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Numerical model of the solidification of alloys with natural convection of the liquid

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Języki publikacji
EN
Abstrakty
EN
The paper deals with comparison of numerical analysis results obtained for binary alloys solidification process in the sand and permanent mould with motion of the fluid in the liquid and mushy zone. The partial differential equations describing mathematical model of the phenomena are presented. Finite Element Method is used for modeling process. Characteristic Based Split (CBS) method is used for solving momentum equation. Such approach allows to uncouple velocities and pressure. Petrov-Galerkin formulation is employed to stabilize heat conductivity equation with convective term. The results of the numerical simulations in the 2D region are discussed. Velocity fields, cooling rates and positions of the liquid, solid-liquid and solid regions are compared.
Rocznik
Strony
109--112
Opis fizyczny
Bibliogr. 14 poz., rys., tab.
Twórcy
Bibliografia
  • [1] W. Kurz, D. J. Fisher, Fundamentals of solidification, Trans. Tech. Publications Ltd, Switzerland 1989.
  • [2] E. Węgrzyn-Skrzypczak, Modelling of solidification with motion of the fluid in liquid and mushy zone, PhD Thesis, Częstochowa 2005 (in Polish).
  • [3] B. Mochnacki, J.S. Suchy, Numerical methods in computations of foundry processes, Polish Foundrymen's Technical Association, Kraków 1995.
  • [4] M. Kaviany, Principles of heat transfer in porous media, Springer-Verlag New York Inc.,1991.
  • [5] K. J. Bathe, Finite element procedures in engineering analysis, Prentice-Hall, 1982.
  • [6] Z. Svoboda, The analysis the convective-conductive heat transfer in the building constructions, In: Proceedings of the 6th Building Simulation Conference, Kyoto (1999) 1: 329-335.
  • [7] P. Bochev, Finite element methods based on least squares and modified variational principles. COM2MAC Lecture Notes, Postech, Pohang, South Korea, 2001.
  • [8] T. J. R. Hughes, Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations, International Journal for Numerical Methods in Fluids , vol. 7 (1987) 1261-1275.
  • [9] A. Bokota, A. Kulawik, Three dimensional model of thermal phenomena determined by moving heat source, Archives of Foundry vol. 2, No. 4 (2002) 74-79 (in Polish).
  • [10] A. J. Chorin, Numerical solution of the Navier-Stokes equation, Math. Comput. (1968) 23:745-762.
  • [11] O. C. Zienkiewicz, R. Codina, A general algorithm for compressible and incompressible flow, Part I. The split characteristic based scheme, International Journal for Numerical Metods in Fluids (1995) 20:869-885.
  • [12] O. C. Zienkiewicz, R.L. Taylor, The finite element method, Volume 3: Fluid dynamics, Butterworth and Hienemann, 2000.
  • [13] J. Chessa, T. Belytschko, An extended finite element method for two-phase fluids, Journal of Applied Mechanics, vol. 70 (2003) 10-17.
  • [14] A. K. Singh, B. Basu, A numerical study of macro-segregation of iron-carbon alloy: the role of double diffusive convection, Metallurgical and Material Transactions (1995) 26(B): 1069-1081.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ3-0028-0022
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