Simulation of convection and macrosegregation in a large steel ingot
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I. INTRODUCTION
MACROSEGREGATION in large steel ingots is one of the most well-known and now classical problems in the field of solidification and casting.[1] It arises from the relative movement of solute-rich or poor liquid and solid phases during solidification over distances much larger than the dendrite arm spacings. Commonly found macrosegregation patterns in steel ingots are a positively segregated zone at the top, negative segregation near the bottom in the equiaxed zone, inverse segregation near the ingot surface, V segregates along the centerline, and A segregates in the columnar zone.[2,3] These inhomogeneities can severely limit the yield in ingot casting and cause problems in the subsequent processing and final steel properties. It is well established that the macroscopic transport of species leading to macrosegregation can occur by a variety of mechanisms, including thermally and solutally driven natural convection of the melt in the mushy zone, flow due to solidification contraction, and the sedimentation of free equiaxed crystals. Fredriksson and co-workers[4,5] provide recent overviews of the solidification, transport phenomena, and macrosegregation in ingot casting. While there exists a relatively good understanding of the physical processes that cause macrosegregation in steel ingots, the mathematical modeling and quantitative numerical prediction of macrosegregation have proven to be difficult. Macrosegregation models were first developed by Flemings and co-workers.[6,7] These models have yielded much insight into macrosegregation due to interdendritic fluid flow. Ohnaka[8] presented a numerical model for predicting macrosegregation in steel ingots, but it was limited to a binary Fe-C alloy. In the study by Olsson et al.,[5] a simple ingot macrosegregation model was developed that J.P. GU, Postdoctoral Researcher, and C. BECKERMANN, Professor, are with the Department of Mechanical Engineering, University of Iowa, Iowa City, IA 52242. Manuscript submitted July 31, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
included consideration of the settling of free crystals and A segregates. Although good agreement with experiments was achieved, the model relied on many approximations (such as estimating the flow velocities). It should also be mentioned that many models have appeared in the literature that are solely concerned with heat transfer during steel ingot casting (for example, Reference 9 and references therein). While these models form the foundation for any realistic ingot casting modeling, they do not address solid/liquid transport during solidification and the resulting macrosegregation. More recently, macrosegregation models have been formulated that rely on fully coupled numerical solutions of the mass, momentum, energy, and species conservation equations for a solid/liquid mixture.[10,11] Beckermann and Wang[12] and Prescott and Incropera[13] have reviewed the progress in this area. Although many basic phenomena, such as the formation of A segregates and the negative segregation due to
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