连铸流动与凝固耦合模拟中糊状区系数的表征及影响
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摘要
分析提出了连铸流动与凝固耦合数值模拟中,钢液在两相区流动时的糊状区系数(Amush)与渗透率的关系;通过建立大方坯连铸结晶器三维耦合数值模型,揭示了不同糊状区系数对钢液流动、传热与凝固进程的影响,以及早期相关研究结果差异的源头.结果表明:糊状区系数越大,钢液在糊状区内的流动阻力越强,凝固时钢液流动速度降低越快.采用较大的糊状区系数时,糊状区呈较窄的"带状"分布在固液相之间;当糊状区系数较小时,糊状区范围变大,钢液在结晶器内温降过快,自由液面处出现过冷现象,凝固坯壳局部发生重熔.结合实验数据验证与模型分析,认为糊状区系数取值1×10~8～5×10~8kg·m~(-3)·s~(-1)可以较可靠地揭示连铸结晶器内的实际凝固现象.
The mushy zone refers to the region of the solid-liquid system where the temperature is between the liquidus and solidus temperatures. In this zone,the turbulence of the interdendritic flow is reduced by blockage of dendrites. The mushy zone coefficient( Amush) is an important calculating parameter in the continuous casting numerical simulation process,which strongly affects the prediction of fluid flow and solidification behavior in the mold zone. However,most researchers have neglected the influence of the mushy zone coefficient,and the correct expression of this coefficient is rarely found in the literature. Generally,the lower default value of 1 ×10~5 kg·~(-3)·s~(-1) is used in the model,which leads to unrealistic results. In this study,the relationship between the mushy zone coefficient and permeability was analyzed,and the expression of the mushy zone coefficient was proposed. A coupled flow and solidification numerical model was developed to evaluate the effect of the mushy zone coefficient on the melt flow and solidification phenomena in a bloom continuous casting mold. Results show that the higher the value of the mushy zone coefficient,the stronger the damping becomes,and the faster the velocity drops as melt solidifies. A relatively high value of the mushy zone coefficient generates a"banded"form of mushy zone sandwiched between the solid and liquid phases in the mold zone. When the mushy zone coefficient is at a lower value,a wider mushy zone is obtained and the melt cools down rapidly in the mold region. In addition,the temperature at free surface is relatively low with supercooling,and the solidified shell remelts locally. The model is validated through comparison with measurements of shell thickness on a breakout shell. The value of the mushy zone coefficient ranging from 1×10~8～5×10~8kg·m~(-3)·s~(-1) is suggested.
The mushy zone refers to the region of the solid-liquid system where the temperature is between the liquidus and solidus temperatures. In this zone,the turbulence of the interdendritic flow is reduced by blockage of dendrites. The mushy zone coefficient( Amush) is an important calculating parameter in the continuous casting numerical simulation process,which strongly affects the prediction of fluid flow and solidification behavior in the mold zone. However,most researchers have neglected the influence of the mushy zone coefficient,and the correct expression of this coefficient is rarely found in the literature. Generally,the lower default value of 1 ×10~5 kg·~(-3)·s~(-1) is used in the model,which leads to unrealistic results. In this study,the relationship between the mushy zone coefficient and permeability was analyzed,and the expression of the mushy zone coefficient was proposed. A coupled flow and solidification numerical model was developed to evaluate the effect of the mushy zone coefficient on the melt flow and solidification phenomena in a bloom continuous casting mold. Results show that the higher the value of the mushy zone coefficient,the stronger the damping becomes,and the faster the velocity drops as melt solidifies. A relatively high value of the mushy zone coefficient generates a"banded"form of mushy zone sandwiched between the solid and liquid phases in the mold zone. When the mushy zone coefficient is at a lower value,a wider mushy zone is obtained and the melt cools down rapidly in the mold region. In addition,the temperature at free surface is relatively low with supercooling,and the solidified shell remelts locally. The model is validated through comparison with measurements of shell thickness on a breakout shell. The value of the mushy zone coefficient ranging from 1×10~8～5×10~8kg·m~(-3)·s~(-1) is suggested.
