Jo_et_al_1993

Prévia do material em texto

Inclusion Behavior and Heat-Transfer Phenomena 
Steelmaking Tundish Operations Part I. Aqueous 
in 
Modeling 
S. JOO and R.I.L. GUTHRIE 
An in-house computer code, METFLO 3D, which can model three-dimensional (3-D) turbulent 
flow, heat transfer, and inclusion flotation, has been developed for steelmaking tundishes. Also, 
sensor equipment has been developed for the continuous detection of particles suspended in 
aqueous systems. The probe, based on the resistive pulse principle, withdraws a continuous 
sample of the feed water to be monitored. A full-scale (isothermal) water model tundish (Stelco 
Research Centre, Burlington, Canada) was used to test experimental data on particle separation 
within the tundish. These experimental data were compared with predictions calculated by the 
mathematical model developed for tundish flows, and satisfactory agreement was achieved. 
I. INTRODUCTION 
TUNDISHES act as distributors of liquid metal be- 
tween the ladle and molds of continuous casting ma- 
chines. They can also act as removal tanks for nonmetallic 
inclusions within liquid steel. To study such matters, de- 
tailed velocity and turbulence fields are required, these 
being specific to a given tundish design, metal flowrate, 
etc. 
There have been, in recent years, a number of studies 
on fluid flow and/or inclusion separation behavior for 
tundish arrangements, using physical (water) models t~ 61 
and/or mathematical models.F ~21 
Using a full-scale water model tundish, Kemeny et al. lu 
carried out a simple fluid dynamic analysis of tundish 
flows with the aim of improving steel cleanness by max- 
imizing fluid retention times. They observed that the flow 
patterns were improved using combinations of dams and 
weirs and that the minimum retention time could be in- 
creased. Tanaka and Guthrie 151 developed a probe based 
on a Coulter counter technique L~gl to detect nonmetallic 
inclusions in aqueous systems. Nakajima 16J extended the 
use of such probes to molten steel systems. Both authors 
analyzed the separation behavior of inclusion particles 
in terms of "tank reactor" models. 
Lai et al. 181 carried out both computational and phys- 
ical modeling of three-dimensional (3-D) fluid flows in 
a symmetrical twin-strand tundish and compared one to 
the other. Szekely and E1-Kaddah t7j also numerically 
predicted 3-D tundish fluid flows and the retention time 
distribution (RTD) curves with and without flow control 
devices (weir/dam arrangements), using the commercial 
PHOENICS code. He and Sahai t9~ performed a compu- 
tation of fluid flows in tundishes under the condition of 
sloping sidewalls, comparing the effect of these with 
vertical walls in terms of flow patterns and RTD curves. 
Tacke and Ludwig I~11 solved a transport equation for par- 
ticles, taking into account their specific buoyancy, con- 
vection, and turbulent dispersion, again using the 
S. JOO, formerly Doctoral Candidate, Department of Mining and 
Metallurgical Engineering, McGill Metals Processing Centre, McGill 
University, is Senior Researcher, Research Institute of Industrial Science 
and Technology, Pohang, Korea. R.I.L. GUTHRIE, Macdonald 
Professor of Metallurgy, is Director, McGill Metals Processing Centre, 
McGill University, Montreal, PQ, Canada H3A 2A7. 
Manuscript submitted March 15, 1990. 
PHOENICS code. There, particle concentration fields 
and the percentage of particles removed were calculated. 
However, none of these authors addressed the question 
of thermal natural convection on flows and inclusion be- 
havior in tundishes. Similarly, the application of math- 
ematical models to tundish design with respect to geometry 
of tundish, location of flow control devices and their 
numbers, etc. has yet to be tackled. More recent con- 
tributions by Joo and Guthrie tl~ and by Sahai and 
Chakraborty, t22j while this article was in revision, con- 
firm the thermal stratification phenomena that take place, 
both during steady operations tl~ and during sequence 
casting with thermal cycles generated by cooling steel in 
teeming ladles, t~71 
Meanwhile, most major steel companies still study the 
change of fluid flow and inclusion particle behavior with 
or without flow control devices using isothermal phys- 
ical modeling in large plexiglass water models. Flow vi- 
sualization with dye, residence time distribution studies, 
and detection of inclusion particles in such physical models 
certainly provide useful information. Nevertheless, such 
full-scale physical modeling often requires expensive 
equipment and significant time and effort. 
