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The existence of forced and natural melt convections in the liquid in front of dendritic tip will Change the thickness of diffusion layer, which can significantly influence the dendrite morphology. Using the cellular automaton method and considering the influences of melt convection and heat transfer on microstructure evolution, a new numerical model is established by coupling the Navier-Stokes equations, the heat transfer equation and the solute convection and diffusion equation. The influences of forced and natural melt convection on dendrite morphology evolution are investigated by this model. The three-dimensional simulations reproduce the equiaxed dendrite growth, and reveal the influence of convection on dendritic growth rate and tip radius. The effect of natural convection on columnar dendrite growth during directional solidification of NH4Cl-H2O solution is simulated via the model. Experimental validation of this solidification process is performed and compared with simulation results. The simulation results accord well with experimental measurements. Hence, the model is reliable and can be extended to the prediction of the behavior of dendrite growth in real alloys.
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Keywords:
- cellular automaton /
- convection /
- NH4Cl-H2O solution /
- directional solidification
[1] Trivedi R, Miyahara H, Mazumder P, Simsek E, Tewari S N 2001 J. Cryst. Growth 222 365
[2] [3] Lu Y, Beckermann C, Ramirez J C 2005 J. Cryst. Growth 280 320
[4] Steinbach I 2009 Acta Mater. 57 2640
[5] [6] Wang W, Lee P D, McLean M 2003 Acta Mater. 51 2971
[7] [8] [9] Shan B W, Huang W D, Lin X, Wei L 2008 Acta Metall. Sin. 44 1042 (in Chinese) [单博炜、黄卫东、林 鑫、魏 雷 2008 金属学报 44 1042]
[10] [11] Shin Y H, Hong C P 2002 ISIJ Int. 42 359
[12] [13] Guo D Y, Yang Y S 2006 Foundry 55 601 (in Chinese) [郭大勇、杨院生 2006铸造 55 601]
[14] Li D M, Li R, Zhang P W 2007 Appl. Math. Model. 31 971
[15] [16] Zhu M F, Dai T, Lee S Y, Hong C P 2008 Comput. Math. Appl. 55 1620
[17] [18] [19] Sun D K, Zhu M F, Yang C R, Pan S Y, Dai T 2009 Acta Phys. Sin. 58 S285 (in Chinese) [孙东科、朱鸣芳、杨朝蓉、潘诗琰、戴 挺 2009 物理学报 58 S285]
[20] Hansen G, Liu S, Lu S Z, Hellawell A 2002 J. Cryst. Growth 234 731
[21] [22] [23] Feng Y H, Nie H, Zhang X X 2008 J. Eng. Thermophys. 29 301 (in Chinese) [冯妍会、聂 红、张欣欣 2008工程热物理学报 29 301]
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[26] Lipton J, Glicksman M E, Kurz W 1984 Mater. Sci. Eng. 65 57
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[29] [30] [31] Liu Y, Xu Q Y, Liu B C 2006 Tsinghua Sci. Tech. 11 495
[32] Yu J, Xu Q Y, Cui K, Liu B C 2007 Acta Metall. Sin. 43 731 (in Chinese) [于 靖、许庆彦、崔 锴、柳百成 2007金属学报 43 731]
[33] [34] Li B, Xu Q Y, Pan D, Liu B C, Xiong Y C, Zhou Y J, Hong R Z 2008 Acta Metall. Sin. 44 243 (in Chinese) [李 斌、许庆彦、潘 冬、柳百成、熊艳才、周永江、洪润洲 2008 金属学报 44 243]
