特大方坯新型结晶器技术的研究
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摘要
随着现代工业的发展，现有普通尺寸规格的方坯难以满足市场的需求，如在桥梁、隧道建造行业，亟需一些大断面尺寸的钢材来满足其基础建设的需要。本文根据实际需要提出建设700mm×700mm特大方坯，并依据大方坯连铸的特点，分析了结晶器传热过程及新型结晶器技术的特点，针对700mm×700mm特大方坯提出了在结晶器内部设置内冷却器的方案。运用CFD技术及ANSYS对复合冷却结晶器内钢水的流场、温度场、钢水的凝固传热行为及结晶器壁的温度场与应力进行了仿真分析，其为以后700mm×700mm特大方坯的建设及新型结晶器技术的深入研究提供了理论指导。
(1)给出了复合冷却结晶器的结构简图，理论分析了设置内冷却器的作用。
(2)利用FLUENT软件，建立了复合冷却结晶器内部铸坯的三维模型，对采用不同结晶器浇注时结晶器内部流场与温度场进行了研究。通过对比分析结果，得到了采用复合冷却结晶器的优点。
(3)运用FLUENT软件中凝固/熔化模型，研究了复合冷却结晶器内钢水的凝固行为。给出了结晶器内不同截面处的温度云图与液相分数云图，绘制了铸坯内部及表面的温度曲线、铸坯坯壳厚度的生长曲线。
(4)建立了外结晶器、内冷却器与钢水流固耦合传热数学模型，对结晶器壁与钢水间的传热热阻进行了深入研究，考虑了气隙热阻及结晶器内钢水流场对结晶器温度场的影响，计算得到了外结晶器、内冷却器的温度场分布；运用ANSYS结合计算所得到的温度场计算了外结晶器、内冷却器的热应力分布，这为以后深入研究内冷却器在连铸结晶器中的应用提供了依据。
With the development of modern industry, the traditional dimension steel can hardlymeet the needs of market, such as bridge and tunnel industry, thus supercolossalcross-section slab is greatly needed to satisfy the infrastructural needs. This papersuggested building700mm×700mm supercolossal bloom continuous casting machine onthe basis of practical needs. The process of heat transfer of mold and the characteristicsof new mold technology were analyzed according to bloom continuous casting. Finally,an inner cooler was applied to the mold of700mm×700mm bloom. CFD technology andANSYS software were used to do simulation of the flow, temperature and solidificationprocess of molten steel in the mold, and the temperature and thermal stress of mold wereanalyzed as well. It has theoretical and practical significance in the built of700mm×700mm bloom continuous casting, doing further research about new moldtechnology.
(1) The drawing of the complex mold was given and analyzed the effects of innercooler.
(2) The CFD software FLUENT was applied to build the3-D model of slab ofcomplex mold, the flow and the temperature of mold were studied when different moldswere used to casting. The advantages of complex were vividly revealed according toresult of simulation.
(3) The processes of solidification of molten steel were in-depth studied with the useof solidification/molten model of FLUENT. The temperature contour and liquid fractioncontour of the different cross-section of mold, the temperature curve of slab and surfacecentral, the curve of shell thickness along mold were given.
(4) Fluid-Solid interaction coupling thermal model of outer mold and inner coolerwith steel were built, which was used to study the temperature distribution of outer moldand inner cooler. The heat resistance was closely investigated, the influence of the heatresistance between steel and mold and the flow of mold were considered in the process of modeling. ANSYS software was applied to calculate the stress and strain distribution oftwo parts of complex mold combined with temperature, which provided reference forfurther research in continuous casting and inner cooler.
