连铸结晶器传热/润滑反问题方法及应用
摘要
结晶器是连铸机的核心部件,实时、准确地了解结晶器传热、铸坯凝固及保护渣润滑状态,对于稳定和提高铸坯表面质量具有重要意义。目前,针对结晶器内传热与保护渣润滑行为的研究已取得很大进展,但大部分都在理想状态下进行,计算结果往往呈现均匀对称特征,不能真实反映实际工况。随着近年来结晶器“可视化”和“智能化”概念的提出,连铸现场对数值模拟准确性和实时性也提出了更为严苛的要求。
针对上述问题,本文以板坯连铸结晶器为研究对象,建立了针对实测的结晶器传热反问题模型与方法,并采用基于OpenMP的并行计算技术,解决在线数值模拟“准确性”和“实时性”间的矛盾,开发出面向在线的连铸反问题方法。将模型应用至不同钢厂与铸机类型的离线模拟与在线检测,对方法的可行性和正确性进行论证。在此基础上,建立保护渣热态润滑模型,研究结晶器内保护渣膜的分布和润滑状态,讨论不同工艺及保护渣物性参数对结晶器内润滑行为的影响。最后,通过定义非均匀性评价方法和坯壳生长速率,分析并考察了结晶器内传热与润滑的非均匀性特征。
基于实测的板坯连铸结晶器温度数据,建立传热反问题模型,结合OpenMP并行计算技术,划分结晶器和铸坯区域分配到4个CPU进行并行计算。结果表明,测点的温度计算值和实测值较为吻合,能够较为准确地反映结晶器内的传热状态；并行后的计算时间约为原来的1/4,基本满足在线计算的速度要求。目前嵌入反问题模型的结晶器监控集成系统已在钢厂调试运行,初步实现结晶器内温度、热流、铸坯凝固行为的在线可视化,对于预测铸坯裂纹、指导和优化连铸生产工艺具有积极意义。
在温度场计算结果的基础上,建立保护渣热态润滑模型,计算结晶器/铸坯间的渣膜和气隙厚度分布。研究表明,针对本文计算的包晶钢种,液渣膜的分布与铸坯表面温度分布一致,结晶器上端的液渣膜厚度较厚,量级为0.1mm。随着铸坯表面温度降低,液渣膜逐渐消失。固渣膜较厚,约为0.5mm,在结晶器出口附近将高于1mm。保护渣熔化温度与黏度对渣膜分布影响显著,液渣膜厚度随拉速升高而变薄。此外,本文还尝试了一种计算结晶器/铸坯间气隙的新方法,为研究气隙行为提供新的思路。
定义了结晶器内传热和润滑非均匀性的评价方法和坯壳生长速率,分析结晶器内传热的非均匀性特征。结果表明,弯月面附近坯壳厚度非均匀性波动较大；距离弯月面0-200mm的区域,坯壳生长速率波动剧烈且达到最大值。结晶器温度、热流、坯壳厚度和液渣膜厚度的不均匀性均随拉速增大,坯壳生长速率也随拉速的升高而增大。
The mould is the core component of continuous caster. Understanding the status of heat transfer, solidification and lubrication within the mould exactly in real-time is very important for improving the slab's quality. At present, there have been many researches about the heat transfer and lubrication behaviors in the mould, but most of them are studied under the idea condition, the calculated results of which are uniform and can't reflect the real casting condition. With appearance of the conceptions of visualization and intellectualization in continuous casting, the'accuracy'and'real-time'of numerical simulation are more important at production field.
In this paper, the mould of continuous slab caster is taken as the research object. Based on the measured data of mould temperature, an inverse problem model is established to analyze the mould heat transfer and the strand solidification. And combining the parallel technology of OpenMP, the conflict of accuracy results and quick computation will be resolved. Corresponding software is developed and applied to different plant and caster for off-line simulation and on-line detection, in order to verify the feasibility and validity of the model. Then the mathematical model of thermal state of slag lubrication is built to study the distribution of slag film and lubrication states, and the influence of process condition and physical properties of powder is also discussed. At last, the relative root mean square (rRMS) and the shell growth rate are presented to investigate the non-uniform characteristic of mould heat transfer and lubrication state.