On the other hand, computations of 3-D fluid flow are 
becoming less expensive and are widely applicable to 
tundish performance. These can provide detailed flow 
information, enabling one to predict inclusion flotation 
together with temperature distributions within tundishes. 
The prediction of such phenomena in a tundish vessel 
by mathematical modeling is useful for determining the 
best design of the vessel with respect to size, shape, and 
the placement of flow control devices (e.g. , weir/dam 
arrangements, baffles, etc.) for a given set of operating 
parameters (e.g., metal flow rate, input temperature, etc.). 
However, their validity has not yet been clearly dem- 
onstrated either through direct comparisons with physi- 
cal models or from actual plant data. It is therefore 
necessary that such predictions continue to be paralleled 
by proper experiments and the results compared with each 
other. 
In the present experimental work (part I), particle re- 
moval rates could be studied thanks to the "in-house" 
development of a novel electric sensing zone (ESZ) sys- 
tem. t~41 This system was capable of detecting inclusions 
on-line and in situ ( i .e. , within the water-filled tundish) 
METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--755 
and provided number densities and size distributions of 
inclusions within the fluid. A full-scale water model of 
a dual-purpose tundish (i.e., single strand for slab cast- 
ing and twin strand for bloom casting) at Stelco Research 
Centre was therefore used to test experimental data against 
computations. A general purpose in-house computer code 
for 3-D turbulent flows in ladles and tundishes, METFLO 
3D, was develope dI15] for the numerical predictions. 
In parts II and III of this series of articles, the roles 
of heat transfer in steel systems (part II) and tundish de- 
sign philosophies (part III) are tackled on the basis of a 
validated code and set of procedures. 
I I . THEORY 
A. Fluid Flow 
The governing equations of continuity and momentum 
balance are represented by 
0 
- - (pUi) : 0 [ 1 ] 
Oxi 
and 
- - - - ~- - - Ixef f ~t_ ~- Pgi [2] 
OX i OX i OXj \ OXj OXi/ .J 
using Cartesian coordinates and index notation. 
For modeling turbulence, the k-e two-equation model 
by Jones and Launder ~161 was used. There, turbulence is 
expressed by two transport equations for the turbulent 
kinetic energy, k, and its rate of dissipation, g. The re- 
lation between the turbulent viscosity Ix, and these two 
characteristics of turbulence is 
Ix, = c~pk21 i [3] 
The governing equations for k and e are 
Oxi pIx~ffk = G - p i cr k 
[41 
and 
puig = (CLOG - C2pC) /k 
O" e 
[51 
where the effective viscosity comprises the laminar and 
turbulent components 
txe. =/x +/x, [6] 
and the viscous stress generation terms, G, are given by 
Ouj ( Ouj __Ou'~ 
G = ~, - - + [7] 
~xi \ Oxi OxJ 
The five empirical constants appearing in Equations 
[3] through [5] were adopted on the basis of suggestions 
by Launder and Spalding, t~7J as given in Table I. 
Tab le I. Constants Used in the k - f Mode l 
C 1 C2 Co o- k o'~ 
1.430 1.92 0.09 1.00 1.30 
B. Energy Conservation 
Under steady flow conditions, the general energy con- 
servation equation for incompressible, nonviscous liquid 
flow can be expressed as 
Oxj Oxj Fe,r [8] 
The effective diffusivity concept was used to represent 
the combinedeffect of molecular and turbulent thermal 
diffusion. The exchange coefficient, Fe,r, is given by 
Ix Ix, 
F~.r = - - + - - [9] 
o" r o-t, r 
C. Dispersion of Fine Particles 
Stokes law provides that the terminal rising velocity, 
us, of a spherical particle in steel is related to size, buoy- 
ancy, and steel viscosity according to 
Apgd 2 
u, - [10] 
18IX 
Here, Ap is the density difference between the fluid and 
the particle, g is the acceleration due to gravity, d is the 
particle diameter, and IX is the viscosity of the fluid. 
