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Melt Flow Control in a Multistrand Tundish Using a
Turbulence Inhibitor
R.D. MORALES, J. de J. BARRETO, S. LO´ PEZ-RAMIREZ, J. PALAFOX-RAMOS, and
D. ZACHARIAS
Water modeling and mathematical simulation techniques were used to study the melt flow under the
influence of turbulence inhibitors in a multistrand bloom caster tundish. Three different cases were
studied: a bare tundish (BT), a tundish with two pairs of baffles and a waved impact pad (BWIP),
and a tundish equipped with turbulence inhibitor and a pair of dams (TI&D). Chemical mixing of
tracer turbulence diffusion was also simulated and compared with actual experimental results. The
TI&D arrangement showed an improvement of the fluid flow characteristics, yielding better tracer
distribution among the outlets, lower values of back mixing flow, and higher values of plug flow. A
mass transfer model coupled with k-« turbulence model predicted acceptably well the experimental
chemical mixing of the tracer in the water model. The water modeling and the numerical simulation
indicated that the TI&D arrangement retains the tracer inside the vessel for longer times, increasing
the minimum residence time. These results encourage the use of turbulence-inhibiting devices in
bloom and billet casters, which pursue excellence in product quality.
I. INTRODUCTION TI on the fluid flow pattern, tracer diffusion, and tracer
distribution in the different strands of a four-strand tundishMELT flow control in tundishes with one or two strands
of a bloom caster. Other important aspects considered were
using dams, weirs, and baffles has been widely studied using
the melt flow performance comparisons, among the bare
water models.[1–8] Melt flow in multiple-strand tundishes
tundish, MFCD consisting of dams and a waved impact pad,for billet and bloom casters has been studied using water
and the TI itself. In order to obtain these objectives, water
modeling and mathematical simulation techniques.[9–14]
and mathematical modeling techniques were applied simul-More recently, these techniques also have been employed
taneously, reaching useful conclusions in a complemen-to develop turbulence inhibitors. These devices are essential
tary fashion.to decrease fluid turbulence in the pouring region in one-
and two-strand tundishes.[15–20]
Turbulence inhibitors have been shown to be very useful II. WATER MODELING
to avoid slag entrapment, pick up of oxygen and nitrogen
A 1/3-scale model, using the Froude criterion, was con-from the surrounding air during ladle changes, and decrease
structed using transparent Perspex (Bodega de Pla´sticos,downgraded steel during grade changes. It is a usual trend
Mexico) plastic sheets with a thickness of 0.0127 m. Figurethat, similar to other melt flow control devices (MFCD), a
1 shows the geometric dimensions of this model. As can beturbulence inhibitor (TI) should be designed and manufac-
seen, the positions of the outlets are nonsymmetrical withtured on a tailor-made basis. Every TI should be designed
respect to the central axis of both sides of the tundish. Threeaccording to the tundish size, melt depth, flow rate, and
types of tundishes were studied: the bare tundish (BT), atundish design.
tundish with MFCD consisting of two pairs of baffles andIn the present work, melt flow control using a turbulence
a waved impact pad (BWIP), and a tundish with MFCDinhibitor in a four-strand tundish of a bloom caster is thor-
consisting of a TI and a pair of dams (TI&D).oughly studied. In this sense, this is the first report dealing
Design of the high baffles for the BWIP arrangement iswith the employment of a TI in a multiple-strand tundish.
shown in Figure 2(a). Figure 2(b) shows the design for theA multiple-strand tundish presents various challenges such
low dams, while Figure 2(c) shows a scheme of the wavedas being able to maintain the same casting temperature,
impact pad. Similarly, the TI&D arrangement is shown inhomogeneous chemistry, and similar steel cleanliness in
Figures 3(a) and (b). The first one shows the dam designevery strand.
and the second one the TI.The objective in this work was to study the effects of a
The positions of the two pairs of dams inside the tundish
for the BWIP arrangement and those corresponding to the
TI&D arrangement are indicated in Figure 4. Stopper rods
R.D. MORALES, Professor, and J. PALAFOX-RAMOS, Postdoctoral perform flow rate control of fluid, one for each outlet. TheStudent, are with the Department of Metallurgy and Materials Engineering,
operating conditions of the tundish are reported in Table I.Institute Polytechnic National, ESIQIE, C.P. 07300, Mexico. J. de J.
