电磁软接触连铸结晶器内多物理场耦合数值模拟研究
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摘要
众所周知在实际连铸生产中常发生非理想的凝固过程,影响铸坯质量。而电磁软接触连铸技术能生产出无振痕无裂纹的连铸坯,这一点已得到冶金工作者的广泛认同,但是钢的电磁软接触连铸技术受众多因素的影响规律尚不清楚。
为了确定合理的工艺参数,提供电磁软接触结晶器结构设计的理论依据,以及丰富电磁软接触技术内容,本文首先建立了电磁软接触结晶器内的三维电磁场有限元模型,研究了软接触结晶器内能重点反映电磁场冶金特性的磁感应强度、焦耳热和电磁体积力等物理量的分布特征。在此基础上,建立了电磁软接触连铸结晶器内钢液湍流流动的三维耦合模型,研究了典型参数下软接触结晶器内的钢液运动规律。并进一步针对圆坯电磁软接触连铸结晶器内钢液的流动凝固和应力应变状态,建立了多物理场耦合的二维轴对称数学模型,研究了高频交变电磁场对钢液传热凝固、受力变形的影响规律,以及对软接触结晶器壁温度分布、受力变形的影响规律。
从描述电磁场的Maxwell方程组出发,建立了软接触结晶器内的三维电磁场有限元模型,研究了典型参数下软接触结晶器内的电磁场分布规律,对比分析了电源频率、电流强度对结晶器内磁感应强度、电磁体积力、焦耳热生成率的影响规律,以期为之后的流动凝固分析计算提供数据支持和理论基础。结果表明：磁感应强度在空间分布不均,圆坯电磁软接触结晶器内钢液上的焦耳热按结晶器分瓣结构呈周期性不均匀分布,由此会造成凝固坯壳厚度的不均匀分布,并得到了实验验证,需在电磁软接触连铸结构设计和电参数制定时充分考虑。圆坯电磁软接触结晶器内钢液自由表面上的周向电磁力按结晶器切缝、分瓣体中心反方向对称分布,会对钢液有一个拉伸或者推挤作用,影响钢液流动形态。
在连续介质模型基础上,建立了软接触结晶器内流体湍流流动的三维数学模型,研究了典型参数下软接触结晶器内的钢液运动规律,并对不同电源频率、电流强度下的流体流动速度、湍动能水平进行了对比分析。结果表明：高频交变电磁场主要对弯月面区域的钢液有力的作用,钢液下段几乎不受电磁场影响。圆坯软接触结晶器自由表面上钢液流动速度按切峰、分瓣体中心反方向对称分布,会使自由表面产生凹凸变形,并得到了实验验证,需在电磁软接触结晶器结构设计和电参数选择时加以充分考虑。钢液纵截面内钢液流动呈现双环流动,上部涡流较常规连铸结晶器涡心位置上移,且漩涡区域扩大,流动速度较常规连铸增加。结晶器内上部熔池的流体速度随电流强度增大而增大,但电流强度大小并不改变熔池中的流动形态。电源频率改变同时影响钢液上部涡流区域速度的大小、方向,提高电源频率,有抑制自由表面波动的作用。
在合理简化模型的基础上,通过双向迭代耦合的方法,建立了软接触结晶器内电磁场、流场、温度场和应力场的二维轴对称多物理场耦合模型,并充分考虑了结晶器壁与坯壳的接触问题,且就不同电源频率、电流强度下钢液的温度和应力场分布以及结晶器的温度、应力场、变形场进行了对比讨论。温度场计算结果表明：①软接触结晶器内钢液初始凝固点下降,初始凝固坯壳减薄,但在结晶器出口处凝固壳厚度较常规连铸增厚。②软接触结晶器铜管高温区域扩大,温度梯度也较常规结晶器加大,外壁温度高于冷却水汽化温度,在电磁软接触连铸过程中,应较常规连铸适当提高冷却水流量。应力场计算结果表明：①软接触结晶器内初始连铸坯壳内外表面等效应力值较常规连铸减小,但在结晶器下段内外表面等效应力又较常规连铸增大。②软接触结晶器壁高应力区及高变形区较常规结晶器扩大,负锥度加大。③软接触结晶器内初始凝固区域的坯壳-结晶器壁间气隙较常规连铸减小,下端气隙却较常规连铸增大。
In the continuous casting process of molten steel, it is well known there are some nonideal solidification phenomena which have harmful to product quality. Now an effective technique of electromagnetic soft contact continuous casting has been introduced to eliminating surface defects for non-cracks and no-oscillation marks billets, which have been proved by many physical experiments and numerical simulations. However, the soft-contact continuous casting of steel has still been a developing question.
