双辊薄带铸轧钢水流动及传热规律的仿真与实验研究
|
摘要
双辊薄带铸轧工艺因其具有众多优点而受世界广泛关注,研究双辊铸轧熔池内钢液的流动、传热、凝固状况对双辊薄带连铸布流系统的设计以及连铸工艺参数的优化都有着非常重要的理论价值与实际意义。
本文以某钢铁公司的双辊薄带铸机为原型,采用楔形布流器,以旋转的结晶辊、侧封板以及布流器围城的熔池区域作为研究对象,考虑铸辊的转动对熔池流场和温度场的影响,把整个铸轧熔池看作空气和钢水的两相自由表面流动,建立了钢水流动传热凝固的数学模型,并分析了布流器的结构和铸轧工艺参数对钢水的流动形式、熔池自由液面温度以及铸坯出口温度分布的影响。
研究表明采用楔形布流器时,双辊铸轧熔池内钢液温度在纵向对称面上根据布流器侧水口的位置近似呈正弦形式分布,并且在侧封板附近,液面温度较高,而出口温度较低；当布流器侧水口倾角在0°到33°之间选取时,铸带宽度方向的温差相对较小,温度分布比较均匀；随着水口高度的提高熔池液面温度增加,同时铸坯出口温度降低；随着拉坯速度的提高熔池自由表面和出口的温度均提高；随着钢水过热度的提高熔池液面温度和铸坯出口温度都有所提高。在实际的铸轧过程中,可利用本文研究结果,通过合理控制铸轧工艺参数来控制钢液的凝固速度和避免液面结壳,以最大化的减少铸带缺陷,提高薄带质量,同时,本文为合理的设计双辊薄带铸轧布流系统提供了重要的理论依据。
As an international frontier technology, the twin-roll strip casting process has a very large potential power in market competition. But so far, most of the thin strips produced by this casting process have a variety of defects. The structure of flow distribution device and the process parameters determine the flow and thermal conduction pattern in the molten pool. The study on flow and thermal conduction of molten steel in twin-roll pool has a very important theoretical and practical significance.
This paper takes the molten pool as research object constructed by twin-roll, side dam and wedge-shaped device. Taking roll rotation into consideration, the mathematical model of flow and solidification is established with the entire casting pool as a two-phase free surface flow of air and molten. In this case, the effects of the structure of wedge-shaped device and casting process parameters on molten steel flow pattern, temperature ditribution on pool surface and the slab temperature distribution are analyzed.
The research results show that the temperature of molten steel in the longitudinal symmetry plane distributes in the approximation cosine pattern bsed on the inlet location. When the nozzle angle is between 0°and 33°, the temperature difference is relatively small in the longitudinal direction of casting strip, so, the temperature distribution is relatively even. The surface temperature of molten pool increases with increasing of nozzle height, while the slab temperature is reduced. In addition, the temperature of free surface and outlets are both increased with the increasing of casting speed pool and superheat temperature. In the actual casting process, the solidification rate of molten steel will be controlled and level surface crusts will be avoided by the rational operating of casting process parameters according to the results. So, the casting defects will be reduced largely. Meanwhile, the results provide a theoretical basis for designing a reasonable flow distribution system in two-roll strip casting.
本文以某钢铁公司的双辊薄带铸机为原型,采用楔形布流器,以旋转的结晶辊、侧封板以及布流器围城的熔池区域作为研究对象,考虑铸辊的转动对熔池流场和温度场的影响,把整个铸轧熔池看作空气和钢水的两相自由表面流动,建立了钢水流动传热凝固的数学模型,并分析了布流器的结构和铸轧工艺参数对钢水的流动形式、熔池自由液面温度以及铸坯出口温度分布的影响。
研究表明采用楔形布流器时,双辊铸轧熔池内钢液温度在纵向对称面上根据布流器侧水口的位置近似呈正弦形式分布,并且在侧封板附近,液面温度较高,而出口温度较低；当布流器侧水口倾角在0°到33°之间选取时,铸带宽度方向的温差相对较小,温度分布比较均匀；随着水口高度的提高熔池液面温度增加,同时铸坯出口温度降低；随着拉坯速度的提高熔池自由表面和出口的温度均提高；随着钢水过热度的提高熔池液面温度和铸坯出口温度都有所提高。在实际的铸轧过程中,可利用本文研究结果,通过合理控制铸轧工艺参数来控制钢液的凝固速度和避免液面结壳,以最大化的减少铸带缺陷,提高薄带质量,同时,本文为合理的设计双辊薄带铸轧布流系统提供了重要的理论依据。
As an international frontier technology, the twin-roll strip casting process has a very large potential power in market competition. But so far, most of the thin strips produced by this casting process have a variety of defects. The structure of flow distribution device and the process parameters determine the flow and thermal conduction pattern in the molten pool. The study on flow and thermal conduction of molten steel in twin-roll pool has a very important theoretical and practical significance.