In order to determine the Residence Time DistributionBARRETO, Professor, is with the Materials Graduate Center, Institute
Tecnologico de Morelia, C.P. 58120-Morelia, Mexico. S. LOPEZ-RAMIREZ, (RTD) curves, tracer experiments were carried out using a
formerly Postdoctoral Student, Department of Metallurgy and Materials red dye that was injected in the inlet stream at a time zero.
Engineering, Institute Polytechnic National, ESIQIE, is Researcher, The tracer concentration was measured in two of the outlets,FOSECO INC., 20200 Sheldon Road, Cleveland, OH 44142.
one called the interior (the nearest one to the inlet) and theD. ZACHARIAS, Research Engineer, is with FOSECO INC.
Manuscript submitted October 18, 1999. other one exterior (the nearest one to the end wall of the
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 31B, DECEMBER 2000—1505
(a)
Fig. 1—Geometric dimensions of the water model (m).
(b)
tundish), using two UV spectrophotometers. The output sig-
nals from these apparatuses were fed to a PC equipped with
a data acquisition card provided with software to process
the raw data into dimensionless variables according to well-
known proce-dures.[21]
Thus, assuming that the volumetric flow rates through
the four strands are identical, the amount of injected tracer
flowing out in a period dt through the i strand will be[22].
dmi 5 Ci (t)Qdt [1]
where Ci is the tracer concentration in the outlet i, Q the
volumetric flow rate, and mi the tracer mass at the strand i
(List of Symbols).
Allowing M to be the total mass of the pulse tracer (c)
injected, we obtain, by definition, the following expression:
Fig. 2—Geometric dimensions for the BWIP tundish arrangement (m): (a)
tall baffles, (b) short baffles, (c) waved impact pad.dmi
M
5 Ei (t)dt [2]
model was designed to simulate the fluid flow of waterIntegrating this equation for all strands,
inside the tundish model as well as the chemical mixing
process of the tracer injected by a pulse in the incominge`0 E1 (t)dt 1 e
`
0
E2 (t)dt 1 . . . . 5 1 [3]
stream. It involves the solution of the three-dimensional (3-
or simply D) Navier–Stokes equations of turbulence, the mass transfer
equation, continuity equation, and two equations for the k-«e`0 E (t)dt 5 1 [4] model chosen to represent turbulent viscosity. The equations
were reduced to their finite-difference equivalents by integ-
Once the RTD curve given by Eq. [4] was determined, the rating over the computational cells into which the 3-D
flow parameters were calculated using the methods dis- domain was divided, as shown in Figure 5. Turbulent
cussed in Reference 21. momentum equations were solved to yield steady-state con-
ditions and the turbulent mass transfer equation was solved
under unsteady-state conditions. This is a similar procedureIII. MATHEMATICAL MODELING
to that employed in the physical model, i.e., the fluid is
A. Fundamental Equations allowed to stabilize at a constant volumetric flow rate and
at an arbitrary tune taken as zero, the tracer is injectedTwo cases were considered in this study, the bare tundish
and the tundish with a TI&D arrangement. A mathematical starting its unsteady chemical mixing in the fluid.
1506—VOLUME 31B, DECEMBER 2000 METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 5—3-D computational mesh employed in the mathematical model.