Based on the measured temperature data and OpenMP, an inverse problem model combining the parallel technology is developed, which is assigned to4CPU for parallel computing after domain decomposition of mould and strand. The results show that there is good agreement between the calculated temperature and the measured temperature, which could reflect the exact situation of heat transfer in the mould. And the computing time reduces three-quarters by using the parallel technology, basically meeting the velocity desire of on-line calculation. Now the software is applied in plants and it preliminarily realizes on-line visualization of the temperature, heat flux and strand solidification within mould, which could predict the generation of strand surface crack and optimize the process condition.
The slag lubrication model is developed on the basis of temperature field to calculate the distribution of slag film and air-gap. The calculation results of peritectic steel in this paper show that the distributions of liquid slag film and strand surface temperature share similar characteristics. The liquid slag film at the upper part of the mould is thicker, the order of magnitude of which thickness is0.1mm. The liquid slag film disappears gradually when the strand surface temperature decreases. The thickness of solid slag film is about0.5mm, while it reaches1mm at the mould outlet. The status of slag film is affected obviously by the slag melting point and viscosity, and the liquid slag film thickness decreases when the casting speed increased. Furthermore, this paper proposes another method to analyze the air-gap between mould and strand.
Non-uniformity and shell growth rate presenting in this paper are all defined to study the non-uniform behaviors in the mould. It shows that the non-uniformity of shell thickness near meniscus fluctuates severely, and the shell growth rate changes abruptly and reaches the maximum in the region of0-200mm below meniscus. The non-uniformity of mould temperature, heat flux, shell thickness and the liquid slag film increases with casting speed, as well as the fluctuation of shell growth rate.
针对上述问题,本文以板坯连铸结晶器为研究对象,建立了针对实测的结晶器传热反问题模型与方法,并采用基于OpenMP的并行计算技术,解决在线数值模拟“准确性”和“实时性”间的矛盾,开发出面向在线的连铸反问题方法。将模型应用至不同钢厂与铸机类型的离线模拟与在线检测,对方法的可行性和正确性进行论证。在此基础上,建立保护渣热态润滑模型,研究结晶器内保护渣膜的分布和润滑状态,讨论不同工艺及保护渣物性参数对结晶器内润滑行为的影响。最后,通过定义非均匀性评价方法和坯壳生长速率,分析并考察了结晶器内传热与润滑的非均匀性特征。
基于实测的板坯连铸结晶器温度数据,建立传热反问题模型,结合OpenMP并行计算技术,划分结晶器和铸坯区域分配到4个CPU进行并行计算。结果表明,测点的温度计算值和实测值较为吻合,能够较为准确地反映结晶器内的传热状态；并行后的计算时间约为原来的1/4,基本满足在线计算的速度要求。目前嵌入反问题模型的结晶器监控集成系统已在钢厂调试运行,初步实现结晶器内温度、热流、铸坯凝固行为的在线可视化,对于预测铸坯裂纹、指导和优化连铸生产工艺具有积极意义。
在温度场计算结果的基础上,建立保护渣热态润滑模型,计算结晶器/铸坯间的渣膜和气隙厚度分布。研究表明,针对本文计算的包晶钢种,液渣膜的分布与铸坯表面温度分布一致,结晶器上端的液渣膜厚度较厚,量级为0.1mm。随着铸坯表面温度降低,液渣膜逐渐消失。固渣膜较厚,约为0.5mm,在结晶器出口附近将高于1mm。保护渣熔化温度与黏度对渣膜分布影响显著,液渣膜厚度随拉速升高而变薄。此外,本文还尝试了一种计算结晶器/铸坯间气隙的新方法,为研究气隙行为提供新的思路。
定义了结晶器内传热和润滑非均匀性的评价方法和坯壳生长速率,分析结晶器内传热的非均匀性特征。结果表明,弯月面附近坯壳厚度非均匀性波动较大；距离弯月面0-200mm的区域,坯壳生长速率波动剧烈且达到最大值。结晶器温度、热流、坯壳厚度和液渣膜厚度的不均匀性均随拉速增大,坯壳生长速率也随拉速的升高而增大。
The mould is the core component of continuous caster. Understanding the status of heat transfer, solidification and lubrication within the mould exactly in real-time is very important for improving the slab's quality. At present, there have been many researches about the heat transfer and lubrication behaviors in the mould, but most of them are studied under the idea condition, the calculated results of which are uniform and can't reflect the real casting condition. With appearance of the conceptions of visualization and intellectualization in continuous casting, the'accuracy'and'real-time'of numerical simulation are more important at production field.
