilliard方程的方法,应用相场法模拟水的溃坝流和水下气泡的上升变形过程,发现水碰到右边壁面时,水面上卷,气泡在浮力作用下逐渐上升,从球形逐渐变为帽形,模拟结果与界面跟踪法模拟结果一致,验证了数值算法的正确性.在此基础上,数值模拟了悬浮熔融硅液滴的流动、变形过程,结果表明,具有初始变形的液滴在表面张力的作用下逐渐收缩,液滴内产生对流,然后,液滴逐渐变为长条状,液滴内分布着4个涡胞,沿纵向排列.

In order to simulate the two-phase flow with high density ratio, the algorithm of Newton iteration was utilized to solve a discretized semi-implicit Cahn-Hilliard equation. The dam-break flow problem and the interface deformation of a rising air bubble in water were numerically simulated using the phase field method. The result exhibits that when the water flow reaches the right side wall, it flows upward along the solid wall. Driven by the buoyant force, the spherical bubble rises up, and deforms into a spherical-cap shape gradually. The results agree well with those obtained by the front tracking method, which indicates the validity of the numerical algorithm. By the phase field method, the internal convection and interface deformation of a levitated droplet of molten silicon is simulated with a given initial amplitude. The result shows that the droplet gradually shrinks and the internal convection occurs, driven by the surface tension force. After a while, the droplet extends again, and four vortexes locate in the droplet, aligning along the vertical direction.