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Three-dimensional modelling and numerical simulation on segregation during Fe-Pb alloy solidification in a multiphase system

Wang Zhe Wang Fa-Zhan Wang Xin He Yin-Hua Ma Shan Wu Zhen

Three-dimensional modelling and numerical simulation on segregation during Fe-Pb alloy solidification in a multiphase system

Wang Zhe, Wang Fa-Zhan, Wang Xin, He Yin-Hua, Ma Shan, Wu Zhen
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  • The three-dimensional mathematical model for a three-phase flow during its horizontai solidification is studied using fluid dynamics method based on Eulerian-Eulerian and volume of fraction methods, in which the mass, momentum, species, and enthalpy conservation equations of the Fe-Pb alloy solidification process are solved simultaneously. Effects of Pb area quadratic gradient (∇ (∇SPb)) and Pb concentration quadratic gradient (∇ (∇CPb)) on the segregation formation are investigated. Results show that the segregation mode is manifested as X-segregates in the upper and V-segregates in the lower part during flow-solidification of liquid phase and gas phase. The X-segregates result from the phase transformation driving force of gas phase and “scattering” is due to the orientation of phase transition. When t >tc the lower ∇ (∇SPb) and ∇ (∇CPb) curves cause a larger yielding rate of Pb with a larger down angle of X-segregates and a smaller up angle of X-segregates and V-segregates. All these are favorable for the formation of a well-dispersed microstructure. In addition, the gas-liquid two-phase flow interaction term has an effect on channel segregation, showing that channels occur only in the region where the flow-phase transition interaction term (ul·∇cl and ug·∇cg) is negative. With a negative flow-phase transition interaction term the increase in flow velocity due to the flow perturbation and flow-phase transition interaction becomes more negative, thus the channel continues to grow and tends to be stable. Calculated results show good agreement with experimental data.
    • Funds: Project supported by the National Key Technology R&D Program during the 12th Five-year Plan Period of China (Grant No. 2011BAE31B02).
    [1]

    Nazábal J L, Urcola J J, Fuentes M 1984 Metallography. 71 439

    [2]

    Murakami Y, Mine K, Usuki H 1988 J. Iron. Steel. Inst. Jpn. 74 1113

    [3]

    Bernsmann G, Bleymehl M, Ehl R 2001 Stahl. Eisen. 121 87

    [4]

    Iwamoto T, Murakami T 2004 JFE. Tech. Rep. 4 74

    [5]

    Guduru R K, Scattergood R O, Koch C C, Murty K L, Guruswamy S, McCarter M K 2006 Scripta. Mater. 54 1879

    [6]

    Yamauchi K, Nakagawa Y 1971 Jpn. J. Appl. Phys. 10 1730

    [7]

    Burton B 1991 J. Phase. Equilib. 12 200

    [8]

    Iwama N, Uchiyama M, Owaki S 1999 Curr. Adv. Mater. Process. 12 1387

    [9]

    Mcdonald R J, Hunt J D 1969 Trans. Metall. Soc. AIME. 245 1993

    [10]

    Mcdonald R J, Hunt J D 1970 Metall. Trans. 1 1787

    [11]

    Sarazin J R, Hellawell A 1988 Metall. Trans. A 19 1861

    [12]

    Shahani H, Amberg G, Fredriksson H 1991 Metall. Trans. A 23 2301

    [13]

    Schneider M C, Beckermann C 1995 Int. J. Heat. Mass. Tran. 38 3455

    [14]

    Belleta M, Combeau H, Fautrelle Y, Gobin D, Rady M, Arquis E, Budenkova O, Dussoubs B, Duterrail Y, Kumar A, Gandin C A, Goyeau B, Mosbah S, Založ nik M 2009 Int. J. Therm. Sci. 48 2013

    [15]

    Wang T M, Yao S, Zhang X G, Jin J Z, Wu M, Ludwig A, Pustal B, B hrig-Polaczek A 2006 Acta. Metall. Sin. 42 584 (in Chinese)[王同敏, 姚山, 张兴国, 金俊泽, Wu M, Ludwig A, Pustal B, Bhrig-Polaczek A 2006 金属学报42 584]

    [16]

    Cockroft S L, Maijer D M 2009 Modeling of Casting Welding and Advanced Solidification Processes (Warrendale: Wiley-IEEE Press) pp250-265

    [17]

    Zhu C S, Wang Z P, Jing T, Xiao R Z 2006 Acta. Phys. Sin. 55 1502 (in chinese) [朱昌盛, 王智平, 荆涛, 肖荣振 2006 物理学报55 1502]

    [18]