Our mathematical model of inclusion population dis- 
tribution employs a standard mass conservation equation 
describing spatial distributions in the mass fraction of 
fine particles within a fluid control volume (Eulerian). 
Thus, in the presence of a steady flow field, the mass 
fraction of particles of a specific size can be expressed 
according to a species conservation equation of the form 
OC O[p(uj-Usj)C] O( O~xj) 
- - + - Fe. c [11] 
Ot Oxj Oxj 
where the effective diffusivity, ['e,C, can be written by 
IX Ixt 
Fe.c = - - +- [12] 
o" c crt. c 
One will note from Eq. [11] that the transient and con- 
vective terms balance the diffusive term to the right-hand 
side of Eq. [11]. Since the flotation of micron-size fine 
particles in metallurgical processing vessels would seem 
to be subject to Stokes law, their dispersion within such 
a system can be described via a 3-D convection-diffusion 
type mass transport equation. The solution of such equa- 
tions requires that the distribution of flow variables (u, 
v, and w) and turbulence variables be known a priori. 
The possibility of inclusions directly affecting the flow 
within the tundish can be discounted owing to their rel- 
atively low volume fraction within the liquid. 
756- -VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B 
D. Boundary Conditions 
1. Fluid flows 
At the tundish walls, the momentum transport pro- 
cesses were modeled using the wall function method, t~71 
For velocity components normal to the wall, zero flux 
or impermeability was imposed. For velocity compo- 
nents parallel to the wall, nonslip conditions were im- 
posed at the wall. 
At the symmetry planes and the free surface boundary, 
which is assumed to be flat, the normal velocity com- 
ponents and normal gradients of all other variables were 
set equal to zero. At the jet entry, the velocity compo- 
nent perpendicular to the free surface was calculated from 
the volumetric flow rate and the cross-sectional area of 
nozzle (ladle shroud): 
Ui. = Q/A .... l~ [13] 
Similar boundary conditions were imposed at the tundish 
outlet nozzles. 
The inlet values of k, the level of turbulence kinetic 
energy, and ~, the rate of turbulence energy dissipation, 
were approximated from the following relationships: 
kin = 0 .0 l U~n [14] 
and 
= b3/211; I [15] ~in n'in /l~'nozzle 
2. Inclusion behavior 
In order to simplify the problem of inclusion flotation, 
the following assumptions were made in the mathemat- 
ical formulation. 
(1) Particles are spherical, and the surface tension of 
particles has no effect on float-out velocity. 
(2) The motion of inclusions/fine particles (in the range 
of 20 to 150 #xm in diameter) follows Stokesian behavior 
within the whole region of a tundish. At the top surface, 
the vertical flux of inclusions leaving the aqueous phase 
was taken to be given by s~/' = Us C* where C* repre- 
sents the dimensionless concentration level of inclusions 
(Ci = nilni, o) at the upper boundary layer to the flow. 
This was approximated by taking the value of C* to be 
that at the first scalar nodal point below the surface. 
(3) There was no modeling of any interactions and/or 
agglomeration/coalescence phenomena between inclu- 
sion particles within the tundish. While the authors be- 
lieve that coalescence is an important factor in the entry 
region where turbulence is high, they suppose that sub- 
sequent coalescence would be minimal in the quieter re- 
gions of the flow. Consequently, if the size distribution 
in the entry region can be specified, subsequent changes 
(in this model) are exclusively related to vertical float- 
out of these variously sized inclusions. 
(4) The sidewalls and bottom of the tundish, as well as 
flow modification devices, are all nonwetting (reflect- 
ing) to inclusions within the melt. Again, this is a sim- 
plification, inclusions such as alumina being known to 
be highly ferrophobic and likely to precipitate in regions 
of flow reversal. 
