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金属学报  2018, Vol. 54 Issue (2): 131-150    DOI: 10.11900/0412.1961.2017.00430
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炼钢与连铸过程数值模拟研究进展
朱苗勇(), 娄文涛, 王卫领
东北大学冶金学院 沈阳 110819
Research Progress of Numerical Simulation in Steelmaking and Continuous Casting Processes
Miaoyong ZHU(), Wentao LOU, Weiling WANG
School of Metallurgy, Northeastern University, Shenyang 110819, China
全文: PDF(4741 KB)   HTML
摘要: 

由于钢的冶炼与连铸过程的复杂性以及现场测试条件的限制,数值模拟已成为解析其过程现象和机理不可或缺的手段,自20世纪80年代以来,这种技术得到了飞速发展。在转炉的冶炼方面,利用氧枪超音速射流特性的模拟研究辅助设计了集束、氦气伴随等新型氧枪,通过对转炉熔池内渣-金-气多相流行为模拟研究有效揭示了混匀效率、炉衬冲刷、金属液滴喷溅等物理现象,同时耦合热力学模拟研究了转炉内脱碳、脱磷化学反应过程;在钢的精炼方面,Euler-Euler模型逐渐替代了准单相和Euler-Lagrange模型,成功描述了底吹Ar气钢包内钢液湍流脉动诱导的气泡扩散行为和气泡上浮诱导钢液湍流等现象,而且钢中夹杂物一些新的传输机理和现象也被提出,并利用CFD-PBM模型有效预测了钢液中夹杂物输运、碰撞聚合及去除行为,丰富了钢包精炼夹杂物去除机理,同时CFD-SRM耦合模型实现了钢包精炼多组分参与渣-金反应和脱硫行为的预测,有效揭示了钢液与顶渣的成分、底吹模式对脱硫效率的影响规律;在钢的连铸方面,坯壳-结晶器Cu板热流模型与坯壳热/力模型的耦合成功预测了结晶器周向和高度方向的保护渣和气隙分布特征,奠定了新型内凸型曲面结晶器设计和微合金钢角部裂纹控制的理论基础,结晶器内流场与电磁场耦合模拟研究阐明了电磁搅拌和电磁制动作用下钢液流动行为、液面波动特征以及夹杂物在连铸坯内分布特征,基于体积平均方法的多场/多相凝固模型成功揭示了连铸坯宏观偏析形成机理,定量预测了不同工艺参数下连铸坯中心偏析指数,此外,连铸坯凝固组织演变模拟在晶粒层面上获得了进展,目前正向枝晶领域扩展。整体上讲,钢的冶炼与连铸过程的数值模拟朝着多物理化学/多场耦合方向发展,且研究尺度逐渐向微观层面过渡。

关键词 炼钢精炼连铸数值模拟    
Abstract

Because of the complexity of steelmaking and continuous casting processes and their limitation condition for direct measuring and testing, numerical simulation has become an indispensable means to analyze the phenomena and mechanisms occurring in the processes, and since the 1980s, it has made a rapid development. For the converter smelting, some new oxygen lances were designed by using the simulation study of the characteristics of the oxygen lance supersonic jet. Some mathematical models have been established to describe the slag-metal-gas multiphase flow behavior in steelmaking converter, and the flow field, mixing efficiency, metal droplet splashing, lining scouring and other physical phenomena. For the ladle refining, the Euler-Euler model gradually replaces the quasi-unidirectional and Euler-Lagrangian models, and successfully describes the phenomena of bubble turbulent dispersion caused by liquid turbulent fluctuation, and bubble-induced turbulence occurring during bubble floating process. So, some new and important inclusion transport mechanisms and phenomena have been presented. The CFD-PBM model was used to predict successfully the inclusion transport, collision growth and removal behavior in the molten steel, which enriches the inclusions removal theory of ladle refining. The CFD-SRM coupled model was used to accurately describe the slag-metal reaction and desulfurization behavior in a gas-stirred ladle, and the effect of the different content of compositions in synthetic slag and liquid steel, arrangement of bottom blowing tuyeres on the slag-metal reactions and desulfurization efficiency were discussed and clarified. For steel continuous casting, as the heat flow model from the solidified shell to the copper plate of mold was coupled with the thermo/mechanical model of the solidified shell, distributions of mold flux and air gap both along circumference and height directions of the mold were successfully predicted, while founded theoretical backgrounds for designing new mold with inner convex surface and controlling the surface corner crack of micro-alloyed steel. The coupled simulation between flow and electromagnetic fields in mold revealed the flow behavior of molten steel with electromagnetic stirring or braking, the fluctuation characteristic of the slag-steel interface and the distribution characteristic of inclusions in the strand. Based on the volume averaged method, multi-field and multi-phase solidification model successfully clarified the formation mechanism of macro-segregation in continuously cast strand and quantitatively predicted central/centerline segregation indexes in the strand under different casting conditions. In addition, the numerical simulation of the evolution of solidification structure of the continuously cast strand mainly focused on the as-cast grain, and its extension to the dendrite structure needed further more endeavors. Generally speaking, the numerical simulation in steelmaking-continuous casting process is moving towards coupling multi-physical/chemistry phenomena and multi-fields and gradually transits to the microscopic scale.

