# 8.- Modeling Flow Phenomena in Tundishes used in DC Casting of Copper Alloys

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8.- Modeling Flow Phenomena in Tundishes used in DC Casting of Copper Alloys
```Case 8
Modeling Flow Phenomena in Tundishes used in DC
Casting of Copper Alloys
In direct chill (DC) casting of copper alloys, the melt is transferred from the furnace onto
a tundish form where it is made to flow in a controlled manner into the DC casting mold.
Inside the tundish, the goal is to fine tune and set to the appropriate level the fluid dynamic,
thermal as well as the chemical conditions of the melt. Specifically, a melt with fairly uniform
temperature and chemistry is desired. Moreover, said melt must be in a streamlined state
of flow and perturbed as little as possible. Maintenance of these conditions during casting
is critical for success of the operation.
To investigate fluid flow behavior in the DC casting tundish, the producer constructed
a 1:1 water model of the system. Segregation phenomena were investigated using tracers.
Various operating conditions were empirically investigated. However, the producer decided
that a mathematical model would be an appropriate complement to the above investigations
particularly since the model could readily incorporate properties and characteristics of the
actual DC casting system. The produced also required the model be developed using a
specific software platform (Ansys-Flotran).
The purpose of modeling was to develop a mathematical representation of the flow,
thermal and solute dispersion phenomena inside the DC casting tundish so that simulation
studies can be undertaken to quantitatively analyze the relationships existing among the
various parameters and variables of the process. Once the model had been developed it had
to be coded for numerical solution using the Ansys software.
After selecting a rectangular Cartesian system of coordinates and assuming steady state
conditions, one proceeds to the statement of the equation of continuity
∇·v =0
the equation of motion
(v · ∇)v = −∇p + µ∇2 v + ρg
the thermal energy balance equation
v∇T = k∇2 T + gE
1
and the solute conservation equation
v∇c = D∇2 c + gC
Since the flow is most likely to be at least mildly turbulent, the above equations must be
supplemented by a turbulence model. In this case the k − model was used that requires
solution of the turbulence kinetic energy equation
ρvj
∂
∂k
∂k
∂ui
= τij
− ρ +
[(µ + µT /σk )
]
∂xj
∂xj
∂xj
∂xj
the dissipation rate equation
ρvj
∂
2
∂
∂
∂ui
= C1 τij
− C2 ρ +
[(µ + µT /σ )
]
∂xj
k ∂xj
k
∂xj
∂xj
and the eddy viscosity
µT = ρCµ
k2
where τij = 2µT Sij − 23 ρkδij is the Reynolds stress tensor, in which Sij is the mean strain
rate tensor and the closure coefficients are assigned the values
C1 = 1.44
C2 = 1.92
Cµ = 0.09
σk = 1.0
σ = 1.3
Boundary conditions for the flow include the given velocity at the melt inlet, no slip at
solid boundaries, zero shear at free boundaries and outflow conditions at the pouring hole.
Boundary conditions for the temperature include the stated inlet melt temperature and the
specification of heat losses into the refractory walls and into the powdered covering at upper
surface as well as the specification of any external source of heat applied. Finally, for the
solute, the external addition must be specified as well as the statement of the loss rate, if
any.
The ultimate goal was to develop a model of the three pouring hole tundish. However,
there was also interest in investigating the single pouring hole tundish and a model for this
was developed first. In fact, the first model was a two dimensional one as this executed
rapidly and allowed appropriate code development and verification. Once the two dimensional model was ready the three dimensional models were developed. Results obtained from
computation using all three models (the 2D, the single hole 3D and the three hole 3D) were
compared against available experimental results from the physical model and also against
results obtained from models developed using the Phoenics software platform. A sample of
selected results is shown in the attached figures.
2
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