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

摘要

A discretization procedure for species equation source terms in mixture models of solidification that has been widely applied to static castings was shown to provide erroneous results when applied to semicontinuous casting systems due to the inconsistent, simultaneous use of both upwind and central-difference assumptions. Through a simplified example, a corrected discretized form for species equation terms was derived using consistent upwinding procedures. Sample calculations performed for DC casting of an Al-4.5 wt% Cu billet revealed that the false segregation arising from inconsistently discretized species equation terms overwhelms true, physical segregation due to the buoyancy-driven flow of solute-rich liquid and the settling of solute-depleted, free-floating dendrites.