(5) Possible erosion of refractories was not taken into 
account. 
(6) An adiabatic free-surface condition was assumed for 
the aqueous system based on visual observations of in- 
clusion float-out behavior (i.e., these hydrophyllic par- 
ticles did not form a separate upper phase). 
The particle concentration was normalized to a value 
of unity at the inlet nozzle. Thus, the resultant concen- 
tration at the outlet nozzles also represents the residual 
ratio of inclusions. 
E. Numerical Solution Procedure 
As already noted, a computer code for 3-D rectangular 
and cylindrical geometry was developed at McGill by 
the authors, llS'2u The partial differential equations for ui, 
k, ~, T, and C were discretized using the finite integral 
volume method employing a hybrid differencing 
scheme. 1~81 The whole set of equations was solved via a 
semi-implicit tri-diagonal matrix algorithm marching 
scheme coupled with a Gauss-Siedal routine. The SIMPLE 
algorithm was used to solve the pressure field, through 
simultaneous satisfaction of the continuity and momen- 
tum equations, within each volume element. 
Only a symmetrical half of the model tundish was 
considered for the present computations. The domain was 
divided into a nonuniform grid of 17 (vertical) x 40 
(longitudinal) • 16 (transverse) in the three orthogonal 
directions. Figures l(a) and (b) illustrate the effect of 
longitudinal grid spacing (which was the coarsest rela- 
tive to vertical and transverse gridding) on the accuracy 
of flow field predictions. Thus, Figure l(a) shows fluid 
vectors along the vertical axis of the penetrating jet, while 
Figure 1 (b) gives corresponding vectors for liquid within 
the vertical axis of the exit port to the tundish. Such tests 
show that the grid field chosen was sufficiently fine to 
render flow field computations independent of grid size. 
The computer runs for the isothermal conditions were 
carried out on a desktop microprocessor (IBM-AT) fitted 
with a Definicon system of 8 MB RAM and 20 MHz 
clock speed. Converged solutions were obtained after 600 
to 1000 iterations requiring 10 to 16 hours machine time. 
III. EXPERIMENT 
A. Experimental Equipment 
The full-scale model tundish at Stelco's Hilton Works 
was constructed of transparent plexiglass, its walls being 
outwardly inclined at an angle of 10 deg to the vertical. 
Filled to a height of l. 1 m, the tundish measured 5.19 m 
in length and 0.68 m in width at the bottom and 1.07 m 
at the free surface. Figure 2 illustrates the experimental 
arrangement used for inclusion detection studies. It con- 
sisted of the full-scale plexiglass tundish, a ladle, and a 
slurry injection system supplying particles at a constant 
feeding rate, together with the novel ESZ system for the 
detection and counting of particles and a personal com- 
puter to record the data sets acquired and to provide par- 
ticle frequency versus size distribution curves. 
For simulating actual inclusions in molten steel, hol- 
low glass microspheres, with an appropriate number 
density of 108 particles/m 3, over the size range 20 to 
110 #xm, were fed continuously at a feeding rate of 
0.5 L/min into the tundish through the inlet shroud. 
The specific density of the glass microspheres was 
METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--757 
1.Z 
E 
"~ 1,0 
.9. ~ 
.~ 0.8 
> 0.1~ 
'8 
"5 0.4 
3 
O.Z 
0.0 
0 .0 
17,~16 
17x4O~le 
~=. . . tundish 
A i , �9 I I 
02 0.4 O.O0.8 
Dis tance f rom sur face of liquid in tundish (m) 
(a) vertical axis of the entry jet 
1.0 
0.10 
E 
O.l~ 
o 
�9 ~ 0.08 
o 
"0 
�9 --~ 0.~ C 
0.0 
........... 17~Z9~ I �9 
. . . . . . . 17x,,~x I 8 
17xalOx10 
17x4~m,c le 
: : : : : : : : : : : : : : : : : : : : : : : : : . . . . . . 