(1)给出了复合冷却结晶器的结构简图，理论分析了设置内冷却器的作用。
(2)利用FLUENT软件，建立了复合冷却结晶器内部铸坯的三维模型，对采用不同结晶器浇注时结晶器内部流场与温度场进行了研究。通过对比分析结果，得到了采用复合冷却结晶器的优点。
(3)运用FLUENT软件中凝固/熔化模型，研究了复合冷却结晶器内钢水的凝固行为。给出了结晶器内不同截面处的温度云图与液相分数云图，绘制了铸坯内部及表面的温度曲线、铸坯坯壳厚度的生长曲线。
(4)建立了外结晶器、内冷却器与钢水流固耦合传热数学模型，对结晶器壁与钢水间的传热热阻进行了深入研究，考虑了气隙热阻及结晶器内钢水流场对结晶器温度场的影响，计算得到了外结晶器、内冷却器的温度场分布；运用ANSYS结合计算所得到的温度场计算了外结晶器、内冷却器的热应力分布，这为以后深入研究内冷却器在连铸结晶器中的应用提供了依据。
With the development of modern industry, the traditional dimension steel can hardlymeet the needs of market, such as bridge and tunnel industry, thus supercolossalcross-section slab is greatly needed to satisfy the infrastructural needs. This papersuggested building700mm×700mm supercolossal bloom continuous casting machine onthe basis of practical needs. The process of heat transfer of mold and the characteristicsof new mold technology were analyzed according to bloom continuous casting. Finally,an inner cooler was applied to the mold of700mm×700mm bloom. CFD technology andANSYS software were used to do simulation of the flow, temperature and solidificationprocess of molten steel in the mold, and the temperature and thermal stress of mold wereanalyzed as well. It has theoretical and practical significance in the built of700mm×700mm bloom continuous casting, doing further research about new moldtechnology.
(1) The drawing of the complex mold was given and analyzed the effects of innercooler.
(2) The CFD software FLUENT was applied to build the3-D model of slab ofcomplex mold, the flow and the temperature of mold were studied when different moldswere used to casting. The advantages of complex were vividly revealed according toresult of simulation.
(3) The processes of solidification of molten steel were in-depth studied with the useof solidification/molten model of FLUENT. The temperature contour and liquid fractioncontour of the different cross-section of mold, the temperature curve of slab and surfacecentral, the curve of shell thickness along mold were given.
(4) Fluid-Solid interaction coupling thermal model of outer mold and inner coolerwith steel were built, which was used to study the temperature distribution of outer moldand inner cooler. The heat resistance was closely investigated, the influence of the heatresistance between steel and mold and the flow of mold were considered in the process of modeling. ANSYS software was applied to calculate the stress and strain distribution oftwo parts of complex mold combined with temperature, which provided reference forfurther research in continuous casting and inner cooler.
引文
[1]罗振才.炼钢机械[M].北京：冶金工业出版社，1989：146-150.
[2]蔡开科，程士富.连续铸钢原理和工艺[M].北京：冶金工业出版社，1994:64-70.
[3]徐少兵,吴建洲.国内外大方坯连铸机新技术发展综述[J].中国冶金,2008,18(4):1-6.
[4]金泽洪. WAMTM公司特殊钢大方坯连铸成套技术的发展[C].中国金属学会2007年大方坯圆坯异型坯连铸技术研讨会,2007:96-102.
[5] Fabio Costanzo.康力斯集团Aldwarke新建5流大方坯连铸机[C].2005中国钢铁年会，2005:304-311.
[6]吴狄峰.大方坯结晶器内钢液流动、传热、夹杂物运动及电磁制动研究[D].北京：北京科技大学钢铁冶炼学科硕士学位论文，2008：8-9.
[7]包燕平,张涛,蒋伟,等.板坯连铸结晶器内钢液流场的三维数学模型[J].北京科技大学学报,2001,23(2):206-210.
[8]李宝宽，赫冀成编著.炼钢中的计算流体力学[M].北京：冶金工业出版社，1998：105-121.
[9]赵静,杨军,邢长虎,等.连铸结晶器内流场研究进展[J].现代铸铁，2003,(6):7-10.
[10] Takatani, K. Tanizawa, Y. Mizukami, H. Mathematical Model for Transient Fluid Flow in aContinuous Casting Mold[J]. ISIJ int,2001,41(10):1252-1261.
