TY - JOUR
T1 - An asymptotic approach to solidification shrinkage-induced macrosegregation in the continuous casting of binary alloys
AU - Vynnycky, M.
AU - Saleem, S.
AU - Fredriksson, H.
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2018/2
Y1 - 2018/2
N2 - The modelling of macrosegregation in the continuous casting of alloys normally requires resource-intensive computational fluid dynamics (CFD). By contrast, here we develop an asymptotic framework for the case when macrosegregation is driven by solidification shrinkage; as a first step, a binary alloy is considered. Systematic asymptotic analysis of the steady-state two-dimensional mass, momentum, heat and solute conservation equations in terms of the shrinkage parameter indicates that the overall problem can be reduced to a hierarchy of decoupled problems: a leading-order problem that is non-linear, and a sequence of linear problems, with the actual macrosegregation of the solute then being determined by means of one-dimensional quadrature. A numerical method that solves this sequence is then developed and implemented, and yields realistic macrosegregation profiles at low computational cost.
AB - The modelling of macrosegregation in the continuous casting of alloys normally requires resource-intensive computational fluid dynamics (CFD). By contrast, here we develop an asymptotic framework for the case when macrosegregation is driven by solidification shrinkage; as a first step, a binary alloy is considered. Systematic asymptotic analysis of the steady-state two-dimensional mass, momentum, heat and solute conservation equations in terms of the shrinkage parameter indicates that the overall problem can be reduced to a hierarchy of decoupled problems: a leading-order problem that is non-linear, and a sequence of linear problems, with the actual macrosegregation of the solute then being determined by means of one-dimensional quadrature. A numerical method that solves this sequence is then developed and implemented, and yields realistic macrosegregation profiles at low computational cost.
KW - Binary alloys
KW - Continuous casting
KW - Macrosegregation
UR - http://www.scopus.com/inward/record.url?scp=85038207280&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2017.10.012
DO - 10.1016/j.apm.2017.10.012
M3 - Article
AN - SCOPUS:85038207280
SN - 0307-904X
VL - 54
SP - 605
EP - 626
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
ER -