EXTENSION OF THE CONTINUUM MODEL FOR TRANSPORT PHENOMENA OCCURRING DURING METAL ALLOY SOLIDIFICATION .1. THE CONSERVATION EQUATIONS

In this study, models for simulating transport phenomena occurring dur ing solidification of a binary metal alloy are reviewed, with emphasis placed on the benefits and shortcomings of existing continuum and two -phase approaches. Linkages between the two approaches are discussed, and volume averaging procedures inherent in the two-phase model are us ed to develop an extension of the continuum model which retains its co mputational convenience, while eliminating its inability to treat impo rtant features such as solutal undercooling, nucleation, stereological characteristics of the solid/liquid interface, solid movement in the form of floating or settling crystals, and shrinkage. Two approaches t o development of a mixture momentum equation are considered, one invol ving evolution from the liquid momentum conservation equation and the other involving summation of the liquid and solid momentum equations. Special features of both approaches are discussed. In a companion pape r, additional models are developed to account for the transport (float ing and settling) of solid crystals in the melt, solutal undercooling, and nucleation.