[11] Shinichiro Yokoya, Shigeo Takagi, Motoki Kaneko, et al. Swirling Effect in Immersion Nozzleon Flow and Heat Transport in Billet Continuous Casting Mold[J]. ISIJ International,1998,38(8):827-833.
[12] Yokoya.S, Jonsson.P.G, Sasaki.K, Tada.K, et al.The Effect of Swirl Flow in an ImmersionNozzle on the Heat and Fluid flow in a Billet Continuous Casting Mold[J]. Scand J metall,2004(4):22-28.
[13] Yokoya.Shinichiro, Takaqi.Siqeo, Tsukaquchi.Yuichi, Lquchi.Manabu. Swirling Flow Effect inImmersion Nozzle on Heat and Mass Transport Phenomena in Continuous Casting Mold[J].Mater Sci Forum,2003(2):1113-1118.
[14] Yokoya.S, Takaqi.S, Jonsson.P. et al Swirling Flow Effect in Immersion Nozzle on Control ofHeat and Mass transport in Casting Teeming[J]. Sohn int. Symp. Adv. Proc. Metals Mater. Proc.Int. Symp,2006:485-498.
[15]崔凤兰，崔小朝，刘凯，等.漩流水口对圆管坯连铸结晶器内流场的影响[J].特殊钢，2009.30(4):36-38.
[16]于湛，任忠鸣，雷作胜，等.小方坯连铸旋流水口模拟研究[C].第十五届全国炼钢学术会议文集，503-506.
[17]陈燕平，范玉妹，张炯明.旋流水口对结晶器流场影响的数值模拟[J].第五届冶金工程科学论坛，2006：122-125.
[18]王维维，张家泉，陈素琼，等.水口侧孔倾角对大方坯结晶器流场和液面波动的影响[J].北京科技大学学报，2007，29(8)：816-820.
[19]张乔英，王书桓，王立涛，等.浸入式水口底部结构对结晶器内钢液流场和温度场的影响[J].钢铁研究，2005(1):17-20.
[20] Thomas B G, Mika L J, Najjar F M. Simulation of Fluid Flow inside a ContinuousSlab-Casting[J]. Machine. Metall Trans B,1990,21B:387-399.
[21] Aboutalebi M R, Hasan M, Guthrie R I L. Coupled Turbulent Flow, Heat and Solute Transport inContinuous Casting Processes[J]. Metall Trans B,1995,26B:731-744.
[22] Fady, M. Najjar, B G. Thomas, D E. Hershey. Numerical Study of Steady Turbulent Flowthrough Bifurcated Nozzles in Continuous Casting[J]. Metallurgical and Materials TransactionsB,1995,26(4):749-765.
[23] Quan Yuan, Bin Zhao, S.P. Vanka. Study of Computational Issues in Simulation of TransientFlow in Continuous Casting[J]. Steel Research International,2005,76(1):33-43.
[24]孙海波,韩占光,钱宏智,等.注流方式对大方坯连铸结晶器内钢水流动与温度状态的影响[J].北京科技大学学报,2010.9(32):1131-1137.
[25]文光华，李刚，张建春.高速板坯连铸结晶器内流场、温度场的数值模拟[J].重庆大学学报(自然科学版)，1997，20(6)：23-29.
[26]杨秉俭，苏俊义.薄板坯连铸结晶器中钢液三维流动的数值模拟[J].应用力学学报，2000，17(1)：18-22.
[27]包燕平，朱建强，蒋伟，等.薄板坯连铸结晶器内流场的三维数值模拟[J].北京科技大学学报，2000，22(5)：409-413.
[28]张大江，陈登福，王翠娜，等.不同宽度板坯结晶器内流场的水模型和数值模拟研究[J].特殊钢，2002，31(1)：14-17.
[29]于湛，张振强，任忠鸣，等.板坯电磁制动结晶器内流体流动的研究[J].金属学报，2010，46(10)：1275-1280.
