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利用渐近方法求出在弱对流熔体中定向凝固棒状共晶生长的浓度场的渐近解, 研究了弱熔体对流对定向凝固中棒状共晶生长的影响. 结果表明, 弱熔体对流对定向凝固中棒状共晶生长有显著的作用; 平均界面过冷度不仅与棒状共晶的棒间距、生长速度有关, 还与流动强度有关; 当生长速度一定时, 随着流动强度增大, 棒状共晶的平均界面过冷度减小. 利用最小过冷原则, 获得棒间距与生长速度和流动强度的关系. 结果表明, 当生长速度比较小时, 随着流动强度增大, 棒状共晶的棒间距增大; 当生长速度比较大时, 随着流动强度增大, 棒状共晶的棒间距变化减弱; 棒状共晶的生长速度越小, 流动对棒状共晶生长的影响越大. 利用本文的解析结果计算在对流条件下Al-Cu共晶的棒间距, 结果显示随着转速增大或径向距离增大, 共晶的间距增大, 这与Junze 等的实验结果相符合.Eutectic solidification is very important for exploring new materials in which the periodic multiphase structures may have a remarkable or enhanced functionality. An asymptotic solution of the solute diffusion equation with flow terms for the rod eutectic in the weak convective melt in directional solidification is obtained by using the asymptotic method, and the effect of weak convection on the rod eutectic growth is studied. The so-called weak convection is defined in this paper as the condition in which the intensity of convection flow ahead of the solid liquid interface is relatively small. The relationships between the intensity of convection flow, the growth velocity, the rod spacing and the average interface undercooling can be derived. The result shows that the weak convection has a significant effect on the rod eutectic growth in directional solidification. The average interface undercooling is related to not only the rod spacing and the growth velocity, but also the intensity of convection flow. When specifically focusing on the effect of the intensity of convection flow on the average undercooling in directional solidification, the growth velocity is kept the same. For a certain growth velocity, the average interface undercooling of the rod eutectic decreases as the intensity of convection flow increases, especially at low growth velocity. The rod spacing, which is formed by solidified melt of eutectic or near-eutectic composition, plays a very important role in determining the properties of final products. In this study, by minimizing the average interface undercooling it is found that the rod spacing is a function of growth velocity and the intensity of convection flow. It is shown that for the small growth velocity, the rod spacing increases as the intensity of convection flow increases; for the large growth velocity, the rod spacing increases very slowly as the intensity of convection flow increases. In other words, the smaller the growth velocity, the greater the effect of the weak convection flow on the rod spacing. Our analytical result is compared with the results from other models, and it is also used to calculate the practical case such as the rod spacing of the typical eutectic alloy, Al-Cu eutectic, under the condition of weak forced convection induced by the accelerated crucible rotation technique. It is shown that the rod spacing increases as the rotation rate or the radial position increases, which is consistent with the experimental results obtained by Junze et al.
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Keywords:
- rod eutectic /
- convection /
- rod spacing /
- average interface undercooling
[1] Jackson K A, Hunt J D 1966 Trans. Metall. Soc. AIME 236 1129
[2] Trivedi R, Magnin P, Kurz W 1987 Acta Metall. 35 971
[3] Liu J, Elliott R 1995 J. Cryst. Growth 148 406
[4] Bai B B, Lin X, Wang L L, Wang X B, Wang M, Huang W D 2013 Acta Phys. Sin. 62 218103 (in Chinese) [白贝贝, 林鑫, 王理林, 王贤斌, 王猛, 黄卫东 2013 62 218103]
