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建立了二维双组分两相流的大密度比格子玻尔兹曼方法 (lattice Boltzmann method, LBM)模型. 该模型基于改进的Shan-Chen伪势多相流LBM模型, 结合采用不同时间步长的方法, 实现密度比达800以上的气液两相流模拟. 为了对模型进行验证, 模拟了在不同气液相互作用系数和密度比条件下气泡内外压力差与其半径之间的关系, 其结果满足Laplace定律. 将所建立的大密度比LBM与介观尺度的元胞自动机(cellular automaton, CA)和有限差分法(FDM)相耦合, 用LBM模拟气液两相流, 用CA方法模拟固相生长, 用有限差分法模拟温度场, 采用LBM-CA-FDM耦合模型对定向凝固过程中凝固前沿的气泡与液-固界面之间的相互作用进行模拟研究. 结果表明, 绝热气泡的存在影响了温度场分布, 使得凝固前沿接近气泡时, 液-固界面凸起, 在不同的固相生长速度条件下, 出现凝固前沿淹没气泡或气泡脱离凝固前沿的不同情况, 模拟结果与实验结果符合良好.A two-dimensional (2D) two-component and two-phase lattice Boltzmann method (LBM) with large density ratio is developed based on a modified Shan-Chen pseudopotential model combined with the deferent time step method. The present LBM model can simulate the gas-liquid two-phase flow with density ratio up to around 800. To validate the model, the pressure difference between the inside and outside of a bubble varying with its radius is simulated with different gas-liquid interact parameters and density ratios. The results are found to obey the Laplace law. Then, the LBM is coupled with the cellular automaton (CA) method used for simulating the solid phase growth, and the finite difference method (FDM) used for calculating the temperature field. The LBM-CA-FDM coupled model is used to simulate the interaction between bubble and the solidification interface. The results show that the existence of adiabatic bubble influences the distribution of temperature field in front of solidification interface, which leads to a bulge of the solid-liquid interface when it is close to the bubble. Under the conditions of different growth rates, the bubble is either engulfed or pushed away by the growing solid-liquid interface. The simulation results agree reasonably well with those observed experimentally.
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Keywords:
- lattice Boltzmann method /
- cellular automaton /
- solidification /
- bubble
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[2] Xing H, Wang J Y Chen C L Shen Z F, Zhao C W 2012 J. Cryst. Growth 338 256
[3] Zhao L, Liao H C, Pan Y, Wang L, Wang Q G 2011 Scripta Mater. 65 795
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[19] Yuan P, Schaefer L 2006 Phys. Fluids 18 042101
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[21] Sbragaglia M, Benzi R, Biferale L, Succi S, Sugiyama K, Toschi F 2007 Phys. Rev. E 75 026702
[22] Zhou F M, Sun D K, Zhu M F 2010 Acta Phys. Sin. 59 3394 (in Chinese) [周丰茂, 孙东科, 朱鸣芳 2010 59 3394]
[23] Shan X, Chen H 1993 Phys. Rev. E 47 1815
[24] Zhang J 2011 Microfluid Nanofluid 10 1
[25] Yang Z R, Sun D K, Pan S Y, Dai T, Zhu M F 2009 Acta Metall. Sin. 45 43 (in Chinese) [杨朝蓉, 孙东科, 潘诗琰, 戴挺, 朱鸣芳 2009 金属学报 45 43]
[26] Li Q, Li D Z, Qian B N 2004 Acta Phys. Sin. 53 3477 (in Chinese) [李强, 李殿忠, 钱百年 2004 53 3477]
[27] Yang Z R 2009 M. S. Dissertation (Nanjing: Southeast University) (in Chinese) [杨朝蓉 2009 硕士学位论文 (南京: 东南大学)]
[28] Zhao L 2012 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese) [赵磊 2012博士学位论文 (南京: 东南大学)]
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[1] Han Q Y 2006 Scripta Mater. 55 871
[2] Xing H, Wang J Y Chen C L Shen Z F, Zhao C W 2012 J. Cryst. Growth 338 256
[3] Zhao L, Liao H C, Pan Y, Wang L, Wang Q G 2011 Scripta Mater. 65 795
[4] Hadji L 2007 Phys. Rev. E 75 042602
[5] Kao J C T, Golovin A A, Davis S H 2009 J. Fluid Mech. 625 299
[6] Atwood R C, Lee P D 2003 Acta Mater. 51 5447
[7] Catalina A V, Stefanescu D M, Sen S, Kaukler W F 2004 Metall Mater. Tran. A 35A 1525
[8] Feng S D, Zhao Y, Gao X L, Ji Z Z 2002 Chin. Phys. Lett. 19 814
[9] Yu Z Q, Zhang Z, Zhang B T 2002 Chin. Phys. Lett. 11 771
[10] Karagadde S, Sundarraj S, Dutta P 2009 Scripta Mater. 61 216
[11] Zhang X M, Zhou C Y, Islam S, Liu J Q 2009 Acta Phys. Sin. 58 8046 (in Chinese) [张新明, 周超英, Islam S, 刘家琦 2009 58 8046]
[12] Zeng J B, Li L J, Liao Q, Jiang F M 2011 Acta Phys. Sin. 60 066401 (in Chinese) [曾建邦, 李隆键, 廖全, 蒋方明 2011 60 066401]
[13] Huang H, Thorne Jr D T, Schaap M G, Sukop M C 2007 Phys. Rev. E 76 066701
[14] Kim L S, Jeong H K, Ha M Y, Kim K C 2008 J. Mech. Sci. Technol. 22 770
[15] Yu Z, Hemminger O, Fan L S 2008 Chem. Eng. Sci. 62 7172
[16] Wu W, Sun D K, Dai T, Zhu M F 2012 Acta Phys. Sin. 61 150501 (in Chinese) [吴伟, 孙东科, 戴挺, 朱鸣芳 2012 61 150501]
[17] Inamuro T, Ogata T, Tajima S, Konishi N 2004 J. Comput. Phys. 198 628
[18] Yan Y Y, Zu Y Q 2007 J. Comput. Phys. 227 763
[19] Yuan P, Schaefer L 2006 Phys. Fluids 18 042101
[20] Liu M, Yu Z, Wang T, Wang J, Fan L S 2010 Chem. Eng. Sci. 65 5615
[21] Sbragaglia M, Benzi R, Biferale L, Succi S, Sugiyama K, Toschi F 2007 Phys. Rev. E 75 026702
[22] Zhou F M, Sun D K, Zhu M F 2010 Acta Phys. Sin. 59 3394 (in Chinese) [周丰茂, 孙东科, 朱鸣芳 2010 59 3394]
[23] Shan X, Chen H 1993 Phys. Rev. E 47 1815
[24] Zhang J 2011 Microfluid Nanofluid 10 1
[25] Yang Z R, Sun D K, Pan S Y, Dai T, Zhu M F 2009 Acta Metall. Sin. 45 43 (in Chinese) [杨朝蓉, 孙东科, 潘诗琰, 戴挺, 朱鸣芳 2009 金属学报 45 43]
[26] Li Q, Li D Z, Qian B N 2004 Acta Phys. Sin. 53 3477 (in Chinese) [李强, 李殿忠, 钱百年 2004 53 3477]
[27] Yang Z R 2009 M. S. Dissertation (Nanjing: Southeast University) (in Chinese) [杨朝蓉 2009 硕士学位论文 (南京: 东南大学)]
[28] Zhao L 2012 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese) [赵磊 2012博士学位论文 (南京: 东南大学)]
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