This paper takes the molten pool as research object constructed by twin-roll, side dam and wedge-shaped device. Taking roll rotation into consideration, the mathematical model of flow and solidification is established with the entire casting pool as a two-phase free surface flow of air and molten. In this case, the effects of the structure of wedge-shaped device and casting process parameters on molten steel flow pattern, temperature ditribution on pool surface and the slab temperature distribution are analyzed.
The research results show that the temperature of molten steel in the longitudinal symmetry plane distributes in the approximation cosine pattern bsed on the inlet location. When the nozzle angle is between 0°and 33°, the temperature difference is relatively small in the longitudinal direction of casting strip, so, the temperature distribution is relatively even. The surface temperature of molten pool increases with increasing of nozzle height, while the slab temperature is reduced. In addition, the temperature of free surface and outlets are both increased with the increasing of casting speed pool and superheat temperature. In the actual casting process, the solidification rate of molten steel will be controlled and level surface crusts will be avoided by the rational operating of casting process parameters according to the results. So, the casting defects will be reduced largely. Meanwhile, the results provide a theoretical basis for designing a reasonable flow distribution system in two-roll strip casting.
引文
[1]邸洪双等,薄带连铸技术发展现状与展望[J],河南冶金,2005,13(1)：3-7
[2]廖建云.双辊薄带钢连铸工艺参数的选择[J].钢铁技术.2006,(3)：8-11
[3]Nippon Steel to Build a Direct Strip Caster at its Hikari Works. Iron&Steelmaker, April 1996,7
[4]Direct Strip Caster for Stainless Steel StartsUp at Nippon, Ironmaking&Steelmaking,1998,(10):13
[5]Nucor to Install Direct Strip Caster. Iron&Steelmaker, March 2000,56-58
[6]W.A. Opalka. BHPAchieves BreakthroughWith ProjectM[J]. Iron-making&Steelmaking, 1998,(10):19
[7]W Blejde, H Fukase, R Mahapatra. RECENT DEVELOPMENTS IN PROJECTMTHE JOINTDEVELOPMENTOFLOWCARBONSTEEL STRIP CASTING BY BHP AND IHI[C]. International Conference on New Developments in Metallurgical Process Technology, METEC Congress 99, Dussldorf, June 13-15,1999:176-181
[8]Europe's first industrial strip caster. Steel Times International, September 1999,350