[30] Asai.S, Szekeyly.J. Turbulent Flow and its Effects in Continuous Casting[J]. Ironmaking andSteelmaking,1975,3:205-213.
[31] S.K.Choudhary, D.Mazumdar. Mathematical Modeling of Transport Phenomena in ContinuousCasting of Steel[J]. ISIJ International,1994,34(7):584-592.
[32] M.R.Aboutalebi, M.Hasan, R.I.L.Guthrie. Coupled Turbulent Flow, Heat, and Solute Transport inContinuous Casting Processes[J]. Metallurgical and Materials Transactions B,1995,26(4):731-744.
[33] M.R.Aboutalebi, M.Hasan, R.I.L.Guthrie. Numerical Study of Coupled Turbulent Flow andSolidification for Steel Slab Caster[J]. Numerical Heat Transfer, Part A,1995,28(3):279-297.
[34] Yang Hongliang. Zhao Loamgang, et al.Mathematical Simulation on Coupled Flow, Heat, andSolute Transport in Slab Continuous Casting Process[J]. Metall Mat TransB Process Metall MatProcess Sci,1998.29:1345-1356.
[35] Zhang.L, Shen.H.F, Rong.Y.M, Huang.T.Y. Numerical Simulation on Solidification and ThermalStress of Continuous Casting Billet in Mold Based on Meshless Methods[J]. Materials Scienceand Engineering A,2007(466):71-78.
[36] Samarasekera.I.V, Brimacomber.J.K. Thermal and Mechanical Behavior of Continuous CastingBillet Moulds[J], Ironmaking and Steelmaking,1982,9(1):1-15.
[37] Spitzer.K.H, Harste.K, Weber.B, et al. Mathematical Model for Thermal Tracking and On-lineControl in Continuous Casting[J]. ISIJ International,1992,32(7):848-856.
[38]王恩刚，杨泽宽，陈海耿，等.结晶器内连铸坯凝固过程的有限元数值模拟[J].东北大学学报(自然科学版)，1996，17(4)：384-387.
[39]李东辉，邱以清，刘相华.模拟连铸过程的数学模型[J].钢铁研究，2004(5)：20-23.
[40]王宝峰，麻永林，丁国，等.大方坯连铸过程中铸坯传热及凝固行为的研究[J].包头钢铁学院学报，2002，21(2)：121-126.
[41]张炯明，张立，杨会涛，等.板坯结晶器钢水凝固的数值模拟[J].北京科技大学学报，2004，26(2)：130-134.
[42]仇圣桃，刘和平，干勇.基于连续模型的板坯连铸凝固过程的数值模拟[J].钢铁研究学报，2003，15(6)：16-20.
[43]任子平,姜茂发.280mmx380mm铸坯结晶器内钢水凝固与传热仿真研究[J].特殊钢,2006,1(27):36-38.
[44]邓安元，赫冀成.小方坯初始凝固三维数值模拟[J].钢铁研究，2001，1：15-17.
[45]杨世铭，陶文铨编著.传热学[M].北京：高等教育出版社，1998：9-12，25-28.
[46]王经编著.传热学与流体力学基础[M].上海：上海交通大学出版社，2007：71-73.
[47]孙蓟泉编著.连铸及连轧工艺过程中的传热分析[M].北京：冶金工业出版社，2010：104-105.
[48] Brimacombe J K. Empowerment with Knowledge Toward the Intelligent Mold for theContinuous Casting of Steel Billets[J]. Metall Trans B,1993,24B(12):917.
[49]胡忠仁.小方坯高速连铸结晶器技术探讨[J].连铸，1998,(5):27-30.
[50] Gianac Gensini. High Speed Casting with a New Mould[J]. MPT International.1995,(6):52-55.
[51] Josef Fuchshuber. Modern High Speed Casting Technology for Billet Casting[J]. Electric FurnaceConference Proceedings.1997:347-350.
[52]区勇铭.高效连铸方坯结晶器的改进[J].炼钢，1999，3(15):15-17.
