Simulation of Convection and Macrosegregation in a Large Steel Ingot

segregates. Although good agreement with experiments was MACROSEGREGATION in large steel ingots is one achieved, the model relied on many approximations (such of the most well-known and now classical problems in the as estimating the flow velocities). It should also be menfield of solidification and casting.[1] It arises from the relative tioned that many models have appeared in the literature that movement of solute-rich or poor liquid and solid phases are solely concerned with heat transfer during steel ingot during solidification over distances much larger than the casting (for example, Reference 9 and references therein). dendrite arm spacings. Commonly found macrosegregation While these models form the foundation for any realistic patterns in steel ingots are a positively segregated zone at ingot casting modeling, they do not address solid/liquid the top, negative segregation near the bottom in the equiaxed transport during solidification and the resulting macrozone, inverse segregation near the ingot surface, V segresegregation. gates along the centerline, and A segregates in the columnar More recently, macrosegregation models have been forzone.[2,3] These inhomogeneities can severely limit the yield mulated that rely on fully coupled numerical solutions of in ingot casting and cause problems in the subsequent prothe mass, momentum, energy, and species conservation equacessing and final steel properties. It is well established that tions for a solid/liquid mixture.[10,11] Beckermann and the macroscopic transport of species leading to macrosegreWang[12] and Prescott and Incropera[13] have reviewed the gation can occur by a variety of mechanisms, including progress in this area. Although many basic phenomena, such thermally and solutally driven natural convection of the melt as the formation of A segregates and the negative segregation in the mushy zone, flow due to solidification contraction, due to settling of equiaxed crystals, have been successfully and the sedimentation of free equiaxed crystals. Fredriksson simulated on laboratory-scale systems, the application of and co-workers[4,5] provide recent overviews of the solidifisuch continuum or multiphase models to multicomponent cation, transport phenomena, and macrosegregation in steel ingot solidification has been very limited. ingot casting. Combeau and co-workers[14–17] attempted to extend recent While there exists a relatively good understanding of the binary alloy solidification models that couple mass, momenphysical processes that cause macrosegregation in steel tum, energy, and species conservation in all regions (solid, ingots, the mathematical modeling and quantitative numerimush, and bulk liquid) to model steel solidification considercal prediction of macrosegregation have proven to be diffiing only buoyancy driven flow. In order to simplify the cult. Macrosegregation models were first developed by calculation procedure, the mass, momentum, and energy Flemings and co-workers.[6,7] These models have yielded conservation equations were solved assuming that the commuch insight into macrosegregation due to interdendritic positions in the mushy zone were given by the lever rule fluid flow. Ohnaka[8] presented a numerical model for pre(for carbon) or Scheil equation (for other elements). With dicting macrosegregation in steel ingots, but it was limited the solid fraction and velocity distribution known, the solid to a binary Fe-C alloy. In the study by Olsson et al.,[5] a and liquid compositions were then determined explicitly at simple ingot macrosegregation model was developed that the end of each time-step. Using a binary Fe-C alloy solidifying in a cylindrical ingot, Vannier et al.[17] compared this