[9]Yong-Gi Lee, Chul Min Park, Hyung-Tae Chung et al. Development of Strip Casting Process at POSCO[C]. International Conference on New Developments in Metallurgical Process Technology, METEC Congress 99, Dussldorf, June 13-15,1999:168-175
[10]潘秀兰,王艳红等.世界薄带连铸技术的最新进展[J].鞍钢技术,2006,(4)：12-19
[11]梁小平等.近终形连铸技术的现状及发展趋势[J].材料导报,1996,4：24-27
[12]潘秀兰,李震等.近终形连铸技术的最新进展[J].冶金信息导刊,2007,(2)：5-9
[13]杨明波.双辊薄带凝固组织的数值模拟和参数表征[D].重庆：重庆大学.重庆大学.2001,10
[14]丁学恭.薄带铸轧工艺参数的分析和动态模拟[J].机械设计与制造.2007(8)：214-216
[1 5]陈远清,文光华.0200mm×380mm双辊薄带连铸机布流的物理模拟[J].特殊钢.2006,27(4)：25-27
[16]肖兴国,谢蕴国.冶金反应工程学基础[M].北京：冶金工业出版社,1997
[17]齐新霞.板坯结晶器流场物理模拟及冶金效果研究[J].钢铁研究.2004,136(2)：12-16
[18]WANG Bo, ZHANG Jie-yu, FAN Jun-fei. Water Modeling of Twin-Roll Strip Casting[J]. JOURAL OF IRON AND STEEL RESEARCH, INTERNATIONAL.2006,13(1):14-17
[19]祝明妹,文光华.双辊薄带连铸熔池布流系统的数理模拟研究[硕士论文].重庆：重庆大学.2002,5
[20]赵顺利.双辊薄带连铸布流系统优化设计及侧封板热应力研究[硕士论文].内蒙古：内蒙古科技大学.2005,6
[21]TAVARES R P, GUTHRIE R I L. Computational fluid dynamics applied to twin roll casting[J]. Canadian Metallurgical Quarterly,1998,37 (324):2412250
[22]GUTHRIE R I L, TAVARES R P. Mathematical and physical modeling of steel flow and solidification in twin roll/horizontal belt thin strip casting machines[J]. Applied Mathematical Modeling,1998,22:8512872
[23]郭俊玉,王波.板坯双辊熔池内钢液流场的数值模拟[J].工艺技术.2007,(2)：12-15
[24]任志峰,孙斌煜.基于Procast的不锈钢双辊铸轧过程中温度场数值模拟[J].山西冶金.2007,(2)：18-20
[25]李东辉,邱以清.连铸凝固传热过程的数值模拟[J].铸造技术,2004,25(7)：529-531
[26]邢长虎,于艳等.双辊薄带连铸熔池传热特性的研究[J].上海大学学报(自然科学版).2002,8(6)：490-494
[27]D Bouchard, F Busque, F G Hamel. Fluid flow study of a twin roll strip caster mold using a water model[C]. Steelmaking Conference Proceeding, Chicago:ISS,1999, (82):427-436
[28]D Bouchard, F G Hamel, S F Turcotte, et al. Water molding evaluation of metal delivery in a twin roll strip caster using pool level and residence time distribution measurements[J]. ISIJ International, 2001,41(12):1465-1472
[29]文光华,祝明妹.双辊薄带连铸熔池液面波动及流体混合特征模拟研究[J].连铸.增刊,2000：20-25
[30]王波,张捷宇,贺友多,安胜利.双辊薄带连铸布流系统的优化设计[J].中国稀土学报.2004,22(8)：138-141
[31]王波,张捷宇,张胤.双辊薄带连铸布流系统的模拟优化研究[J].铸造技术.2006,27(7)：707-710
[32]Ohler C, Odenthal H J, Pfeifer H, et al. Laser-optical measurements and CFD simulation of a twin-roll strip caster water model with a roll width of 150mm.4th European Continuous Casting Conference, Brimingham(UK),2002:945-955
[33]Brummayer M, Hohenbichler G, Javurek M, et al. Numerical and experimental study of the turbulent flow and particle behavior inside the mold of a twin-roll caster.5th World Congress on Computational Mechanics, Vienna(Austria),2002,7
