Binary alloy solidification and freckle formation: Effect of shrinkage induced flow on solutal instability and macro-segregation

Abstract

Freckle formation during directional solidification of binary alloy is a well-researched subject area. However, the influence of shrinkage induced flow (SIF) on freckling phenomena is barely reported. The focus of this work is to investigate this effect during bottom-up solidification of binary alloys. A fixed grid-based numerical scheme involving volume averaging of conserved parameters is proposed. The solidification geometry under consideration is a two-dimensional mold cavity with a central riser allowing continuous melt flow into the cavity. Model validation is obtained against existing numerical results involving directional solidification of Al-4.1 wt. % Cu alloy. However, heavier solute (Cu) rejection in the melt during solidification renders the validation case study devoid of freckling phenomena. The postvalidation investigations involve bottom up solidification of Al-30 wt. % Mg alloy with lighter solute (Mg) rejection, leading to solutal instability and freckle formation. The effect of SIF on solutal instability, channel formation, and overall macro-segregation is investigated. The intensity of SIF hinges on both cooling condition and opening size. The penetration depth of SIF into the solidification domain gives rise to either early or late onset of solutal instability. SIF penetration depth till the melt domain adjacent to the mushy layer promotes early onset of solutal instability. However, SIF penetration into the mushy layer itself triggers redistribution of solute-rich melt inside this layer, leading to delayed onset of solutal instability. Since the macro-segregation is a direct consequence of advection of solute inside and adjacent to the mushy region, the influence of SIF is manifested by unprecedented macro-segregation pattern.

On macrosegregation in a binary alloy undergoing solidification shrinkage

“…where ∂χ/∂t > 0 locally. Although solidification shrinkage is not responsible for this, it may nevertheless act to moderate it, by delaying the onset of thermosolutal convection, if not preventing it completely [27]. use the lowest value possible of τ 0 , in view of the need to compute C solid correctly; thus, all subsequent computations were carried out with τ 0 = 10 −4 .…”