Continuity equation:
(a) ­r
­t
1
­
­xj
(ruj) 5 0 [5]Momentum equation:
­
­t
(rui)1 ­
­xj
(rui uj)52­P
­xi
1
­
­xj
Fmeff1­ui­uj 1­uj­xi2Grg [6]
Mass transfer equation:
­C
­t
1 u
­C
­x
1 v
­C
­y
1 w
­C
­z
5 Deff 1­
2C
­x2
1
­2C
­y2
1
­2C
­z22 [7]
Equation that describes the turbulent kinetic energy:
­
­t
(rk) 1 ­
­xi 1rui k 2
meff
sk
­k
­xi2 5 G 2 r« [8]
Equation that describes the dissipation rate of turbulence
energy:(b)
Fig. 3—Geometric dimensions for the TI&D tundish arrangement (m): (a) ­
­t
(r«) 1 ­
­xi 1rui« 2
meff
ss
­k
­xi2 5
1
k (C1 G 2 C2 r«
2) [9]baffles and (b) turbulence inhibitor.
where
G 5 mt
­ui
­xi 1
­ui
­xi
1
­ui
­xj2 [10]
Effective viscosity is the sum of laminar viscosity and turbu-
lent viscosity:(a)
meff 5 ml 1 mt [11]
Turbulent viscosity is related to the turbulent energy and
dissipation rate of turbulent energy by
mt 5 CDrk2/« [12]
The values for the constants in this k-« model C1, C2, CD ,(b)
sk , and s« are 1.43, 1.92, 0.09, 1.00, and 1.30, respectively;
Fig. 4—Schematics of tundish arrangements employed in this study (m): these values were taken from Spalding.[23]
(a) BWIP arrangement and (b) TI&D arrangement. In the mass transfer equations, Deff 5 Dm 1 Dt is the
effective mass transfer diffusivity, which is the summation
of molecular and turbulent diffusivities, respectively. The
Table I. Basic Parameters for the Water Model turbulent diffusivity Dt is related to the turbulent viscosity
mt byParameter Model
st 5 mt /(rDt) [13]Water volume for 27 ton 0.1475 m3
Water model depth at 27 ton 0.253 m Since turbulent flow generally carries mass over an equiva-
Nozzle penetration 0.065 m lent Prandtl mixing length,[24] this coefficient was assumedWater flow rate 0.02 m3 min21 to equal one. Then, from Eq. [13], we obtain
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 31B, DECEMBER 2000—1507
Dt 5 mt /r [14] explained previously, until reaching the steady state of the
fluid flow. The velocity field calculated was then employed
to solve Eq. [7] for the tracer concentration under unsteady-B. Boundary Conditions
state conditions. Here, it is implicitly assumed that the pres-
Nonslipping conditions were applied as boundary condi- ence of the tracer does not affect the water density to an
tions to all solid surfaces of the tundish including baffles, appreciable extent. The initial condition to solve Eq. [7] is
dams, and interior walls of the tundish. Near any solid sur- stated as follows:
face, there is a very thin laminar sublayer. Between the
laminar sublayer and the turbulent core, there is also a buffer at t 5 0 and x0, y0, z0 C 5
M
Vnozzle
[23]
sublayer, which is in a state between laminar and turbulent
flow. Consequently, for nodes near a solid wall, the so-
where M is the total mass of the tracer and V is the volume
called wall functions are required to calculate the values of
of the water column in the ladle nozzle from the injection
a variable, since in those places, very steep gradients occur. point to the nozzle tip assuming a perfect mixing. The termsIf a node in the 3-D domain is in the laminar sublayer, a
x0, y0, and z0 are the coordinates of the nozzle tip in the 3-linear relationship between the wall stress and the velocity D domain.gradient is assumed:
tw 5 m
Dv
Dn
[15] D. Numerical Solution
The continuity equation, the momentum and mass transferIf the node is beyond the laminar sublayer, the logarithmic
equations, and the initial and all boundary conditions werelaw is applied in order to calculate the wall shear stress:
rewritten in a finite difference scheme using the 3-D mesh
shown in Figure 5. A dense mesh was employed near thevp
v*
5
1
kv
ln (Ey+) [16] tundish bottom and near the tundish walls just to avoid
inconsistencies when the wall function is applied as a bound-
where ary condition. A dense mesh was also employed in the outlet-
longitudinal planes as well as in the proximity of the stopper
v* 5 !twr [17] rods. The total number of cells in this 3-D domain counted
80,000, which ensures reliable calculations of fluid flow and
and mass transfer.