[34]文光华,祝明妹,何俊范等.双辊薄带连铸熔池液面波动物理模拟[J].金属学报,2000,36(9)：1001-1004
[35]文光华,祝明妹等.双辊薄带连铸熔池液面波动及流体混合特征模拟研究[J].钢铁研究.2001,(123)：21-26
[36]赵顺利,张捷宇.双辊薄带连铸中分配器的优化设计[J].包头钢铁学院学报.2004,23(3)：219-221
[37]樊俊飞,赵顺利等.双辊薄带连铸熔池液面波动物理模拟[J].中国稀土学报.2004,22(8)：
279-282
[38]张晓明,赵晓红等.双辊铸轧过程中水口对熔池内温度场和流场的影响[J].东北大学学报(自然科学版).2006,27(6)：654-657
[39]王波,张捷宇等.双辊薄带连铸布流系统的模拟优化研究[J].铸造技术.2006,27(7)：707-710
[40]王波.双辊薄带连铸布流系统的数学物理模拟[D].北京：北京科技大学.2006
[41]王波,张捷宇等.双辊薄带连铸过程数值模拟[J].特种铸造及有色合金.2007,27(3)：204-206
[42]梁小平,丁培道等.双辊薄带连铸的极限工艺参数计算[J].钢铁.1999,34(suppl)：619-620
[43]冯巍,朱传运,李德强,刘承军,姜茂发.IF钢板坯连铸结晶器内钢液流场的模拟与优化[J].中国冶金.2007,17(12)：29-31
[44]杜艳平,杨建伟等.铸轧熔池内三维流场与温度场耦合数值模拟[J].特种铸造及有色合金.2004,(1)：41-43
[45]侯仕东.双辊薄带连铸凝固组织仿真模拟及工艺分析的研究[D].重庆：重庆大学机械工程学院,2000
[46]Burgo J A,Conarty T J,Hlinka J W. Thermal Design and Analysis of a twin-roll Caste[J]. Iron and Steel Eng,1990,67(7):51-55
[47]Arai T,Yamada M,Nakashima H,et al. Quality aspects of sheet product cast by the twin roller process [A].77th Steelmaking Conference Proceedings[C].1994,77(3):357-364
[48]韩华伟,吴巍,仇圣桃等.双辊薄带连铸的数值模拟[J].钢铁,2001,36(10)：75-77
[49]Fujita Y,Sato H,Kitagawa,et al. Solidification and Roll-bonding of Shells in Twin-roll Casting Process[J]. ISIJ inter,1989,29(6):495-502
[50]Bagshaw M J,Hunt J D,Jordan R M. Heat line formation in roll caster[J]. Applied Science Research,1987,44:161-168
[51]Hibrohiko T,Natsuo H,Masayaki T. Simple Model for Thermal Calculation in Twin-roll Strip Casting Process [J]. Steel Research,1990,61(7):312-317
[52]Miyazawa K,Szedely J. A Mathermatical Model of the Splat Cooling Process Casting the Twin-roll Technique[J]. MetallTrans,1981,12A(6):1047-1057
[53]Tavares R P.Computational Fluid Dynamics Applied to Twin-roll Casting [J]. Canadian Metallurigical Quarterly,1998,37(34):241-250
[54]Mo A,Hoydal S H. Proc of the Modelling of Casting,Welding and advanced Solidification Processing Ⅵ[C].USA,1993:671-679
[55]金珠梅,赫翼成,徐广携.双辊连铸铸轧工艺中流场、温度场和热应力场的数值计算[J].金属学报,2000,36(4)：391-394
[56]吴德铭,郜冶.实用计算流体力学基础[M].哈尔滨：哈尔滨工程大学出版社.2006,6
[57]刘儒勋,王志峰.数值模拟方法和运动界面追踪[M].合肥：中国科学技术大学出版社.2001, 10
[58]杨明波,潘复生,彭晓东等.双辊薄带凝固组织的数值模拟(Ⅰ)[J].钢铁研究学报,2001,13(4)：19-24
[59]孙斌煜.板带铸轧理论与技术[M].北京：冶金工业出版社,2002
[60]张奇,许嘉龙,孙祖庆等.双辊薄带连铸工艺热传输的计算机模拟[J].钢铁,1992,27(12)：15-20
[61]周建兴,刘瑞祥等.凝固过程数值模拟中的潜热处理方法[J].铸造.2001,50(7)：404-407
[62]陈海清,李华基,曹阳.铸件凝固过程数值模拟[M].重庆：重庆大学出版社,1991