[53]崔小朝，晋艳娟，张柱，等.板坯连铸内外复合冷却流场和温度场耦合数值模拟[J].钢铁研究学报，2007.19(8):14-18.
[54]唐红伟，陶红标.低温度梯度结晶器的传热分析及其工业应用试验[J].钢铁研究学报，2010，10(10):20-24.
[55]王福军.计算流体动力学分析——CFD软件原理与应用[M].北京：清华大学出版社，2004：1-3，185-188.
[56]韩占忠，王敬，兰小平. FLUENT流体工程仿真计算实例与应用[M].北京：北京理工大学出版社，2004：19-24.
[57] B.E. Launder, D.B. Spalding. Lectures in Mathematical Models of Turbulence[C]. AcademicPress, London, England,1972:189-195.
[58] J.Savage, W.H.Pritchard, The Problem of Rupture of the Billet in the Continuous Casting ofSteel[J]. Journal of the Iron and Steel Institute,1954,11:269-277.
[59] B.G. Thomas, G.Li, A.Moitra, D.Habing. Analysis of Thermal and Mechanical Behavior ofCopper Molds during Continuous Casting of Steels Labs[J]. Ironmaking and Steelmaking,1998,12:125-143.
[60] Huespe A.E, Cardona A, Fachinotti V. Thermomechanical Model of a Continuous CastingProcess[J]. Comput. Methods Appl. Mech. Eng.,2000(182):439-455.
[61] Davies, Tieu A.K, Kim I.S. Simulation of the Continuous Casting Process by MathematicalModel[J]. Int. J. Mech. Sci.,1997,39(2):53-62.
[62]盛义平.新型高速连铸结晶器的理论研究与实际应用[D].秦皇岛：燕山大学机械电子工程学科博士学位论文，2007：19-24,40-43.
[63]蔡少武，王同敏，李军，等.基于钢水凝固收缩数值模拟优化设计连铸结晶器锥度[J].特种铸造及有色合金，2008，专刊107-119.
[64]王哲，沈厚发，柳百成.连铸结晶器中坯壳生长有限元分析[J].清华大学学报(自然科学版)，2004，44(11):1448-1451.
[65]干勇，仇圣桃，萧泽强著.连续铸钢过程数学物理模拟[M].北京：冶金工业出版社，2004：108-111,121-124.
[66]冯科，徐楚韶，陈登福，等.板坯连铸结晶器铜板温度场的数值仿真[J].特殊钢，2005.26(1):12-15.
[67]杨刚，李宝宽，于洋，等.薄板坯连铸结晶器铜板的三维传热分析[J].金属学报，2007.43(3):332-336.
[68]那贤昭，张慧，干勇，等.薄板坯连铸结晶器铜板的传热及变形数值分析与结构优化研究[J].钢铁，2000,35:233-238.
[69] L. Jung-Eui, H. Heung Nam, O. Kyu Hwan. A Fully Coupled Analysis of Fluid Flow, HeatTransfer and Stress in Continuous Round Billet Casting[J]. ISIJ International,1999,39(5):435-444.
[70]段明南，冯长宝，杨建华，等.板坯连铸结晶器铜板热机耦合应力分析[J].钢铁,2008，5(43)：30-34.
[71]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(11)：1137-1142.
[2]蔡开科，程士富.连续铸钢原理和工艺[M].北京：冶金工业出版社，1994:64-70.
[3]徐少兵,吴建洲.国内外大方坯连铸机新技术发展综述[J].中国冶金,2008,18(4):1-6.
[4]金泽洪. WAMTM公司特殊钢大方坯连铸成套技术的发展[C].中国金属学会2007年大方坯圆坯异型坯连铸技术研讨会,2007:96-102.
[5] Fabio Costanzo.康力斯集团Aldwarke新建5流大方坯连铸机[C].2005中国钢铁年会，2005:304-311.
[6]吴狄峰.大方坯结晶器内钢液流动、传热、夹杂物运动及电磁制动研究[D].北京：北京科技大学钢铁冶炼学科硕士学位论文，2008：8-9.
