Simulation of channel segregation using a two-phase columnar solidification model – Part II: Mechanism and parameter study

Abstract

In Part II of this investigation the two-phase columnar solidification model, described in Part I, is applied to study channel segregation in a Sn–10wt.% Pb benchmark. Channel segregation originates from the thermo-solutal convection and the flow perturbations. The onset of a flow perturbation and subsequent channel segregation was previously analyzed with a mushy zone Rayleigh number by Beckermann et al. [Worster, Ann. Rev. Fluid Mech. (1997); Beckermann et al., Metall. Mater. Trans. A (2000)]. The current study has justified the Rayleigh number as a qualitative indicator for characterizing the origin of segregation channels. Numerical parameter study has shown that an enhanced mushy zone Rayleigh number by increasing the secondary dendrite arm spacing and/or solutal expansion coefficient is prone to the formation of the channel segregation. Newly formed channels are sustained via growth under certain preferential conditions of the resulting flow-solidification interactions, which can be characterized by a flow-solidification interaction term, u⇀ℓ·∇cℓ. Depending on the flow direction, the sign of this term can be positive or negative. Channels occur only in the region where the flow-solidification interaction term is negative. With a negative flow-solidification interaction term the increase in flow velocity due to a flow perturbation suppresses the local solidification rate, promoting the growth of the channel. In return the growing channel strengthens the flow perturbation, and the flow-solidification interaction term becomes more negative; thus the channel continues to grow and becomes stable. The current model indicates that remelting is not a necessary condition for channel segregation.