方坯连铸结晶器电磁搅拌的数值模拟
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摘要
在连铸生产中应用电磁搅拌技术，可以扩大铸坯的等轴晶区，减轻铸坯的中心疏松、中心偏析和中心缩孔，大幅度减少铸坯表面和皮下夹杂、气孔等缺陷。电磁搅拌技术的诸多优势，吸引着研究者在多个方面对电磁搅拌理论开展了大量的研究工作。电磁搅拌的实质是在电磁搅拌器的线圈内通以低频交变电流，产生变化的磁场，变化的磁场在钢液中产生感应电流，感应电流与磁场相互作用在钢液中产生洛伦兹力，驱动坯壳内部钢液的流动。因此对电磁搅拌过程中电磁场和流场的分布进行研究是非常必要的。单纯的物理模拟方法对其进行理论解析比较困难，数值模拟方法更加广泛地用来研究连铸过程中电磁搅拌技术，它成为了连铸工作者进行电磁搅拌结构设计和确定工艺参数的一种有效而且相对简单的方法。
本文以某钢厂方坯结晶器的旋转型电磁搅拌器为研究对象，忽略钢水流动对电磁场的影响，以麦克斯韦方程组为基础建立了连铸电磁搅拌过程的电磁场数学模型；确定钢水流动的湍流状态，以连续方程、动量方程、纳维－斯托克斯方程为基础，并选择低Re数k ε模型方程作为结晶器钢水流动模型来建立连铸结晶器电磁搅拌流场的数学模型；利用ANSYS有限元软件对搅拌器内磁场、流场的二维、三维数值模拟，分析了其分布特征及变化规律；考察了电流强度大小、电流频率等搅拌参数对磁感应强度、电磁力的影响。采用ANSYS耦合分析的物理环境法将电磁场模拟得到的电磁力作为体积力载荷加入流场分析中，将磁场耦合到流场中，得到了流场的分布规律，确定合理的电磁搅拌参数。
When electromagnetic stirring technology is applied to continuous castingproduction,it can expand equiaxial crystal area,reduce center loose, segregation andshrinkage,greatly reduce casting surface and subcutaneous inclusion,porosity and otherdefects.The advantages attraced researchers carrying out lots of research work. Theessence of the electromagnetic stirring is that coil passing into low-frequency alternatingcurrent can produce the changing magnetic field. The changing magnetic field cangenerate induced current in the liquid steel. The interaction between induced current andmagnetic field produces Lorenz force in the liquid steel to drive liquid steel flow.Physicalsimulation of its theoretical analysis is difficult, numerical simulation has been aeffective mean to study electromagnetic stirring technology in the process of continuouscasting.The numerical simulation method became an effective and relatively simplemethod to determine electromagnetic stirring structure and process parameter.
Taking a mold electromagnetic stirring in a steel plant as a research object，in thispaper,I ignored the influence of the flowing liquid steel on the electromagnetic field. Onthe basis of Maxwell's equation set,I established electromagnetic flied mathematicalmodel.Then,I confirmed the steel flow state as turbulence,chose low Reynolds model asliquid steel flow model,and established flow flied mathematical model on the basis ofcontinuous equation, momentum equations and Navier-Stokes equations.By finiteelement software ANSYS,I carried out2d and3d numerical stimulation forelectromagnetic flied and flow flied，as well as analyzed its distribution and changingrule. I investigated the influence of current strength and current frequency on magneticinduction and electromagnetic force.Using physical environmental law in the coupledanalysis,I applied electromagnetic force to flow field analysis as volume force,thencoupled flow field with electromagnetic field so that I got its distribution and deteminnethe technical parameters.
本文以某钢厂方坯结晶器的旋转型电磁搅拌器为研究对象，忽略钢水流动对电磁场的影响，以麦克斯韦方程组为基础建立了连铸电磁搅拌过程的电磁场数学模型；确定钢水流动的湍流状态，以连续方程、动量方程、纳维－斯托克斯方程为基础，并选择低Re数k ε模型方程作为结晶器钢水流动模型来建立连铸结晶器电磁搅拌流场的数学模型；利用ANSYS有限元软件对搅拌器内磁场、流场的二维、三维数值模拟，分析了其分布特征及变化规律；考察了电流强度大小、电流频率等搅拌参数对磁感应强度、电磁力的影响。采用ANSYS耦合分析的物理环境法将电磁场模拟得到的电磁力作为体积力载荷加入流场分析中，将磁场耦合到流场中，得到了流场的分布规律，确定合理的电磁搅拌参数。
When electromagnetic stirring technology is applied to continuous castingproduction,it can expand equiaxial crystal area,reduce center loose, segregation andshrinkage,greatly reduce casting surface and subcutaneous inclusion,porosity and otherdefects.The advantages attraced researchers carrying out lots of research work. Theessence of the electromagnetic stirring is that coil passing into low-frequency alternatingcurrent can produce the changing magnetic field. The changing magnetic field cangenerate induced current in the liquid steel. The interaction between induced current andmagnetic field produces Lorenz force in the liquid steel to drive liquid steel flow.Physicalsimulation of its theoretical analysis is difficult, numerical simulation has been aeffective mean to study electromagnetic stirring technology in the process of continuouscasting.The numerical simulation method became an effective and relatively simplemethod to determine electromagnetic stirring structure and process parameter.