Key wordssteelmaking    refining    continuous casting    numerical simulation
收稿日期: 2017-10-16     
ZTFLH:  TF7  
基金资助:国家重点研发计划项目No.2016YFB0300105和国家自然科学基金项目No.U1560208
作者简介:

作者简介 朱苗勇,男,1965年生,教授,博士

引用本文:

朱苗勇, 娄文涛, 王卫领. 炼钢与连铸过程数值模拟研究进展[J]. 金属学报, 2018, 54(2): 131-150.
Miaoyong ZHU, Wentao LOU, Weiling WANG. Research Progress of Numerical Simulation in Steelmaking and Continuous Casting Processes. Acta Metall Sin, 2018, 54(2): 131-150.

链接本文:

https://www.ams.org.cn/CN/10.11900/0412.1961.2017.00430      或      https://www.ams.org.cn/CN/Y2018/V54/I2/131

图1  转炉冶炼过程炉内现象示意图
图2  氧枪射流流动结构示意图
图3  钢包精炼过程多相流传输行为及反应动力学数值模拟研究[23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80]
图4  夹杂物碰撞及去除行为示意图
图5  钢包精炼过程中夹杂物行为
图6  钢包中组分元素质量传输和化学反应示意图
图7  连铸坯典型质量缺陷示意图
图8  凝固坯壳-结晶器热/力耦合数值模拟研究[92,93]
[1] Sumi I, Kishimoto Y, Kikuchi Y, et al.Effect of high-temperature field on supersonic oxygen jet behavior[J]. ISIJ Int., 2006, 46: 1312
[2] Alam M, Naser J, Brooks G.Computational fluid dynamics simulation of supersonic oxygen jet behavior at steelmaking temperature[J]. Metall. Mater. Trans., 2010, 41B: 636
[3] Tago Y, Higuchi Y.Fluid flow analysis of jets from nozzles in top blown process[J]. ISIJ Int., 2003, 43: 209
[4] Li M M, Li Q, Kuang S B, et al.Coalescence characteristics of supersonic jets from multi-nozzle oxygen lance in steelmaking BOF[J]. Steel Res. Int., 2015, 86: 1517
[5] Li C L, Zhu R, Wang H X, et al.Oxygen jet technology in BOF[J]. J. Univ. Sci. Technol. Beijing, 2009, 31(S1): 32(李存牢, 朱荣, 王慧霞等. 转炉炼钢氧气射流技术[J]. 北京科技大学学报, 2009, 31(S1): 32)
[6] Liu K, Zhu M Y, Wang Y B.Simulation of flow field of convergent jet[J]. J. Iron Steel Res., 2008, 20(12): 14(刘坤, 朱苗勇, 王滢冰. 聚合射流流场的仿真模拟[J]. 钢铁研究学报, 2008, 20(12): 14)
[7] Sambasivam R, Lenka S N, Durst F, et al.A new lance design for BOF steelmaking[J]. Metall. Mater. Trans., 2007, 38B: 45
[8] Wang H, Zhu R, Gu Y L, et al.Behaviours of supersonic oxygen jet injected from four-hole lance during top-blown converter steelmaking process[J]. Can. Metall. Quart., 2014, 53: 367
[9] Szekely J, Asai S.Turbulent fluid flow phenomena in metals processing operations: Mathematical description of the fluid flow field in a bath caused by an impinging gas jet[J]. Metall. Trans., 1974, 5: 463
[10] Li Y Z, Li D Y.The modeling of fluid flow fields in a bath caused by imping gas jet[J]. J. Iron Steel Res. Beijing, 1983, (4): 48(李有章, 李顶宜. 顶吹气体射流冲击下熔池内液体流场的研究[J]. 北京钢铁学院学报, 1983, (4): 48)
[11] Olivares O, Elias A, Sánchez R, et al.Physical and mathematical models of gas-liquid fluid dynamics in LD converters[J]. Steel Res., 2002, 73: 44
[12] Asahara N, Naito K I, Kitagawa I, et al.Fundamental study on interaction between top blown jet and liquid bath[J]. Steel Res. Int., 2011, 82: 587
[13] Ersson M, Tilliander A, Jonsson L, et al.A mathematical model of an impinging air jet on a water surface[J]. ISIJ Int., 2008, 48: 377
[14] Dong K, Zhu R, He C L, et al.Numerical simulation of three-phase flow in an oxygen top-blown convertor[J]. Chin. J. Process Eng., 2011, 11(1): 20(董凯, 朱荣, 何春来等. 氧气顶吹转炉的三相流数值模拟[J]. 过程工程学报, 2011, 11(1): 20)
[15] Lv M, Zhu R, Guo Y G, et al.Simulation of flow fluid in the BOF steelmaking process[J]. Metall. Mater. Trans., 2013, 44B: 1560
[16] Li Q, Li M M, Kuang S B, et al.Numerical simulation of the interaction between supersonic oxygen jets and molten slag-metal bath in steelmaking BOF process[J]. Metall. Mater. Trans., 2015, 46B: 1494
[17] Du S C, Zhang J Y, Wei S K.A mathematical model for fluid flow in molten bath agitated by impinging gas jet[J]. Acta Metall. Sin., 1986, 22: 137(杜嗣琛, 张家芸, 魏寿昆. 顶吹气体射流冲击下熔池流动的数学模型[J]. 金属学报, 1986, 22: 137)
[18] Wei J H, Zhu H L, Yan S L, et al.Preliminary investigation of fluid mixing characteristics during side and top combined blowing AOD refining process of stainless steel[J]. Steel Res. Int., 2005, 76: 362
[19] Odenthal H J, Emling W H, Kempken J, et al.Advantageous numerical simulation of the converter blowing process[J]. Iron Steel Technol., 2007, 4: 71
[20] Li Y, Lou W T, Zhu M Y.Numerical simulation of gas and liquid flow in steelmaking converter with top and bottom combined blowing[J]. Ironmak. Steelmak., 2013, 40: 505
[21] Ersson M, H?glund L, Tilliander A, et al.Dynamic coupling of computational fluid dynamics and thermodynamics software: Applied on a top blown converter[J]. ISIJ Int., 2008, 48: 147
