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Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 www.me‐journal.org doi: 10.14355/me.2014.0303.03
109
Physical and Mathematical Simulation of
Fluid Flow in a Wide Single‐strand Tundish
for Slab Continuous‐casting Zhong Liangcai*1, Hao Ruichao2 Li Junzhe3 Li Lei1 Zhu Yingxiong4 Xu Ninghui5
1‐4 School of Materials and Metallurgy, Northeastern University, Shenyang 110004, China; 5Pinggang Jiujiang
Branch Corporation, Jiujiang 332000, Jiangxi, China.
*[email protected]; [email protected]; [email protected]; [email protected]
Received 16 July, 2013; Accepted 22 September, 2013; Published 9 June, 2014
© 2014 Science and Engineering Publishing Company
Abstract
Molten steel flow in a wide single‐strand tundish with
different flow control devices (FCDs) for slab continuous‐
casting was investigated by physical and mathematical
simulations in this work. The effects of different FCDs on the
flow characteristics and velocity and temperature fields in
the tundish with larger width, shorter length and larger
depth were studied. The results showed that locations and
dimensions of weirs and dams and geometry of turbulence
inhibitors (TIs) have a large effect on the flow characteristics
and velocity and temperature profiles. Adoption of a square
turbulence inhibitor without extending top lips can improve
the molten steel flow better than that with top extending lips
in the tundish. In comparison with the former tundish
configuration, the flow characteristics are improved to a
great extent in the optimum case. A big “spring uprush”
forms on the free surface around the long shroud when
molten steel flows into a turbulence inhibitor with extending
top lips and rushes up reversely out of the TI, while four
small “spring uprushes” appear on the surface when a
square TI without extending top lips is adopted because the
liquid steel flows mainly out of the 4 corners of the square TI.
The flow of liquid steel in the former tundish configuration
is not reasonable and the height of an area where
temperature is less than 1819 K is about half of liquid surface
height at the right side of the stopper, which means that big
dead zone exited in the former tundish configuration. In the
optimum case, the height of such area was only one seventh
of the liquid surface height. The RTD curves obtained from
the mathematical simulation are agreed with those from the
physical modeling and the flow characteristics obtained
from these two methods in this work are coincident with
each other.
Keywords
Slab Continuous‐casting; Wide Single‐strand Tundish;
Mathematical Simulation; Physical Modelling; Fluid Flow
Characteristic; Velocity Field; Temperature Profile; Flow Control
Device
Introduction
Tundishes in continuous casting have very important
effects for steel cleanness. Tundish metallurgy has
been paid more and more attentions.1 It is well known
that molten steel flow characteristics in tundishes have
great effects on non‐metallic inclusion removal from
the liquid steel, slag and air entrainment minimization,
and new inclusion formation prevention. Different
flow control devices (FCDs), such as weirs, dams,
baffles and turbulence inhibitors (TIs), have been
applied in continuous‐casting tundishes for
improvement of the characteristics of molten steel flow.
Many researchers2‐10 have applied TIs with other FCDs
to optimize the tundish configurations since 1990s by
physical modeling and/or mathematical simulation.
Generally, the TIs used have extending top lips in
these researches and good flow characteristics have
been achieved. But not all tundishes are suitable to use
such TIs with extending top lips. What kinds of TIs in
geometry should be adopted in a tundish lies on the
inside profile of tundishes.
The geometry characteristics of the single‐strand slab
tundish profile studied in the present work are larger
width, shorter length and larger depth, being 1513 mm
(upper width)×4035 mm(upper length)×1215(working
liquid surface depth). For such tundish, different TIs
with or without extending top lips were applied to
optimize the tundish configuration together with a
weir and a dam through physical modeling
experiments and mathematical simulation calculations,
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110
and the flow characteristics of the tundish with
different tundish configurations and their velocity and
temperature fields are investigated in this work.
Physical Modeling Method
In order to ensure that the fluid flowing between a
model tundish and a prototype tundish for isothermal
and non‐reactive systems is similar, geometrical and
dynamic similarities must be satisfied between the two
vessels. In the present work, the ratio of geometrical
similarity of model tundish to the prototype, λ was
chosen to be 1:2.5. Dynamic similarity required
simultaneous equality of both turbulent Reynolds and
Froude numbers, but it was impossible to keep the
condition satisfied in reduced scale modeling studies.