The numerical algorithm used to solve those equations isy+ 5 rv* Dnp /m [18]
known as PISO[26,27] (pressure implicit with splitting opera-
where kv is the Von Karman’s constant (0.42), E is an empiri- tions). This is a time marching procedure: a predictor is
cal constant (9.81) taken from Reference 25, and vp is the followed by one or more corrector steps for each time-step,
velocity of the fluid near the wall. using a noniterative splitting of operations of discretized
The boundary conditions for k and « in this sublayer were continuity, momentum, kinetic energy, dissipation rate of
calculated with the previous knowledge of y+ through kinetic energy, and pressure equations. In this way, the veloc-
ity fields at the end of each step are close approximations
y+ 5
rk1/2p C1/4m Dnp
m
[19] of the turbulent change equations.
A criterion for convergence was established when the sum
where kp is the turbulent kinetic energy at the near-wall grid of all residuals for the variables was less than 1026. Velocity
point p and Dnp is the distance of point p to the wall. Equation fields at steady state were first calculated and later they were
[19] is an empirical fit of turbulent flow data for y+ between employed to solve the mass transfer equation.
values of 10 to 20. In this study, Eq. [15] is used when y+ The mathematical model was run in a workstation Silicon
is smaller than 12, and Eq. [19] is used when y+ is larger Graphics (Silicon Graphics S.A. de C.V., Mexico) Model O2
than this value. with R 10000 processors at the Laboratory for Simulation of
On the top free surface of the bath and in symmetry Materials Processing of IPN-ESIQIE, Department of Metallurgy
planes, the fluxes of momentum and mass, as well as the and Materials Engineering. The computer results were stored
gradients of the turbulent kinetic energy and the dissipation in magnetic tapes to be arranged in a special format for further
rate of kinetic energy, were set equal to zero. analysis by feeding them into commercial plotting software
At the entry jet, the flow profile was assumed to be flat known as Tecplot (Adaptive Research, Alhambra, CA).
and calculated by
Uin 5 Q/Anozzle [20] IV. RESULTS AND DISCUSSION
The inlet values for k and « were calculated with the follow- A. Water Modeling Experimentsing equations:
Figures 6(a) through (c) show the experimental RTDkin 5 0.01U 2in [21] curves for the BT and the tundishes with the BWIP and
TI&D arrangements, respectively, showing the interior and«in 5 2k3/2in /Dnozzle [22]
exterior outlet signals. The BT shows an unequal distribution
of the tracer to both outlets and the minimum residence isC. Initial Conditions smaller in the interior outlet than in the exterior one. The
concentration peak is higher in the exterior outlet and theEquations [5], [6], [8], and [9] were solved together with
their boundary conditions using the auxiliary expressions, difference between maximum concentration time and the
1508—VOLUME 31B, DECEMBER 2000 METALLURGICAL AND MATERIALS TRANSACTIONS B
(a)
(a)
(b)
(b)
Fig. 8—Experimental RTD curves for two distances between the dam and
the entry nozzle using the TI&D arrangement: (a) 0.23 m and (b) 0.24 m.
Table II. Flow Characteristics Results from the
Experimental Total RTD Curves
Arrangement VDead VPlug VMixed tcalc su2 D/UL
BT 0.0755 0.2071 0.7174 304.18 0.2171 0.123(c) BWIP 0.1054 0.2761 0.6185 362.06 0.2427 0.141
TI&D 0.0693 0.3461 0.5846 318.44 0.1961 0.110Fig. 6—Experimental RTD curves for the tundish arrangements: (a) BT,
(b) BWIP, and (c) TI&D.