[22] Zhang T B.Study on high-efficiency and low-cost dephosphorization process of 80t converter in Xinxing ductile iron pipes LTD. [D]. Beijing: University of Science and Technology Beijing, 2015(张同波. 新兴铸管80t转炉高效低成本脱磷工艺研究 [D]. 北京: 北京科技大学, 2015)
[23] Grevet J H, Szekely J, El-Kaddah N.An experimental and theoretical study of gas bubble driven circulation systems[J]. Int. J. Heat Mass Transfer, 1982, 25: 487
[24] Sahai Y, Guthrie R I L. Hydrodynamics of gas stirred melts: Part II. Axisymmetric flows[J]. Metall. Trans., 1982, 13B: 203
[25] Mazumdar D, Guthrie R I L. Hydrodynamic modeling of some gas injection procedures in ladle metallurgy operations[J]. Metall. Trans., 1985, 16B: 83
[26] Castillejos A H, Salcudean M E, Brimacombe J K.Fluid flow and bath temperature destratification in gas-stirred ladles[J]. Metall. Trans., 1989, 20B: 603
[27] Joo S, Guthrie R I L. Modeling flows and mixing in steelmaking ladles designed for single- and dual-plug bubbling operations[J]. Metall. Trans., 1992, 23B: 765
[28] Zhu M Y, Inomoto T, Sawada I, et al.Fluid-flow and mixing phenomena in the ladle stirred by argon through multi-tuyere[J]. ISIJ Int., 1995, 35: 472
[29] Zhu M Y, Sawada I, Yamasaki N, et al.Numerical simulation of three-dimensional fluid flow and mixing process in gas-stirred ladles[J]. ISIJ Int., 1996, 36: 503
[30] Johansen S T, Boysan F.Fluid dynamics in bubble stirred ladles: Part II. Mathematical modeling[J]. Metall. Mater. Trans., 1988, 19B: 755
[31] Mazumdar D, Guthrie R I L. An assessment of a two phase calculation procedure for hydrodynamic modelling of submerged gas injection in ladles[J]. ISIJ Int., 1994, 34: 384
[32] Sheng Y Y, Irons G A.Measurement and modeling of turbulence in the gas/liquid two-phase zone during gas injection[J]. Metall. Trans., 1993, 24B: 695
[33] Sheng Y Y, Irons G A.The impact of bubble dynamics on the flow in plumes of ladle water models[J]. Metall. Mater. Trans., 1995, 26B: 625
[34] Guo D, Irons G A.Modeling of gas-liquid reactions in ladle metallurgy: Part II. Numerical simulation[J]. Metall. Mater. Trans., 2000, 31B: 1457
[35] Türko?lu H, Farouk B.Numerical computations of fluid flow and heat transfer in a gas-stirred liquid bath[J]. Metall. Trans., 1990, 21B: 771
[36] Ilegbusi O J, Szekely J, Iguchi M, et al.A comparison of experimentally measured and theoretically calculated velocity fields in a water model of an argon stirred ladle[J]. ISIJ Int., 1993, 33: 474
[37] Ilegbusi O J, Iguchi M, Nakajima K, et al.Modeling mean flow and turbulence characteristics in gas-agitated bath with top layer[J]. Metall. Mater. Trans., 1998, 29B: 211
[38] Sheng D Y, S?der M, J?nsson P, et al.Modeling micro-inclusion growth and separation in gas-stirred ladles[J]. Scand. J. Metall., 2002, 31: 134
[39] Qu T, Jiang M, Liu C, et al.Transient flow and inclusion removal in gas stirred ladle during teeming process[J]. Steel Res. Int., 2010, 81: 434
[40] Lou W T, Zhu M Y.Numerical simulation of gas and liquid two-phase flow in gas-stirred systems based on Euler-Euler approach[J]. Metall. Mater. Trans., 2013, 44B: 1251
[41] Lindborg U, Torssell K.A collision model for the growth and separation of deoxidation products[J]. Trans. Metall. Soc. AIME, 1968, 242: 94
[42] Nakanishi K, Szekely J.Deoxidation kinetics in a turbulent flow field[J]. Trans. Iron Steel Inst. Jpn., 1975, 15: 522
[43] Miki Y, Shimada Y, Thomas B G, et al.Model of inclusion removal during RH degassing of steel[J]. Iron Steelmaker, 1997, 8: 31
[44] S?der M, J?nsson P, Jonsson L.Growth and removal of inclusions during ladle refining[J]. Steel Res. Int., 2004, 75: 128
[45] Zhang L F, Taniguchi S, Cai K K.Fluid flow and inclusion removal in continuous casting tundish[J]. Metall. Mater. Trans., 2000, 31B: 253
[46] Arai H, Matsumoto K, Shimasaki S I, et al.Model experiment on inclusion removal by bubble flotation accompanied by particle coagulation in turbulent flow[J]. ISIJ Int., 2009, 49: 965
[47] Lei H, Nakajima K, He J C.Mathematical model for nucleation, Ostwald ripening and growth of inclusion in molten steel[J]. ISIJ Int., 2010, 50: 1735
[48] De Santis M, Ferretti A.Thermo-fluid-dynamics modelling of the solidification process and behaviour of non-metallic inclusions in the continuous casting slabs[J]. ISIJ Int., 1996, 36: 673
[49] Bouris D, Bergeles G.Investigation of inclusion re-entrainment from the steel-slag interface[J]. Metall. Mater. Trans., 1998, 29B: 641