[63]Xiaoming ZHANG, Zhengyi JIANG, Xianghua LIU. Simulation of Fluid Flow, Heat Transfer and Micro-Segregation in Twin-roll Strip Casting of Stainless Steel[J]. Journal of Materials Science and Technology,2006,22(3):295-300
[64]王文明,钟掘.双辊铸轧区内流动凝固传热的有限元模拟[J].矿冶工程.2007,27(2)：61-63
[65]M. Zhang, Z.Y. Jiang, L.M. Yang. Modelling of coupling flow and temperature fields in molten pool during twin-roll strip casting process[J]. Journal of Materials Processing Technology,2007, (187-188):339-343
[66]廖建云,韩志伟,冯科.双辊薄带连铸凝固过程的数值模拟与分析[J].计算机辅助工程.2006,15(Suppl)：444-446
[67]王金录,邸洪双等.双辊铸轧薄带钢温度场的有限元数值模拟[J].塑性工程学报.2002,9(3)：58-61
[68]黄福祥,张炯明,王新华等.双辊薄带连铸304不锈钢铸带表面横裂纹成因研究[J].钢铁.2008,43(2)：47-50
[69]张彩东,丁培道.双辊薄带连铸不锈钢铸带组织特征研究[J].材料导报.2004,18(8A)：158-160
[70]康向东,邸洪双,张晓明.双辊铸轧薄带钢裂纹形成原因分析[J].材料与冶金学报.2002,1(2)：106-109
[2]廖建云.双辊薄带钢连铸工艺参数的选择[J].钢铁技术.2006,(3)：8-11
[3]Nippon Steel to Build a Direct Strip Caster at its Hikari Works. Iron&Steelmaker, April 1996,7
[4]Direct Strip Caster for Stainless Steel StartsUp at Nippon, Ironmaking&Steelmaking,1998,(10):13
[5]Nucor to Install Direct Strip Caster. Iron&Steelmaker, March 2000,56-58
[6]W.A. Opalka. BHPAchieves BreakthroughWith ProjectM[J]. Iron-making&Steelmaking, 1998,(10):19
[7]W Blejde, H Fukase, R Mahapatra. RECENT DEVELOPMENTS IN PROJECTMTHE JOINTDEVELOPMENTOFLOWCARBONSTEEL STRIP CASTING BY BHP AND IHI[C]. International Conference on New Developments in Metallurgical Process Technology, METEC Congress 99, Dussldorf, June 13-15,1999:176-181
[8]Europe's first industrial strip caster. Steel Times International, September 1999,350
[9]Yong-Gi Lee, Chul Min Park, Hyung-Tae Chung et al. Development of Strip Casting Process at POSCO[C]. International Conference on New Developments in Metallurgical Process Technology, METEC Congress 99, Dussldorf, June 13-15,1999:168-175
[10]潘秀兰,王艳红等.世界薄带连铸技术的最新进展[J].鞍钢技术,2006,(4)：12-19
[11]梁小平等.近终形连铸技术的现状及发展趋势[J].材料导报,1996,4：24-27
[12]潘秀兰,李震等.近终形连铸技术的最新进展[J].冶金信息导刊,2007,(2)：5-9
[13]杨明波.双辊薄带凝固组织的数值模拟和参数表征[D].重庆：重庆大学.重庆大学.2001,10
[14]丁学恭.薄带铸轧工艺参数的分析和动态模拟[J].机械设计与制造.2007(8)：214-216
[1 5]陈远清,文光华.0200mm×380mm双辊薄带连铸机布流的物理模拟[J].特殊钢.2006,27(4)：25-27
[16]肖兴国,谢蕴国.冶金反应工程学基础[M].北京：冶金工业出版社,1997
[17]齐新霞.板坯结晶器流场物理模拟及冶金效果研究[J].钢铁研究.2004,136(2)：12-16
[18]WANG Bo, ZHANG Jie-yu, FAN Jun-fei. Water Modeling of Twin-Roll Strip Casting[J]. JOURAL OF IRON AND STEEL RESEARCH, INTERNATIONAL.2006,13(1):14-17
[19]祝明妹,文光华.双辊薄带连铸熔池布流系统的数理模拟研究[硕士论文].重庆：重庆大学.2002,5