引文
[1] Thomas B G,Mika L J,Najjar F M. Simulation of fluid flow inside a continuous slab-casting machine. Metall Trans B,1990,21(2):387
[2] Thomas B G,Zhang L F. Mathematical modeling of fluid flow in continuous casting. ISIJ Int,2001,41(10):1181
[3] Fujisaki K. Magnetohydrodynamic solidification calculation in Darcy flow[steel casting]. IEEE Trans Magn,2003,39(6):3541
[4] Chakraborty S,Dutta P. Effects of dendritic arm coarsening on macroscopic modelling of solidification of binary alloys. Mater Sci Technol,2001,17(12):1531
[5] Pfeiler C,Thomas B G,Wu M,et al. Solidification and particle entrapment during continuous casting of steel. Steel Res Int,2008,79(8):599
[6] Gu J P,Beckermann C. Simulation of convection and macrosegregation in a large steel ingot. Metall Mater Trans A,1999,30(5):1357
[7] Yang H L,Zhang X Z,Deng K W,et al. Mathematical simulation on coupled flow,heat,and solute transport in slab continuous casting process. Metall Mater Trans B,1998,29(6):1345
[8] Aboutalebi M R,Hasan M,Guthrie R I L. Coupled turbulent flow,heat,and solute transport in continuous casting processes.Metall Mater Trans B,1995,26(4):731
[9] Seyedein S H,Hasan M. A three-dimensional simulation of coupled turbulent flow and macroscopic solidification heat transfer for continuous slab casters. Int J Heat Mass Transfer,1997,40(18):4405
[10] Aboutalebi M R,Guthrie R I L,Seyedein S H. Mathematical modeling of coupled turbulent flotw and solidification in a single belt caster with electromagnetic brake. Appl Math Modell,2007,31(8):1671
[11] Netto P G Q,Guthrie R I L. Modelling of a novel configuration for single-belt caster:the influence of empirical parameters on the solidification profile. ISIJ Int,2000,40(5):460
[12] Sun H B,Zhang J Q. Study on the macrosegregation behavior for the bloom continuous casting:model development and validation.Metall Mater Trans B,2014,45(3):1133
[13] Sun H B,Zhang J Q. Effect of feeding modes of molten steel on the mould metallurgical behavior for round bloom casting. ISIJ Int,2011,51(10):1657
[14] He M L,Wang N,Chen M,et al. Physical and numerical simulation of the fluid flow and temperature distribution in bloom continuous casting mold. Steel Res Int,2017,88(9):1600447
[15] Trindade L B,Nadalon J E A,Contini A C,et al. Modeling of solidification in continuous casting round billet with mold electromagnetic stirring(M-EMS). Steel Res Int,2017,88(4):1600319
[16] Hietanen P T,Louhenkilpi S,Yu S. Investigation of solidification,heat transfer and fluid flow in continuous casting of steel using an advanced modeling approach. Steel Res Int,2017,88(7):1600355
[17] Wang Q Q. Stundy on the Multiphase Flow,Heat Transfer and Solidification,Motion and Entrapment of Inclusions during Continuous Casting[Dissertation]. Beijing:University of Science and Technology Beijing,2016(王强强.连铸过程多相流、传热凝固及夹杂物运动捕获的研究[学位论文].北京:北京科技大学,2016)
[18] Voller V R,Prakash C. A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems. Int J Heat Mass Transfer,1987,30(8):1709
[19] Carman P C. Fluid flow through granular beds. Trans Inst Chem Eng,1937,15:150
[20] Minakawa S,Samarasekera I V,Weinberg F. Centerline porosity in plate castings. Metall Trans B,1985,16(4):823
[21] Won Y M,Thomas B G. Simple model of microsegregation during solidification of steels. Metall Mater Trans A,2001,32(7):1755
[22] Jiang D B,Zhu M Y. Flow and solidification in billet continuous casting machine with dual electromagnetic stirrings of mold and the final solidification. Steel Res Int,2015,86(9):993
[23] Ji Y,Tang H Y,Lan P,et al. Effect of dendritic morphology and central segregation of billet castings on the microstructure and mechanical property of hot-rolled wire rods. Steel Res Int,2017,88(8):1600426
[24] Jones W P,Launder B E. The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence. Int J Heat Mass Transfer,1973,16(6):1119
[25] Lai K Y M,Salcudean M,Tanaka S,et al. Mathematical modeling of flows in large tundish systems in steelmaking. Metall Trans B,1986,17(3):449
[26] Savage J,Pritchard W H. The problem of rupture of the billet in the continuous casting of steel. J Iron Steel Inst,1954,178(3):269
[27] Cai K K. Continuous Casting Mold. Beijing:Metallurgical Industry Press,2008(蔡开科.连铸结晶器.北京:冶金工业出版社,2008)