[50] Miki Y, Thomas B G.Modeling of inclusion removal in a tundish[J]. Metall. Mater. Trans., 1999, 30B: 639
[51] Yuan Q, Thomas B G, Vanka S P.Study of transient flow and particle transport in continuous steel caster molds: Part II. Particle transport[J]. Metall. Mater. Trans., 2004, 35B: 703
[52] López-Ramirez S, Palafox-Ramos J, Barreto J D, et al.Modeling study of the influence of turbulence inhibitors on the molten steel flow, tracer dispersion, and inclusion trajectories in tundishes[J]. Metall. Mater. Trans., 2001, 32B: 615
[53] Zhang L F, Wang Y F, Zuo X J.Flow transport and inclusion motion in steel continuous-casting mold under submerged entry nozzle clogging condition[J]. Metall. Mater. Trans., 2008, 39B: 534
[54] Zhu M Y, Zheng S G, Huang Z Z, et al.Numerical simulation of nonmetallic inclusions behaviour in gas-stirred ladles[J]. Steel Res. Int., 2005, 76: 718
[55] Lei H, Wang L Z, Wu Z N, et al.Collision and coalescence of alumina particles in the vertical bending continuous caster[J]. ISIJ Int., 2002, 42: 717
[56] Geng D Q, Lei H, He J C.Numerical simulation for collision and growth of inclusions in ladles stirred with different porous plug configurations[J]. ISIJ Int., 2010, 50: 1597
[57] Sheng D Y, S?der M, J?nsson P, et al.Modeling micro-inclusion growth and separation in gas-stirred ladles[J]. Scand. J. Metall., 2002, 31: 134
[58] Wang L T, Zhang Q Y, Peng S H, et al.Mathematical model for growth and removal of inclusion in a multi-tuyere ladle during gas-stirring[J]. ISIJ Int., 2005, 45: 331
[59] Wang L T, Zhang Q Y, Deng C H, et al.Mathematical model for removal of inclusion in molten steel by injecting gas at ladle shroud[J]. ISIJ Int., 2005, 45: 1138
[60] Kwon Y J, Zhang J, Lee H G.A CFD-based nucleation-growth-removal model for inclusion behavior in a gas-agitated ladle during molten steel deoxidation[J]. ISIJ Int., 2008, 48: 891
[61] Shirabe K, Szekely J.A mathematical model of fluid flow and inclusion coalescence in the R-H vacuum degassing system[J]. Trans. Iron Steel Inst. Jpn., 1983, 23: 465
[62] Sinha A K, Sahai Y.Mathematical modeling of inclusion transport and removal in continuous casting tundishes[J]. ISIJ Int., 1993, 33: 556
[63] Chen G J, He S P, Li Y G, et al.Modeling dynamics of agglomeration, transport, and removal of Al2O3 clusters in the Rheinsahl-Heraeus reactor based on the coupled computational fluid dynamics-population balance method model[J]. Ind. Eng. Chem. Res., 2016, 55: 7030
[64] Ling H T, Zhang L F, Li H.Mathematical modeling on the growth and removal of non-metallic inclusions in the molten steel in a two-strand continuous casting tundish[J]. Metall. Mater. Trans., 2016, 47B: 2991
[65] Lou W T, Zhu M Y.Numerical simulations of inclusion behavior in gas-stirred ladles[J]. Metall. Mater. Trans., 2013, 44B: 762
[66] Hassal G J, Jackaman D P, Hawkins R T.Phosphorus and sulphur removal from liquid steel in ladle steelmaking processes[J]. Ironmaking Steelmaking, 1991, 18: 359
[67] Reifferscheid M, Pluschkell W.Development of a numerical model simulating the desulphurisation of liquid steel[J]. Steel Res., 1994, 65: 309
[68] Wei J H, Zhu S J, Yu N W.Kinetics of desulphurization by powder injection and blowing in RH refining of molten steel[J]. Acta Metall. Sin., 1998, 34: 497(魏季和, 朱守军, 郁能文. 钢液RH精炼中喷粉脱硫的动力学[J]. 金属学报, 1998, 34: 497)
[69] Zhu R, Wang X H, Di L, et al.Study on desulphurization refining by powder injection with ladle-immersion cover[J]. Spec. Steels, 2000, 21: 9(朱荣, 王新华, 迪林等. 钢包浸渍罩钢液喷粉脱硫试验研究 [J]. 特殊钢, 2000, 21: 9)
[70] Wu K, Liang Z G, Zhang E H, et al.Research on the slag-metal sulfur partition and the kinetics equation of desulfurization in LF refining process[J]. Acta Metall. Sin., 2001, 37: 1069(吴铿, 梁志刚, 张二华等. LF精炼过程中硫分配比和脱硫动力学方程研究[J]. 金属学报, 2001, 37: 1069)
[71] Li S Q, Xiong G H, Li S Q, et al.Dynamic model applied in ultra-low sulphur steel refining desurlfurization process[J]. J. Univ. Sci. Technol. Beijing, 2004, 26: 244(李素芹, 熊国宏, 李士琦等. 极低硫钢的精炼脱硫动力学模型[J]. 北京科技大学学报, 2004, 26: 244)
[72] Roy D, Pistorius P C, Fruehan R J.Effect of silicon on the desulfurization of Al-killed steels: Part I. Mathematical model[J]. Metall. Mater. Trans., 2013, 44B: 1086
[73] Jonsson L, Du S C, J?nsson P.A new approach to model sulphur refining in a gas-stirred ladle—A coupled CFD and thermodynamic model[J]. ISIJ Int., 1998, 38: 260