[7]包燕平,张涛,蒋伟,等.板坯连铸结晶器内钢液流场的三维数学模型[J].北京科技大学学报,2001,23(2):206-210.
[8]李宝宽，赫冀成编著.炼钢中的计算流体力学[M].北京：冶金工业出版社，1998：105-121.
[9]赵静,杨军,邢长虎,等.连铸结晶器内流场研究进展[J].现代铸铁，2003,(6):7-10.
[10] Takatani, K. Tanizawa, Y. Mizukami, H. Mathematical Model for Transient Fluid Flow in aContinuous Casting Mold[J]. ISIJ int,2001,41(10):1252-1261.
[11] Shinichiro Yokoya, Shigeo Takagi, Motoki Kaneko, et al. Swirling Effect in Immersion Nozzleon Flow and Heat Transport in Billet Continuous Casting Mold[J]. ISIJ International,1998,38(8):827-833.
[12] Yokoya.S, Jonsson.P.G, Sasaki.K, Tada.K, et al.The Effect of Swirl Flow in an ImmersionNozzle on the Heat and Fluid flow in a Billet Continuous Casting Mold[J]. Scand J metall,2004(4):22-28.
[13] Yokoya.Shinichiro, Takaqi.Siqeo, Tsukaquchi.Yuichi, Lquchi.Manabu. Swirling Flow Effect inImmersion Nozzle on Heat and Mass Transport Phenomena in Continuous Casting Mold[J].Mater Sci Forum,2003(2):1113-1118.
[14] Yokoya.S, Takaqi.S, Jonsson.P. et al Swirling Flow Effect in Immersion Nozzle on Control ofHeat and Mass transport in Casting Teeming[J]. Sohn int. Symp. Adv. Proc. Metals Mater. Proc.Int. Symp,2006:485-498.
[15]崔凤兰，崔小朝，刘凯，等.漩流水口对圆管坯连铸结晶器内流场的影响[J].特殊钢，2009.30(4):36-38.
[16]于湛，任忠鸣，雷作胜，等.小方坯连铸旋流水口模拟研究[C].第十五届全国炼钢学术会议文集，503-506.
[17]陈燕平，范玉妹，张炯明.旋流水口对结晶器流场影响的数值模拟[J].第五届冶金工程科学论坛，2006：122-125.
[18]王维维，张家泉，陈素琼，等.水口侧孔倾角对大方坯结晶器流场和液面波动的影响[J].北京科技大学学报，2007，29(8)：816-820.
[19]张乔英，王书桓，王立涛，等.浸入式水口底部结构对结晶器内钢液流场和温度场的影响[J].钢铁研究，2005(1):17-20.
[20] Thomas B G, Mika L J, Najjar F M. Simulation of Fluid Flow inside a ContinuousSlab-Casting[J]. Machine. Metall Trans B,1990,21B:387-399.
[21] Aboutalebi M R, Hasan M, Guthrie R I L. Coupled Turbulent Flow, Heat and Solute Transport inContinuous Casting Processes[J]. Metall Trans B,1995,26B:731-744.
[22] Fady, M. Najjar, B G. Thomas, D E. Hershey. Numerical Study of Steady Turbulent Flowthrough Bifurcated Nozzles in Continuous Casting[J]. Metallurgical and Materials TransactionsB,1995,26(4):749-765.
[23] Quan Yuan, Bin Zhao, S.P. Vanka. Study of Computational Issues in Simulation of TransientFlow in Continuous Casting[J]. Steel Research International,2005,76(1):33-43.
[24]孙海波,韩占光,钱宏智,等.注流方式对大方坯连铸结晶器内钢水流动与温度状态的影响[J].北京科技大学学报,2010.9(32):1131-1137.
[25]文光华，李刚，张建春.高速板坯连铸结晶器内流场、温度场的数值模拟[J].重庆大学学报(自然科学版)，1997，20(6)：23-29.