Fig. 9—Experimental total RTD curves.
minimum residence time is smaller for this outlet. It is appar-
ent from Figure 6(a) that the interior outlet exhibits larger
dispersion data for the concentration of the tracer with some
characteristics of bypass flow.
Using the BWIP arrangement, the RTD curves exhibitFig. 7—Schematic representation of the flow behavior using a step in the
upper side of the dam. considerable improvements,as can be seen in Figure 6(b).
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 31B, DECEMBER 2000—1509
(a) (b)
(c) (d)
Fig. 10—Velocity fields of water in the tundish model: (a) entry plane in the BT arrangement, (b) plane located between both outlets in the BT arrangement,
(c) entry plane in the TI&D arrangement, and (d ) plane located between both outlets in TI&D arrangements.
Although there is still some difference between the minimum distribution in both outlets. This step is expected to influence
the fluid flow by driving it toward the upper surface of theresidence times for both outlets, this difference is smaller
than in the precedent case. The minimum residence time for bath, as is schematically shown in Figure 7. It is envisaged
that in this step flow, the fluid, flowing downstream, firstthe interior outlet prevails smaller than the exterior one.
Both curves show apparent similar statistical dispersion and hits the upper edge of the dam and changes its direction
upward, suffering a further impulse when it hits the step.the curve for the exterior outlet reports an irregular shape
after the concentration peak. This phenomenon was consis- This allows the tracer to follow a longer path, increasing its
residence time inside the tundish.tently observed in all the experimental trials. Furthermore,
it was observed that its origin lies in the fact that the holes Figures 8(a) and (b) show the RTD curves for the interior
and exterior outlets when the positions of the dams arein the multiple-hole baffles promoted the downstream pas-
sage of the tracer by packages. An intense bath surface 0.23 and 0.24 m (one position before and another after the
optimum position whose results are reported in Figure 6(c))turbulence in the pouring box zone was observed.
With the TI&D arrangement (Figure 6(c)), the fluid flow from the entry nozzle, respectively. As seen, in contrast to
the RTD curves when the dams are located 0.235 m fromis markedly improved. The minimum residence times in both
outlets are practically equal and so are the peak concentration the entry nozzle (Figure 6(c)), these new positions change
appreciably the tracer distribution in both nozzles. However,values. These latter values are also higher than the respective
concentration peaks for the BWIP arrangement. Besides it should be said that the flow characteristics for the outlets
in both cases remain superior to those corresponding to thethese improvements, the TI&D arrangement has the advan-
tage over the BWIP that it employs only three pieces in the bare tundish and the tundish with the BWIP arrangement
(compare Figures 6(a) and (b) with Figures 8(a) and (b)).tundish furniture instead of five. The bath surface turbulence
in the pouring box decreased considerably in comparison Table II shows a summary of the flow quantification
parameters for the BT and the tundish with the BWIP andwith the two previous cases.
The special design of the dams in the TI&D arrangement, TI&D arrangements; these values were calculated from the
experimental total RTD curves in Figure 9, using Eq. [3]using a step in their upper side, and their position inside
the tundish play a determinant role to control the tracer and following the procedure of Sahai and Emi.[21] It can be
1510—VOLUME 31B, DECEMBER 2000 METALLURGICAL AND MATERIALS TRANSACTIONS B
(a) (b)
(c) (d)
Fig. 11—Velocity fields of water in the tundish model: (a) interior outlet in BT arrangement, (b) exterior outlet in BT arrangement, (c) interior outlet in
TI&D arrangement, and (d ) exterior outlet in TI&D arrangement.