[74] Andersson M, Hallberg M, Jonsson L, et al.Slag-metal reactions during ladle treatment with focus on desulphurisation[J]. Ironmak. Steelmak., 2013, 29: 224
[75] Andersson M A T, Jonsson L T I, J?nsson P G. A thermodynamic and kinetic model of reoxidation and desulphurisation in the ladle furnace[J]. ISIJ Int., 2000, 40: 1080
[76] Singh U, Anapagaddi R, Mangal S, et al.Multiphase modeling of bottom-stirred ladle for prediction of slag-steel interface and estimation of desulfurization behavior[J]. Metall. Mater. Trans., 2016, 47B: 1804
[77] Wang Q, He Z, Li G Q, et al.Numerical investigation of desulfurization behavior in electroslag remelting process[J]. Int. J. Heat Mass Transf., 2017, 104: 943
[78] Lou W T, Zhu M Y.Numerical simulation of desulfurization behavior in gas-stirred systems based on computation fluid dynamics-simultaneous reaction model (CFD-SRM) coupled model[J]. Metall. Mater. Trans., 2014, 45B: 1706
[79] Lou W T, Zhu M Y.Numerical simulation of slag-metal reactions and desulfurization efficiency in gas-stirred ladles with different thermodynamics and kinetics[J]. ISIJ Int., 2015, 55: 961
[80] Lou W T, Zhu M Y.A mathematical model for the multiphase transport and reaction kinetics in a ladle with bottom powder injection[J]. Metall. Mater. Trans., 2017, 48B: 3196
[81] Mahapatra R B, Brimacombe J K, Samarasekera I V, et al.Mold behavior and its influence on quality in the continuous casting of steel slabs: Part I. Industrial trials, mold temperature measurements, and mathematical modeling[J]. Metall. Mater. Trans., 1991, 22B: 861
[82] Wang X D, Tang L, Zang X Y, et al.Mold transient heat transfer behavior based on measurement and inverse analysis of slab continuous casting[J]. J. Mater. Process. Technol., 2012, 212: 1811
[83] Park J K, Samarasekera I V, Thomas B G, et al.Thermal and mechanical behavior of copper molds during thin-slab casting (I): Plant trial and mathematical modeling[J]. Metall. Mater. Trans., 2002, 33B: 425
[84] Liu X D, Zhu M Y, Cheng N L.An analysis of thermal elastoplastic behavior of continuous casting slab mold[J]. Acta Metall. Sin., 2006, 42: 1137(刘旭东, 朱苗勇, 程乃良. 板坯连铸结晶器的热弹塑性力学分析[J]. 金属学报, 2006, 42: 1137)
[85] Kim K, Han H N, Yeo T, et al.Analysis of surface and internal cracks in continuously cast beam blank[J]. Ironmak. Steelmak., 1997, 24: 249
[86] Han H N, Lee J E, Yeo T J, et al.A finite element model for 2-dimensional slice of cast strand[J]. ISIJ Int., 1999, 39: 445
[87] Park J K, Thomas B G, Samarasekera I V.Analysis of thermo-mechanical behaviour in billet casting with different mould corner radii[J]. Ironmak. Steelmak., 2002, 29: 359
[88] Jing D J, Cai K K.Finite element simulation of thermo-mechanically coupled states in continuous casting mold[J]. Acta Metall. Sin., 2000, 36: 403(荆德君, 蔡开科. 连铸结晶器内热-力耦合状态有限元模拟[J]. 金属学报, 2000, 36: 403)
[89] Zhang J Q, Cui L X, Chen Z P, et al.Coupling model for temperature/stress fields analysis in slab casting moulds[J]. J. Univ. Sci. Technol. Beijing, 2004, 26: 373(张家泉, 崔立新, 陈志平等. 板坯连铸结晶器内温度/应力场耦合模型 [J]. 北京科技大学学报, 2004, 26: 373)
[90] Meng Y A, Thomas B G.Heat-transfer and solidification model of continuous slab casting: CON1D[J]. Metall. Mater. Trans., 2003, 34B: 685
[91] Li C S, Thomas B G.Thermomechanical finite-element model of shell behavior in continuous casting of steel[J]. Metall. Mater. Trans., 2004, 35B: 1151
[92] Cai Z Z, Zhu M Y.Simulation of thermal behavior during steel solidification in slab continuous casting mold I. Mathematical model[J]. Acta Metall. Sin., 2011, 47: 671(蔡兆镇, 朱苗勇. 板坯连铸结晶器内钢凝固过程热行为研究 I. 数学模型[J]. 金属学报, 2011, 47: 671)
[93] Cai Z Z, Zhu M Y.Simulation of thermal behavior during steel solidification in slab continuous casting mold II. Model verification and results analysis[J]. Acta Metall. Sin., 2011, 47: 678(蔡兆镇, 朱苗勇. 板坯连铸结晶器内钢凝固过程热行为研究 II. 模型验证与结果分析[J]. 金属学报, 2011, 47: 678)
[94] Cai Z Z, Zhu M Y.Thermo-mechanical behavior of peritectic steel solidifying in slab continuous casting mold and a new mold taper design[J]. ISIJ Int., 2013, 53: 1818
[95] Yang J, Meng X N, Wang N, et al.Oscillation-mark formation and liquid-slag consumption in continuous casting mold[J]. Metall. Mater. Trans., 2017, 48B: 1230
[96] Ma J C, Xie Z, Jia G L.Applying of real-time heat transfer and solidification model on the dynamic control system of billet continuous casting[J]. ISIJ Int., 2008, 48: 1722
