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A novel front tracking algorithm in FEM modelling of continous casting of pure metals

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Języki publikacji
EN
Abstrakty
EN
The mathematical model of temperature field in the process of continuous casting of metals is presented in the paper. The Finite Element Method (FEM) is applied to formulate steady state heat conduction problem with phase change. A modified front-tracking approach with an automatic mesh generation in the deforming finite element technique is used to determine temperature field and interface location within an ingot. The modified weighting functions were used to avoid spatial oscillations due to a strong convective nature of the problem. Paper presents a new method for the correction to the interface location at each step of the iteration process (through the energy balance at the interface). The main advantage of this technique is its ability to continuously track the interface position. The capability of the presented method is demonstrated on the example of the continuous casting of a cylindrical ingot made of copper.
Rocznik
Strony
21--41
Opis fizyczny
Bibliogr. 30 poz.,
Twórcy
autor
  • Politechnika Śląska, Gliwice
autor
  • Politechnika Śląska, Gliwice
Bibliografia
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  • [3] CARSLAW H. J. AND JÄGER, J. C.: Conduction of heat in solids, Oxford University Press, Oxford, 1959.
  • [4] COMINI G., DEL GUIDICE, G., LEWIS, R. W., ZIENKIEWICZ, O. C.: Finite Element Solution of Non-linear Heat Conduction Problems with Special Reference to Phase Change, Int. J. Numer. Meth. Eng., 8(1974), 613-624.
  • [5] CRANK J.: Free and moving boundary problems, Claredon Press, Oxford, 1984.
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  • [7] DALHUIJSEN A. J., SEGAL A.: Comparison of Finite Element Techniques for Solidification Problems, Int. J. Numer. Meth. Eng., 23(1986), 1807-1829.
  • [8] DAVIES V. DE L., WESTBY O.: Numerical computation of the solidification of continuously cast aluminium rod, The British Foundryman, 1974, 259-267.
  • [9] DONEA, J.: Recent Advances in Computational Methods for Steady and Transient Transport Problems, Nuclear Engineering and Design, North Holland, Amsterdam, 80(1984), 141-162.
  • [10] ENGL H.W., LANGTHALER T., LINZ: Numerical Solution of an Inverse Problem Connected with Continuous Casting of Steel, ZOR-Zeitschrift Operations Research, 29(1985), 185-199.
  • [11] ENGL H. W., LANGTHALER T., MANSELLI P.: On an inverse problem for a non- linear heat equation connected with continuous casting of steel, [in:] Optimal control of partial differential equations II: theory and applications, Hoffmann K. H., Krabs W., ed., Birkhäuser Basel, 1987, 67-89.
  • [12] GORDON W. J., HALL C. A.: Construction of Curvelinear Coordinate Systems and Application to Mesh Generation, Int. J. Numer. Meth. Eng., 7(1973), 461-477.
  • [13] HEINRICH J.C., ZIENKIEWICZ O.C.: Quadratic finite element schemes for two- dimensional convective transport problems, Computer Methods in Applied Me- chanics & Engineering, 11(1977), North Holland, 1831-1844.
  • [14] Ho-LE K.: Finite Element Mesh Generation Methods: A Review and Classification, Computer Aided Design, 20(1988), 27-38.
  • [15] KIKUCHI N.: Finite element methods in mechanics, Cambridge University Press, Cambridge, 1987.
  • [16] LEWIS R.W., MORGAN K., THOMAS H.R., SEETHARAMU K.N.: The Finite Element Method in Heat Transfer Analysis, J. Wiley & Sons, West Sussex, 1996.
  • [17] LYNCH D.R., O'NEILL K.: Continuously Deforming Finite Elements for the Solution of Parabolic Problems, with and without Phase Change, Int. J. Numer. Meth. Eng., 17(1981), 81-96.
  • [18] LYNCH D.R., SULLIVAN J.M.: Heat Conservation in Deforming Element Phase Change Simulation, J. Comp. Phys., 57(1985), 303-317.
  • [19] MILLER K., MILLER R. N.: Moving Finite Elements. 1, SIAM J. Numer. Anal., 18(1981), no. 6, 1019-1057.
  • [20] NAWRAT A., GRZYMKOWSKI R.: Automatic mesh generation for curved two- dimensional domains, European Congress on Computational Methods in Applied Science and Engineering, ECCOMASS 2000, Barcelona, 2000.
  • [21] ÖZISIK M. N.: Heat Conduction, Wiley, New York, 1980.
  • [22] PARDO E., WECKMAN D. C.: A Fixed Grid Finite Element Technique for Modelling Phase Change in Steady-State Conduction-Advection Problems, Int. J. Num. Meth. Eng., 29(1990), no. 5, 969-984.
  • [23] REDDY J. N.: An Introduction to The Finite Element Method, McGraw-Hill, USA,
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  • [26] SKOREK, J.: Model matematyczny pola temperatury w procesie ciągłego odlewania miedzi, PhD dissertation, Gliwice, 1976, (in Polish).
  • [27] VOLLER V.R., CROSS M.: Accurate Solutions of Moving Boundary Problems Using the Enthalpy Method, Int. J. Heat Mass Transfer, 24(1981), 5435-5456.
  • [28] ZABARAS N., RUAN Y.: A Deforming Finite Element Method Analysis of Inverse Stefan Problems, Int. J. Numer. Meth. Eng., 28(1989), 295-313.
  • [29] ZABARAS N., RUAN Y.: Moving and Deforming Finite-Element Simulation of Two-Dimensional Stefan Problems, Commun. Appl. Numer. Meth., 6(1990), 495-506.
  • [30] ZABARAS N., RUAN Y., RICHMOND O.: Front Tracking Thermomechanical Model for Hypoelastic Viscoplastic Behavior in a Solidifying Body, Uni. of Minnesota Supercomputer Institute, UMSI 89/91, Minnesota, 1989.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BGPK-0379-2418
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