[2] Thomas B G,Zhang L F. Mathematical modeling of fluid flow in continuous casting. ISIJ Int,2001,41(10):1181
[3] Fujisaki K. Magnetohydrodynamic solidification calculation in Darcy flow[steel casting]. IEEE Trans Magn,2003,39(6):3541
[4] Chakraborty S,Dutta P. Effects of dendritic arm coarsening on macroscopic modelling of solidification of binary alloys. Mater Sci Technol,2001,17(12):1531
[5] Pfeiler C,Thomas B G,Wu M,et al. Solidification and particle entrapment during continuous casting of steel. Steel Res Int,2008,79(8):599
[6] Gu J P,Beckermann C. Simulation of convection and macrosegregation in a large steel ingot. Metall Mater Trans A,1999,30(5):1357
[7] Yang H L,Zhang X Z,Deng K W,et al. Mathematical simulation on coupled flow,heat,and solute transport in slab continuous casting process. Metall Mater Trans B,1998,29(6):1345
[8] Aboutalebi M R,Hasan M,Guthrie R I L. Coupled turbulent flow,heat,and solute transport in continuous casting processes.Metall Mater Trans B,1995,26(4):731
[9] Seyedein S H,Hasan M. A three-dimensional simulation of coupled turbulent flow and macroscopic solidification heat transfer for continuous slab casters. Int J Heat Mass Transfer,1997,40(18):4405
[10] Aboutalebi M R,Guthrie R I L,Seyedein S H. Mathematical modeling of coupled turbulent flotw and solidification in a single belt caster with electromagnetic brake. Appl Math Modell,2007,31(8):1671
[11] Netto P G Q,Guthrie R I L. Modelling of a novel configuration for single-belt caster:the influence of empirical parameters on the solidification profile. ISIJ Int,2000,40(5):460
[12] Sun H B,Zhang J Q. Study on the macrosegregation behavior for the bloom continuous casting:model development and validation.Metall Mater Trans B,2014,45(3):1133
[13] Sun H B,Zhang J Q. Effect of feeding modes of molten steel on the mould metallurgical behavior for round bloom casting. ISIJ Int,2011,51(10):1657
[14] He M L,Wang N,Chen M,et al. Physical and numerical simulation of the fluid flow and temperature distribution in bloom continuous casting mold. Steel Res Int,2017,88(9):1600447
[15] Trindade L B,Nadalon J E A,Contini A C,et al. Modeling of solidification in continuous casting round billet with mold electromagnetic stirring(M-EMS). Steel Res Int,2017,88(4):1600319
[16] Hietanen P T,Louhenkilpi S,Yu S. Investigation of solidification,heat transfer and fluid flow in continuous casting of steel using an advanced modeling approach. Steel Res Int,2017,88(7):1600355
[17] Wang Q Q. Stundy on the Multiphase Flow,Heat Transfer and Solidification,Motion and Entrapment of Inclusions during Continuous Casting[Dissertation]. Beijing:University of Science and Technology Beijing,2016(王强强.连铸过程多相流、传热凝固及夹杂物运动捕获的研究[学位论文].北京:北京科技大学,2016)
[18] Voller V R,Prakash C. A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems. Int J Heat Mass Transfer,1987,30(8):1709
[19] Carman P C. Fluid flow through granular beds. Trans Inst Chem Eng,1937,15:150
[20] Minakawa S,Samarasekera I V,Weinberg F. Centerline porosity in plate castings. Metall Trans B,1985,16(4):823
[21] Won Y M,Thomas B G. Simple model of microsegregation during solidification of steels. Metall Mater Trans A,2001,32(7):1755
[22] Jiang D B,Zhu M Y. Flow and solidification in billet continuous casting machine with dual electromagnetic stirrings of mold and the final solidification. Steel Res Int,2015,86(9):993
[23] Ji Y,Tang H Y,Lan P,et al. Effect of dendritic morphology and central segregation of billet castings on the microstructure and mechanical property of hot-rolled wire rods. Steel Res Int,2017,88(8):1600426
[24] Jones W P,Launder B E. The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence. Int J Heat Mass Transfer,1973,16(6):1119
[25] Lai K Y M,Salcudean M,Tanaka S,et al. Mathematical modeling of flows in large tundish systems in steelmaking. Metall Trans B,1986,17(3):449
[26] Savage J,Pritchard W H. The problem of rupture of the billet in the continuous casting of steel. J Iron Steel Inst,1954,178(3):269
[27] Cai K K. Continuous Casting Mold. Beijing:Metallurgical Industry Press,2008(蔡开科.连铸结晶器.北京:冶金工业出版社,2008)
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