The computational work of Sahai and Burval11 and the
experimental work of Singh and Koria12‐13 showed that
the magnitude of turbulent Reynolds number under
turbulent flow range in different tundishes was very
similar. Therefore, Froude number between the model
tundish and the prototype was maintained to be
equivalent in this work. With this condition, the water
flow rate, Qm in the experiments was calculated from
the liquid steel flow rate, Qp by the following equation:
2.5m pQ Q (1)
The experimental apparatus was shown in Fig. 1. 0.2
g/ml NaCl solution of 500 ml was used as the tracer in
the physical modeling experiments. After fluid flow in
the model tundish reached stable, the tracer was
injected into the tundish though the ladle shroud. A
probe was located under the outlets of the tundish to
measure the variation of water conductivity with time,
that is, residence time distribution (RTD) curves. The
probe was connected to a conductivity meter and the
signals were recorded with a data acquisition system
and a computer. From the RTD curves measured, fluid
flow characteristics in a certain tundish configuration
were calculated with the following equations:
Average residence time tav
0
0
n
i i ii
av n
i ii
tc t dt t c t tt
c t tc t dt
(2)
Plug flow volume fraction vp
p min maxp 2
Vv
V
(3)
Dead zone volume fraction vd 14
d ad a1
V Qv
V Q
(4)
Mixing flow volume fraction vm
mm d p1
Vv v v
V (5)
FIG. 1 SCHEMATIC OF EXPERIMENTAL APPARATUS
Mathematical Simulation Method
Governing Equations
The liquid steel flow in the continuous casting tundish
can be considered to be three‐dimensional, turbulent.
The flow is treated as steady by neglecting the
phenomena involved during filling and emptying of
the tundish. The effect of surface slag to the flow is
ignored and the melt surface is assumed to be flat. The
molten steel is Newtonian and incompressible fluid.
Therefore, the governing equations in Cartesian
tensional form for the liquid steel flow in the tundish
can be written as:
Continuity ( ) 0ii
ux
(6)
Momentum
( ) jii j eff i
i i i j i
uupu u g
x x x x x
(7)
where, ρ is the density of melt, u the velocity, p the
pressure, g the gravitation acceleration, and μeff the
effective viscosity. i and j represent the three
coordinate directions. μeff is equal to the sum of
molecular and turbulent viscosity of steel as follows:
eff t (8)
The turbulent viscosity is calculated through its
relationship with the turbulent kinetic energy and its
dissipation rate. The turbulent kinetic energy, k and its
dissipation rate, ε can be expressed with the following
equations:
Turbulent kinetic energy
effi
i i k i
ku k G
x x ο x
(9)
Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 www.me‐journal.org
111
Dissipation rate of turbulent kinetic energy
1 2eff
ii i i
u C G Cx x x k
(10)
The generation term, G in Equs. (9) and (10) can be
given as: 22
2 ji it t
i j i
uu uG
x x x
(11)
The turbulent viscosity, μt can be written as:
2
t
C k
(12)
C1, C2, Cμ, σk and σε are the empirical constants of the k‐
ε model and were assigned to their standard values
from Launder and Spalding15: 1.44, 1.92, 0.09, 1.0 and
1.30, respectively.
The heat transfer in the tundish is governed by energy
equation as follows:
Peff
( )i
i i i
C u T T
x x x
(13)
where the effective thermal conductivity, λeff, is the
sum of two components:
Prp t
efft
C (14)
here, Prt is the turbulent Prandtl number, λ is thermal
conductivity, Cp is heat capacity and T is temperature.
To calculate the residence time distribution curves of
the molten steel in the tundish with different
configurations and compare them to the RTD curves
obtained from the physical modeling experiments, a
pulse of tracer was introduced into the melt through
the inlet and allowed to flow with the melt. By
monitoring the change in tracer concentration of the
melt at the tundish outlet, the residence time
distribution curve was obtained. The transport of the
tracer and the variation in tracer concentration are
governed by the mass transport equation as follows:
( )ieff
i i i
u cc cD
t x x x
(15)
where c represents the concentration of the tracer, t is
the time and Deff is the effective mass diffusion
coefficient and is the sum of the molecular and
turbulent diffusivity (D+DT). Under the condition
where turbulent Schmidt number is equal to 1, one has:
eff
eff
1D
(16)
Boundary Conditions
The whole volume filled with molten steel in the
tundish was chosen as the numerical calculation
domain. The above continuity, momentum and energy
equations were solved with the equations for k and ε
by using the boundary conditions. Non‐slipping
conditions were applied as boundary conditions to all
solid walls. Frictionless conditions were used to the
free surface of liquid steel. The logarithmic law was
employed to all nodes closest to any solid walls. The
vertical velocity profiles of the liquid steel at the inlet
as well as at the outlet of the tundish were assumed to
be uniform through the cross sections and the other
two velocity components were assumed to be zero.