seen that the TI&D arrangement reduces the dead volume same two planes, respectively, in the tundish with the TI&
D arrangement. At the entry plane of the bare tundish, thefraction, in contrast to the arrangement BWIP. It also
increases the plug flow volume fraction, reducing the mixed fluid observes a recirculating flow with highest velocities,
directed to the upper bath surface, near the wall after strikingvolume fraction. Using these traditional MFCDs promotes
the formation of undesirable zones. Another important flow the tundish floor (Figure 10(a)). In the same plane, the TI
controls the fluid turbulence and the recirculating flowcharacteristic of the TI&D arrangement is that it exhibits
lower fluid dispersion, represented by the dispersion parame- remains, but with smaller velocity vectors directed toward
the tundish floor located near the walls (Figure 10(c)). Inter (D/UL). These results support the contention that the
traditional MFCD are not as effective in controlling the the plane between the outlets, the recirculating pattern
remains as an influence of the high turbulence promoted byflow as the turbulence-inhibiting device. In addition to the
metallurgical and operational advantages of using turbulence the entry liquid jet (Figure 10(b)). The corresponding flow
pattern using the TI&D arrangement shown in Figure 10(d)inhibitors, their employment in multistrand tundishes can
help to obtain homogeneous steel chemistries. Implicit with indicates that the recirculating flow is eliminated, indicating
that transverse mixing is decreased.this there is also the possibility to obtain equal temperatures
and steel cleanliness in all strands of tundishes belonging Water flow characteristics in the planes of both outlets
(interior and exterior) are shown in Figures 11(a) throughto billet and bloom casters, opening a much wider application
of this device. Mainly, billet casters pursuing excellence in (d). Figure 11(a) shows a strong recirculating nonsymmetric
flow, due to the position of the outlets, as indicated by theproduct quality will find this an important tool for flow,
temperature, chemistry, and cleanliness controls. stopper rods, in the plane of the interior outlet of the BT.
Essentially, the same features mentioned previously for the
entry plane are also observed here. The highest fluid veloci-B. Mathematical Modeling of Fluid Flow ties are directed toward the upper bath surface near the
tundish walls. In the exterior outlet, the same flow patternFigures 10(a) and (b) show the velocity field of water in
the entry plane and at a plane located between both outlets is formed, although velocity vectors are smaller because the
fluid loses momentum further downstream.in the bare tundish, while Figures 10(c) and (d) show the
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 31B, DECEMBER 2000—1511
(a)(a)
(b)
(b)
(c)
(c)
(d)
Fig. 13—Front view of the velocity field of water in the tundish model:
(a) outlet plane in BT arrangement, (b) outlet plane in TI&D arrangement,(d) (c) near wall plane in TI&D arrangement, and (d ) near wall plane in TI&
D arrangement.Fig. 12—Upper views of the velocity fields of water in the tundish model:
(a) upper bath surface in BT arrangement, (b) upper bath surface in TI&
D arrangement, (c) center plane of the bath height in BT arrangement, and
(d ) center plane of the bath height in TI&D arrangement.
D arrangement. Figures 13(c) and (d) show the same type
of information for planes located near the wall.
Figures 11 through 13 indicate clearly the three-dimen-For a TI&D arrangement, the velocity vectors do not
sional nature of this flow. The flow is nonsymmetric alsopresent recirculating flow characteristics as can be seen for
in the horizontal planes because of the nonsymmetric posi-the interior and exterior outlets in Figures 11(c) and (d),
tion of the outlets. In the BT, the liquid jet entrains waterrespectively. Flow patterns are very similar in both outlets.
in the pour box area (Figure 13(a)). In the tundish with theFrom Figures 10 and 11, the higher dispersion observed in
TI&D arrangement, there is the formation of a recirculatingFigure 6(a) for the BT, in comparison to the TI&D arrange-
flow, but the velocity vectors are small due to the influencement (Figure 6(c)) and reported in Table II, can be clearly
of the inhibitor (Figure 13(b)). Near the wall, the fluidexplained as follows. In the BT, the fluid keeps arecirculat-
velocities are high and directed upward in a plane locateding flow pattern from the entry plane until, at least, the
near the wall (Figure 13(c)) for the BT, and these velocitiesexterior outlet promoting transverse mixing in addition to
are considerably lower and slightly directed toward thelongitudinal mixing (Figures 12(a), 12(c), 13(a), and 13(c)).
tundish floor (Figure 13(d)) for the tundish with a TI&Meanwhile, using a tundish with the TI&D arrangement,
D arrangement.transverse mixing is only observed in the pouring box and,
after the dam, the fluid behaves as a plug flow.