[97] Louhenkilpi S, M?kinen M, Vapalahti S, et al.3D steady state and transient simulation tools for heat transfer and solidification in continuous casting[J]. Mater. Sci. Eng., 2005, A413: 135
[98] Liu K Z.Research and numerical simulation of new continuous straightening curve [D]. Qinhuangdao: Yanshan University, 2011(刘克仲. 新型连续矫直曲线的研究及数值模拟 [D]. 秦皇岛: 燕山大学, 2011)
[99] Lin Q Y, Zhu M Y.Analysis of reduction efficiency in soft reduction for continuous casting slab[J]. Acta Metall. Sin., 2007, 43: 1301(林启勇, 朱苗勇. 连铸板坯轻压下过程中的压下效率分析[J]. 金属学报, 2007, 43: 1301)
[100] Lin Q Y, Zhu M Y.Theoretical model and analysis of soft reduction gradient for continuous casting slab[J]. Acta Metall. Sin., 2007, 43: 847(林启勇, 朱苗勇. 连铸板坯轻压下过程压下率理论模型及其分析 [J]. 金属学报, 2007, 43: 847)
[101] Luo S, Zhu M Y, Ji C, et al.Characteristics of solute segregation in continuous casting bloom with dynamic soft reduction and determination of soft reduction zone[J]. Ironmak. Steelmak., 2010, 37: 140
[102] Ji C, Wu C H, Zhu M Y.Thermo-mechanical behavior of the continuous casting bloom in the heavy reduction process[J]. JOM, 2016, 68: 3107
[103] Wu C H, Ji C, Zhu M Y.Analysis of the thermal contraction of wide-thick continuously cast slab and the weighted average method to design a roll gap[J]. Steel Res. Int., 2017, 88: 1600514
[104] Cukierski K, Thomas B G.Flow control with local electromagnetic braking in continuous casting of steel slabs[J]. Metall. Mater. Trans., 2008, 39B: 94
[105] Chaudhary R, Thomas B G, Vanka S P.Effect of electromagnetic ruler braking (EMBr) on transient turbulent flow in continuous slab casting using large eddy simulations[J]. Metall. Mater. Trans., 2012, 43B: 532
[106] Genma N, Soejima T, Saito T, et al.The linear-motor type in-mold electromagnetic stirring technique for the slab continuous caster[J]. ISIJ Int., 1989, 29: 1056
[107] Li B K, Tsukihashi F.Numerical estimation of the effect of the magnetic field application on the motion of inclusion in continuous casting of steel[J]. ISIJ Int., 2003, 43: 923
[108] Li B K, Tsukihashi F.Effects of electromagnetic brake on vortex flows in thin slab continuous casting mold[J]. ISIJ Int., 2006, 46: 1833
[109] Liu Z Q, Li B K, Jiang M F.Transient asymmetric flow and bubble transport inside a slab continuous-casting mold[J]. Metall. Mater. Trans., 2014, 45B: 675
[110] Liu Z Q, Li B K, Zhang L, et al.Analysis of transient transport and entrapment of particle in continuous casting mold[J]. ISIJ Int., 2014, 54: 2324
[111] Liu H P, Xu M G, Qiu S T, et al.Numerical simulation of fluid flow in a round bloom mold with in-mold rotary electromagnetic stirring[J]. Metall. Mater. Trans., 2012, 43B: 1657
[112] Yu H Q, Zhu M Y.Numerical simulation of the effects of electromagnetic brake and argon gas injection on the three-dimensional multiphase flow and heat transfer in slab continuous casting mold[J]. ISIJ Int., 2008, 48: 584
[113] Yu H Q, Zhu M Y, Wang J.Interfacial fluctuation behavior of steel/slag in medium-thin slab continuous casting mold with argon gas injection[J]. J. Iron Steel Res. Int., 2010, 17: 5
[114] Trindade L B, Vilela A C F, Filho A F F, et al. Numerical model of electromagnetic stirring for continuous casting billets[J]. IEEE Trans. Magn., 2002, 38: 3658
[115] Natarajan T T, El-Kaddah N.Finite element analysis of electromagnetic and fluid flow phenomena in rotary electromagnetic stirring of steel[J]. Appl. Math. Model., 2004, 28: 47
[116] Ren B Z, Chen D F, Wang H D, et al.Numerical analysis of coupled turbulent flow and macroscopic solidification in a round bloom continuous casting mold with electromagnetic stirring[J]. Steel Res. Int., 2015, 86: 1104
[117] Yu H Q, Zhu M Y.3-D numerical simulation of flow field and temperature field in a round billet continuous casting mold with electromagnetic stirring[J]. Acta Metall. Sin., 2008, 44: 1465(于海岐, 朱苗勇. 圆坯结晶器电磁搅拌过程三维流场与温度场数值模拟[J]. 金属学报, 2008, 44: 1465)
[118] Yu H Q, Zhu M Y.Influence of electromagnetic stirring on transport phenomena in round billet continuous casting mould and macrostructure of high carbon steel billet[J]. Ironmak. Steelmak., 2012, 39: 574
[119] Jiang D B, Zhu M Y.Flow and solidification in billet continuous casting machine with dual electromagnetic stirrings of mold and the final solidification[J]. Steel Res. Int., 2015, 86: 993