The values of k and ε at the inlet were calculated from
the inlet average velocity through the well known
equations. A constant mass flow rate of steel from the
ladle to the tundish was 2.98 ton/min for the
mathematical simulation.
For the boundary conditions of temperature field,
uniform and constant heat flow rates were used at
every wall surface of the tundish and liquid surface.
The heat flow rates used in this work were those
recommended by Chakraborty and Sahai16 and related
parameters were listed in Table 1.
TABLE 1 PARAMETERS FOR MATHEMATICAL SIMULATION OF LIQUID
STEEL FLOW IN THE TUNDISH
Parameters Values Parameters Values
Liquid steel
density/kg∙m‐3 7000
Liquid steel
viscosity/kg∙m‐1∙s‐1 0.0067
Liquid steel
conductivity/W∙m‐1∙K‐141
Liquid steel specific
heat /J∙kg‐1∙K‐1 750
Inlet temperature/K 1823 Heat flux at walls
inside tundish/kW∙m‐21.75
Heat flux at
bottom/kW∙m‐2 1.4
Heat flux at liquid
surface/kW∙m‐2 15
Heat flux at transverse
walls /kW∙m‐2 3.8
Heat flux at
longitudinal
walls/kW∙m‐2
3.2
Zero mass transfer fluxes were used at all walls and
liquid surface for mass equation solution. At t=0 s the
mass fraction of tracer at inlet of the tundish was set to
be 0.1. After t=1 s it was given as zero. The
concentration of the tracer at the outlet of the tundish
was monitored from t=0 and the RTD curves would be
obtained from the numerical calculation.
The commercial CFD package FLUENT® was used to
solve the above governing equations with the
boundary conditions. In the numerical solution
scheme Semi Implicit Method for Pressure Linked
Equation (SIMPLE) algorithm was used for pressure
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112
and velocity coupling and first order upwind scheme
for momentum and scalar transport equations. Once
the flow and temperature fields were converged to
steady state the problem defined module of the
FLUENT solver was changed to unsteady state for
solving the transient tracer dispersion Eq. (15) with
appropriate initial and boundary conditions.
Results and Discussion
Physical Modeling
FIG. 2 SCHEMATIC OF TUNDISH CONFIGURATIONS IN THE
EXPERIMANTS
TABLE 2 TYPICAL TUNDISH CONFIGURATIONS IN EXPERIMENTS
Case TI S1/mm S2/mm H1/mm H2/mm
C0 TI1 632 108 96 136
C1 TI1 590 108 96 136
C2 TI1 590 200 130 205
C3 TI2 590 150 55 205
C4 TI3 590 150 55 205
C5 TI4 540 200 55 225
C6 ‐ 390 150 55 250
C7 TI1 390 150 55 250
C8 TI5 540 200 55 250
C9 TI5 440 200 55 250
C10 TI5 390 200 55 250
C11 TI5 390 150 55 250
FIG. 3 SCHEMATIC OF SOME TURBULENCE INHIBITORS IN
THE EXPERIMENTS
Different tundish configuration studied in this work is
shown in Fig. 2. The tundish configurations consisted
of different turbulent inhibitors (TIs), different
locations of a weir and a dam (S1 and S2) and their
different heights (H1 and H2). A lot of tundish
configurations had been experimented in the present
work, but for space limited only some typical tundish
configurations are listed in Table 2 where C0 is the
former tundish arrangement. Figure 3 presents some
TIs used in the physical modeling experiments. These
TIs are all square at horizontal cross‐section except TI3
whose horizontal cross‐section is rectangle with 280
mm short sides.