[20]赵顺利.双辊薄带连铸布流系统优化设计及侧封板热应力研究[硕士论文].内蒙古：内蒙古科技大学.2005,6
[21]TAVARES R P, GUTHRIE R I L. Computational fluid dynamics applied to twin roll casting[J]. Canadian Metallurgical Quarterly,1998,37 (324):2412250
[22]GUTHRIE R I L, TAVARES R P. Mathematical and physical modeling of steel flow and solidification in twin roll/horizontal belt thin strip casting machines[J]. Applied Mathematical Modeling,1998,22:8512872
[23]郭俊玉,王波.板坯双辊熔池内钢液流场的数值模拟[J].工艺技术.2007,(2)：12-15
[24]任志峰,孙斌煜.基于Procast的不锈钢双辊铸轧过程中温度场数值模拟[J].山西冶金.2007,(2)：18-20
[25]李东辉,邱以清.连铸凝固传热过程的数值模拟[J].铸造技术,2004,25(7)：529-531
[26]邢长虎,于艳等.双辊薄带连铸熔池传热特性的研究[J].上海大学学报(自然科学版).2002,8(6)：490-494
[27]D Bouchard, F Busque, F G Hamel. Fluid flow study of a twin roll strip caster mold using a water model[C]. Steelmaking Conference Proceeding, Chicago:ISS,1999, (82):427-436
[28]D Bouchard, F G Hamel, S F Turcotte, et al. Water molding evaluation of metal delivery in a twin roll strip caster using pool level and residence time distribution measurements[J]. ISIJ International, 2001,41(12):1465-1472
[29]文光华,祝明妹.双辊薄带连铸熔池液面波动及流体混合特征模拟研究[J].连铸.增刊,2000：20-25
[30]王波,张捷宇,贺友多,安胜利.双辊薄带连铸布流系统的优化设计[J].中国稀土学报.2004,22(8)：138-141
[31]王波,张捷宇,张胤.双辊薄带连铸布流系统的模拟优化研究[J].铸造技术.2006,27(7)：707-710
[32]Ohler C, Odenthal H J, Pfeifer H, et al. Laser-optical measurements and CFD simulation of a twin-roll strip caster water model with a roll width of 150mm.4th European Continuous Casting Conference, Brimingham(UK),2002:945-955
[33]Brummayer M, Hohenbichler G, Javurek M, et al. Numerical and experimental study of the turbulent flow and particle behavior inside the mold of a twin-roll caster.5th World Congress on Computational Mechanics, Vienna(Austria),2002,7
[34]文光华,祝明妹,何俊范等.双辊薄带连铸熔池液面波动物理模拟[J].金属学报,2000,36(9)：1001-1004
[35]文光华,祝明妹等.双辊薄带连铸熔池液面波动及流体混合特征模拟研究[J].钢铁研究.2001,(123)：21-26
[36]赵顺利,张捷宇.双辊薄带连铸中分配器的优化设计[J].包头钢铁学院学报.2004,23(3)：219-221
[37]樊俊飞,赵顺利等.双辊薄带连铸熔池液面波动物理模拟[J].中国稀土学报.2004,22(8)：
279-282
[38]张晓明,赵晓红等.双辊铸轧过程中水口对熔池内温度场和流场的影响[J].东北大学学报(自然科学版).2006,27(6)：654-657
[39]王波,张捷宇等.双辊薄带连铸布流系统的模拟优化研究[J].铸造技术.2006,27(7)：707-710
[40]王波.双辊薄带连铸布流系统的数学物理模拟[D].北京：北京科技大学.2006
[41]王波,张捷宇等.双辊薄带连铸过程数值模拟[J].特种铸造及有色合金.2007,27(3)：204-206
[42]梁小平,丁培道等.双辊薄带连铸的极限工艺参数计算[J].钢铁.1999,34(suppl)：619-620
[43]冯巍,朱传运,李德强,刘承军,姜茂发.IF钢板坯连铸结晶器内钢液流场的模拟与优化[J].中国冶金.2007,17(12)：29-31
[44]杜艳平,杨建伟等.铸轧熔池内三维流场与温度场耦合数值模拟[J].特种铸造及有色合金.2004,(1)：41-43
[45]侯仕东.双辊薄带连铸凝固组织仿真模拟及工艺分析的研究[D].重庆：重庆大学机械工程学院,2000
