The numerical micro/macro model of solidification process

In the paper the problems connected with numerical modelling of the solidification and cooling processes in a system casting-mould are discussed. The task is treated as a boundary-initial problem in which the crystallization process (in micro scale) is taken into account, in other words the component describing a capacity of internal heat sources in adequate energy equation results from the analysis of crystallization process on a microscopic level. The mathematical model of crystallization process was constructed on a basis of the theory given by Kolmogorov. The number of nuclei and also their temporary dimensions (i.e. crystallization model) result from the local values of undercooling below the equilibrium temperature [1, 2, 3]. Such approach is widely known - but the numerical procedures worked out by the authors make possible to 'follow' the vicissitudes of successive grains generations and it is a new element in mathematical modelling of crystallization process. Numerical solution of the boundary-initial problem discussed has been obtained on the basis of the Boundary Element Method. It is well known that this method assures a relatively good approximation of geometrical and boundary conditions. In the case of solidification process modelling this advantage is very essential because of the great values of temperature gradients near the casting-mould contact surface. As an example the tasks concerning the aluminium plate solidifying in the typical sand moulds will be presented, at the same time it is possible (in a simple way) to widen the algorithm in the direction of 2D or 3D problems and more complex materials (e.g. binary alloys)(*)).