Comparison of mathematical models for the turbulent fluid flow, heat transfer and solidification in the continuous casting process

Comparison of mathematical models for the turbulent fluid flow, heat transfer and solidification in the continuous casting process

Rodrigo Ottoni Da Silva Pereira, Roberto Parreiras Tavares

Federal University of Minas Gerais, Belo Horizonte, Brazil.

DOI:

https://doi.org/10.7494/cmms.2007.3.0175

Abstract:

In the present work a mathematical model for the continuous casting process and its principal phenomena was developed. The model takes into account: heat transfer, fluid flow and mass transfer. The model allows the calculation of temperature, velocity, carbon concentration and turbulence variables profiles and the variation of the solidified shell thickness along the caster. The new features of the present model are the inclusion of the effects of nozzle port configuration on the fluid flow and the possibility to perform calculations for the entire casting length. The effect of fluid flow and segregation was evaluated and it was shown that the mathematical model should take the fluid flow into account and that segregation has a minor effect in the temperature and fluid flow profiles. The introduction of the effect of segregation in the model indicates that the carbon content is lower near the surface and higher in the center of the strand. The model also showed that the strand becomes completely solid at approximately 13m below the meniscus in the case studied. The fluid flow affects the process in the first 4 to 5 m of the strand, being important only in the first 2 m. Different nozzle port angles were simulated and it was shown that a port with a downward angle leads to lower turbulence at the meniscus level in the mould.

Cite as:

Pereira, R., & Tavares, R., (2007). Comparison of mathematical models for the turbulent fluid flow, heat transfer and solidification in the continuous casting process. Computer Methods in Materials Science, 7(3), 352 – 365. https://doi.org/10.7494/cmms.2007.3.0175

Article (PDF):

Keywords:

Continuous casting, Mathematical modelling, Fluid flow, Segregation, Turbulence

References:

Aboutalebi, R., 1994, Modelling of turbulent transport phenomena and solidification in continuous casting systems, PhD thesis, McGill University, Montreal.

Aboutalebi, R., Hasan, M., Guthrie, R.I.L., 1995, Coupled turbulent flow, heat, and solute transport in continuous casting processes, Metall. Mater. Trans. B, 26B, 731-744.

Bennon, W.D., Incropera, F.P., 1987, Numerical analysis of binary solid-liquid phase change using a continuum model, Int. J. Heat and Mass Transfer, 30, 2161-70.

Bennon, W.D., Incropera, F.P., 1988, Numerical analysis of binary solid-liquid phase change using a continuum model, Numerical Heat Transfer, 13, 277-296.

Brimacombe, J.K., 1984, Design of continuous casting machines based on a heat-flow analysis: state-of-art review, in: Brimacombe, J.K., Samarasekera, I.V., Lait, J.E., Continuous Casting: Heat Flow, Solidification and Crack Formation, 2, Iron and Steel Society, Warrendale, 17-28.

Brimacombe, J.K., Batista, L.A., 1984, Continuous Casting. Heat Flow, Solidification and Crack Formation, Iron and Steel Society, Warrendale, 1, 109-123.

Brimacombe, J.K., Weinberg, F., Hawbolt, E.B., 1984, Formation of longitudinal, midface cracks in continuously-cast slabs. in: Brimacombe, J.K.; Samarasekera, I.V., Lait J.E., Continuous Casting: Heat Flow, Solidification and Crack Formation, 2, Warrendale, Iron and Steel Society, 215-227.

Chen, H.S., Pehlke, R.D., 1996, Mathematical modeling of tundish operation and flow control to reduce transition slabs, Metall. Mater. Trans. B, 27B, 745-756.

Farouk, B., Apelian, D., Kim, Y. G., 1992, A numerical and experimental study of the solidification rate in a twin-belt caster, Metall. Mater. Trans. B, 23B, 477-492.

Ingerslev, P., Henein, H., 1997, An integral boundary approach for 1- and 2-D modeling of ingot reheating and cooling, Iron and Steelmaker, 24, 5, 75-85.

Joo, S., Guthrie, R.I.L., 1993, Inclusion behavior and heat-transfer phenomena in steelmaking tundish operations: part I. Aqueous modeling, Metall. Mater. Trans. B, 24B, 755-765.

Lait, J.E., Continuous Casting. Heat Flow, Solidification and Crack Formation, Iron and Steel Society, Warrendale, 2, 17-28.

Patankar, S.V., 1980, Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, 197.

Prescott, P.J., Incropera, F. P., 1995, The effect of turbulence on solidification of a binary metal alloy with electromagnetic stirring, Trans. ASME – J. Heat Transfer, 117, 716-724.

Prescott, P. J., Incropera, F. P., Bennon, W. D., 1991, Modelling of dendritic solidification systems : reassessment of the continuum momentum equation, Int. J. Heat and Mass Transfer, 34, 9, 2351-2359.

Qiu, S., Liu, H., Peng, S., Gan, Y., 2004, Numerical analysis of thermal-driven buoyancy flow in the steady macrosolidification process of a continuous slab caster, ISIJ Int., 44, 1376-1383.

Samarasekera, I.V., Lait, J.E., Continuous Casting. Heat Flow, Solidification and Crack Formation, Iron and Steel Society, Warrendale, 2, 215-227.

Schwerdtfeger, K. J., 2003, Heat Withdrawal in Continuous Casting of Steel, The Making, Shaping and Treating of Steel, 11th Edition, Casting Volume, The AISE Steel Foundation Pittsburgh, 1-41.

Seyedein, S. H., Hasan, M., 1996, A 3-D numerical prediction of turbulent flow, heat transfer and solidification in a continuous slab caster for steel, Computational Fluid Dynamics and Heat/Mass Transfer Modelling in the Metallurgical Industry, eds, Argyropoulos, S. A., Mucciardi, F., 146-163.

Shyy, W., Pang, Y., Hunter, G.B., Wei, D.Y., Chen, M.-H., 1992, Modeling of turbulent transport and solidification during continuous ingot casting, Int. J. Heat and Mass Transfer, 35, 5, 1229-1245.

Suzuki, M., Yamaguchi, R., Murakami, K., Nakada, M., 2001, Inclusion particle growth during solidification of stainless steel, ISIJ Int., 41, 247-256.

Thomas, B.G., Mika, L.J., Najjar, F.M., 1990, Simulation of fluid flow inside a continuous slab-casting machine, Metall. Trans. B, 21B, 387-400.

Yang, H., Zhao, L., Zhang, X., Deng, K., Li, W., Gan, Y., 1998, Mathematical simulation on coupled flow, heat, and solute transport in slab continuous casting process, Metall. Trans. B, 29B, 1345-1356.

Yeh, J.L., Hwang, W.S., Chou, C.L., 1994, An improved fluid flow model for slab tundishes and its comparison with a full-scale water model, Applied Mathematical Modelling, 18, 39-45.