In this paper, the mould of continuous slab caster is taken as the research object. Based on the measured data of mould temperature, an inverse problem model is established to analyze the mould heat transfer and the strand solidification. And combining the parallel technology of OpenMP, the conflict of accuracy results and quick computation will be resolved. Corresponding software is developed and applied to different plant and caster for off-line simulation and on-line detection, in order to verify the feasibility and validity of the model. Then the mathematical model of thermal state of slag lubrication is built to study the distribution of slag film and lubrication states, and the influence of process condition and physical properties of powder is also discussed. At last, the relative root mean square (rRMS) and the shell growth rate are presented to investigate the non-uniform characteristic of mould heat transfer and lubrication state.
Based on the measured temperature data and OpenMP, an inverse problem model combining the parallel technology is developed, which is assigned to4CPU for parallel computing after domain decomposition of mould and strand. The results show that there is good agreement between the calculated temperature and the measured temperature, which could reflect the exact situation of heat transfer in the mould. And the computing time reduces three-quarters by using the parallel technology, basically meeting the velocity desire of on-line calculation. Now the software is applied in plants and it preliminarily realizes on-line visualization of the temperature, heat flux and strand solidification within mould, which could predict the generation of strand surface crack and optimize the process condition.
The slag lubrication model is developed on the basis of temperature field to calculate the distribution of slag film and air-gap. The calculation results of peritectic steel in this paper show that the distributions of liquid slag film and strand surface temperature share similar characteristics. The liquid slag film at the upper part of the mould is thicker, the order of magnitude of which thickness is0.1mm. The liquid slag film disappears gradually when the strand surface temperature decreases. The thickness of solid slag film is about0.5mm, while it reaches1mm at the mould outlet. The status of slag film is affected obviously by the slag melting point and viscosity, and the liquid slag film thickness decreases when the casting speed increased. Furthermore, this paper proposes another method to analyze the air-gap between mould and strand.
Non-uniformity and shell growth rate presenting in this paper are all defined to study the non-uniform behaviors in the mould. It shows that the non-uniformity of shell thickness near meniscus fluctuates severely, and the shell growth rate changes abruptly and reaches the maximum in the region of0-200mm below meniscus. The non-uniformity of mould temperature, heat flux, shell thickness and the liquid slag film increases with casting speed, as well as the fluctuation of shell growth rate.
引文
[1]胡胜亮.方坯连铸结晶器内钢液行为的数值模拟[D].唐山：河北理工大学,2005.
[2]干勇,仇圣桃,萧泽强.连续铸钢过程数学物理模拟[M].北京：冶金工业出版社,2001.
[3]蔡开科等.连铸结晶器[M].北京：冶金工业出版社,2008.
[4]高妮.板坯连铸结晶器传热行为的理论研究[D].沈阳：东北大学,2009.
[5]Brimacombe J K. Empowerment with knowledge toward the intelligent mold for the continuous casting of steel billets [J]. Metallurgical and Materials Transactions B,1993,24B(6):917-934.
[6]Bakshi I A, Brendzy J L, Walker N, et al. Mould-strand interaction in continuous casting of steel billets Part 1 Industrial trials [J]. Ironmaking and Steelmaking,1993,20(1):54-62.
[7]Huang X, Thomas B G. Modeling of transient flow phenomena in continuous casting of steel [J]. Canadian Metallurgical Quarterly,1998,37(3):197-212.
[8]Araki T, Dkeda M. Optimization of mold oscillation for high speed casting-new criteria for mold oscillation [J]. Canadian Metallurgical Quarterly,1999,38(5):295-300.
[9]Mahapatra R B, Brimacombe J K, Samatrasekera I V, et al. Mold behavior and its influence on quality in the continuous casting of steel slabs:Part 1. Industrial trials, mold temperature measurements, and mathematical modeling [J]. Metallurgical and Materials Transactions B,1991,22B(6):561-874.
[10]Kumar S, Meech J A, Samarasekera I V, et al. Development of intelligentmould for online detection of defects in steel billets [J]. Ironmaking and Steelmaking,1999,26(4):269-284.
[11]de Toledo G A, Ciriza J, Laraudogoitia J J, et al. Abnormal transient phenomena in the continuous casting process:Part 2 [J]. Ironmaking and Steelmaking,2003,30(5):360-368.
