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EFFECT OF TEMPERATURE CHANGE ON THE STEEL FLOW IN THE FIVE-STRAND
ASYMMETRIC TUNDISH USING NUMERICAL MODELLING
1Jiří CUPEK, 1Karel MICHALEK, 2Jacek PIEPRZYCA, 3Tomáš HUCZALA
1VSB - Technical University of Ostrava, Ostrava, Czech Republic, EU,
jiri.cupek@vsb.cz, karel.michalek@vsb.cz
2Silesian University of Technology, Gliwice, Poland, EU, jacek.pieprzyca@polsl.pl
3Třinecké železárny a.s., Třinec, Czech Republic, EU, tomas.huczala@trz.cz
https://doi.org/10.37904/metal.2022.4383
Abstract
Numerical modelling is becoming an essential part of research in the field of steel metallurgy at present. In
numerical modelling, the operating equipment is replaced by a mathematical model, which consists of a system
of partial differential equations. Numerical modelling is used to display processes and results that cannot be
monitored under operating conditions. From numerical modelling we can obtain the results of the flow field, we
can monitor the change in temperature and monitor the wear of the refractory lining, etc. This paper deals with
numerical modelling of steel flow in the tundish. The tundish is a very important part of continuous casting. It
supplies liquid steel during the ladle change and distributes steel between casting strands. The tundishes are
made of a welded steel shell and lined with a refractory material. During casting steel, the tundish is the last
reactor where it is possible to influence the quality and purity of the cast steel. It is necessary to know the
processes in the tundish. This presented paper compares the results obtained by flowing steel in the tundish
at non-isothermal conditions. A five-strand asymmetric tundish for bloom casting was used for numerical
simulations. The paper also provides an overview of the issues of numerical simulations and their applicability
in practice. Fluent software, which is part of the ANSYS package, was used for numerical simulations.
Keywords: Numerical modelling, steel flow, tundish, temperature
1. INTRODUCTION
The tundish is a very important part of continuous casting. It supplies liquid steel and distributes steel between
casting strands. The tundishes are made of a welded steel shell and lined with a refractory material. The steel
flows into the tundish from the ladle through a ladle shroud made of ceramic material, which ensures the inlet
flow conditions and prevents reoxidation of the melt. The surface of the steel melt in the tundish is covered
with slag, which prevents reoxidation and heat loss of the melt. Another task of the slag is to ensure the ideal
course of chemical reactions and the absorption of non-metallic inclusions from the melt. To control the flow
of steel from the tundish, each casting strand is equipped with a stopper rod or a slide valve [1,2].
Optimum steel flow in the tundish is essential for continuous casting equipment. Impact pads, baffles, dams
and weirs can be used to optimize the flow. The tundish is the last reactor where we can influence the final
quality and purity of the steel. It is necessary to optimize the flow of steel in the tundish. Under operating
conditions, monitoring the nature of the flow is very difficult. Numerical and physical modeling methods are
used to monitor the flow behavior in the tundish. In the numerical model, the prototype is replaced by a
mathematical model, which consists of a system of partial differential equations. In the case of physical
modeling, the prototype is replaced by a physical model that has the same physical behavior [1,2].
Numerical modelling is suitable for optimizing the steel flow in the tundish. The main advantage of numerical
modelling is the possibility of visualizing the steel casting process. In this paper, the behaviour of steel flow
May 18 - 19, 2022, Brno, Czech Republic, EU
with changes in temperature will be assessed by numerical modelling [1,3,4]. The main objective of the present
publication is to assess the effect of non-isothermal flow in the tundish.
2. PRINCIPLE OF NUMERICAL MODELLING
Numerical modeling is the process by which a prototype is replaced by a mathematical model. Partial
differential equations of a mathematical model can describe, for example, heat transfer, liquid and gas flow or
chemical reactions in the model. Processes in a mathematical model are described as a function of time [1,3].
The system of differential equations is solved in the mesh. The equations are solved for each cell of the mesh
separately. Depending on the accuracy and fineness of the mesh, the number of equations that are solved in
numerical modeling increases [1,3,4].