    Kumar A, Dussoubs B, Založ nik M, Combeau H 2009 Phys. J. Appl. Phys. 42 105503

    [19]

    Li J, Wu M, Hao J, Ludwig A 2012 Comp. Mater. Sci. 55 407

    [20]

    Wu M, Ludwig A 2006 Metall. Mater. Trans. A 37 1613

    [21]

    Kumar A, Založ nik M, Combeau H 2012 Int. J. Therm. Sci. 54 33

    [22]

    Schneider M C, Beckermann C 1995 Int. J. Heat. Mass. Tran. 38 3455

    [23]

    Wu M, Ludwig A 2007 Metall. Mater. Trans. A 38 1465

    [24]

    Xu D, Bai Y, Guo J, Fu H, Guo J J 2004 Int. J. Heat. Mass. Tran. 46 767

    [25]

    Beckermann C, Viskanta R 1993 Appl. Mech. Rev. 46 1

    [26]

    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 物理学报58 104]

    [27]

    Založ nik M, Combeau H 2010 Comp. Mater. Sci. 48 1

    [28]

    Wang K F, Guo J J, Mi G F, Li B S, Fu H Z 2008 Acta. Phys. Sin. 57 3048 (in chinese) [王狂飞, 郭景杰, 米国发, 李邦盛, 傅恒志2008 物理学报57 3048]

    [29]

    Li Q, Guo Q Y, Li R D 2003 Chin. Phys. 15 778

    [30]

    Monchoux J P, Rabkin E 2002 Acta. Mater. 50 3159

    [31]

    Hu G X, Cai X, Rong Y H 2010 Fundamentals of Materials Science (Shanghai: Shanghai Jiao-tong University Press) pp131-140 (in Chinese) [胡赓祥, 蔡珣, 戎咏华2010 材料科学基础(上海: 上海交通大学出版社) 第131–140 页]

    [32]

    Wu M, Könözsy L, Ludwig A, Schtzenhöfer W, Tanzer R 2008 Steel. Res. Int. 79 637

    [33]

    Tong J S 1999 Theory of Molecular Aggregation and Application (BeiJing: Science Press) pp37-68 (in Chinese)[童景山1999 分子聚集理论及其应用(北京: 科学出版社) 第37–68 页]

    [34]

    Yaguchi H 1986 J. Applied. Metalworking. 4 214

  • [1]

    Nazábal J L, Urcola J J, Fuentes M 1984 Metallography. 71 439

    [2]

    Murakami Y, Mine K, Usuki H 1988 J. Iron. Steel. Inst. Jpn. 74 1113

    [3]

    Bernsmann G, Bleymehl M, Ehl R 2001 Stahl. Eisen. 121 87

    [4]

    Iwamoto T, Murakami T 2004 JFE. Tech. Rep. 4 74

    [5]

    Guduru R K, Scattergood R O, Koch C C, Murty K L, Guruswamy S, McCarter M K 2006 Scripta. Mater. 54 1879

    [6]

    Yamauchi K, Nakagawa Y 1971 Jpn. J. Appl. Phys. 10 1730

    [7]

    Burton B 1991 J. Phase. Equilib. 12 200

    [8]

    Iwama N, Uchiyama M, Owaki S 1999 Curr. Adv. Mater. Process. 12 1387

    [9]

    Mcdonald R J, Hunt J D 1969 Trans. Metall. Soc. AIME. 245 1993

    [10]

    Mcdonald R J, Hunt J D 1970 Metall. Trans. 1 1787

    [11]

    Sarazin J R, Hellawell A 1988 Metall. Trans. A 19 1861

    [12]

    Shahani H, Amberg G, Fredriksson H 1991 Metall. Trans. A 23 2301

    [13]

    Schneider M C, Beckermann C 1995 Int. J. Heat. Mass. Tran. 38 3455

    [14]

    Belleta M, Combeau H, Fautrelle Y, Gobin D, Rady M, Arquis E, Budenkova O, Dussoubs B, Duterrail Y, Kumar A, Gandin C A, Goyeau B, Mosbah S, Založ nik M 2009 Int. J. Therm. Sci. 48 2013

    [15]

    Wang T M, Yao S, Zhang X G, Jin J Z, Wu M, Ludwig A, Pustal B, B hrig-Polaczek A 2006 Acta. Metall. Sin. 42 584 (in Chinese)[王同敏, 姚山, 张兴国, 金俊泽, Wu M, Ludwig A, Pustal B, Bhrig-Polaczek A 2006 金属学报42 584]

    [16]