[26]杨秉俭，苏俊义.薄板坯连铸结晶器中钢液三维流动的数值模拟[J].应用力学学报，2000，17(1)：18-22.
[27]包燕平，朱建强，蒋伟，等.薄板坯连铸结晶器内流场的三维数值模拟[J].北京科技大学学报，2000，22(5)：409-413.
[28]张大江，陈登福，王翠娜，等.不同宽度板坯结晶器内流场的水模型和数值模拟研究[J].特殊钢，2002，31(1)：14-17.
[29]于湛，张振强，任忠鸣，等.板坯电磁制动结晶器内流体流动的研究[J].金属学报，2010，46(10)：1275-1280.
[30] Asai.S, Szekeyly.J. Turbulent Flow and its Effects in Continuous Casting[J]. Ironmaking andSteelmaking,1975,3:205-213.
[31] S.K.Choudhary, D.Mazumdar. Mathematical Modeling of Transport Phenomena in ContinuousCasting of Steel[J]. ISIJ International,1994,34(7):584-592.
[32] M.R.Aboutalebi, M.Hasan, R.I.L.Guthrie. Coupled Turbulent Flow, Heat, and Solute Transport inContinuous Casting Processes[J]. Metallurgical and Materials Transactions B,1995,26(4):731-744.
[33] M.R.Aboutalebi, M.Hasan, R.I.L.Guthrie. Numerical Study of Coupled Turbulent Flow andSolidification for Steel Slab Caster[J]. Numerical Heat Transfer, Part A,1995,28(3):279-297.
[34] Yang Hongliang. Zhao Loamgang, et al.Mathematical Simulation on Coupled Flow, Heat, andSolute Transport in Slab Continuous Casting Process[J]. Metall Mat TransB Process Metall MatProcess Sci,1998.29:1345-1356.
[35] Zhang.L, Shen.H.F, Rong.Y.M, Huang.T.Y. Numerical Simulation on Solidification and ThermalStress of Continuous Casting Billet in Mold Based on Meshless Methods[J]. Materials Scienceand Engineering A,2007(466):71-78.
[36] Samarasekera.I.V, Brimacomber.J.K. Thermal and Mechanical Behavior of Continuous CastingBillet Moulds[J], Ironmaking and Steelmaking,1982,9(1):1-15.
[37] Spitzer.K.H, Harste.K, Weber.B, et al. Mathematical Model for Thermal Tracking and On-lineControl in Continuous Casting[J]. ISIJ International,1992,32(7):848-856.
[38]王恩刚，杨泽宽，陈海耿，等.结晶器内连铸坯凝固过程的有限元数值模拟[J].东北大学学报(自然科学版)，1996，17(4)：384-387.
[39]李东辉，邱以清，刘相华.模拟连铸过程的数学模型[J].钢铁研究，2004(5)：20-23.
[40]王宝峰，麻永林，丁国，等.大方坯连铸过程中铸坯传热及凝固行为的研究[J].包头钢铁学院学报，2002，21(2)：121-126.
[41]张炯明，张立，杨会涛，等.板坯结晶器钢水凝固的数值模拟[J].北京科技大学学报，2004，26(2)：130-134.
[42]仇圣桃，刘和平，干勇.基于连续模型的板坯连铸凝固过程的数值模拟[J].钢铁研究学报，2003，15(6)：16-20.
[43]任子平,姜茂发.280mmx380mm铸坯结晶器内钢水凝固与传热仿真研究[J].特殊钢,2006,1(27):36-38.
[44]邓安元，赫冀成.小方坯初始凝固三维数值模拟[J].钢铁研究，2001，1：15-17.
[45]杨世铭，陶文铨编著.传热学[M].北京：高等教育出版社，1998：9-12，25-28.
[46]王经编著.传热学与流体力学基础[M].上海：上海交通大学出版社，2007：71-73.
[47]孙蓟泉编著.连铸及连轧工艺过程中的传热分析[M].北京：冶金工业出版社，2010：104-105.