The RTD curves in the tundish with configurations of
C0, C6, C7 and C11are shown in Fig. 4 and the flow
characteristics of different tundish configurations are
given in Table 3. It is known from Table 2 that C0 and
C7 used the same TI, i.e., TI1, and the difference
between these two cases was their weir and dam
locations and heights, i.e., S1, S2, H1 and H2. As shown
in Fig. 4, there are high peaks in the RTD curves for C0
and C7 cases, which indicates that a lot of tracers flow
out of the tundish and large dead zone volumes exit in
the tundish with C0 and C7 configurations, as seen in
Table 3. Even though C7 and C11 have the same
values of S1, S2, H1 and H2, the peak of the RTD curve
in C11 case is lowered apparently due to the different
TI and its RTD curve moves towards right side in Fig.
4. These results indicate that TI1 is not suitable for this
kind of tundish studied in present work. The
difference among C6, C7 and C11 cases in
configuration is that there is no TI in C6 case. It is
known from Fig. 4 that the minimum residence and
peak concentration times in C6 case are short. Short
minimum residence and peak concentration times are
not expected even though its peak concentration is low.
Therefore, the adoption of turbulent inhibitor without
extending top lips, TI5, in this tundish can distribute
molten steel well to larger space of the tundish and
prolong residence time of liquid steel in the tundish,
which is favorable to removal of non‐metal inclusions.
Such result is determined by the characteristic of this
tundish profile.
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0
0.5
1.0
1.5
2.0
C/-
/-
C0
C6
C7
C11
FIG. 4 RTD CURVES IN SOME DIFFERENT TUNDISH
CONFIGURATIONS
As shown in Table 3, the fluid flow in the tundish with
the former configuration, C0, is not perfect. Its
Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 www.me‐journal.org
113
minimum residence is 64 s, its peak concentration and
average residence times are short and its dead zone
volume is larger, being 35%, which decreases largely
the effective volume of the tundish. The same TI1 was
used in C1 and C2 cases and the locations and heights
of the weir and dam were adjusted, but the flow
characteristics in these two cases change less. Their
average residence times increase a little and their dead
zone volumes decrease less, and all of their fractions
were over 30%.
TABLE 3 FLOW CHARACTERISTICS IN DIFFERENT TUNDISH
CONFIGURATIONS
Case tmin/s tmax/s tav/s vp/% vd/% vm/%
C0 64 81 237 20 35 45
C1 64 81 241 20 34 46
C2 70 108 249 24 32 44
C3 78 113 279 26 24 50
C4 80 130 280 29 23 48
C5 78 134 289 29 21 50
C6 54 91 286 20 21 59
C7 63 99 273 22 25 53
C8 88 121 291 29 20 51
C9 82 139 303 30 17 53
C10 79 141 307 30 16 54
C11 81 163 314 33 14 53
Turbulent inhibitors of TI2, TI3 and TI4 were applied
in tundish configurations of C3, C4 and C5,
respectively. The outlet areas of these three TIs are
incremental. It can be seen from Table 2 and 3 that
flow characteristics in such tundish are improved by
changing TIs and adjusting locations and heights of
the weir and dam. The minimum, peak and average
residence times are increased and the dead zone
volume is lowered, being below 25%.
There was no TI in C6 case and its dead zone volume
is low obviously, lower 40% than that in the former
case C0. The peak and average residence times are
prolonged in some degree, but the minimum residence
time becomes shorter by 10 s due to no TI, as
compared to that in C0 case. When fluid flows into the
tundish, a part of it flows to the dam along the tundish
bottom if no TI is used in the tundish. As a result, the
flowing distance of this part of fluid is short and the
minimum residence time in such tundish
configuration becomes low.
It can be concluded from Table 2 and 3 that reduction
in S1 and H1 and increase in S2 and H2 are favorable to
improvement for fluid flow characteristics in this
tundish. Average residence time is increased and dead
zone volume is decreased. Lowering H1 and S1 and
increasing S2 and H2 can prolong fluid’s flowing
distance, reduce its flowing velocity between the weir
and dam and let fluid flow toward upper part of the
right end wall, which increases residence times and
decreases dead zone volume in the tundish.
C7 case was obtained by applying TI1 to C6 case.
Comparing to C6 case, minimum residence and peak
concentration times in C7 case are prolonged, but its
dead zone volume fraction is enlarged from 21% to
25%, which means that this TI1 is not favorable to
decreasing dead zone volume in this tundish.
Application of TI in C7 case, in comparison with C6,
prolongs distance of fluid flow in the tundish.