    Cockroft S L, Maijer D M 2009 Modeling of Casting Welding and Advanced Solidification Processes (Warrendale: Wiley-IEEE Press) pp250-265

    [17]

    Zhu C S, Wang Z P, Jing T, Xiao R Z 2006 Acta. Phys. Sin. 55 1502 (in chinese) [朱昌盛, 王智平, 荆涛, 肖荣振 2006 物理学报55 1502]

    [18]

    Kumar A, Dussoubs B, Založ nik M, Combeau H 2009 Phys. J. Appl. Phys. 42 105503

    [19]

    Li J, Wu M, Hao J, Ludwig A 2012 Comp. Mater. Sci. 55 407

    [20]

    Wu M, Ludwig A 2006 Metall. Mater. Trans. A 37 1613

    [21]

    Kumar A, Založ nik M, Combeau H 2012 Int. J. Therm. Sci. 54 33

    [22]

    Schneider M C, Beckermann C 1995 Int. J. Heat. Mass. Tran. 38 3455

    [23]

    Wu M, Ludwig A 2007 Metall. Mater. Trans. A 38 1465

    [24]

    Xu D, Bai Y, Guo J, Fu H, Guo J J 2004 Int. J. Heat. Mass. Tran. 46 767

    [25]

    Beckermann C, Viskanta R 1993 Appl. Mech. Rev. 46 1

    [26]

    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 物理学报58 104]

    [27]

    Založ nik M, Combeau H 2010 Comp. Mater. Sci. 48 1

    [28]

    Wang K F, Guo J J, Mi G F, Li B S, Fu H Z 2008 Acta. Phys. Sin. 57 3048 (in chinese) [王狂飞, 郭景杰, 米国发, 李邦盛, 傅恒志2008 物理学报57 3048]

    [29]

    Li Q, Guo Q Y, Li R D 2003 Chin. Phys. 15 778

    [30]

    Monchoux J P, Rabkin E 2002 Acta. Mater. 50 3159

    [31]

    Hu G X, Cai X, Rong Y H 2010 Fundamentals of Materials Science (Shanghai: Shanghai Jiao-tong University Press) pp131-140 (in Chinese) [胡赓祥, 蔡珣, 戎咏华2010 材料科学基础(上海: 上海交通大学出版社) 第131–140 页]

    [32]

    Wu M, Könözsy L, Ludwig A, Schtzenhöfer W, Tanzer R 2008 Steel. Res. Int. 79 637

    [33]

    Tong J S 1999 Theory of Molecular Aggregation and Application (BeiJing: Science Press) pp37-68 (in Chinese)[童景山1999 分子聚集理论及其应用(北京: 科学出版社) 第37–68 页]

    [34]

    Yaguchi H 1986 J. Applied. Metalworking. 4 214

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  • Received Date:  15 November 2013
  • Accepted Date:  01 January 2014
  • Published Online:  05 April 2014

Three-dimensional modelling and numerical simulation on segregation during Fe-Pb alloy solidification in a multiphase system

  • 1. College of Material and Mineral Resources, Xi’an University of Architecture and Technology, Xi’an 710055, China;
  • 2. School of Mechanical and Electrical Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
Fund Project:  Project supported by the National Key Technology R&D Program during the 12th Five-year Plan Period of China (Grant No. 2011BAE31B02).

Abstract: The three-dimensional mathematical model for a three-phase flow during its horizontai solidification is studied using fluid dynamics method based on Eulerian-Eulerian and volume of fraction methods, in which the mass, momentum, species, and enthalpy conservation equations of the Fe-Pb alloy solidification process are solved simultaneously. Effects of Pb area quadratic gradient (∇ (∇SPb)) and Pb concentration quadratic gradient (∇ (∇CPb)) on the segregation formation are investigated. Results show that the segregation mode is manifested as X-segregates in the upper and V-segregates in the lower part during flow-solidification of liquid phase and gas phase. The X-segregates result from the phase transformation driving force of gas phase and “scattering” is due to the orientation of phase transition. When t >tc the lower ∇ (∇SPb) and ∇ (∇CPb) curves cause a larger yielding rate of Pb with a larger down angle of X-segregates and a smaller up angle of X-segregates and V-segregates. All these are favorable for the formation of a well-dispersed microstructure. In addition, the gas-liquid two-phase flow interaction term has an effect on channel segregation, showing that channels occur only in the region where the flow-phase transition interaction term (ul·∇cl and ug·∇cg) is negative. With a negative flow-phase transition interaction term the increase in flow velocity due to the flow perturbation and flow-phase transition interaction becomes more negative, thus the channel continues to grow and tends to be stable. Calculated results show good agreement with experimental data.

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