Effects of calculation approaches for thermal conductivity on the simulation accuracy of billet continuous casting

Abstract

An unsteady, two-dimensional, explicitly solved finite difference heat transfer model of a billet caster was presented to clarify the influence of the thermal conductivity of steel on model accuracy. Different approaches were utilized for calculating the thermal conductivity of solid, mushy and liquid steels. Model results predicted by these approaches were compared, and the advantages of advocated approaches were discussed. It is found that the approach for calculating the thermal conductivity of solid steel notably influences model predictions. Convection effects of liquid steel should be considered properly while calculating the thermal conductivity of mushy steel. Different values of the effective thermal conductivity of liquid steel adopted could partly be explained by the fact that different models adopted dissimilar approaches for calculating the thermal conductivity of solid and mushy steels.

Keywords

continuous casting / solidification / heat transfer / thermal / conductivity / mathematical models

References

[1] Mizikar EA. Mathematical heat transfer model for solidification of continuously cast steel slabs. Trans. Metall. Soc. AIME, 1967, 239(11): 1747

[2] Ramírez-López A, Aguilar-López R, Palomar-Pardavé M, Romero-Romo MA, Muñoz-Negrón D. Simulation of heat transfer in steel billets during continuous casting. Int. J. Miner. Metall. Mater., 2010, 17(4): 403.

[3] Lou JJ, Bao YP, Liu JH, Sun W, Du SL, Huang SQ. Numerical simulation of thermal processing in continuously cast beam blank. J. Univ. Sci. Technol. Beijing, 2005, 27(2): 173

[4] Hardin RA, Liu K, Beckermann C, Kapoor A. A transient simulation and dynamic spray cooling control model for continuous steel casting. Metall. Mater. Trans. B, 2003, 34(3): 297.

[5] Lally B, Biegler L, Henein H. Finite difference heat-transfer modeling for continuous casting. Metall. Trans. B, 1990, 21(4): 761.

[6] Louhenkilpi S, Mäkinen M, Vapalahti S, Räisänen T, Laine J. 3D steady state and transient simulation tools for heat transfer and solidification in continuous casting. Mater. Sci. Eng. A, 2005, 413–414, 135.

[7] Thomas BG, Samarasekera IV, Brimacombe JK. Comparison of numerical modeling techniques for complex, two-dimensional, transient heat-conduction problems. Metall. Trans. B, 1984, 15(2): 307.

[8] Szekely J, Stanek V. On heat transfer and liquid mixing in the continuous casting of steel. Metall. Trans. B, 1970, 1(1): 119

[9] Liu Q, Wang LZ, Zhang LQ, Cao LG, Ding XZ, Liang M, Qi Y. Mathematical model of heat transfer for bloom continuous casting. J. Univ. Sci. Technol. Beijing, 2008, 15(1): 17.

[10] Zheng Z, Hu Y. Advance in mathematic model of solidification heat transfer process in continuous casting. J. Chongqing Univ. Nat. Sci. Ed., 2006, 29(10): 100

[11] Louhenkilpi S, Laitinen E, Nieminen R. Real-time simulation of heat transfer in continuous casting. Metall. Trans. B, 1993, 24(4): 685.

[12] Wang HM, Li GR, Lei YC, Zhao YT, Dai QX, Wang JJ. Mathematical heat transfer model research for the improvement of continuous casting slab temperature. ISIJ Int., 2005, 45(9): 1291.

[13] Ramírez-López A, Aguilar-López R, Kunold-Bello A, González-Trejo J, Palomar-Pardavé M. Simulation factors of steel continuous casting. Int. J. Miner. Metall. Mater., 2010, 17(3): 267.

[14] Wang YC, Li DY, Peng YH, Zhu LG. Computational modeling and control system of continuous casting process. Int. J. Adv. Manuf. Technol., 2007, 33(1–2): 1.

[15] Mazumdar D. A consideration about the concept of effective thermal conductivity in continuous casting. ISIJ Int., 1989, 29(6): 524.

[16] Xia YJ, Wang FM, Wang JL, Li GZ. Simulation of the continuous casting process in a mold of free-cutting steel 38MnVS based on a MiLE method. Int. J. Miner. Metall. Mater., 2011, 18(5): 562.

[17] Tieu AK, Kim IS. Simulation of the continuous casting process by a mathematical model. Int. J. Mech. Sci., 1997, 39(2): 185.

[18] Zou DJ, Zou ZS. Discussion on effective thermal conductivity of molten steel in numerical simulation of solidification in continuous casting. Continuous Cast., 2009 5

[19] Choudhary SK, Mazumdar D, Ghosh A. Mathematical modelling of heat transfer phenomena in continuous casting of steel. ISIJ Int., 1993, 33(7): 764.

[20] El-Bealy MO. Mold thermo-mechanical rigidity criterion for surface quality of continuous casting of steel. Mater. Sci. Appl., 2013, 4, 39

[21] Huang X, Thomas BG. Modeling of transient flow phenomena in continuous casting of steel. Can. Metall. Q., 1998, 37(3–4): 197.

[22] Tao WQ. Numerical Heat Transfer, 2001, Xi’an, Xi’an Jiaotong University Press, 80

[23] Kawawa T, Sato H, Miyahara S, Koyano T, Nemoto H. Determination of solidifying shell thickness of continuously cast slab by rivet pin shooting. Tetsu-to-Hagané, 1974, 60(2): 206

[24] Long MJ, Chen DF, Wang QX, Luo DH, Han ZW, Liu Q, Gao WX. Determination of CC slab solidification using nail shooting technique. Ironmaking Steelmaking, 2012, 39(5): 370.