To determine the reasonable operation parameters, and provide the fundamental theories of optimal design for soft-contact mould and rich the contents of soft-contact technique, a three dimensional finite element model of electromagnetic field was developed to investigate the distribution of magnetic flux density and heat generation and electromagnetic volum force, which can represent the casting action of electromagnetic field. Then a three dimensional coupled mathematical model of electromagnetic field and flow field had been founded to simulate the fluid flow behaviors of molten steel under typical simulation parameters. At last, a coupled two dimensional finite element model had been established, for the effective calculations of electromagnetic field, fluid flow, heat transfer, and stress distribution under complex conditions of soft contact. By using this model, the effects of high frequency electromagnetic field on temperature and thermo-mechanical behaviors of steel and mould had also been studied.
Based on the Maxwell equations of basic equations for electromagnetic field, a three dimensional finite element model of electromagnetic field was developed to investigate the distribution of electromagnetic field in the mold under typical simulation parameters. And the effects of frequencies and currents on the distributions of magnetic flux density and electromagnetic force density and heat generation ratio had been emphasized. The results showed the magnetic flux density distributed unevenly in space. The joule heat indicated the character of periodic symmetry of uneven distribution to result in the uneven thickness of shell in EMC mold, which had been approved by experiment. The electromagnetic force circumferential component indicates periodical antisymmetric distribution at the center of slit and segment to make the jostling or drawing function in EMC mold, which would affect the flow pattern of liquid steel.
From the Bennon's continuum model, a three dimensional coupled mathematical model of electromagnetic field and flow field had been founded to simulate the fluid flow behaviors of molten steel under typical simulation parameters. And the effects of frequencies and currents on flow velocity and turbulence kinetic energy had been compared and analyzed. The results showed high frequency electromagnetic field mainly had effects on billet in meniscus zone, and the bottom of it was not worked on. In the process of EMC, flow velocities were periodical antisymmetric distribution at the center of slit and segment to result in the concavo-convex deformation at free surface, which had been made sure by experiment. So it was necessary for choices of EMC parameters to considerate this phonomena. There were two vortexes forming in longitudinal section, and the center of upper recirculation moved towards free surface, and circulation zone extended, and flow velocities increased, compared with continuous casing. The flow velocity increased when the currents enhanced, but the flow patterns nearly remain unchanged. When frequencies changed, the magnitude and direction of fluid velocity vector also altered, and the higher frequency electromagnetic field can retrain the fluctuation of free surface of liquid steel.
By reasonable simplification of mold's configuration, a coupled two dimensional finite element model had been founded, for the effective calculations of electromagnetic field, fluid flow, heat transfer, and stress distribution under complex conditions. Moreover, the intermittent contact behaviors between the shell and the mold were considered. And the effects of frequencies and currents on temperature and stress for both billet and mold had been discussed and analyzed. The results of temperature field showed with the high frequency electromagnetic field, the solidification start point moved downwards and initial shell thickness got thinner, but the shell thickness increased at the outlet of mold. The temperature and its gradient of EMC mold also enhanced, and the temperature of outer wall was beyond the boiloff temperature of cooling water. It mean the flux of cooling water must be increased in EMC process. The results of stress showed the equivalent stress of initial solidification shell both at its outer and inner surface decreased, but at the bottom the equivalent stress of two sides of shell both increased. The high-stress zone and the high-deformation zone of EMC mold extended, and the negative taper added. Under the high frequency electromagnetic field, the gap size reduced at the initial solidification zone and then grew at the lower position.
