Numerical discretization of species equation source terms in binary mixture models of solidification and their impact on macrosegregation in semicontinuous, direct chill casting systems

A discretization procedure for species equation source terms in mixture mod els of solidification that has been widely applied to static castings was s hown to provide erroneous results when applied to semicontinuous casting sy stems due to the inconsistent simultaneous use of both upwind a,ld central- difference assumptions. Through a simplified example, a corrected discretiz ed form for species equation terms,uas derived using consistent upwinding p rocedures. Sample calculations performed for DC casting of an Al-4.5 wt% Cu billet revealed that the false segregation arising from inconsistently dis cretized species equation terms overwhelms true, physical segregation due t o the buoyancy-driven flow of solute-rich liquid and the settling of solute -depleted, free-floating dendrites.