[5] Meng G H, Lin X 2014 Acta Phys. Sin. 63 068104 (in Chinese) [孟广慧, 林鑫 2014 63 068104]
[6] Wang L, Wang N, Ji L, Yao W J 2013 Acta Phys. Sin. 62 216801 (in Chinese) [王雷, 王楠, 冀林, 姚文静 2013 62 216801]
[7] Ravishankar P S, Wilcox W R, Larson D J 1980 Acta Metall. 28 1583
[8] Baskaran V, Eisa G F, Wilcox W R 1984 Computational Methods and Experimental Measurements (Berlin Heidelberg: Springer) pp123-134
[9] Kumar P, Chakraborty S, Srinivasan K, Dutta P 2002 Metall. Mater. Trans. B 33 605
[10] Thiele R, Anglart H 2013 Nucl. Eng. Des. 254 111
[11] Pirich R G, Larson D J 1981 MRS Proceedings (Cambridge: Cambridge University Press) p523
[12] Muller G, Kyr P 1984 Results of Spacelab 1, Proceeding of the 5th European Symposium on Materials Sciences under Microgravity Schloss Elmau, FRG, November 5-7, 1984 p141
[13] Quenisset J M, Naslain R 1981 J. Cryst. Growth 54 465
[14] Baskaran V, Wilcox W R 1984 J. Cryst. Growth 67 343
[15] Caram R, Chandrasekhar S, Wilcox W R 1990 J. Cryst. Growth 106 294
[16] Ma D, Jie W Q, Li Y, Ng S C 1998 Acta Mater. 46 3203
[17] Coriell S R, McFadden G B, Mitchell W F, Murray B T, Andrews J B, Arikawa Y 2001 J. Cryst. Growth 224 145
[18] Zhang W Q, Yang Y S, Hu Z Q 1998 Acta Metall. Sin. 34 1 (in Chinese) [张伟强, 杨院生, 胡壮麒 1998 金属学报 34 1]
[19] Zhang W Q, Fu H, Yang Y S, Hu Z Q 1998 J. Cryst. Growth 194 263
[20] Greenspan H P 1990 The Theory of Rotating Fluids (Cambridge: Cambridge University Press) p354
[21] Junze J, Kobayashi K F, Shingu P H 1984 Metall. Trans. A 15 307
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[1] Jackson K A, Hunt J D 1966 Trans. Metall. Soc. AIME 236 1129
[2] Trivedi R, Magnin P, Kurz W 1987 Acta Metall. 35 971
[3] Liu J, Elliott R 1995 J. Cryst. Growth 148 406
[4] Bai B B, Lin X, Wang L L, Wang X B, Wang M, Huang W D 2013 Acta Phys. Sin. 62 218103 (in Chinese) [白贝贝, 林鑫, 王理林, 王贤斌, 王猛, 黄卫东 2013 62 218103]
[5] Meng G H, Lin X 2014 Acta Phys. Sin. 63 068104 (in Chinese) [孟广慧, 林鑫 2014 63 068104]
[6] Wang L, Wang N, Ji L, Yao W J 2013 Acta Phys. Sin. 62 216801 (in Chinese) [王雷, 王楠, 冀林, 姚文静 2013 62 216801]
[7] Ravishankar P S, Wilcox W R, Larson D J 1980 Acta Metall. 28 1583
[8] Baskaran V, Eisa G F, Wilcox W R 1984 Computational Methods and Experimental Measurements (Berlin Heidelberg: Springer) pp123-134
[9] Kumar P, Chakraborty S, Srinivasan K, Dutta P 2002 Metall. Mater. Trans. B 33 605
[10] Thiele R, Anglart H 2013 Nucl. Eng. Des. 254 111
[11] Pirich R G, Larson D J 1981 MRS Proceedings (Cambridge: Cambridge University Press) p523
[12] Muller G, Kyr P 1984 Results of Spacelab 1, Proceeding of the 5th European Symposium on Materials Sciences under Microgravity Schloss Elmau, FRG, November 5-7, 1984 p141
[13] Quenisset J M, Naslain R 1981 J. Cryst. Growth 54 465
[14] Baskaran V, Wilcox W R 1984 J. Cryst. Growth 67 343
[15] Caram R, Chandrasekhar S, Wilcox W R 1990 J. Cryst. Growth 106 294
[16] Ma D, Jie W Q, Li Y, Ng S C 1998 Acta Mater. 46 3203
[17] Coriell S R, McFadden G B, Mitchell W F, Murray B T, Andrews J B, Arikawa Y 2001 J. Cryst. Growth 224 145
[18] Zhang W Q, Yang Y S, Hu Z Q 1998 Acta Metall. Sin. 34 1 (in Chinese) [张伟强, 杨院生, 胡壮麒 1998 金属学报 34 1]
[19] Zhang W Q, Fu H, Yang Y S, Hu Z Q 1998 J. Cryst. Growth 194 263
[20] Greenspan H P 1990 The Theory of Rotating Fluids (Cambridge: Cambridge University Press) p354
[21] Junze J, Kobayashi K F, Shingu P H 1984 Metall. Trans. A 15 307
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