为了确定合理的工艺参数,提供电磁软接触结晶器结构设计的理论依据,以及丰富电磁软接触技术内容,本文首先建立了电磁软接触结晶器内的三维电磁场有限元模型,研究了软接触结晶器内能重点反映电磁场冶金特性的磁感应强度、焦耳热和电磁体积力等物理量的分布特征。在此基础上,建立了电磁软接触连铸结晶器内钢液湍流流动的三维耦合模型,研究了典型参数下软接触结晶器内的钢液运动规律。并进一步针对圆坯电磁软接触连铸结晶器内钢液的流动凝固和应力应变状态,建立了多物理场耦合的二维轴对称数学模型,研究了高频交变电磁场对钢液传热凝固、受力变形的影响规律,以及对软接触结晶器壁温度分布、受力变形的影响规律。
从描述电磁场的Maxwell方程组出发,建立了软接触结晶器内的三维电磁场有限元模型,研究了典型参数下软接触结晶器内的电磁场分布规律,对比分析了电源频率、电流强度对结晶器内磁感应强度、电磁体积力、焦耳热生成率的影响规律,以期为之后的流动凝固分析计算提供数据支持和理论基础。结果表明：磁感应强度在空间分布不均,圆坯电磁软接触结晶器内钢液上的焦耳热按结晶器分瓣结构呈周期性不均匀分布,由此会造成凝固坯壳厚度的不均匀分布,并得到了实验验证,需在电磁软接触连铸结构设计和电参数制定时充分考虑。圆坯电磁软接触结晶器内钢液自由表面上的周向电磁力按结晶器切缝、分瓣体中心反方向对称分布,会对钢液有一个拉伸或者推挤作用,影响钢液流动形态。
在连续介质模型基础上,建立了软接触结晶器内流体湍流流动的三维数学模型,研究了典型参数下软接触结晶器内的钢液运动规律,并对不同电源频率、电流强度下的流体流动速度、湍动能水平进行了对比分析。结果表明：高频交变电磁场主要对弯月面区域的钢液有力的作用,钢液下段几乎不受电磁场影响。圆坯软接触结晶器自由表面上钢液流动速度按切峰、分瓣体中心反方向对称分布,会使自由表面产生凹凸变形,并得到了实验验证,需在电磁软接触结晶器结构设计和电参数选择时加以充分考虑。钢液纵截面内钢液流动呈现双环流动,上部涡流较常规连铸结晶器涡心位置上移,且漩涡区域扩大,流动速度较常规连铸增加。结晶器内上部熔池的流体速度随电流强度增大而增大,但电流强度大小并不改变熔池中的流动形态。电源频率改变同时影响钢液上部涡流区域速度的大小、方向,提高电源频率,有抑制自由表面波动的作用。
在合理简化模型的基础上,通过双向迭代耦合的方法,建立了软接触结晶器内电磁场、流场、温度场和应力场的二维轴对称多物理场耦合模型,并充分考虑了结晶器壁与坯壳的接触问题,且就不同电源频率、电流强度下钢液的温度和应力场分布以及结晶器的温度、应力场、变形场进行了对比讨论。温度场计算结果表明：①软接触结晶器内钢液初始凝固点下降,初始凝固坯壳减薄,但在结晶器出口处凝固壳厚度较常规连铸增厚。②软接触结晶器铜管高温区域扩大,温度梯度也较常规结晶器加大,外壁温度高于冷却水汽化温度,在电磁软接触连铸过程中,应较常规连铸适当提高冷却水流量。应力场计算结果表明：①软接触结晶器内初始连铸坯壳内外表面等效应力值较常规连铸减小,但在结晶器下段内外表面等效应力又较常规连铸增大。②软接触结晶器壁高应力区及高变形区较常规结晶器扩大,负锥度加大。③软接触结晶器内初始凝固区域的坯壳-结晶器壁间气隙较常规连铸减小,下端气隙却较常规连铸增大。
In the continuous casting process of molten steel, it is well known there are some nonideal solidification phenomena which have harmful to product quality. Now an effective technique of electromagnetic soft contact continuous casting has been introduced to eliminating surface defects for non-cracks and no-oscillation marks billets, which have been proved by many physical experiments and numerical simulations. However, the soft-contact continuous casting of steel has still been a developing question.
