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Mathematical and numerical model of directional solidification including initial and terminal transients of the process

Kapturkiewicz W., Burbelko A. A., Fraś E.

Archives of Foundry Engineering

2008

Vol. 8, iss. 4

65-70

The, developed in this study, simple model and numerical solution of diffusion growth of the solid phase under the conditions of directional solidification allow for the effect of constituent diffusion in both liquid and solid phase and assume the process run in which (like in reality) the preset parameter is the velocity of sample (pulling velocity) at a preset temperature gradient. The solid/liquid interface velocity is not the process parameter (like it is in numerous other solutions proposed so far) but a function of this process. The effect of convection outside the diffusion layer has been included in mass balance under the assumption that in the zone of convection the mixing is complete. The above assumptions enabled solving the kinetics of growth of the solid phase (along with the diffusion field in solid and liquid phase) under the conditions of diffusion well reflecting the process run starting with the initial transient state, going through the steady state period in central part of the casting, and ending in a terminal transient state. In the numerical solution obtained by the finite difference method with variable grid dimensions, the error of the mass control balance over the whole process range was 1- 2%.