VAR ingot solidification model and its verification

Our recent works are devoted to simple thermal model concerning the ingot solidification during vacuum arc remelting (VAR). The nonlinear PDE solving algorithm of model implementation has been tested by analytical solutions within constrained systems. To obtain these solutions a special linearization method of the heat equation is first proposed. The obtained solutions can be specifically applied to hypothetical alloys with peculiar thermo-physical properties, meeting the rigid linearization requirements. The VAR model of the kind has been verified. In order to validate the model, a mixed experimental and theoretical technique has been applied to determine certain thermo-physical properties of Ti-10V-2Fe-3Al alloy, required for the model calculations. The technique is based on the liquid pool profiles analyzing in fully solidified VAR ingots. The experimental part of the technique enables easy estimate of liquid pool contours. The theoretical part is based on solving the inverse heat conduction problem for a solidifying ingot by means of represented VAR model. The results have been applied to calculate pool profiles for Ti-10V-2Fe-3Al titanium alloy. The results of the model calculations prove to be in sufficient agreement with the experimental data.