Velocity fields in horizontal planes are shown in Figures C. Mathematical Model of Mass Transfer12(a) through (d). Figure 12(a) shows the velocity field of
water in the upper bath surface in a bare tundish and Figure Dynamics of chemical mixing of the tracer after 30 sec-
onds of its injection in the ladle nozzle are shown in Figures12(b) the corresponding field in the tundish with a TI&D
arrangement. Figures 12(c) and (d) show the same type of 14(a) and (b) as isoconcentration lines expressed in mass
fractions units for longitudinal-vertical planes. Figures 14(a)information for a plane located at half the bath depth.
Velocity fields in longitudinal-vertical fields are shown and (b) correspond to the jet entry plane for a BT and a
tundish with the TI&D arrangement, respectively. It is seenin Figures 13(a) through (d). Figure 13(a) shows the velocity
field at the outlet plane for the bare tundish and Figure 13(b) that, at this short time, the tracer has been dispersed, reaching
the interior outlet completely and the exterior one partiallyshows the corresponding field for the tundish with the TI&
1512—VOLUME 31B, DECEMBER 2000 METALLURGICAL AND MATERIALS TRANSACTIONS B
(a) (a)
(b) (b)
(c) (c)
(d) (d)
Fig. 14—Front view of the isoconcentration lines of tracer at 30 s. After
Fig. 15—Upper view of the isoconcentration lines of the tracer at 30 s.the injection: (a) inlet plane in BT arrangement, (b) inlet plane in TI&D
After the injection: (a) near the floor plane in BT arrangement, (b) neararrangement, (c) outlet plane in BT arrangement, and (d ) outlet plane in
the floor plane in TI&D arrangement, (c) center plane of the bath heightTI&D arrangement.
in BT arrangement, and (d ) center plane of the bath height in TI&D
arrangement.
in the bare tundish. In the tundish with a TI&D arrangement,
the tracer remains in a mixing process in the entry zone,
and further downstream, it has just passed over the upper
side of the dam. Figures 14(c) and (d) show the same type
of information for the outlet plane in both kinds of tundishes
where the same comments are applicable.
Horizontal views of the chemical mixing 30 seconds after
injection of the tracer can be seen in Figure 15. Figures
15(a) and (b) show the isoconcentration lines in a plane
located near the tundish floor for a bare tundish and the TI&
D arrangement, respectively. In the first case, the tracer has
already reached the position of the interior outlet and is a
little more than halfway from the exterior outlet. In the
second case, the tracer is just exiting from the hole in the
dam.
Figures 15(c) and (d) show the chemical mixing of the
tracer, 30 seconds after the injection, in the upper planes of
Fig. 16—Mathematically calculated total RTD curves.a bare tundish and the TI&D tundish, respectively. The tracer
dispersion has reached the lateral wall of the bare tundish
since the momentum transfer and the turbulence are high
enough to promote transverse and longitudinal mixing pro- outlets. The tracer is still away from the lateral tundish
wall, as can be seen in Figure 15(d). The results of thecesses. In the TI&D arrangement, the tracer is driven toward
the top bath surface, but with a lower turbulence, and the mathematical simulations for the total RTD curves at both
outlets are shown in Figure 16 for the BT and with a TI&isoconcentration lines are deformed by the presence of the
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 31B, DECEMBER 2000—1513
Table III. Flow Characteristics Results from the 4. Tracer diffusion under turbulent conditions was simulated
Calculated Total RTD Curves acceptably well through the mathematical model using
the standard k-« model.Arrangement VDead VPlug VMixed tcalc su2 D/UL 5. These results prove that a simple arrangement composed
BT 0.1309 0.2112 0.6579 284.0 0.3196 0.1992 of a TI and a pair of dams has a better performance
TI&D 0.0785 0.370 0.5515 315.82 0.1596 0.0874 than the complex furniture usually employed in actual
tundishes such as weirs, dams, vortex killers, and sophis-
ticated impact pads.