Taking a mold electromagnetic stirring in a steel plant as a research object，in thispaper,I ignored the influence of the flowing liquid steel on the electromagnetic field. Onthe basis of Maxwell's equation set,I established electromagnetic flied mathematicalmodel.Then,I confirmed the steel flow state as turbulence,chose low Reynolds model asliquid steel flow model,and established flow flied mathematical model on the basis ofcontinuous equation, momentum equations and Navier-Stokes equations.By finiteelement software ANSYS,I carried out2d and3d numerical stimulation forelectromagnetic flied and flow flied，as well as analyzed its distribution and changingrule. I investigated the influence of current strength and current frequency on magneticinduction and electromagnetic force.Using physical environmental law in the coupledanalysis,I applied electromagnetic force to flow field analysis as volume force,thencoupled flow field with electromagnetic field so that I got its distribution and deteminnethe technical parameters.
引文
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[15]商跃进.有限元原理与ANSYS应用指南[M].北京:清华大学出版社，2005:12-13.
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[19]冯慈璋.电磁场[M].北京：人民教育出版社,1985:32-34.
[20]王哲峰.电磁搅拌过程中电磁场、流场的有限元模拟[D].沈阳:东北大学,2002:26-28.
[21]江家麟,周佩白,钱秀英等.电磁场与电磁能[M].北京:高等教育出版社,1992:156-159.
[22]汤蕴缪.电机内的电磁场[M].北京:科学出版社,1998:135-137.
[23]胡之光.电机电磁场的分析与计算[M].北京:机械工业出版社,1989:196-199.
[24]倪光正.电磁场数值方法[M].北京：高等教育出版社,1995:168-171.
[25] Meyer J L, Szekely J, E l-Kzddzh N. Calculation of the Electromagnetic Force Field forInduction Stirring in Continuous Casting[J]. Transactions ISIJ,1987(27):25-33
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[27]陶文铨．数值传热学（第二版）[M].西安:西安交通大学出版社,2001:333-392.
[28]任兵芝.电磁搅拌大方坯连铸结晶器内电磁场与流场及温度场耦合过程数值模拟[D].沈阳:东北大学,2008:35.
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[30] Levdansky V V,Kim HC,Smolik J,Moravec P.Effect of electromagnetic field on transferprocesses in heterogeneous system[J]. International Journal of Heat and MassTransfer,2001,44:1065-1071.
[31] Alboussiere T,Neurand A C,Garandet J P,Moreau R.Segregation during horizontal bridgmangrowth under an axial magnetic field[J]. Journal of Crystal Growth,1997,181:133-144.
[32] Versteeg H K,Malalasekera W.An Introduction to Computational Fluid Dynamics:The FiniteVolume Method[M]. New York:Wiley,1995.
[33] Thomas B G,Mika L J,Najjar F M. Simulation of fluid flow inside a continuous slab-castingmachine[J]. Metall. Trans. B.,1990,21B:387-400.
[34] Brian G Thomas,Zhang Lifeng.Mathematical modeling of fluid flow in continuous casting[J].ISIJ International,2001,41(10):1181-1191.
[35] Cho Y W,Chung S H,Shim J D,Dementev S,Ivanov S.Fluid flow and heat transfer in moltenmetal stirred by a circular inductor[J]. International Journal of Heat and MassTransfer,1999,42:1317-1326.
[36]王福军.计算流体动力学[M].北京:清华大学出版社,2004，146-148.
[37] Brinkmeyer Ll.Fluid dynamics of continuous casting tundishes[J]. Steelmaking ConferenceProceeding,1992:293-294.
[38]吴扣根.圆坯连铸结晶器电磁搅拌过程数学模拟与实验研究[D].上海:上海大学,2004.
[39] Brian G. Modeling of the continuous casting of steel-past,present and future[J]. ElectricFurnace Conf.Proc.2011,59:3-30.
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