02 0.4 O.O 0.8 
Dis tance f rom sur face of l iquid in tundish (m) 
tundish 
bottom 
L_. 
i 
1.0 
(b) vertical axis of the exit port 
Fig. 1--(a) and (b) The effect of grid spacing on the accuracy of 
flow field predictions. 
Ladle Mixing box 
~ , Stopper 
I E.S.Z.Uo , ). I I 
/ 
[ Plotter Computer I [ Printer I 
Personal 
Fig. 2--Schematic diagram of experimental arrangement. 
295 kg/m 3. The important parameters and properties of 
the present model prototype tundish are summarized in 
Table II. 
B. ESZ Technique 
It is appropriate to briefly describe the principle, il- 
lustrated in Figure 3, of particle detection by the ESZ 
method, which began with the invention of Coulter 
counters. ['9] When small nonconducting particles pass 
through an electrically insulated orifice, the electrical re- 
sistance of a fluid electrolyte flowing through this orifice 
increases in direct proportion to a particle's volume. 
Voltage pulses generated in the presence of an electrical 
current can then be measured and both the number and 
size of particles counted. 
The signal produced consists of a steady voltage base- 
line with a bell-shaped transient related to a particle's 
passage through the ESZ. The change in resistance, AR, 
caused by the introduction of a nonconducting particle 
into an orifice is given by DeBlois et al.: t2~ 
4pd3 F( d ~ 
~kR = 7TD4 \~/ [ 16] 
where p is the fluid's electrical resistivity, d is the par- 
ticle diameter, D is the orifice diameter, and F(d/D) is 
a geometric correction factor. It has been proposed by 
DeBlois that this correction factor be expressed as 
As most of the time only particles smaller than 40 pct 
of the orifice diameter can be analyzed without frequent 
orifice blockage, the error involved in ignoring this 
correction factors is, in the worst case, on the order of 
5 pct. Consequently, F(d/D) is often taken as unity. 
The ESZ device developed for this work is shown 
schematically in Figure 4. It consists of a glass probe for 
sampling the liquid, a current feeding circuit, and signal 
processing analysis equipment. A high-pass filter (HPF) 
removes the DC content of the signal taken at Rb, and 
the AC content is first linearly amplified to bring the 
signal amplitude to a suitable level and then logarith- 
mically amplified to increase the detection efficiency of 
small particles. A peak detector device is used to rec- 
ognize pulses, and this triggers the pulse height analyzer 
(PHA) to measure, sort, and count them, thereby pro- 
viding particle size distribution data. A microcomputer, 
connected to the PHA, was used for data acquisition 
control and for storage. 
Taking the difference of the potentials across Rb be- 
tween the case of no particle within the ESZ (resistivity 
of the orifice = Rorinoe) and that when a particle is present 
(resistivity of orifice = Rorifice + ~) and noting that 
~g "~ (e b + eorifice ) 
it is readily shown that the variation of potential at Rb, 
relative to a change in orifice resistivity, is given by [6] 
Rb 
AV - I" AR [18] 
eorifice + R b 
758--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B 
Table II. Important Parameters and Properties of Model and Prototype 
Model Prototype 
Geometry tundish length 5.19 m 5.19 m 
tundish depth 1.10 m 1.10 m 
bottom width 0.68 m 0.68 m 
surface width 1.07 m 1.07 m 
Fluid properties liquid water steel 
temperature 15 ~ 1580 ~ 
density 1000 kg/m 3 7000 kg/m 3 
viscosity 1.14 x 10 -3 kg/ms 6.7 x 10 3 kg/ms 
volumetric flow rate 6.9 • 10 -3 m3/S 6.9 • 10 -3 m3/s 
Inclusion properties inclusions glass microspheres AI203 and/or SiO2 
size range 20 to 110 p.m - - 
density 295 kg/m 3 ---3000 kg/m 3 
INCLUSION 
PARTICLE d 
oooo Io 
1 2 ~ zt . . . . . . . . 5 ............... 
