Abstract
The modelling of the continuous casting of metals is known to involve the complex interaction of non-isothermal fluid and solid mechanics. However, using asymptotic methods and an earlier numerical result obtained via computational fluid dynamics, we demonstrate how the motion of the liquid metal can be systematically decoupled from the stresses induced in the solidified shell. The resulting asymptotically reduced model can then serve as a computationally efficient module for stress mechanics models that aim to predict segregation and crack formation in the solid metal.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aboutalebi, M.R., Hasan, M., Guthrie, R.I.L.: Coupled turbulent flow, heat and solute transport in continuous casting processes. Metall. Trans. B 26B, 731–744 (1995)
Aboutalebi, M.R., Hasan, M., Guthrie, R.I.L.: Numerical study of coupled turbulent flow and solidification for steel slab casters. Numer. Heat Transfer A 28, 279–297 (1995)
Amin, M.R., Greif, D.: Conjugate heat transfer during two-phase solidification process in a continuously moving metal using average heat capacity method. Int. J. Heat Mass Transfer 42, 2883–2985 (1999)
Das, S.K., Sarkar, A.: Computational modelling of thermal transport phenomena in continuous casting process based on non-orthogonal control volume approach. Commun. Numer. Methods Eng. 12, 657–671 (1996)
Lee, J.E., Han, H.N., Oh, K.H., Yoon., J.K.: A fully coupled analysis of fluid flow, heat transfer and stress in continuous round billet casting. ISIJ Int. 39, 435–444 (1999)
Mahmoudi, J.: Mathematical modelling of fluid flow, heat transfer and solidification in a strip continuous casting process. Int. J. Cast Met. Res. 19, 223–236 (2006)
Mahmoudi, J., Vynnycky, M., Fredriksson, H.: Modelling of fluid flow, heat transfer, solidification in the strip casting of copper base alloy. Part 3. Solidification – a theoretical study. Scand. J. Metall. 30(3), 136–145 (2001)
Mahmoudi, J., Vynnycky, M., Sivesson, P., Fredriksson, H.: An experimental and numerical study on the modelling of fluid flow, heat transfer and solidification in a copper continuous strip casting process. Mater. Trans. 44(9), 1741–1751 (2003)
Mitchell, S.L., Vynnycky, M.: An accurate finite-difference method for ablation-type stefan problems. J. Comput. Appl. Math. 236, 4181–4192 (2012)
Mitchell, S.L., Vynnycky, M.: On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions. J. Comput. Appl. Math. 264, 49–64 (2014)
Vynnycky, M.: An asymptotic model for the formation and evolution of air gaps in vertical continuous casting. Proc. R. Soc. A 465, 1617–1644 (2009)
Vynnycky, M.: On the onset of air-gap formation in vertical continuous casting with superheat. Int. J. Mech. Sci. 73, 69–76 (2013)
Yao, M., Yin, H.B., Fang, D.C.: Real-time analysis on non-uniform heat transfer and solidification in mould of continuous casting round billets. ISIJ Int. 44, 1696–1704 (2004)
Yao, M., Yin, H., Wang, J.C., Fang, D.C., Liu, X., Yu, Y., Liu, J.J.: Monitoring and analysis of local mould thermal behaviour in continuous casting of round billets. Ironmaking Steelmaking 32, 359–368 (2005)
Zhang, L.F.: Computational fluid dynamics modeling: application to transport phenomena during the casting process. JOM 64, 1059–1062 (2012)
Acknowledgements
SLM, BJF and SBGO’B acknowledge the support of the Mathematics Applications Consortium for Science and Industry (http://www.macsi.ul.ie), funded by the Science Foundation Ireland grant 12/IA/1683.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Vynnycky, M., Mitchell, S.L., Florio, B.J., O’Brien, S.B.G. (2016). Decoupling the Interaction of Solid and Fluid Mechanics in the Modelling of Continuous Casting Processes. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds) Progress in Industrial Mathematics at ECMI 2014. ECMI 2014. Mathematics in Industry(), vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-23413-7_35
Download citation
DOI: https://doi.org/10.1007/978-3-319-23413-7_35
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23412-0
Online ISBN: 978-3-319-23413-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)