Therefore, its minimum residence time increases. But
such TI with extending top lips makes the fluid flow
out of the TI in a concentrative way and can not
transfer the fluid to the whole tundish volume. For
this reason, the tracers added into the tundish with C7
configuration flow out of the tundish quickly due to
its larger width, which makes its RTD curve have
short peak concentration time and high peak
concentration, as shown in Fig. 4. As a result, there is
larger dead zone volume in the tundish with C7 case.
It was found from the experiments that increase in TI’s
outlet area can improve fluid flow characteristics in
this tundish. TI5 was achieved by canceling TI’s
extending top lips. C8, C9, C10 and C11 configurations
consist of TI5 and different locations and heights of a
weir and a dam. It is known from Table 2 and 3 that
the peak concentration and average residence times
are prolonged greatly by using TI5 and moving the
weir and dam towards the direction of the tundish
outlet and the dead zone volume is reduced greatly,
being less 20%. The dead zone volume fraction in the
tundish with C11 case is lowered to 14%, less by 60%
than that in the former tundish configuration C0.
350 400 450 500 550 600 650
15
20
25
30
35
TI: TI5, S2=150 mm, H
1=55 mm, H
2=250 mm
v d /%
S1/mm
TI: TI1, S2=108 mm, H
1=96 mm, H
2=136 mm
FIG. 5 RELATIONSHIP BETWEEN DEADZONE VOLUME
FRACTION IN THE TUNDSIH AND S1
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Fig. 5 presents the variation of dead zone volume
fraction in the tundish with the distance S1 between
the dam and the centre line of the tundish outlet under
the condition of the same TI, S2, H1 and H2. When S1 is
reduced from 632 mm to 390 mm, the dead zone
volume fraction is lowered from 35% to 30% for the
former tundish configuration C0, while the fraction is
decreased from 20% to 14% for the optimum tundish
configuration C11 when S1 is reduced from 540 mm to
390 mm. As described above, the fluid flowing over
the dam can moves towards the end wall at higher
velocity when the weir and the dam are moved to the
side of the tundish outlet. The same effect is also
obtained if the dam’s height is increased. Therefore,
the dead zone at that end wall is reduced.
The research results in this work indicate that FCDs
and their locations in tundishes should be optimized
carefully to determine an optimum tundish
configuration according to tundish inside profile and
molten steel flow rate so that the optimum fluid flow
characteristics in tundishes can be achieved for the
sufficient removal of inclusions from liquid steel.
Mathematical Simulation
0 1 2 3 40.0
0.5
1.0
1.5
C /
-
/ -
Physical result for C6
Nmerical result for C6
Physical result for C7
Nmerical result for C7
FIG. 6 RTD CURVES FROM MATHEMATICAL AND PHYSICAL
SIMULATIONS IN C6 AND C7 TUNDISH CONFIGURATIONS
0 1 2 3 40.0
0.5
1.0
1.5
Physical result for C11
Numerical result for C11
Numerical result for C0
C/-
/-
Physical result for C0
FIG. 7 RTD CURVES FROM MATHEMATICAL AND PHYSICAL
SIMULTIONS IN C0 AND C11 TUNDISH CONFIGURATIONS
RTD curves obtained from physical modeling
experiments and mathematical simulations in different
tundish configurations are given in Figs. 6 and 7. It is
shown in these figures that the RTD curves obtained
from mathematical simulations are agreed basically
with those from corresponding physical modeling
experiments. Only some differences between these
two methods in this work exist in the vicinity of the
peaks of the curves, but the results in the
mathematical simulations can reflect fluid flow
characteristics in different tundish configurations.
Table 4 gives a comparison of flow characteristics from
mathematical simulation to those from physical
modeling. It is obvious in this table that the calculated
flow characteristics from the RTD curves in
mathematical simulations are coincident with those
from the measured RTD curves.