1ram 
SIGNAL , 
............... AV /L" ~ BASE 
LINE 
T IME 
Fig, 3--Principle of particle detection by the ESZ technique. 
Vp=9V 
I Ii 
(4 (+) 
- . 
- PROBE _ �9 
~ AblIVI:ETER 
Pre-~plifier ~1 pe~: deteet~r 
lo p,i r 
Fig. 4--Schematic diagram of the ESZ system for aqueous systems. 
METALLURGICAL TRANSACTIONS B 
where Rb is the ballast resistance at which the potential 
is taken, Ronnce is the resistivity of the ESZ with no par- 
ticle present, and I is the current through the orifice. The 
resistance, AR, is given by Eq. [16]. The accuracy of 
this technique depends on a number of factors, the most 
sensitive being orifice diameter variability as well as 
variations in aqueous electrical conductivity. A special 
circuit for aqueous systems was adopted to ensure that 
the voltage drop across the ESZ was maintained inde- 
pendent of water temperature and source (e.g., Montreal 
water vs Toronto water). Generally, the volumes of par- 
ticles sensed are expected to be accurate within 8 pct of 
their true volumes (or diameters within 2 pct). 
The voltage pulse measurement system operated as 
follows: the voltage difference between the two elec- 
trodes was carried to an oscilloscope (Tektronics No. 
5223) which allows one to observe electrical signals (i.e., 
voltage pulses) and also serves as a preamplifier. Typical 
pulses could be observed and validated from the oscil- 
loscope's traces. Preamplified signals were then carried 
to a logarithmic amplifier (TRACOR-NORTHERN* No. 
*TRACOR-NORTHERN is a trademark of Noran Instruments, Inc., 
Middleton, WI. 
TN1246) which was used as a peak detector. The pulse 
height analyzer was a multichannel analyzer (TRACOR- 
NORTHERN No. TN7200) which provided a 512-chan- 
nel histogram of particle size distribution. These data, 
acquired over preselected time periods, were then trans- 
ferred to an IBM-compatible personal computer and saved 
on disk. 
C. Measurement of lnclusions 
Once the water level in the tundish had been estab- 
lished for a steady flow of liquid at 1.1-m bath depth, 
glass bubbles were fed continuously into the tundish 
through the inlet shroud. The separation behavior of par- 
ticles was then measured using the ESZ method just 
described. 
Alternate sensing of particles over 10-second intervals 
at the inlet and outlet nozzles to the tundish was carried 
out, until a total data acquisition time of 60 seconds had 
been accumulated for each nozzle. The data sets thus 
VOLUME 24B, OCTOBER 1993--759 
acquired were transferred to an IBM compatible personal 
computer and saved on diskettes, using a data acquisi- 
tion code for the TN-7200 multichannel analyzer devel- 
oped by Sebo et al. 041 Data on particle population densities 
were monitored for about 40 minutes. This includes all 
particles greater than 50 /zm in diameter which were 
counted. 
Figure 5 shows a typical comparison of the PHA re- 
cordings of particles at inlet and outlet nozzles. The upper 
curve provides the number and size distribution of par- 
ticles at the intake to the tundish, while the lower curve 
gives the number of such particles leaving in the ef- 
fluent. The relationship between channel number and in- 
clusion diameter is given by I61 
10 oh#/64o 
d = [lOOk(T)]J/3 [19] 
where k(T) assumes a fixed value when the temperature 
and amplifier gain are constant. Its value can be obtained 
directly, rather than by theory, by passing particles of 
known size distribution through the ESZ system. 
Figure 6 plots the relative number of particles at the 
intake and outlet ports to the tundish vs time. It can be 
seen that the particle number feeding rate was constant 
during the course of an experiment. It is noteworthy that 
pseudo-steady state was only reached after about 25 min- 
utes (i.e., three mean residence times) for the output curve. 
