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In the paper the thermal processes proceeding in the solidifying metal are analyzed. The basic energy equation determining the course of solidification contains the component (source function) controlling the phase change. This component is proportional to the solidi-fication rate afs/at(fs E [0,1], is a temporary and lo cal volumetric fraction of solid state). The value of fs can be found, among others, on the basic of laws determining the nucleation and nuclei growth. This approach leads to the so called micro/macro models (the second generation models). The capacity of internal heat source appearing in the equation concerning the macro scale (solidification and cooling of domain considered) results from the phenomena proceeding in the micro scale (nuclei growth). The function fs can be defined as a product of nuclei density N and single grain volume V (a linear model of crystallization) and this approach is applied in the paper presented. The problem discussed consists in the simultaneous identification of two parameters determining a course of solidification. In particular it is assumed that nuclei density N (micro scale) and volumetric specific heat of metal (macro scale) are unknown. Formulated in this way inverse problem is solved using the least squares criterion and gradient methods. The additional information which allows to identify the unknown parameters results from knowledge of cooling curves at the selected set of points from solidifying metal domain. On the stage of numerical realization the boundary element method is used. In the final part of the paper the examples of computations are presented.
Rocznik
Tom
Strony
107--113
Opis fizyczny
Bibliogr. 20 poz., rys.
Twórcy
autor
autor
- Czestochowa University of Technology, 68 Dabrowskiego St., 42-200 Częstochowa, Poland, moch@imi.pcz.pl
Bibliografia
- [1] D.M. Stefanescu, "Critical reviews of the second generation of solidification models for casting", Modelling of Casting, Welding and Advanced Solidification Process VI, 3-20 (1993).
- [2] J. Crank, Free and Moving Boundary Problems, Claredon Press, Oxford, 1984.
- [3] B. Mochnacki and J.S. Suchy, Numerical Methods in Computations of Foundry Processes, PFTA, Cracow, 1995.
- [4] N.A. Awdonin, Mathematical Deseription of Crystallization, Zinatne, Riga, 1980, (in Russian).
- [5] C. Chang, D.M. Stefanescu and D. Shangguan, "Modelling of the liquid/solid and the eutectoid phase transformation", Metall. Transactions A 23 A(4), 1333-1346 (1992).
- [6] E. Fras, W. Kapturkiewicz and H.F. Lopez, "Macro and micro modelling of the solidification kinetics of casting", AFS Transactions 92(48), 583-591 (1993).
- [7] W. Kapturkiewicz, Modelling of Cast Iron Solidification, Akapit, Cracow, 2003.
- [8] R. Szopa, "Application of the boundary element method in numerical modelling of solidification - Part II. The micro/macro approach", J. Theoretical and Appl. Mechanics 2(36), 469-478 (1998).
- [9] E. Majchrzak and J. Mendakiewicz, "Identification of cast iron substitute thermal capacity", Archives of Foundry 6(22), 310-315 (2006).
- [10] E. Majchrzak and J. Mendakiewicz, "Estimation of cast steel thermal conductivity on the basis of cooling curves from the casting domain", Archives of Foundry 5(15), 265-270 (2005).
- [11] E. Majchrzak, J.S. Suchy and R Szopa, "Linear model of crystallization - identification of nuclei density", Giessereiforschung, International Foundry Research 2, 29-32 (2006).
- [12] K. Kurpisz and A. Nowak, Inverse Thermal Problems, Computational Mechanics Publ., Southampton, Boston, 1995.
- [13] K. Dems and E. Rousselet, "Sensitivity analysis for transient beat conduction in a solid body. Part l", Structural Optimization 17, 36-45 (1999).
- [14] K. Dems and B. Rousselet, "Sensitivity analysis for transient beat conduction in a solid body. Part 2", Structural Optimization 17, 46-54 (1999).
- [15] O.M. Alifanov, Inverse Beat Transfer Problems, Springer Verlag, London, 1994.
- [16] M.N. Ozisik and H.R.B. Orlande, Inverse heat transfer: fundamentals and applications, Taylor and Francis, Pennsylvania, 1999.
- [17] E. Majchrzak, Boundary Element Method In Beat Transfer, Publ. of the Czest. Univ of Technology, Częstochowa, 2001.
- [18] C.A. Brebbia and J. Dominguez, Boundary Elements, An Introductory Course, McGraw-Hill, London, 1992.
- [19] P.K. Banerjee, Boundary Element Methods In Engineering, McGraw-Hill, London, 1994.
- [20] D. Janisz, Inverse Problems in Transient Heat Conduction, Doctoral Thesis, Gliwice, 2004.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG5-0021-0019