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

石万元; 张凤超; 田小红; 塚田隆夫

doi:10.3969/j.issn.0258-2724.2012.04.025

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

doi: 10.3969/j.issn.0258-2724.2012.04.025

基金项目:

国家自然科学基金资助项目(50976128,51176210)

中国博士后基金特别资助项目(201003309)

教育部留学回国人员启动基金资助项目(教外司留[2009]1001-1)

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出版历程
- 收稿日期: 2012-03-05
- 刊出日期: 2012-08-25

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

摘要

摘要: 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.
- 相场模拟 /
- 硅熔体 /
- 液滴 /
- 半隐式格式 /
- 牛顿迭代
Abstract: 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.
- phase field modeling /
- molten silicon /
- droplet /
- semi-implicit scheme /
- Newton iteration

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参考文献(14)

范建峰,袁章福,柯家骏. 高温熔体表面张力测量方法的进展[J]. 化学通报,2004(11): 802-807. FAN Jianfeng, YUAN Zhangfu, KE Jiajun. Development in measuring surface tension of high temperature molten liquid[J]. Chemistry, 2004(11): 802-807.

鄢振麟,解文军,魏炳波. 声悬浮条件下扇谐振荡液滴的内部流动规律 [J]. 中国科学: 物理学力学天文学,2011,41(9): 1096-1103. YAN Zhenlin, XIE Wenjun, WEI Bingbo. Internal flow of acoustically levitated water drops during sectorial oscillations[J]. Scientia Sinica Phys, Mech & Astron, 2011, 41(9): 1096-1103.

ASAKUMA Y, HIRATA T, TSUKADA T, et al. Nonlinear oscillations of molten silicon drops in electromagnetic levitator[J]. J. Chemical Engineering of Japan, 2000, 33(6): 861-868.

BOJAREVICS V, PERICLEOUS K. Modelling electromagnetically levitated liquid droplet oscillation[J]. ISIJ International, 2003, 43: 890-898.

WATANABE T. Nonlinear oscillations and rotations of a liquid droplet[J]. International J. Geology, 2010, 4(1): 5-13.

JACQMIN D. Calculation of two-phase Navier-Stokes using phase-field modelling[J]. J. Computational Physics, 1999, 155(1): 96-127.

DING H, SPELT P D M, SHU C. Diffuse interface model for incompressible two-phase flows with large density ratios[J]. J. Computational Physics, 2007, 226(2): 2078-2095.

TAKADA N, MATSUMOTO J, Matsumoto S, et al. Application of a phase-field method to the numerical analysis of motions of a two-phase fluid with high density ratio on a solid surface[J]. J. Computational Science and Technology, 2008, 2(2): 318-329.

EYRE D J. An unconditionally stable one-step scheme for gradient systems. Salt Lake: Department of Mathematics University of Utah, 1998.

BADALASSV E I, CENICEROS H D, BANERJEE S. Computation of multiphase systems with phase field models[J]. J. Computational Physics, 2003, 190: 371-397.

ASCHER U M, RUUTH S J, WETTON B T R. Implicit-explicit methods for time dependent partial differential equations[J]. SIAM Journal on Numerical Analysis, 1995, 32(3): 797-823.

JIANG G S, SHU C W. Efficient implementation of weighted ENO schemes[J]. J. Computational Physics, 1996, 126: 202-228.

Van Der VORST H A. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems[J]. SIAM Journal on Scientific and Statistical Computing, 1992, 13: 631-644.

HUA J, HOU J. Numerical simulation of bubble riding in viscous liquid[J]. J. Computational Physics, 2007, 222: 769-795.

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文章访问数: 1146
HTML全文浏览量: 64
PDF下载量: 405
被引次数: 0

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

doi: 10.3969/j.issn.0258-2724.2012.04.025

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出版历程

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

计量

出版历程

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