To determine the reasonable operation parameters, and provide the fundamental theories of optimal design for soft-contact mould and rich the contents of soft-contact technique, a three dimensional finite element model of electromagnetic field was developed to investigate the distribution of magnetic flux density and heat generation and electromagnetic volum force, which can represent the casting action of electromagnetic field. Then a three dimensional coupled mathematical model of electromagnetic field and flow field had been founded to simulate the fluid flow behaviors of molten steel under typical simulation parameters. At last, a coupled two dimensional finite element model had been established, for the effective calculations of electromagnetic field, fluid flow, heat transfer, and stress distribution under complex conditions of soft contact. By using this model, the effects of high frequency electromagnetic field on temperature and thermo-mechanical behaviors of steel and mould had also been studied.
Based on the Maxwell equations of basic equations for electromagnetic field, a three dimensional finite element model of electromagnetic field was developed to investigate the distribution of electromagnetic field in the mold under typical simulation parameters. And the effects of frequencies and currents on the distributions of magnetic flux density and electromagnetic force density and heat generation ratio had been emphasized. The results showed the magnetic flux density distributed unevenly in space. The joule heat indicated the character of periodic symmetry of uneven distribution to result in the uneven thickness of shell in EMC mold, which had been approved by experiment. The electromagnetic force circumferential component indicates periodical antisymmetric distribution at the center of slit and segment to make the jostling or drawing function in EMC mold, which would affect the flow pattern of liquid steel.
From the Bennon's continuum model, a three dimensional coupled mathematical model of electromagnetic field and flow field had been founded to simulate the fluid flow behaviors of molten steel under typical simulation parameters. And the effects of frequencies and currents on flow velocity and turbulence kinetic energy had been compared and analyzed. The results showed high frequency electromagnetic field mainly had effects on billet in meniscus zone, and the bottom of it was not worked on. In the process of EMC, flow velocities were periodical antisymmetric distribution at the center of slit and segment to result in the concavo-convex deformation at free surface, which had been made sure by experiment. So it was necessary for choices of EMC parameters to considerate this phonomena. There were two vortexes forming in longitudinal section, and the center of upper recirculation moved towards free surface, and circulation zone extended, and flow velocities increased, compared with continuous casing. The flow velocity increased when the currents enhanced, but the flow patterns nearly remain unchanged. When frequencies changed, the magnitude and direction of fluid velocity vector also altered, and the higher frequency electromagnetic field can retrain the fluctuation of free surface of liquid steel.
By reasonable simplification of mold's configuration, a coupled two dimensional finite element model had been founded, for the effective calculations of electromagnetic field, fluid flow, heat transfer, and stress distribution under complex conditions. Moreover, the intermittent contact behaviors between the shell and the mold were considered. And the effects of frequencies and currents on temperature and stress for both billet and mold had been discussed and analyzed. The results of temperature field showed with the high frequency electromagnetic field, the solidification start point moved downwards and initial shell thickness got thinner, but the shell thickness increased at the outlet of mold. The temperature and its gradient of EMC mold also enhanced, and the temperature of outer wall was beyond the boiloff temperature of cooling water. It mean the flux of cooling water must be increased in EMC process. The results of stress showed the equivalent stress of initial solidification shell both at its outer and inner surface decreased, but at the bottom the equivalent stress of two sides of shell both increased. The high-stress zone and the high-deformation zone of EMC mold extended, and the negative taper added. Under the high frequency electromagnetic field, the gap size reduced at the initial solidification zone and then grew at the lower position.
引文
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47 Tanaka T, Kurita K, Kuroda A. Liquid metal flow with heat transfer in a cold crucible confined by a free surface and a solidification front [J]. ISIJ International,1991,31(12): 1416-1423.