[35] [36] [37] Li B 2007 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese) [李 斌 2007博士学位论文 (北京: 清华大学)]
[38] Nastac L 1999 Acta Mater. 47 4253
[39] [40] Beltran-Sanchez L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[41] [42] Trivedi R, Kurz W 1994 Int. Mater. Rev. 39 49
[43] [44] [45] Stefanescu D M 2009 Science and Engineering of Casting Solidification (New York: Springer) p163
[46] [47] Barbieri A, Langer J S 1989 Phys. Rev. A 39 5314
[48] [49] Pan S Y, Zhu M F 2009 Acta Phys. Sin. 58 S278 (in Chinese) [潘诗琰、朱鸣芳 2009 物理学报 58 S278]
[50] Beltran-Sanchez L 2003 Ph. D. Dissertation (Tuscaloosa: University of Alabama)
[51] -
[1] Trivedi R, Miyahara H, Mazumder P, Simsek E, Tewari S N 2001 J. Cryst. Growth 222 365
[2] [3] Lu Y, Beckermann C, Ramirez J C 2005 J. Cryst. Growth 280 320
[4] Steinbach I 2009 Acta Mater. 57 2640
[5] [6] Wang W, Lee P D, McLean M 2003 Acta Mater. 51 2971
[7] [8] [9] Shan B W, Huang W D, Lin X, Wei L 2008 Acta Metall. Sin. 44 1042 (in Chinese) [单博炜、黄卫东、林 鑫、魏 雷 2008 金属学报 44 1042]
[10] [11] Shin Y H, Hong C P 2002 ISIJ Int. 42 359
[12] [13] Guo D Y, Yang Y S 2006 Foundry 55 601 (in Chinese) [郭大勇、杨院生 2006铸造 55 601]
[14] Li D M, Li R, Zhang P W 2007 Appl. Math. Model. 31 971
[15] [16] Zhu M F, Dai T, Lee S Y, Hong C P 2008 Comput. Math. Appl. 55 1620
[17] [18] [19] Sun D K, Zhu M F, Yang C R, Pan S Y, Dai T 2009 Acta Phys. Sin. 58 S285 (in Chinese) [孙东科、朱鸣芳、杨朝蓉、潘诗琰、戴 挺 2009 物理学报 58 S285]
[20] Hansen G, Liu S, Lu S Z, Hellawell A 2002 J. Cryst. Growth 234 731
[21] [22] [23] Feng Y H, Nie H, Zhang X X 2008 J. Eng. Thermophys. 29 301 (in Chinese) [冯妍会、聂 红、张欣欣 2008工程热物理学报 29 301]
[24] [25] Bennon W D, Incropera F P 1987 Metall. Trans. B 18 611
[26] Lipton J, Glicksman M E, Kurz W 1984 Mater. Sci. Eng. 65 57
[27] [28] Lipton J, Glicksman M E, Kurz W 1987 Metall. Mater. Trans. A 18 341
[29] [30] [31] Liu Y, Xu Q Y, Liu B C 2006 Tsinghua Sci. Tech. 11 495
[32] Yu J, Xu Q Y, Cui K, Liu B C 2007 Acta Metall. Sin. 43 731 (in Chinese) [于 靖、许庆彦、崔 锴、柳百成 2007金属学报 43 731]
[33] [34] Li B, Xu Q Y, Pan D, Liu B C, Xiong Y C, Zhou Y J, Hong R Z 2008 Acta Metall. Sin. 44 243 (in Chinese) [李 斌、许庆彦、潘 冬、柳百成、熊艳才、周永江、洪润洲 2008 金属学报 44 243]
[35] [36] [37] Li B 2007 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese) [李 斌 2007博士学位论文 (北京: 清华大学)]
[38] Nastac L 1999 Acta Mater. 47 4253
[39] [40] Beltran-Sanchez L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[41] [42] Trivedi R, Kurz W 1994 Int. Mater. Rev. 39 49
[43] [44] [45] Stefanescu D M 2009 Science and Engineering of Casting Solidification (New York: Springer) p163
[46] [47] Barbieri A, Langer J S 1989 Phys. Rev. A 39 5314
[48] [49] Pan S Y, Zhu M F 2009 Acta Phys. Sin. 58 S278 (in Chinese) [潘诗琰、朱鸣芳 2009 物理学报 58 S278]
[50] Beltran-Sanchez L 2003 Ph. D. Dissertation (Tuscaloosa: University of Alabama)
[51]
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