D arrangement, and the flow quantification parameters are
presented in Table III. These values were calculated from
ACKNOWLEDGMENTSthe calculated total RTD curves in Figure 16 and following
the procedure of Sahai and Emi.[21] The experimental and The authors give thanks to the institutions SNI, CoNaCyT,
the simulated results exhibit similar flow characteristics, as COFAA, and IPN for the partial financial support. One of
can be seen by comparing Tables II and III. Therefore, us (JdeJB) gives thanks to Instituto Tecnolo´gico de Morelia
similar conclusions can be reached from the water model for allowing him a leave of absence at IPN. Thanks are also
and the mathematical simulations in a complementary fash- given to FOSECO INC., whose support was determinant to
ion. Even the calculated curves (Figure 16) and the experi- perform this study.
mental ones (Figure 9) may look physically different. This
supports the contention that the mass transfer model
LIST OF SYMBOLSdescribes adequately the turbulent chemical mixing of the
tracer inside the water model for a BT and a tundish with A cross-sectional area
rather complex furniture. C tracer concentration
From the analysis of Figures 10 through 15 and the visual Ci tracer concentration at strand i
observations of the tracer dispersion during the experimental C1, C2, constants in the turbulence model
trials, brief descriptions about the tracer dispersion in the and CD
tundish with the TI&D arrangement can be made. E empirical constant in Eq. [16]
Just after the injection, the tracer is driven upward to the Ei RTD curve at strand ibath surface without appreciable turbulence. At an interme- Dm molecular tracer diffusivitydiate time after the injection, the tracer strikes the baffle Dt turbulent tracer diffusivity
and is re-directed again toward the top bath surface and Deff effective tracer diffusivitydriven along the tundish length. When the front of the tracer G generation term (Eq. [10])
dispersion reaches the level between both outlets, the fluid k turbulent kinetic energy
has lost momentum and the tracer descends toward the tun- mi mass of tracer exiting through strand idish floor. Once there, the tracer is diffused toward the M total mass of tracer injected into the vessel
outlets obtaining, in this way, a very similar mass of tracer P pressure
in both outlets. Moreover, the hole in the dam, located in Q volumetric flow rate
the opposite side of the outlets, removes the dead zones very t time
efficiently, which would form downstream otherwise. tcalc mean calculated time
These fluid flow characteristics are observed neither in VDead dead volume fraction
the BT nor in the tundish with a BWIP arrangement; these VPlug plug volume fractiondevices were not as effective as the TI&D arrangement. VMixed mixed volume fraction
v+ as defined in Eq. [17]
u, v, w velocity vectorsV. CONCLUSIONS
y+ as defined in Eq. [18]
Water and mathematical modeling techniques have been
Greek Symbolsapplied to study the flow of liquid steel in a multiple-strand
« dissipation rate of the turbulent kinetic energytundish of a bloom caster and the conclusions derived from
m fluid viscositythe results are as follows.
meff effective fluid viscosity
1. The employment of an arrangement consisting of a TI mt turbulent fluid viscosity
and a pair of dams is more effective to increase the plug rfluid density
volume fraction than a BT or a tundish using two pairs st turbulent Schmidt number
of dams and a waved impact pad. s« constant in the k-« model
2. The combination of a TI and a pair of dams yields very
similar RTD curves for the four strands of this tundish.
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1514—VOLUME 31B, DECEMBER 2000 METALLURGICAL AND MATERIALS TRANSACTIONS B
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