[46]Burgo J A,Conarty T J,Hlinka J W. Thermal Design and Analysis of a twin-roll Caste[J]. Iron and Steel Eng,1990,67(7):51-55
[47]Arai T,Yamada M,Nakashima H,et al. Quality aspects of sheet product cast by the twin roller process [A].77th Steelmaking Conference Proceedings[C].1994,77(3):357-364
[48]韩华伟,吴巍,仇圣桃等.双辊薄带连铸的数值模拟[J].钢铁,2001,36(10)：75-77
[49]Fujita Y,Sato H,Kitagawa,et al. Solidification and Roll-bonding of Shells in Twin-roll Casting Process[J]. ISIJ inter,1989,29(6):495-502
[50]Bagshaw M J,Hunt J D,Jordan R M. Heat line formation in roll caster[J]. Applied Science Research,1987,44:161-168
[51]Hibrohiko T,Natsuo H,Masayaki T. Simple Model for Thermal Calculation in Twin-roll Strip Casting Process [J]. Steel Research,1990,61(7):312-317
[52]Miyazawa K,Szedely J. A Mathermatical Model of the Splat Cooling Process Casting the Twin-roll Technique[J]. MetallTrans,1981,12A(6):1047-1057
[53]Tavares R P.Computational Fluid Dynamics Applied to Twin-roll Casting [J]. Canadian Metallurigical Quarterly,1998,37(34):241-250
[54]Mo A,Hoydal S H. Proc of the Modelling of Casting,Welding and advanced Solidification Processing Ⅵ[C].USA,1993:671-679
[55]金珠梅,赫翼成,徐广携.双辊连铸铸轧工艺中流场、温度场和热应力场的数值计算[J].金属学报,2000,36(4)：391-394
[56]吴德铭,郜冶.实用计算流体力学基础[M].哈尔滨：哈尔滨工程大学出版社.2006,6
[57]刘儒勋,王志峰.数值模拟方法和运动界面追踪[M].合肥：中国科学技术大学出版社.2001, 10
[58]杨明波,潘复生,彭晓东等.双辊薄带凝固组织的数值模拟(Ⅰ)[J].钢铁研究学报,2001,13(4)：19-24
[59]孙斌煜.板带铸轧理论与技术[M].北京：冶金工业出版社,2002
[60]张奇,许嘉龙,孙祖庆等.双辊薄带连铸工艺热传输的计算机模拟[J].钢铁,1992,27(12)：15-20
[61]周建兴,刘瑞祥等.凝固过程数值模拟中的潜热处理方法[J].铸造.2001,50(7)：404-407
[62]陈海清,李华基,曹阳.铸件凝固过程数值模拟[M].重庆：重庆大学出版社,1991
[63]Xiaoming ZHANG, Zhengyi JIANG, Xianghua LIU. Simulation of Fluid Flow, Heat Transfer and Micro-Segregation in Twin-roll Strip Casting of Stainless Steel[J]. Journal of Materials Science and Technology,2006,22(3):295-300
[64]王文明,钟掘.双辊铸轧区内流动凝固传热的有限元模拟[J].矿冶工程.2007,27(2)：61-63
[65]M. Zhang, Z.Y. Jiang, L.M. Yang. Modelling of coupling flow and temperature fields in molten pool during twin-roll strip casting process[J]. Journal of Materials Processing Technology,2007, (187-188):339-343
[66]廖建云,韩志伟,冯科.双辊薄带连铸凝固过程的数值模拟与分析[J].计算机辅助工程.2006,15(Suppl)：444-446
[67]王金录,邸洪双等.双辊铸轧薄带钢温度场的有限元数值模拟[J].塑性工程学报.2002,9(3)：58-61
[68]黄福祥,张炯明,王新华等.双辊薄带连铸304不锈钢铸带表面横裂纹成因研究[J].钢铁.2008,43(2)：47-50
[69]张彩东,丁培道.双辊薄带连铸不锈钢铸带组织特征研究[J].材料导报.2004,18(8A)：158-160
[70]康向东,邸洪双,张晓明.双辊铸轧薄带钢裂纹形成原因分析[J].材料与冶金学报.2002,1(2)：106-109