Abstract

In the present work, a thermodynamic framework incorporating coupling of phase field theory is proposed to model the formation of the shrinkage during the cooling. Initially we assumed that the flow is laminar and we model only the solidification phase. The proposed formulation is defined according to the order parameter C (liquid or gas), it ensures the separation of a binary mixture and the formation of shrinkage in the hottest areas coupling all physical phenomena such as, the kinematics induced by phase separation (liquid - gas), the change of phases related of the properties evolution (viscosity density mass) and the heat exchanges. Thus, we have succeeded to capture some important aspects for the shrinkage formation. The numerical results obtained are accompanied by experimental tests which will be presented in the article.

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