[48] Brimacombe J K. Empowerment with Knowledge Toward the Intelligent Mold for theContinuous Casting of Steel Billets[J]. Metall Trans B,1993,24B(12):917.
[49]胡忠仁.小方坯高速连铸结晶器技术探讨[J].连铸，1998,(5):27-30.
[50] Gianac Gensini. High Speed Casting with a New Mould[J]. MPT International.1995,(6):52-55.
[51] Josef Fuchshuber. Modern High Speed Casting Technology for Billet Casting[J]. Electric FurnaceConference Proceedings.1997:347-350.
[52]区勇铭.高效连铸方坯结晶器的改进[J].炼钢，1999，3(15):15-17.
[53]崔小朝，晋艳娟，张柱，等.板坯连铸内外复合冷却流场和温度场耦合数值模拟[J].钢铁研究学报，2007.19(8):14-18.
[54]唐红伟，陶红标.低温度梯度结晶器的传热分析及其工业应用试验[J].钢铁研究学报，2010，10(10):20-24.
[55]王福军.计算流体动力学分析——CFD软件原理与应用[M].北京：清华大学出版社，2004：1-3，185-188.
[56]韩占忠，王敬，兰小平. FLUENT流体工程仿真计算实例与应用[M].北京：北京理工大学出版社，2004：19-24.
[57] B.E. Launder, D.B. Spalding. Lectures in Mathematical Models of Turbulence[C]. AcademicPress, London, England,1972:189-195.
[58] J.Savage, W.H.Pritchard, The Problem of Rupture of the Billet in the Continuous Casting ofSteel[J]. Journal of the Iron and Steel Institute,1954,11:269-277.
[59] B.G. Thomas, G.Li, A.Moitra, D.Habing. Analysis of Thermal and Mechanical Behavior ofCopper Molds during Continuous Casting of Steels Labs[J]. Ironmaking and Steelmaking,1998,12:125-143.
[60] Huespe A.E, Cardona A, Fachinotti V. Thermomechanical Model of a Continuous CastingProcess[J]. Comput. Methods Appl. Mech. Eng.,2000(182):439-455.
[61] Davies, Tieu A.K, Kim I.S. Simulation of the Continuous Casting Process by MathematicalModel[J]. Int. J. Mech. Sci.,1997,39(2):53-62.
[62]盛义平.新型高速连铸结晶器的理论研究与实际应用[D].秦皇岛：燕山大学机械电子工程学科博士学位论文，2007：19-24,40-43.
[63]蔡少武，王同敏，李军，等.基于钢水凝固收缩数值模拟优化设计连铸结晶器锥度[J].特种铸造及有色合金，2008，专刊107-119.
[64]王哲，沈厚发，柳百成.连铸结晶器中坯壳生长有限元分析[J].清华大学学报(自然科学版)，2004，44(11):1448-1451.
[65]干勇，仇圣桃，萧泽强著.连续铸钢过程数学物理模拟[M].北京：冶金工业出版社，2004：108-111,121-124.
[66]冯科，徐楚韶，陈登福，等.板坯连铸结晶器铜板温度场的数值仿真[J].特殊钢，2005.26(1):12-15.
[67]杨刚，李宝宽，于洋，等.薄板坯连铸结晶器铜板的三维传热分析[J].金属学报，2007.43(3):332-336.
[68]那贤昭，张慧，干勇，等.薄板坯连铸结晶器铜板的传热及变形数值分析与结构优化研究[J].钢铁，2000,35:233-238.
[69] L. Jung-Eui, H. Heung Nam, O. Kyu Hwan. A Fully Coupled Analysis of Fluid Flow, HeatTransfer and Stress in Continuous Round Billet Casting[J]. ISIJ International,1999,39(5):435-444.
[70]段明南，冯长宝，杨建华，等.板坯连铸结晶器铜板热机耦合应力分析[J].钢铁,2008，5(43)：30-34.
[71]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(11)：1137-1142.