[12]Watzinger J, Pesek A, Huebner N, et al. MoldExpert-operational experience and future development [J]. Ironmaking and Steelmaking,2005,32(3):208-212.
[13]Normanton A S, Hewitt P N, Hunter N S, et al. Mould thermal monitoring:a window on the mould [J]. Ironmaking and Steelmaking,2004,31(5):357-363.
[14]Castiaux E, Gruenzner G. Breakout detection/prevention for slab and bloom caster:a new step forward with ?MARTINE?:XL Steelmaking Seminar International [C]. Diisseldorf:2011.
[15]张立,王俊,孙宝德.宝钢板坯连铸结晶器平均热流[J].上海交通大学学报,2003,37(12)：891-1894.
[16]雷作胜,任忠鸣,等.连铸结晶器弯月面区温度波动的模拟研究[J].上海大学学报：自然科学版,2002,8(4)：317-320.
[17]刘晓,姚曼,于艳,等.圆坯连铸机状态在线检测装置：中国,200420082415.X[P].2005,09,14.
[18]方大成,姚曼,王金城,等.一种多点热电偶传感器：中国,03143933.0[P].2004,03,10.
[19]Mizikar G A. Mathematical heat transfer model for solidification of continuously cast steel slabs [J]. Trans. TMS-AIME,1967(239):1747-1753.
[20]Thomas B G, Najjar F M. Finite element modelling of turbulent fluid flow and heat transfer in continuous casting [J]. Applied Mathematical Modelling,1991,15(5):226-243.
[21]Meng Y, Thomas B G. Heat transfer and solidification model of continuous slab casting:CONID [J]. Metallurgical and Materials Transactions B,2003,34B(5):685-705.
[22]蔡开科,吴元增.连续铸钢板坯凝固传热数学模型[J].金属学报,1983,19(1)：1333.
[23]蔡开科,刘凤荣.连铸坯凝固冷却过程的控制[J].金属学报,1984,20(3)：146-154.
[24]金俊泽,郑贤淑,郭可切,等.连铸钢坯凝固进程的数值模拟[J].钢铁,1985,20(5)：19-27.
[25]陈克,徐宝升.连铸结晶器动态热流及其影响,第四届连续铸钢学术会议[C].桂林：1990.
[26]王恩刚,杨泽宽.气隙对连铸坯凝固影响的有限元数据模拟[J].钢铁,1996,31(11)：22-26.
[27]刘旭东,朱苗勇,邹俊苏,等.连铸板坯凝固传热过程的计算机模拟[J].材料与冶金学报,2002,1(3)：195-199.
[28]张炯明,张立,王新华,等.板坯连铸结晶器热流量分布的研究[J].金属学报,2003,39(12)：1285-1290.
[29]尹合壁,姚曼.圆坯连铸结晶器传热的反算法[J].金属学报,2005,41(6)：638-644.
[30]Yamauchi A, Emi T, Seetharaman S. A mathematical model for prediction of thickness of mould flux film in continuous casting mould [J]. ISIJ International,2002,42:1084-1093.
[31]Meng Y, Thomas B G. Modeling transient slag-layer phenomena in the shell/mold gap in continuous casting of steel [J]. Metallurgical and Materials Transactions B,2003,34B:707-725.
[32]Cho J W, Jeong H T. Infiltration of Slag Film into the Grooves on a Continuous Casting Mold:4th International Conference on Modelling and Simulation of Metallurgy Processes in Steelmaking [C]. Dusseldorf:2011.
[33]朱立光,金山同.连铸结晶器内保护渣渣膜状态的数学模拟[J].北京科技大学学报,1999,21(1)：13-16.
[34]张玉文,丁伟中,朱立光.方坯连铸保护渣渣膜润滑行为的理论研究[J].炼钢,2002(02)：25-28.
[35]蔡娥,谢,兵,王雨.保护渣物化性能对铸坯与结晶器间摩擦的影响[J].连铸,2007,(1)：35-38.
[36]郝守卫,柳百成,张卓其,等.凝固过程中热传导的反问题[J].清华大学学报(自然科学版),1989,29(2)：36-43.
[37]李岗,刘伟涛,许云华.板坯连铸结晶器传热反算方法研究[J].特种铸造及有色合金,2007(04)：267-270.