48 Cha P R, Hwang Y S, Nam H S, et al.3D numerical analysis on electromagnetic and fluid dynamic phenomena in a soft contact electromagnetic slab caster [J]. ISIJ International,1998, 38(5):403-410.
49 Zhu X R, Harding R A, Campbell J. Electromagnetic confinement including the dynamic effect due to melt glow [J]. ISIJ International,1999,39(1):1-5.
50 Miyoshino I, Takeuchi E, Yano H, et al. Influence of electromagnetic pressure on the early solidification in a continuous casting mold [J]. ISIJ International,1989,29(12):1040-1047.
51 Kageyama R, Evans J W. Development of a three dimensional mathematical model of the electromagnetic casting of steel [J]. ISIJ International,2002,42(2):163-170.
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54 Li T J, Sassa K, Asai S. Surface quality improvement of continuously cast metals by imposing intermittent high frequency magnetic field and synchronizing the field with mold oscillation [J]. ISIJ International,1996,36(4):410-416.
55 Cho Y W, Oh Y J, Chung S H, et al. Mechanism of surface quality improvement in continuous cast slab with rectangular cold crucible mold [J]. ISIJ International,1998,38(7): 723-729.
56 Ayata K, Miyazawa K, Takenuchi E, et al. Outline of national project on application of electromagnetic force to continuous casting of steel [A]. The 3rd International Symposium on EPM [C]. Nagoya, Japan,2000,376-280.
58 Li T J, Nagaya S, Sassa K, ea al. Study of meniscus behavior and surface properties during casting in a high in a high-frequency magnetic field [J]. Metall. Mater. Trans.,1995,26B(4): 353-359.
59 Nakata H, Etay J. Meniscus shape of molten steel under alternating magnetic field [J]. ISIJ International,1992,32(4):521-528.
60 Toh T, Takeuchi E, Sakane J I, et al. Study of menisicus behavior and surface properties during casting in a high-frequency magnetic field [J]. Metallurgical Transactions B,1995, 26(2):353-359.
61 Joonpyo P, Hoyoung K, Heetae J, et al. Continuous casting of steel billet with high frequency electromagnetic field [J]. ISIJ International,2003,43(6):813-819.
62雷作胜,任忠鸣,杨松华.连铸保护渣渣道动态压力的研究[J].上海金属,2001,32(3)：14-18.
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64 Mizikar E A. Mathematical heat transfer model for solidification of continuously cast steel slabs [J]. Trans. TMS-AIIVIE,1967,239:1747-1753.
65 Lait J E, Brimacombe J K, Weinberg F. Mathematical modeling of heat flow in the continuous casting of steel [J]. Ironmaking and Steelmaking,1974,1(2):90-97.
66 Gartling D K. Finite element analysis of convective heat transfer problems with change of phase [A]. Computer Methods in Fluids [C]. Pentech, London,1980,257-284.
67 Weiner J. Elasto-plastic thermal stresses in a solidifying body [J]. Mech.Phys.Solids,1963, 1(11):145-154.
68 Gill A, Brimacombe J K, Weiberg F. Mathematical analysis of stresses in continuous casting of steel [J], Ironmaking and Steelmaking,1977,4(4):240-245.
69 Grill A, Schwerdtfeger K. Finite element analysis of bulging produced by creep in continuously cast steel slabs [J]. Ironmaking and Steelmaking,1979,6(3):131-135.
70 Barber B, Lewis B A, Leckenby B M. Finite element analysis of strand deformation and strain distribution in solidifying shell during continuous slab casting [J]. Ironmaking and Steelmaking,1985,12(4):131-135.
71 Tszeng T C, Kobayashi S. Stress analysis in solidification processes:application to continuous casting [J] International Journal of Machine Tools & Manufacture,1989,29(1): 121-140.
72 Kelly J E, Michalek K P, O'Connor T G.Initial development of thermal and stress fields in continuously cast steel billets [J]. Metallurgical Transactions A,1988,19(10):2589-2602.
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