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On the interactive effects of mould taper and superheat on air gaps in continuous casting

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Abstract

The formation of an air gap in continuous casting systems is detrimental to the process efficiency as it acts to thermally insulate the cast from the water-cooled mould. By tapering the mould wall, the thermal contraction of the cooling cast can be accommodated so that the thickness of the air gap is decreased. We consider a coupled thermomechanical model to investigate the effect of mould tapering on the formation and thickness of the air gap in an axisymmetric mould. Using asymptotic techniques, the model is reduced to allow analytic and inexpensive numerical investigations while maintaining the essential characteristics of the thermomechanical process. This work improves on previous models by including superheat, where the incoming molten metal is at a higher temperature than its melting point. The degree of superheating also affects the formation and thickness of the air gap and presents a viable alternative for control of the system. The efficacy of mould tapering in the presence of superheat is examined.

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References

  1. Schwerdtfeger, K., Sato, M., Tacke, K.-H.: Stress formation in solidifying bodies. Solidification in a round continuous casting mold. Metall. Mater. Trans. B 29B, 1057–1068 (1998)

    Article  Google Scholar 

  2. Kron, J., Bellet, M., Ludwig, A., Pustal, B., Wendt, J., Fredriksson, H.: Comparison of numerical simulation models for predicting temperature in solidification with reference to air gap formation. Int. J. Cast Metals Res. 17, 295–310 (2004)

    Article  Google Scholar 

  3. Kron, J., Fredriksson, H.: Measurements and modelling of air gap formation in Cu-based alloys. Int. J. Cast Metals Res. 18, 21–28 (2005)

    Article  Google Scholar 

  4. Fredriksson, H., Åkerlind, U.: Materials Processing During Casting. Wiley, New York (2006)

    Book  Google Scholar 

  5. Kim, K.Y.: Analysis of gap formation at mold–shell interface during solidification of aluminium alloy plate. ISIJ Int. 43, 647–652 (2003)

    Article  Google Scholar 

  6. Kelly, J.E., Michalek, K.P., O’Connor, T.G., Thomas, B.G., Dantzig, J.A.: Initial development of thermal and stress fields in continuously cast steel billets. Metall. Trans. A 19A, 2589–2602 (1988)

    Article  Google Scholar 

  7. Savage, J.: A theory of heat transfer and air gap formation in continuous casting molds. J. Iron Steel Inst. 198, 41–47 (1962)

    Google Scholar 

  8. Richmond, O., Tien, R.H.: Theory of thermal stresses and air-gap formation during the early stages of solidification in a rectangular mold. J. Mech. Phys. Solids 19, 273–284 (1971)

    Article  Google Scholar 

  9. Kristiansson, J.-O.: Thermal stresses in the early stage of the solidification of steel. J. Therm. Stress. 5, 315–330 (1982)

    Article  Google Scholar 

  10. Tien, R.H., Richmond, O.: Theory of maximum tensile stresses in the solidifying shell of a constrained regular casting. J. Appl. Mech. 49, 481–486 (1982)

    Article  Google Scholar 

  11. Grill, A., Sorimachi, K., Brimacombe, J.K.: Heat flow, gap formation and break-outs in the continuous casting of steel slabs. Metall. Mater. Trans. B 7B, 177–189 (1976)

    Article  Google Scholar 

  12. Bellet, M., Decultieux, F., Menai, M., Bay, F., Levaillant, C., Chenot, J.L., Schmidt, P., Svensson, I.L.: Thermomechanics of the cooling stage in casting processes: three-dimensional finite element analysis and experimental validation. Metall. Mater. Trans. B 27B, 81–99 (1996)

    Article  Google Scholar 

  13. Huespe, A.E., Cardona, A., Fachinotti, V.: Thermomechanical model of a continuous casting process. Comput. Methods Appl. Mech. Eng. 182, 439–455 (2000)