[38]黄光远,刘小军.数学物理反问题[M].济南：山东科学技术出版社,1993.
[39]李永兵.并行编程环境与工具[J].长治学院学报,2009(2)：41-43.
[40]潘伟华,沈云付,颜鹤.基于MPI的连铸模拟并行计算[J].计算机工程与设计,2005,26(2)：348-350.
[41]赵建华,胡黎辉,秦树人.MPI并行计算在金属凝固温度场模拟中的实现[J].铸造,2007,56(7)：708-711.
[42]贾启忠,王旭东,刘永贞,等.并行计算应用于连铸结晶器传热数值模拟[J].热加工工艺,2009(01)：55-59.
[43]贾启忠,王旭东,刘永贞,等.基于MPI的结晶器传热并行计算方法[J].微计算机信息,2009,25(6)：180,188-189.
[44]Acadams W H. Heat transmission:3rd Ed., McGraw-Hill [C]. New York:1954.
[45]臧欣阳.板坯连铸结晶器内传热与摩擦行为研究[D].大连：大连理工大学,2009.
[46]Won Y M, Yeo T J, Oh K H, et al. Analysis of mold wear during continuous casting of slab [J]. ISIJ International,1998,38(1):53-62.
[47]肖洪波.圆坯连铸结晶器保护渣传热及其相关问题研究[D].大连：大连理工大学,2005.
[48]周伟明.多核计算与程序设计[M].武汉：华中科技大学出版社,2009.
[49]李正浩,周俊,刘大刚.基于OpenMP的电磁场FDTD并行程序性能分析[J].现代电子技术,2008,31(14)：135-138.
[50]孙洪迪,高柱.基于OpenMP技术的多核处理器程序的开发实现[J].北京工业职业技术学院学报,2010,9(1)：19-22.
[51]黄猛OpenMP的多核并行程序设计[J].电脑编程技巧与维护,2009(17)：35-38.
[52]胡越明.多核计算机的程序设计[J].电子产品世界,2007(C00)：39-43.
[53]卢盛意.连铸板坯包晶钢的纵裂问题[J].连铸,2003(6)：22-23,34.
[54]刁承民,刘建伟,张茂存.特厚板坯连铸机表面大纵裂产生原因分析及预防[J].连铸,2010(6)：2-15.
[55]王恩刚,赫冀成.气隙对连铸坯应力分布影响的有限元数值模拟[J].钢铁,1999,34(7)：25-27.
[56]盛义平,孔祥东,杨永利.连铸结晶器传热边界条件研究[J].中国机械工程,2007,18(13)：1615-1618.
[57]康丽,王洋,王恩刚,等.结晶器内连铸坯的热和应力状态数值模拟[J].中国冶金,2007(5)：28-32.
[58]杜方.连铸保护渣渣膜润滑模拟研究[D].重庆：重庆大学,2009.
[59]尹合壁.圆坯连铸结晶器内热—力学行为的分析[D].大连：大连理工大学,2005.
[60]Hanao M, Kawamoto M, Yamanaka A. Growth of solidified shell just below the meniscus in continuous casting mold [J]. ISIJ International,2009,49(3):365-374.
[61]杨建伟,曹晓兵,梁爱生.异型坯连铸二冷区配水模型研究[J].重型机械,2001,1(1)：18-21.
[62]邢淑清,白亮,麻永林,等.316不锈钢连铸工艺参数对结晶器内坯壳厚度影响模拟[J].过程工程学报,2010,10(6)：1163-1167.
[2]干勇,仇圣桃,萧泽强.连续铸钢过程数学物理模拟[M].北京：冶金工业出版社,2001.
[3]蔡开科等.连铸结晶器[M].北京：冶金工业出版社,2008.
[4]高妮.板坯连铸结晶器传热行为的理论研究[D].沈阳：东北大学,2009.
[5]Brimacombe J K. Empowerment with knowledge toward the intelligent mold for the continuous casting of steel billets [J]. Metallurgical and Materials Transactions B,1993,24B(6):917-934.
[6]Bakshi I A, Brendzy J L, Walker N, et al. Mould-strand interaction in continuous casting of steel billets Part 1 Industrial trials [J]. Ironmaking and Steelmaking,1993,20(1):54-62.
[7]Huang X, Thomas B G. Modeling of transient flow phenomena in continuous casting of steel [J]. Canadian Metallurgical Quarterly,1998,37(3):197-212.
