<p><a>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. </a></p>
<p>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 </p>
<p>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.
</p>
<p>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.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/13084949 |
| Date | 16 December 2020 |
| Creators | John Coleman (9154625) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Numerical_Modeling_of_Equiaxed_Solidification_in_Direct_Chill_Casting/13084949 |
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