TABLE 4 COMPARISON OF FLUID FLOW CHARACTERISTICS IN DIFFERENT
TUNDISH CASES FROM NUMERICAL AND PHYSICAL SIMULATIONS
Case Method tmin/s tmax/s tav/s vp/% vd/% vm/%
C0 Numerical 68 123 285 26 28 46
Physical 63 76 235 19 35 45
C11 Numerical 86 185 320 37 17 46
Physical 82 165 313 34 14 52
C7 Numerical 70 113 297 25 24 51
Physical 63 99 273 22 25 53
C6 Numerical 54 169 321 31 19 50
Physical 54 91 286 20 21 59
In order to compare the velocity and temperature
fields in the tundish with different configurations, the
former tundish configuration and the optimum one
were chosen to conduct such comparison in the
mathematical simulation. The velocity fields and
streamlines at symmetrical longitudinal plane and
liquid surface in the former tundish configuration are
presented in Figs. 8 and 9, respectively. It is known
from the two figures that the liquid steel flowing out
of the long shroud impinges the bottom of the TI with
extending top lips and then flows out of the TI at the
opposite direction towards the liquid surface. There is
a big recirculation region around the stream entering
the tundish through the long shroud with the
recirculation “eye” near the TI bottom. When the
molten steel reaches the free surface, it forms a big
“spring uprush” and then flows along the surface and
against the long shroud towards to the side walls and
the weir. As the molten steel reaches these solid walls,
it turns downward. There are two other recirculation
zones near the liquid surface in the area between the
left tundish side wall and the weir, as can be seen in
Fig. 8(b). After the melt reach the tundish bottom,
some part of steel flow along the tundish bottom
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toward the dam. Then this part of liquid steel is forced
to move upwards to the liquid surface due to the
obstruction effect of the dam. The melt flows along the
free surface toward the right side wall. Finally, it turns
down near the stopper and flows toward the tundish
outlet. A large recirculation region is formed between
the dam and the right tundish side wall. A small
recirculation flow exists in the right side of the weir.
Although some recirculation regions are formed on
the free surface near the right tundish side wall, as can
be found in Fig. 9(b), they would not lead to slag
entrapment because the velocity here is very small.
0.5m/s
(a) Velocity field
(b) Streamline
FIG. 8 FLOW FIELD AND STREAMLINES AT VERTICAL
SECTION IN THE FORMER TUNDISH CONFIGURATION
0.5m/s
(a) Flow field
(b) Streamline
FIG. 9 FLOW FIELD AND STREAMLINES AT FREE SURFACE IN
THE FORMER TUNDISH CONFIGURATION
Flow fields and corresponding streamlines in the
tundish with the optimum configuration in the
symmetrical longitudinal plane and on the free surface
are shown in Figs. 10 and 11, respectively. It can be
found from these two figures that the stream from the
long shroud impinges the bottom of the TI without
extending top lips and diverts along its bottom. The
melt rushes reversely up mainly out of the 4 corners of
the TI toward the free surface where 4 small “spring
uprushes” are formed, as can be seen in Fig. 11(b).
Such phenomena could be observed visually in the
physical modeling experiments with the TI without
extending top lips. A recirculation region with small
height is formed around the shroud stream near the
TI’s bottom. The melts reached at the free surface flow
all around along the surface and turn downward at
the around walls and the symmetrical plane of the
tundish when they encounter. No other recirculation
zones are found under the free surface as those in the
former tundish configuration in the vertical
symmetrical plane. Only several very small
recirculation flowing zones can be observed on the
free surface at the left side of the weir. Such flowing
characteristics in the optimum tundish case are
different from those in the former tundish case. With
the reduction in distance between the dam and the
tundish outlet, the recirculation flow region between
the dam and the stopper becomes small, while with
increase in distance between the weir and the dam, the
recirculation zone behind the weir becomes large.
0.5m/s
(a) Flow field
(b) Streamline
FIG. 10 FLOW FIELD AND STREAMLINES AT VERTICAL
SECTION IN THE OPTIMAL TUNDISH CONFIGURATION
0.5m/s
(a) Flow field
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(b) Streamline
FIG. 11 FLOW FIELD AND STREAMLINES AT FREE SURFACE IN
THE OPTIMAL TUNDISH CONFIGURATION
(a) Vertical symmetrical plane
(b) Free surface
FIG. 12 TEMPERATURE FIELD IN THE FORMER TUNDISH
CONFIGURATION
(a) Vertical symmetrical plane
(b) Free surface
FIG. 13 TEMPERATURE FIELD IN THE OPTIMAL TUNDISH
CONFIGURATION
Temperature distributions in the tundish with the
former and the optimum configurations are presented
in Figs. 12 and 13, respectively. It can be seen from Fig.
