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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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[7] Catalina A V, Stefanescu D M, Sen S, Kaukler W F 2004 Metall Mater. Tran. A 35A 1525
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[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 物理学报 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 物理学报 60 066401]
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[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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