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Calculation of phase-change boundary position in continuous casting

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The problem of determination of the phase-change boundary position at the mathematical modeling of continuous ingot temperature field is considered. The description of the heat transfer process takes into account the dependence of the thermal physical characteristics on the temperature, so that the mathematical model is based on the nonlinear partial differential equations. The boundary position between liquid and solid phase is given by the temperatures equality condition and the Stefan condition for the two-dimensional case. The new method of calculation of the phase-change boundary position is proposed. This method based on the finite-differences with using explicit schemes and on the iteration method of solving of non-linear system equations. The proposed method of calculation is many times faster than the real time. So that it amenable to be used for model predictive control of continuous semifinished product solidification.
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Bibliogr. 9 poz., rys., tab., wykr.
  • Institute of Applied Mathematics and Mechanics of NASU, R. Luxemburg Str., 74, Donetsk, 83114, Ukraine
  • [1] Vapalahti, S., Thomas B.G., Louhenkilpi, S., Castillejos, A.H., Acosta F.A., Hernandez, C.A. (2007). Heat Transfer Modelling of Continuous Casting: Numerical Considerations, Laboratory Measurements and Plant Validation. STEELSIM 2007, Graz, Austria, Sept. 12-14.
  • [2] Mauder, T., Šandera, Č. & Štětina, J. (2012). A fuzzy-based optimal control algorithm for a continuous casting process. Materials and technology. 46(4), 325-328. ISSN 1580-2949, Institute of metals and technology.
  • [3] Stefanescu, D.M. (2009). Science and Engineering of Casting Solidification. New York: Second Edition, Springer Science.
  • [4] Meirmanov, A.M. (1992). The Stefan problem. Berlin: Walter de Gruyter.
  • [5] Tikhonov, A.N., Samarskii, A.A. (1990). Equations of Mathematical Physics. Dover Publications. ISBN 0-486-66422-8.
  • [6] Li Yaoyong & Zhang Zhili. (1995). Solving the Free Boundary Problem in Continuous Casting by Using Boundary Element Method. Applied Mathematics and Mechanics. (English Edition). 16(12), 1201-1208.
  • [7] Grzymkowski, R., Pleszczyński, M. & Hetmaniok, E. (2013). Problem of the moving boundary in continuous casting solved by the analytic-numerical method. Archives of Foundry Engineering. 13(1), 33-38. DOI: 10.2478/afe-2013-0007.
  • [8] Tkachenko, V.N. & Ivanova, A.A. (2008). Modeling and analysis of temperature field of ingot of curvilinear continuous casting machine (Моделирование и анализ теплового поля непрерывного слитка криволинейной машины непрерывного литья заготовок). Electronical modeling (Электронное моделирование). 30(3), 87-103.
  • [9] Ivanova, A. (2010). Identification of Convection Heat Transfer Coefficient of Secondary Cooling Zone of CCM based on Least Squares Method and Stochastic Approximation Method. Retrieved June 30, 2013, from
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