Numerical Modelling Of Fe-C AlloysCrystallization

Abstract

The boundary element method is applied to micro/macro modelling of solidification process proceeding in 2D iron casting domain. The heat transfer process is described by the Fourier equation with additional term determining the kinetics of crystallization (the so-called source function). The model bases on the laws determining the course of nucleation and nuclei growth, while the relation between linear growth rate and the liquid fraction in casting volume is given by the Johnson Mehl Avrami Kolmogorov formulas. In the paper the mathematical description of the process, the method of numerical solution and also the example of computations are presented. 1 Governing equations Solidification of pure metals and eutectic alloys A differential equation describing the course of solidification process (a micro/macro model) is the parabolic one with additional term qy(X, t) called a source function: cp . 0 = div[Agrad7(X, t)] + q^(X, t) (1) dt where c, p, X are the specific heat, mass density and thermal conductivity, 7, X, t are the temperature, spatial co-ordinate and time. Because the solidification process proceeds in a rather small interval of temperature one can assume the constant values of thermophysical parameters of material considered and finally the following energy equation should be taken into account 0 , , dt cp Transactions on Engineering Sciences vol 12, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533