Fluid flow is an important process for ensuring the course of chemical reactions, removing non-metallic
inclusions and homogenizing steel. It is essential to know the types of flows that can occur during steel casting.
Flow can be divided into laminar or turbulent. Depending on the time, it can be stationary or non-stationary,
where the quantities change in the time [5,6].
The Navier-Stokes equations together with the continuity equation and the so-called turbulence models are
used to describe both flows (laminar and turbulent) [5,6,7].
2.1. Methods of numerical modelling
Finite difference method (FDM) - the essence is the conversion of the investigated system into a system of
differential equations and subsequent solution within certain limits. The limits are determined by the boundary
and initial conditions of the model. Derivatives at node points are replaced by differences [1,3,4,7,8,9].
Finite element method (FEM) - has the greatest importance among numerical methods. The essence lies in
the division into the mesh of elements of finite number, which can be unstructured. The solution on each
element has the shape of a quadratic polynomial or a linear function. [5-8].
Finite volume method (FVM) - when calculating the finite volume method, the object is first divided into a
certain number of non-overlapping finite volumes. The calculation usually takes place at one point, which
characterizes the given final volume. The representative point is located in the middle of the final volume. The
method does not require too much hardware [1,3,5,6,7].
2.2. Expected effect of non-isothermal flow
During the ladle change, the so-called non-isothermal flow occurs. Steel with a higher temperature than the
steel in the tundish enters the tundish and a positive temperature difference is created. The change in
temperature will also be reflected in the change in the nature of the flow, which will be a combination of forced
convection and natural convection, as a result of which there are differences in melt densities and the resulting
buoyancy forces. In this case, natural convection results in the formation of reverse flow [10,12].
Non-isothermal flow pattern persists until the temperature of the mixed existing and newly fed steel stabilizes
and the conditions approach an isothermal steady state. Non-isothermal flow contributes to better separation
of non-metallic inclusions into the cover slag. The resulting product at times of non-isothermal flow can achieve
significantly higher homogeneity and purity [10,12].
3. EXPERIMENTAL CONDITIONS
All simulation preparations and calculations themselves took place in the Ansys Workbench software package,
which includes for example the Ansys Fluent software for CFD (Computational Fluid Dynamics) simulation
solutions.
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3.1. Geometry
The 3D geometry of the five-strand tundish was constructed in the CAD system of the Ansys DesignModeler
software. For numerical simulations, only the inner part of the tundish was constructed. The created geometry
of the tundish is schematically shown in Figure 1.
Figure 1 Geometry of the five-strand tundish
3.2. Computing mesh
As part of the preparation of the numerical model for the simulation, two different computing meshes were
designed (see Table 1). For a computing mesh, it is important to follow the criteria of orthogonal quality and
skewness. Orthogonal quality describes the quality of the created computing mesh, so it is necessary to
achieve the highest possible value. In the case of the skewness criteria, it is an asymmetry that assesses the
degree of cell deformation. In the case of skewness, it is necessary to reach the lowest possible value. Both
criteria can take values in the range 0-1, we can also express them in percentages. Of the proposed variants,
the mesh variant created using the CutCell method proved to be much better. With a significantly lower number
of cells, a higher network quality was achieved and asymmetry was eliminated compared to the original
tetrahedral mesh. With a lower number of cells, the calculation was significantly accelerated. Both variants are
shown schematically in Figure 2.
Table 1 Variants of computing mesh
Computing mesh
Number of nodes
Number of cells
Orthogonal Quality
Skewness
Tetrahedral
248,977
1,331,930
0.7824
0.2162
CutCell
735,713
680,460
0.9827
0.0243
a)
b)
Figure 2 Computing meshes: a) Tetrahedral; b) CutCell method
3.3. Model setting
Set boundary conditions for numerical simulations is shown in Table 2. The calculations were performed in
SW Ansys Fluent and were solved by the finite volume method. Steel with a defined heat flux through the
tundish walls and the steel surface was chosen as the material for the calculation. The steady flow
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for 1753.15 K was first calculated, then the temperature was raised to 1788.15 K and the change in flow was
monitored. The material properties of the steel were set depending on the temperature [1,11].