[120] Wu M H, Kharicha A, Ludwig A.Discussion on modeling capability for macrosegregation[J]. High Temp. Mater. Process (London), 2017, 36: 531
[121] Mehrabian R, Keane M, Flemings M C.Interdendritic fluid flow and macrosegregation; influence of gravity[J]. Metall. Mater. Trans., 1970, 1B: 1209
[122] Bennon W D, Incropera F P.A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems—I. Model formulation[J]. Int. J. Heat Mass Transf., 1987, 30: 2161
[123] Aboutalebi M R, Hasan M, Guthrie R I L. Coupled turbulent flow, heat, and solute transport in continuous casting processes[J]. Metall. Mater. Trans., 1995, 26B: 731
[124] Yang H L, Zhao L G, Zhang X Z, et al.Mathematical simulation on coupled flow, heat, and solute transport in slab continuous casting process[J]. Metall. Mater. Trans., 1998, 29B: 1345
[125] Li Z Y, Zhao J Z.Coupled numberical simulation on solidification and solute transport in thin slab continuous casting process[J]. Acta Metall. Sin., 2006, 42: 211(李中原, 赵九洲. 平行板型薄板坯连铸结晶器中钢液流动、凝固及溶质分布的三维耦合数值模拟[J]. 金属学报, 2006, 42: 211)
[126] Sun H B, Zhang J Q.Study on the macrosegregation behavior for the bloom continuous casting: Model development and validation[J]. Metall. Mater. Trans., 2014, 45B: 1133
[127] Sun H B, Zhang J Q.Macrosegregation improvement by swirling flow nozzle for bloom continuous castings[J]. Metall. Mater. Trans., 2014, 45B: 936
[128] Zhao X K, Zhang J M, Lei S W, et al.The position study of heavy reduction process for improving centerline segregation or porosity with extra- thickness slabs[J]. Steel Res. Int., 2014, 85: 645
[129] Dong Q P, Zhang J M, Qian L, et al.Numerical modeling of macrosegregation in round billet with different microsegregation models[J]. ISIJ Int., 2017, 57: 814
[130] Li B K.Prediction model of the centerline macro-segregation in slab continuous casting of steel[J]. J. Northeast. Univ., 2001, 22: 652(李宝宽. 板坯连铸中心线偏析的预测模型[J]. 东北大学学报, 2001, 22: 652)
[131] Zhang H W, Wang E G, He J C.Coupled numerical simulation on fluid flow, solidification and solute transport in billet continuous casting process[J]. Acta Metall. Sin., 2002, 38: 99(张红伟, 王恩刚, 赫冀成. 方坯连铸过程中钢液流动、凝固及溶质分布的耦合数值模拟[J]. 金属学报, 2002, 38: 99)
[132] Murao T, Kajitani T, Yamamura H, et al.Simulation of the center-line segregation generated by the formation of bridging[J]. ISIJ Int., 2014, 54: 359
[133] Janssen R J A, Bart G C J, Cornelissen M C M, et al. Macrosegregation in continuously cast steel billets and blooms[J]. Appl. Sci. Res., 1994, 52: 21
[134] Lesoult G, Sella S. Spongy behaviour of alloys during solidification: Flow of liquid metal and segregation in the mushy zone [J]. Solid State Phenom., 1988, 3-7: 167
[135] Beckermann C, Viskanta R.Double-diffusive convection during dendritic solidification of a binary mixture[J]. Physicochem. Hydrodyn., 1988, 10: 195
[136] Wang C Y, Beckermann C.Equiaxed dendritic solidification with convection: Part I. Multiscale/multiphase modeling[J]. Metall. Mater. Trans., 1996, 27A: 2754
[137] Ahmadein M, Wu M, Ludwig A.Analysis of macrosegregation formation and columnar-to-equiaxed transition during solidification of Al-4wt.%Cu ingot using a 5-phase model[J]. J. Cryst. Growth, 2015, 417: 65
[138] Tu W T, Shen H F, Liu B C.Two-phase modeling of macrosegregation in a 231 t steel ingot[J]. ISIJ Int., 2014, 54: 351
[139] Li D Z, Chen X Q, Fu P X, et al.Inclusion flotation-driven channel segregation in solidifying steels[J]. Nat. Commun., 2014, 5: 5572
[140] Wang T M, Yao S, Zhang X G, et al.Modelling of the thermo-solutal convection, shrinkage flow and grain movement during globular equiaxed solidification in a multi-phase system—I. Three-phase flow model[J]. Acta Metall. Sin., 2006, 42: 584(王同敏, 姚山, 张兴国等. 等轴球晶凝固多相体系内热溶质对流、补缩流及晶粒运动的数值建模 I. 三相流模型[J]. 金属学报, 2006, 42: 584)
[141] Wu M, Ludwig A, Kharicha A.A four phase model for the macrosegregation and shrinkage cavity during solidification of steel ingot[J]. Appl. Math. Model., 2017, 41: 102
[142] Mayer F, Wu M, Ludwig A.On the formation of centreline segregation in continuous slab casting of steel due to bulging and/or feeding[J]. Steel Res. Int., 2010, 81: 660
[143] Domitner J, Wu M H, Kharicha A, et al.Modeling the effects of strand surface bulging and mechanical softreduction on the macrosegregation formation in steel continuous casting[J]. Metall. Mater. Trans., 2014, 45A: 1415
