Finite Element Analysis of
the Temperature of a
Continuous Casting Mold
MANE 6960 – ADVANCED TOPICS IN FINITE ELEMENT
ANALYSIS
THOMAS PROVENCHER
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Introduction:
Continuous casting is a metal forming process which is able to provide a steady stream of simple
metal shapes like box or I beams for use in the creation of engineered structures. Molten metal,
steel in this case, is poured into a tank which feeds a water cooled open copper mold that
removes a sufficient amount of heat from the metal to solidify the casting’s outer shell. The
freshly formed beam exits the bottom of the mold and is further cooled by water jets until the
whole casting solidifies. This report will analyze the temperature profile of the copper open
mold using heat transfer data and a thermal Finite Element Analysis model completed in
ABACUS. Figure 1 illustrates the continuous casting process.
Figure 1: Continuous casting process
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Formulation and Solution:
The general shape of the continuous casting mold being analyzed is that of a narrow, tall box
with no top or bottom. The molten steel can therefore pour into the entire top of the mold and
exit the bottom in the shape of the interior of the mold. The Finite Element Analysis (FEA)
model chosen took advantage of the inherent symmetry of this shape by dividing the mold into
four parts, half the width and half the thickness, and assuming no heat transfer across the cut
surfaces. The complete mold’s dimensions are shown in Figure 2 and the FEA quarter model is
shown in Figure 3.
Figure 2: Dimensions of the copper mold
Figure 3: Quarter model of the mold
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The back surfaces of the quarter model were given a set temperature boundary condition profile
of 30°C at the bottom and a linear temperature rise to 38.5°C at the top to simulate the
temperature rise of the cooling water. The interior surface of the mold, where the molten steel is
poured and begins to solidify, was given a heat transfer flow rate dependent on its vertical
location on the mold and the 0.8 meters per minute casting speed heat transfer profile provided in
Figure 4. Figures 5 and 6 show the locations where the water temperature and heat transfer
boundary conditions were placed on the model, respectively. Figure 7 shows the heat transfer
values assigned to the model. The top and bottom surfaces, as well as the cut surfaces created by
the quarter model symmetry were set to have no heat flux and their temperatures were not
controlled.
Figure 4: Heat transfer rates dependent on casting rate
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Figure 5: Temperature controlled surfaces
Figure 6: Various heat transfer zones
Figure 7: Heat transfer rates used within the ABACUS model as shown in Figure 6
The quarter model was meshed using 4 different mesh densities which had 132, 920, 7360, or
66600 elements total with varying number of elements through the thickness. All of the
elements were either linear or quadratic rectangular cuboids, depending on the analysis method
chosen. Figure 8 shows an example of a “medium” mesh, the second least dense mesh analyzed.
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Figure 8: "Medium" mesh density of the quarter mold
The variational formulation is shown below:
(𝑢′ , 𝜐′) = (𝑓, 𝜐)
The ABACUS model of the quarter mold was run eight times, twice for each mesh density to
allow for the elements to be either liner or quadratic. The general graphical temperature profile
output from each of these analyses can be seen in Figures 9 and 10. The different mesh densities
did each have certain select variances, but they were very subtle and hard to discern without
magnification. Table 1 shows the maximum temperature of the quarter mold for each analysis.
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Figure 9: “Coarse” mesh with quadratic elements
Figure 10: “Fine” mesh with quadratic elements
Table 1: Continuous casting copper mold maximum temperature
Mesh Density
Coarse
Medium
Fine
Extra Fine
Copper Mold Maximum Temperature (C) and Relative Error
Linear % Difference to Extra Fine Quadratic % Difference to Extra Fine
180.32
4.965
186.97
1.481
192.23
1.312
189.65
0.069
189.98
0.126
189.61
0.090
189.74
N/A
189.78
N/A
The data provided in Table 1 shows that linear thermal elements are able to provide accurate
results even with extremely low mesh densities, unlike linear mechanical elements which must
be sufficiently plentiful and dense. The quadratic elements were even more consistent when
provided with the same coarse mesh. As the mesh density increased both the linear and
quadratic elements converged to one temperature, approximately 189.75 degrees Celsius.
Conclusions:
Continuous casting provides a fast and cost effective way to create beam sections of various
shapes of any length. The mold defining the shape must be designed such that it can successfully
extract huge amounts of heat from the molten steel such that a solid outer casing can hold its
shape while the molten core is cooled. The analysis showed that when steel is cast into a copper
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mold creating an approximately 1.9 x .2 meter slab at at 0.8 meters/minute the maximum
temperature of the mold will be approximately 190 degrees Celsius provided that sufficient
quantities of 30 degree Celsius water can cool the mold. Both the linear and quadratic elements
converged on this temperature quickly and were still quite accurate with a very coarse mesh.
References:
"Continuous Casting." SSAB -. Web. 22 June 2015. < http://www.ssab.com/en/Investor-Media/About-SSAB/Steel-making-process/The-metallurgical-process/Continuous-casting/>.
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