12 that larger temperature gradients exist along the
flow direction of liquid steel and its temperature
changes from 1821 K to 1807 K at the right side of the
weir on the free surface. The high temperature region
concentrates around the shroud stream. The molten
steel temperature range in the area of 1/2 height of the
bath near the free surface at the right side of the
stopper varies from 1819 K to 1813 K and the lowest
melt temperatures at the two side walls on the free
surface at the right side of the tundish are only 1807 K
and 1808 K, respectively. Therefore, in such areas the
molten steel flows slowly and dead zones are formed,
resulting in lower temperature regions and reduction
in effective tundish volume and being unfavorable to
making full use of metallurgical functions of tundishes.
It can be known from Fig. 13 that the temperature
gradients along the melt flow direction in the
optimum tundish configuration becomes smaller than
those in the former tundish case. The high
temperature zones disperse at the 4 gushes above the 4
corners of the TI. There are larger areas where the
temperature is between 1822 K and 1821 K in the
vertical symmetrical plane and on the free surface. The
molten steel temperature range in the area of 1/7
height of the bath near the free surface at the right side
of the stopper varies from 1819 K to 1816 K and the
lowest melt temperature at the two side walls on the
free surface at the right side of the tundish is 1813 K. It
is indicated from the above results that the molten
steel flow is reasonable and dead volume and low
temperature regions are reduced in the optimum
tundish configuration.
Conclusions
Molten steel flow in a wide single‐strand tundish with
different FCDs for slab continuous‐casting was
investigated by physical and mathematical
simulations in this work. The following conclusions
can be drawn out from this investigation.
(1) The former tundish configuration and the former
FCDs are not reasonable, resulting in poor flow
characteristics. The residence times are short and the
dead zone volume is large, being 35%. Such tundish
configuration is unfavorable to the inclusion removal.
(2) Adoption of a TI without extending top lips in this
tundish can improve flow characteristics in
comparison to the former TI with extending top lips in
this special tundish. Increase in the height of weir and
dam and movement of the weir and dam toward the
outlet of the tundish can prolong residence times and
reduce dead zone volume.
(3) In comparison with the former tundish
configuration, the flow characteristics in the optimum
tundish case are improved to a great extent; minimum
residence time, peak concentration time and average
Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 www.me‐journal.org
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residence time are increased from 64 s, 81 s and 237 s
to 81 s, 163 s and 314s, respectively, and the fraction of
dead zone volume decreases from 35% to 14%, being
reduced by 60%.
(4) Liquid steel flowing out of the long shroud
impinges the bottom of the TI with extending top lips
and then flows out of the TI at the opposite direction
towards the liquid surface. A big recirculation region
around the stream entering the tundish through the
long shroud is formed. A big “spring uprush” appears
around the long shroud on the free surface.
(5) Liquid steel from the long shroud impinges the
bottom of the TI without extending top lips and rushes
reversely up mainly out of the 4 corners of the TI
toward the free surface where 4 small “spring
uprushes” are formed. The recirculation region
around the stream entering the tundish becomes small.
(6) Larger temperature gradients in the former tundish
configuration exist along the flow direction of liquid
steel and its temperature changes from 1821 K to 1807
K at the right side of the weir on the free surface.
There is a larger low temperature zone in the area of
1/2 height of the bath near the free surface at the right
side of the stopper and the lowest melt temperatures
at the two side walls on the free surface at the right
side of the tundish are only 1807 K and 1808 K,
respectively. This indicates that the velocity of liquid
steel in this area is low and large dead zone volume
exists.
(7) The molten steel temperature ranging from 1819 K
to 1816 K in the optimum tundish configuration only
occupies the area of 1/7 height of the bath near the free
surface at the right side of the stopper and the lowest
melt temperatures at the two side walls on the free
surface at the right side of the tundish is 1813 K. The
molten steel flow is reasonable and dead volume and
low temperature regions are reduced.
(8) RTD curves obtained from the mathematical
simulations are in basic agreement with those from the
corresponding physical modeling experiments. The
calculated flow characteristics from the RTD curves in
mathematical simulations are coincident with those
from the measured RTD curves. The results of the
mathematical simulations can reflect fluid flow
characteristics in different tundish configurations.
ACKNOWNLEDGMENTS
The authors are very grateful to National Natural
Science Foundation of China for financial support of
this key research project (No. 61333006).
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