[144] Wu M H, Domitner J, Ludwig A.Using a two-phase columnar solidification model to study the principle of mechanical soft reduction in slab casting[J]. Metall. Mater. Trans., 2012, 43A: 945
[145] Jiang D, Zhu M.Solidification structure and macrosegregation of billet continuous casting process with dual electromagnetic stirrings in mold and final stage of solidification: A numerical study[J]. Metall. Mater. Trans., 2016, 47B: 3446
[146] Jiang D B, Zhu M Y.Center segregation with final electromagnetic stirring in billet continuous casting process[J]. Metall. Mater. Trans., 2017, 48B: 444
[147] Jang D B, Wang W L, Luo S, et al.Mechanism of macrosegregation formation in continuous casting slab: A numerical simulation study[J]. Metall. Mater. Trans., 2017, 48B: 3120
[148] B?ttger B, Schmitz G J, Santillana B.Multi-phase-field modeling of solidification in technical steel grades[J]. Trans. Indian Inst. Met., 2012, 65: 613
[149] B?ttger B, Apel M, Santillana B, et al.Phase-field modelling of microstructure formation during the solidification of continuously cast low carbon and HSLA steels[J]. IOP Conf. Ser. Mater. Sci. Eng., 2012, 33: 012107.
[150] Hou Z B, Jiang F, Cheng G G.Solidification structure and compactness degree of central equiaxed grain zone in continuous casting billet using cellular automaton-finite element method[J]. ISIJ Int., 2012, 52: 1301
[151] Hou Z B, Cheng G G, Jiang F, et al.Compactness degree of longitudinal section of outer columnar grain zone in continuous casting billet using cellular automaton-finite element method[J]. ISIJ Int., 2013, 53: 655
[152] Burbelko A, Falkus J, Kapturkiewicz W, et al.Modeling of the grain structure formation in the steel continuous ingot by CAFE method[J]. Arch. Metall. Mater., 2012, 57: 379
[153] Yamazaki M, Natsume Y, Harada H, et al.Numerical simulation of solidification structure formation during continuous casting in Fe-0.7mass%C alloy using cellular automaton method[J]. ISIJ Int., 2006, 46: 903
[154] Jing C L, Wang X H, Jiang M.Study on solidification structure of wheel steel round billet using FE-CA coupling model[J]. Steel Res. Int., 2011, 82: 1173
[155] Wang J, Wang F, Li C, et al.Simulation of solidification microstructure and columnar to equiaxed transition in free-cutting steel 9SMn28 based on a cafe method[J]. Steel Res. Int., 2010, 81: 150
[156] Luo S, Zhu M Y, Louhenkilpi S.Numerical simulation of solidification structure of high carbon steel in continuous casting using cellular automaton method[J]. ISIJ Int., 2012, 52: 823
[157] Michelic S C, Thuswaldner J M, Bernhard C.Polydimensional modelling of dendritic growth and microsegregation in multicomponent alloys[J]. Acta Mater., 2010, 58: 2738
[158] Pan S Y, Zhu M F.A three-dimensional sharp interface model for the quantitative simulation of solutal dendritic growth[J]. Acta Mater., 2010, 58: 340
[159] Zhao Y, Qin R S, Chen D F, et al.A three dimensional cellular automata model for dendrite growth in non-equilibrium solidification of binary alloy[J]. Steel Res. Int., 2015, 86: 1490
[160] Wang W L, Luo S, Zhu M Y.Numerical simulation of three-dimensional dendritic growth of alloy: Part II—Model application to Fe-0.82WtPctC alloy[J]. Metall. Mater. Trans., 2016, 47A: 1355
[161] Luo S, Zhu M Y.A two-dimensional model for the quantitative simulation of the dendritic growth with cellular automaton method[J]. Comput. Mater. Sci., 2013, 71: 10
[162] Wang W L, Luo S, Zhu M Y.Numerical simulation of three-dimensional dendritic growth of alloy: Part I—model development and test[J]. Metall. Mater. Trans., 2016, 47A: 1339
[163] Wang W L, Luo S, Zhu M Y.Development of a CA-FVM model with weakened mesh anisotropy and application to Fe-C alloy[J]. Crystals, 2016, 6: 147
[164] Wang W L, Ji C, Luo S, et al.Modeling of Dendritic Evolution of Continuously Cast Steel Billet with Cellular Automaton[J]. Metall. Mater. Trans., 2018, 49B: 200
[165] Zuo X J, Meng X N, Huang S, et al.Morphology simulation and mechanical analysis of primary dendrites for continuously cast low carbon steel[J]. Acta Phys. Sin., 2016, 65: 166101(左晓静, 孟祥宁, 黄烁等. 连铸低碳钢一次枝晶演变数值模拟及其受力分析[J]. 物理学报, 2016, 65: 166101)
[166] Pan S Y, Zhu M F, Rettenmayr M.A phase-field study on the peritectic phase transition in Fe-C alloys[J]. Acta Mater., 2017, 132: 565
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