    Article  MATH  Google Scholar 

  14. Li, C., Thomas, B.G.: Thermomechanical finite-element model of shell behavior in continuous casting of steel. Metall. Mater. Trans. B 35B, 1151–1172 (2004)

    Article  Google Scholar 

  15. Sun, D., Annapragada, S.R., Garimella, S.V., Singh, S.K.: Analysis of gap formation in the casting of energetic materials. Numer. Heat Trans. A 51, 415–444 (2007)

    Article  Google Scholar 

  16. Bland, D.R.: Flux and the continuous casting of steel. IMAJ. Appl. Math. 32, 89–112 (1984)

    Article  Google Scholar 

  17. Hill, J.M., Wu, Y.-H.: On a nonlinear Stefan problem in the continuous casting of steel. Acta Mech. 107, 183–198 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  18. DiLellio, J.A., Young, G.W.: An asymptotic model of the mold region in a continuous steel caster. Metall. Mater. Trans. B 26B, 1225–1241 (1995)

    Article  Google Scholar 

  19. Smelser, R.E., Johnson, R.E.: An asymptotic model of slab casting. Int. J. Mech. Sci. 37, 793–814 (1995)

    Article  MATH  Google Scholar 

  20. Johnson, R.E., Cherukuri, H.P.: Vertical continuous casting of bars. Proc. R. Soc. A 455, 227–244 (1999)

    Article  MATH  Google Scholar 

  21. Cherukuri, H.P., Johnson, R.E.: Modelling vertical continuous casting with temperature-dependent material properties. Int. J. Mech. Sci. 43, 1243–1257 (2001)

    Article  MATH  Google Scholar 

  22. 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)

    Article  MATH  Google Scholar 

  23. Vynnycky, M.: A mathematical model for air-gap formation in vertical continuous casting: the effect of superheat. Trans. Ind. Inst. Met. 62, 495–498 (2009)

    Article  Google Scholar 

  24. Vynnycky, M.: Air gaps in vertical continuous casting in round moulds. J. Eng. Math. 68, 129–152 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  25. Vynnycky, M.: On the role of radiative heat transfer in air gaps in vertical continuous casting. Appl. Math. Mod. 37, 2178–2188 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  26. Vynnycky, M.: On the onset of air-gap formation in vertical continuous casting with superheat. Int. J. Mech. Sci. 73, 69–76 (2013)

    Article  Google Scholar 

  27. Florio, B.J., Vynnycky, M., Mitchell, S.L., O’Brien, S.B.G.: Mould-taper asymptotics and air gap formation in continuous casting. Appl. Math. Comput. 268, 1122–1139 (2015)

    MathSciNet  Google Scholar 

  28. Vynnycky, M., Mitchell, S.L., Florio, B.J., O’Brien, S.B.G.: 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 (2014)

  29. Jablonka, A.: Spannungen und Deformationen in Elektro-Schlacke-Umschmelzblöcken während des Umschmelzens, der nachfolgenden Abkühlung und der sich anschliessenden Wärmebehandlung. PhD thesis, Technische Universität Clausthal, Clausthal-Zellerfeld, Germany (1995)

  30. 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)

    Article  MathSciNet  MATH  Google Scholar 

  31. Mitchell, S.L., Vynnycky, M.: An accurate finite-difference method for ablation-type Stefan problems. J. Comput. Appl. Math. 236, 4181–4192 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  32. Mitchell, S.L., Vynnycky, M.: Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems. Appl. Math. Comput. 215, 1609–1621 (2009)

    MathSciNet  MATH  Google Scholar 

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Florio, B.J., Vynnycky, M., Mitchell, S.L. et al. On the interactive effects of mould taper and superheat on air gaps in continuous casting. Acta Mech 228, 233–254 (2017). https://doi.org/10.1007/s00707-016-1717-z

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  • DOI: https://doi.org/10.1007/s00707-016-1717-z

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