[8]Araki T, Dkeda M. Optimization of mold oscillation for high speed casting-new criteria for mold oscillation [J]. Canadian Metallurgical Quarterly,1999,38(5):295-300.
[9]Mahapatra R B, Brimacombe J K, Samatrasekera I V, et al. Mold behavior and its influence on quality in the continuous casting of steel slabs:Part 1. Industrial trials, mold temperature measurements, and mathematical modeling [J]. Metallurgical and Materials Transactions B,1991,22B(6):561-874.
[10]Kumar S, Meech J A, Samarasekera I V, et al. Development of intelligentmould for online detection of defects in steel billets [J]. Ironmaking and Steelmaking,1999,26(4):269-284.
[11]de Toledo G A, Ciriza J, Laraudogoitia J J, et al. Abnormal transient phenomena in the continuous casting process:Part 2 [J]. Ironmaking and Steelmaking,2003,30(5):360-368.
[12]Watzinger J, Pesek A, Huebner N, et al. MoldExpert-operational experience and future development [J]. Ironmaking and Steelmaking,2005,32(3):208-212.
[13]Normanton A S, Hewitt P N, Hunter N S, et al. Mould thermal monitoring:a window on the mould [J]. Ironmaking and Steelmaking,2004,31(5):357-363.
[14]Castiaux E, Gruenzner G. Breakout detection/prevention for slab and bloom caster:a new step forward with ?MARTINE?:XL Steelmaking Seminar International [C]. Diisseldorf:2011.
[15]张立,王俊,孙宝德.宝钢板坯连铸结晶器平均热流[J].上海交通大学学报,2003,37(12)：891-1894.
[16]雷作胜,任忠鸣,等.连铸结晶器弯月面区温度波动的模拟研究[J].上海大学学报：自然科学版,2002,8(4)：317-320.
[17]刘晓,姚曼,于艳,等.圆坯连铸机状态在线检测装置：中国,200420082415.X[P].2005,09,14.
[18]方大成,姚曼,王金城,等.一种多点热电偶传感器：中国,03143933.0[P].2004,03,10.
[19]Mizikar G A. Mathematical heat transfer model for solidification of continuously cast steel slabs [J]. Trans. TMS-AIME,1967(239):1747-1753.
[20]Thomas B G, Najjar F M. Finite element modelling of turbulent fluid flow and heat transfer in continuous casting [J]. Applied Mathematical Modelling,1991,15(5):226-243.
[21]Meng Y, Thomas B G. Heat transfer and solidification model of continuous slab casting:CONID [J]. Metallurgical and Materials Transactions B,2003,34B(5):685-705.
[22]蔡开科,吴元增.连续铸钢板坯凝固传热数学模型[J].金属学报,1983,19(1)：1333.
[23]蔡开科,刘凤荣.连铸坯凝固冷却过程的控制[J].金属学报,1984,20(3)：146-154.
[24]金俊泽,郑贤淑,郭可切,等.连铸钢坯凝固进程的数值模拟[J].钢铁,1985,20(5)：19-27.
[25]陈克,徐宝升.连铸结晶器动态热流及其影响,第四届连续铸钢学术会议[C].桂林：1990.
[26]王恩刚,杨泽宽.气隙对连铸坯凝固影响的有限元数据模拟[J].钢铁,1996,31(11)：22-26.
[27]刘旭东,朱苗勇,邹俊苏,等.连铸板坯凝固传热过程的计算机模拟[J].材料与冶金学报,2002,1(3)：195-199.
[28]张炯明,张立,王新华,等.板坯连铸结晶器热流量分布的研究[J].金属学报,2003,39(12)：1285-1290.
[29]尹合壁,姚曼.圆坯连铸结晶器传热的反算法[J].金属学报,2005,41(6)：638-644.
[30]Yamauchi A, Emi T, Seetharaman S. A mathematical model for prediction of thickness of mould flux film in continuous casting mould [J]. ISIJ International,2002,42:1084-1093.
[31]Meng Y, Thomas B G. Modeling transient slag-layer phenomena in the shell/mold gap in continuous casting of steel [J]. Metallurgical and Materials Transactions B,2003,34B:707-725.
[32]Cho J W, Jeong H T. Infiltration of Slag Film into the Grooves on a Continuous Casting Mold:4th International Conference on Modelling and Simulation of Metallurgy Processes in Steelmaking [C]. Dusseldorf:2011.
