Numerical Modeling of Equiaxed Solidification in Direct Chill Casting
Direct chill (DC) casting is the main production method for wrought aluminum alloys. In this semi-continuous process, significant heat is extracted through a narrow, solidified shell by impinging water jets. A combination of rapid cooling and inoculation of the liquid metal with heterogenous nucleation sites (grain refiner) produces the proper conditions for equiaxed solidification. As equiaxed grains nucleate and grow in the slurry, they are transported by natural convection until their eventual coalescence into a rigid mush. The preferential accumulation of these solute-depleted grains in localized regions of the casting can lead to long range composition differences known as macrosegregation. Because macrosegregation cannot be mitigated by subsequent processing, it is critical to understand and prevent its development during casting.
Numerical models are often used to gain insight into the interplay of the different transport phenomena that cause macrosegregation. The formation of mobile equiaxed grains creates a multiphase system with many moving interfaces, causing several modeling challenges. In principle, a model could be formulated in terms of local instantaneous variables describing the evolution of these interfaces, however the associated computational cost prohibits its extension to the length scale of industrial castings. For this reason, macroscopic transport equations are mathematically formulated using volume averaging methods. Two different volume-averaged model formulations can be distinguished in the solidification literature. The first approach is the multiphase formulation, which solves separate sets of governing equations for each phase that are coupled using microscale interfacial balances. While this approach retains closure models to describe the behavior of the sub-grid interfaces, these interfacial models introduce significant uncertainty that is propagated through the model. The second approach is the mixture formulation, which solves a single set of governing equations for the mixture and utilizes more pragmatic closure relationships. While this approach significantly reduces the complexity and computational cost of the model, previous formulations have oversimplified the microscale transport. Recognizing the advantages and disadvantages of both formulations, a mixture model is rigorously derived, retaining appropriate relationships for the grain structure and microsegregation behavior in equiaxed solidification
Implementation of this model into a 3-D finite volume method (FVM) code using a co-located grid is discussed along with appropriate treatment of the discontinuous body forces and phase mass fluxes across the interface between the slurry and rigid mush. More specifically, body forces in the momentum equation are treated at the face-centers of a control volume to prevent erroneous velocity oscillations near this interface, and a diffuse phase flux method is proposed to reduce the sensitivity of composition predictions to the numerical grid. The proposed methods are verified across a wide range of conditions present in equiaxed solidification.
This model is then used to investigate the role of grain motion on macrosegregation development in equiaxed solidification, specifically in horizontal and vertical DC casting. In horizontal DC casting, the casting axis is perpendicular to gravity and there is a tendency for grains to accumulate along the bottom of the ingot. Feeding liquid metal through a constrained inlet near the bottom suspends grains in the slurry, both reducing the overall macrosegregation and improving the macrosegregation symmetry in the ingot. In vertical DC casting, the casting axis is parallel to gravity and there is a tendency for grains to accumulate in the center of the ingot. It is determined by a combination of simulations in the current work and previous experimental results that a strong localized jet at the centerline can suspend grains in the slurry and reduce negative centerline segregation. The change in segregation is attributed to a combination of reducing the accumulation of solute-depleted grains near the centerline and thinning the rigid mush where solidification shrinkage pulls enriched liquid away from the centerline. The strong localized jet also causes significant refinement and homogenization of the grain structure, which improves the mechanical properties of the ingot. These studies indicate that it is beneficial for DC casting practices to move towards agitated or stirred melts, and away from conventional practices which promote thermal stratification and localized accumulation of equiaxed grains.