Table 2 Boundary conditions of model setting [1,11]
Parameter
Value
Casting speed – velocity inlet (m·s-1)
1.04
Casting temperature (°C)
1,753.15 / 1,788.15
Gravity (m·s-2)
-9.81
Operating pressure (Pa)
101,325
Heat flux of free surface (W·m-2)
15,000
Heat flux of tundish walls (W·m-2)
2,500
4. RESULTS AND DISCUSSION
The basic result is residence time distribution (RTD) analysis. The residence time determines the time that a
certain element of the melt spends in the tundish and is essential for further flow optimization. The result of the
RTD analysis is shown in Figure 3. In numerical simulations, it was determined using a species model [5,9].
a)
b)
Figure 3 RTD analysis: a) Steady flow; b) Temperature change
A minimum retention time is necessary for flow optimization, which is determined as time until the first response
on the strands [9,10].
The minimum retention time is shown in the Table 3. For optimization, it is necessary to increase the residence
time on all casting strands and at the same time keep the variability low, which is expressed by the coefficient
of variation.
The result shows that the residence times at the nearest nozzles (CS3, CS4) to the ladle shroud were
increased after the temperature change. At the same time, low variability was obtained after the temperature
change. Flow after temperature change achieves better results.
Table 3 Results of residence time distribution
Variant
Minimal residence time - 𝜏min
CS1 (s)
CS2 (s)
CS3 (s)
CS4 (s)
CS5 (s)
v (%)
Steady flow
180
68
58
52
56
66
Temperature change
93
82
68
63
52
22
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Figure 4 shows the flow velocity vectors of the tundish in steady flow and 100 seconds after the temperature
change. The highest velocity is seen at the entrance to the tundish around the ladle shroud. Around the first
casting strand, the flow is significantly slowed down. There are obvious zones in which steel circulates. After
the temperature changes, the newly supplied warmer steel flows due to the density mainly at the surface. The
stagnant flow zone near the CS1 is gradually removed.
a)
b)
Figure 4 Velocity vectors in the tundish: a) Steady flow; b) Temperature change (100 secs)
From the flow of steel in the tundish, it is also possible to predict places prone to lining wear. A wall shear
stress model was used. The model is based on velocity vectors. Figure 5 shows the results of steady flow and
flow 100 seconds after the temperature change. The biggest problems in the steady flow occur between CS4
and CS5 and also between CS2 and CS3. After the temperature change, the problem area is shifted to the
side walls of the tundish until it is completely removed.
a)
b)
Figure 5 Wall shear stress: a) Steady flow; b) Temperature change (100 secs)
Another result is the temperature field in the tundish. From the front and side view. Figure 6 shows the results
100 seconds after the temperature increased from 1753.15 K to 1788.15 K. From the temperature field we see
the removal of stagnant flow around CS1. Warmer steel flows near the surface.
b)
a)
Figure 6 Temperature field in the tundish 100 secs after temperature change:
a) Front view; b) Side view
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CONCLUSION
In this paper were compared steady and unsteady flow after temperature change. Temperature change is a
process that always accompanies the continuous casting of steel during ladle change. In several cases, the
flow was better after the temperature change. Especially when removing stagnant flow. An increase in casting
temperature affects the flow and has a positive effect on the wear of the lining. Based on RTD analysis, low
flow variability was achieved after temperature change, leading to better product homogeneity.
ACKNOWLEDGEMENTS
This work was supported by the Doctoral grant competition VŠB-TU´Ostrava grant number
CZ.02.2.69/0.0/0.0/19_073/0016945 of the project DGS/TEAM/2021-002 of the MEYS of the Czech
Republic. The work was created within the solution of the Student Grant Competition of numbers
SP2022/15, SP2022/68, SP2022/83. The work was supported No. CZ.02.1.01/0.0/0.0/17_049/0008399
from EU and Czech financial funds provided by the " OP RDE, Calls 02_17_049 Long-term cross-
sectoral cooperation for ITI, Managing Authority: Czech Republic - MEYS".
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