Fe-Pb合金凝固多相体系内偏析形成过程的三维数值模拟

王哲; 王发展; 王欣; 何银花; 马姗; 吴振

doi:10.7498/aps.63.076101

摘要

基于Eulerian-Eulerian方法和流体体积技术，建立了三维多相流体动力学凝固模型，并将其与质量、动量、溶质和热焓守恒方程相耦合，对Fe-Pb合金侧向凝固过程进行了数值模拟. 首先，分析了分布面积二次梯度（∇（∇SPb））和浓度二次梯度（∇（∇CPb））对偏析模式的影响，结果表明：液、气两相的流动相变使偏析模式表现为上端X形下端V形，X偏析由气相相变驱动力和多取向相变作用下的“散射”形成；t >tc时，随∇（∇SPb）和∇（∇CPb）曲线降低，X偏析的下偏析角增大，上偏析角和V偏析角减小，Pb收得率增大，有利于获得含量稳定弥散的凝固组织. 此外，还研究了液、气两相交互流动下通道偏析的形成机理，结果表明：通道偏析仅存在于流动-相变交互作用（ul·∇cl 和ug·∇cg）为负值的区域，该区域的流动扰动抑制合金的局部凝固，促进偏析通道生长；流动-相变交互作用负值越小，偏析通道持续增长越稳定. 模拟结果与实验结果相符合，验证了模型的准确性.

关键词:

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.

Keywords:

作者及机构信息

1.
西安建筑科技大学, 材料与矿资学院, 西安 710055;

2.
西安建筑科技大学, 机电工程学院, 西安 710055

基金项目: 十二五期间国家科技支撑计划项目（批准号：2011BAE31B02）资助的课题.

Authors and contacts

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

Funds: Project supported by the National Key Technology R&D Program during the 12th Five-year Plan Period of China (Grant No. 2011BAE31B02).

参考文献

[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

施引文献

[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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