[33]朱立光,金山同.连铸结晶器内保护渣渣膜状态的数学模拟[J].北京科技大学学报,1999,21(1)：13-16.
[34]张玉文,丁伟中,朱立光.方坯连铸保护渣渣膜润滑行为的理论研究[J].炼钢,2002(02)：25-28.
[35]蔡娥,谢,兵,王雨.保护渣物化性能对铸坯与结晶器间摩擦的影响[J].连铸,2007,(1)：35-38.
[36]郝守卫,柳百成,张卓其,等.凝固过程中热传导的反问题[J].清华大学学报(自然科学版),1989,29(2)：36-43.
[37]李岗,刘伟涛,许云华.板坯连铸结晶器传热反算方法研究[J].特种铸造及有色合金,2007(04)：267-270.
[38]黄光远,刘小军.数学物理反问题[M].济南：山东科学技术出版社,1993.
[39]李永兵.并行编程环境与工具[J].长治学院学报,2009(2)：41-43.
[40]潘伟华,沈云付,颜鹤.基于MPI的连铸模拟并行计算[J].计算机工程与设计,2005,26(2)：348-350.
[41]赵建华,胡黎辉,秦树人.MPI并行计算在金属凝固温度场模拟中的实现[J].铸造,2007,56(7)：708-711.
[42]贾启忠,王旭东,刘永贞,等.并行计算应用于连铸结晶器传热数值模拟[J].热加工工艺,2009(01)：55-59.
[43]贾启忠,王旭东,刘永贞,等.基于MPI的结晶器传热并行计算方法[J].微计算机信息,2009,25(6)：180,188-189.
[44]Acadams W H. Heat transmission:3rd Ed., McGraw-Hill [C]. New York:1954.
[45]臧欣阳.板坯连铸结晶器内传热与摩擦行为研究[D].大连：大连理工大学,2009.
[46]Won Y M, Yeo T J, Oh K H, et al. Analysis of mold wear during continuous casting of slab [J]. ISIJ International,1998,38(1):53-62.
[47]肖洪波.圆坯连铸结晶器保护渣传热及其相关问题研究[D].大连：大连理工大学,2005.
[48]周伟明.多核计算与程序设计[M].武汉：华中科技大学出版社,2009.
[49]李正浩,周俊,刘大刚.基于OpenMP的电磁场FDTD并行程序性能分析[J].现代电子技术,2008,31(14)：135-138.
[50]孙洪迪,高柱.基于OpenMP技术的多核处理器程序的开发实现[J].北京工业职业技术学院学报,2010,9(1)：19-22.
[51]黄猛OpenMP的多核并行程序设计[J].电脑编程技巧与维护,2009(17)：35-38.
[52]胡越明.多核计算机的程序设计[J].电子产品世界,2007(C00)：39-43.
[53]卢盛意.连铸板坯包晶钢的纵裂问题[J].连铸,2003(6)：22-23,34.
[54]刁承民,刘建伟,张茂存.特厚板坯连铸机表面大纵裂产生原因分析及预防[J].连铸,2010(6)：2-15.
[55]王恩刚,赫冀成.气隙对连铸坯应力分布影响的有限元数值模拟[J].钢铁,1999,34(7)：25-27.
[56]盛义平,孔祥东,杨永利.连铸结晶器传热边界条件研究[J].中国机械工程,2007,18(13)：1615-1618.
[57]康丽,王洋,王恩刚,等.结晶器内连铸坯的热和应力状态数值模拟[J].中国冶金,2007(5)：28-32.
[58]杜方.连铸保护渣渣膜润滑模拟研究[D].重庆：重庆大学,2009.
[59]尹合壁.圆坯连铸结晶器内热—力学行为的分析[D].大连：大连理工大学,2005.
[60]Hanao M, Kawamoto M, Yamanaka A. Growth of solidified shell just below the meniscus in continuous casting mold [J]. ISIJ International,2009,49(3):365-374.
[61]杨建伟,曹晓兵,梁爱生.异型坯连铸二冷区配水模型研究[J].重型机械,2001,1(1)：18-21.
[62]邢淑清,白亮,麻永林,等.316不锈钢连铸工艺参数对结晶器内坯壳厚度影响模拟[J].过程工程学报,2010,10(6)：1163-1167.