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Adopting the Euler and the volume averaging methods, a three-phase mathematical model with parent melt as the primary phase, columnar dendrites and equiaxed grains as two different secondary phases is developed, and the coupled macroscopic mass, momentum, energy and species conservation equations are obtained separately. Taking the Al-4.7 wt% Cu binary alloy ingots for example, the flow field, temperature field, solute field, columnar-to-equiaxed-transition and grain sedimentation in two-dimension are simulated, and the simulated result of ingot and macrosegregation result are compared with their experimental values. The simulation results of temperature field, flow field and structure are basically consistent with the theoretical results, but the result of solute field shows that the simulated values is lower than the measured value on the edge, this is because the model does not take the shrinkage and forced convection into account, and the inner results is higher than the results on edge. The shrinkage and inverse segregation therefore should not be neglected. This model are still necessarily improved. Besides, based on the analysis of simulation results, the advantages and the disadvantages of the volume averaging method to simulate the solidification in a ingot are evaluated.
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Keywords:
- macrosegregation /
- fluid flow /
- heat transfer /
- mass transfer
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[2] Beckermann C, Viskanta R 1988 Physicochem. Hydrodyn. 10 195
[3] Ni J, Beckermann C 1991 Metall. Trans. B 22 349
[4] Wang C Y, Beckermann C 1996 Metall. Trans. A 27 2754
[5] Wu M H, Andreas L 2006 Metall. Trans. A 37 1613
[6] Wang T M, Yao S, Zhang X G, Jin J Z 2006 Acta Metall. Sin. 42 584 (in Chinese) [王同敏, 姚山, 张兴国, 金俊泽 2006 金属学报 42 584]
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[8] Wu M, Ludwig A 2009 Acta Mater. 57 5632
[9] Liu D R, Sang B G, Kang X H, Li D Z 2009 Acta Phys. Sin. 58 104 (in Chinese) [刘东戎, 桑宝光, 康秀红, 李殿中 2009 58 104]
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[13] Wang Z, Wang F Z, Wang X, He Y H, Ma S, Wu Z 2014 Acta Phys. Sin. 63 076101 (in Chinese) [王哲, 王发展, 王欣, 何银花, 马姗, 吴振 2014 63 076101]
[14] Hunt J D 1984 Mater. Sci. Eng. 65 75
[15] Li R, Shen H D, Feng C H, Pan H, Feng C N 2013 Acta Phys. Sin. 62 188106 (in Chinese) [李日, 沈焕弟, 冯长海, 潘红, 冯传宁 2013 62 188106]
[16] Sun D K, Zhu M F, Yang C R, Pan S Y, Dai T 2009 Acta Phys. Sin. 58 285 (in Chinese) [孙东科, 朱鸣芳, 杨朝蓉, 潘诗琰, 戴挺 2009 58 285]
[17] Pan S Y, Zhu M F 2009 Acta Phys. Sin. 58 278 (in Chinese) [潘诗琰, 朱鸣芳 2009 58 278]
[18] 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]
[19] Li J J, Wang J C, Yang G C 2008 Chin. Phys. B 17 3516
[20] Wang Y Q, Wang J C, Li J J 2012 Acta Phys. Sin. 61 118103 (in Chinese) [王雅琴, 王锦程, 李俊杰 2012 61 118103]
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[1] Bennon W D, Incropera F P 1987 Int. J. Heat Mass Transfer. 30 2161
[2] Beckermann C, Viskanta R 1988 Physicochem. Hydrodyn. 10 195
[3] Ni J, Beckermann C 1991 Metall. Trans. B 22 349
[4] Wang C Y, Beckermann C 1996 Metall. Trans. A 27 2754
[5] Wu M H, Andreas L 2006 Metall. Trans. A 37 1613
[6] Wang T M, Yao S, Zhang X G, Jin J Z 2006 Acta Metall. Sin. 42 584 (in Chinese) [王同敏, 姚山, 张兴国, 金俊泽 2006 金属学报 42 584]
[7] Wu M, Ludwig A 2009 Acta Mater. 57 5621
[8] Wu M, Ludwig A 2009 Acta Mater. 57 5632
[9] Liu D R, Sang B G, Kang X H, Li D Z 2009 Acta Phys. Sin. 58 104 (in Chinese) [刘东戎, 桑宝光, 康秀红, 李殿中 2009 58 104]
[10] Wu M, Fjeld A, Ludwig A 2010 Comp. Mater. Sci. 50 32
[11] Wu M, Fjeld A, Ludwig A 2010 Comp. Mater. Sci. 50 43
[12] Zhang H W, Nakajima K, Wang E G, He J C 2012 Chin. J. Nonfer. Metal 22 1883 (in Chinese) [张红伟, Nakajima Keiji, 王恩刚, 赫冀成 2012 中国有色金属学报 22 1883]
[13] Wang Z, Wang F Z, Wang X, He Y H, Ma S, Wu Z 2014 Acta Phys. Sin. 63 076101 (in Chinese) [王哲, 王发展, 王欣, 何银花, 马姗, 吴振 2014 63 076101]
[14] Hunt J D 1984 Mater. Sci. Eng. 65 75
[15] Li R, Shen H D, Feng C H, Pan H, Feng C N 2013 Acta Phys. Sin. 62 188106 (in Chinese) [李日, 沈焕弟, 冯长海, 潘红, 冯传宁 2013 62 188106]
[16] Sun D K, Zhu M F, Yang C R, Pan S Y, Dai T 2009 Acta Phys. Sin. 58 285 (in Chinese) [孙东科, 朱鸣芳, 杨朝蓉, 潘诗琰, 戴挺 2009 58 285]
[17] Pan S Y, Zhu M F 2009 Acta Phys. Sin. 58 278 (in Chinese) [潘诗琰, 朱鸣芳 2009 58 278]
[18] 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]
[19] Li J J, Wang J C, Yang G C 2008 Chin. Phys. B 17 3516
[20] Wang Y Q, Wang J C, Li J J 2012 Acta Phys. Sin. 61 118103 (in Chinese) [王雅琴, 王锦程, 李俊杰 2012 61 118103]
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