Details of experimental results will be described in the 
following sectorsfor comparison with theoretical 
predictions. 
the central longitudinal plane (plane A), the inlet vertical 
plane (plane B), and the outlet vertical plane (plane C) 
are given in Figure 7. As seen, the predicted flow pat- 
terns agreed well with the observations. It is appropriate 
to note that the mean speed of flows within the tundish 
was predicted to be 4.8 mm/s , while the measured mean 
flow speed was reported to be about 5 mm/s on the basis 
of laser doppler anemometry measurements. ~8~ 
General features of the flow field induced in the Stelco 
full-scale water model tundish (isothermal condition) when 
no flow control devices are employed are indicated by 
the predicted vector plots in Figure 8. Figure 8(a) pre- 
sents an isometric view of the flows generated in a half 
section of the tundish, and these may be interpreted in 
terms of Figure 8(b), where a collage of two-dimensional 
plots of velocity components along selected longitudinal, 
transverse, and horizontal axes of the tundish are given. 
IV. RESULTS AND DISCUSSION 
A. Fluid F lows 
In order to verify the code, a computation was carried 
out for a rectangular 1/6 scale water model tundish, Jsl 
which measured 1.16 m in length, 0. t67 m in width, 
with a filled height of 0.214 m. The water flow rate was 
19 L/min. Comparisons between predictions and obser- 
vations of the flow patterns in some selected planes of 
Fig. 6 - -Changes in the number density of particles with respect to 
time, monitored at inlet (input) and outlet (output) ports. 
Fig. 5- -Compar ison of PHA recordings of particles at inlet and out- 
let nozzles. 
Fig. 7- -Compar ison of predicted flow vectors and flow visualization 
with silk tuft. 
760--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B 
>O. SM/S ~ >0. 1H/S -- =O. 05M/S 
]1N/ i i iT i i i i : :: : 
J ' " " t ; ' " " . . . . . . . . . . . . " ' . . . . . / 
1 -l- 
f l l CENTER 
~ . . . . ~.~.o.:~ at.":- : : : : : : : : : : : : : : : : : : : : : : 
IL'k~... . t,f t= , /~ f I , . . . . 
~ , . fPT iT j / .7_ / x . . . . ; ' ' ' : , " . . . . 
�9 " -~ . = . 
"0 , , 
*<' , , ~,. - .~ - ~.-,:-... o, . . . . ,, o . . . . . . . . . . . . . . . . . . . . . . 
"" "~".' ~,"" ":~.~ i l ' , o i l . . . . . . . . . . . . . . . . . . . . . . 
"~,~.~.r ," : , :" . . , 0 , 
. . . . . . . . . . 7 t:. ....... il titl I . . . . . . . . . . . . . . . . . I l l i l l l I l l i l i l . . . . . . . . . " F 
CI INLET Ol H IDDLE E1 tIUTLET 
_ . - - : ?" : : : : .: : : : : := : : ~ 
I - - . . - - : : : : : : : : : : : : : - - : : : : " - L ' . : ' . : : : : : ' . : : ' . ' . " . : ' . : " =_,.=_.. - - - - - :.. :. :. " - ' := - " : i 
F l SURFRCE 
G] BflTTOH 
(b) 
Fig. 8 - - (a ) An isometric view of flow fields predicted in the longitudinally bisected single-strand water model tundish (isothermal conditions) 
of slab casting without flow modification device. (b) Predicted flow fields in some (A) and (B) selected longitudinal planes, (C) through (E) 
transverse planes, and (F) and (G) horizontal planes for the single-strand water model tundish (isothermal conditions) with no flow modification 
device. 
While scientific flow visualization is by far the most 
informative way of presenting the data, t~~ careful in- 
spection of the flow fields shows that the entering jet 
hits the bottom of the tundish and then flows down- 
stream or sideways toward the walls of tundish. This ris- 
ing fluid then moves up the tundish sidewalls to the free 
surface, part moving downstream in the direction of the 
exit and the rest recirculating back toward the incoming 
jet. It is clear that maximum velocities drop significantly 
with increasing distance from the incoming jet. Indeed, 
at the edge, near the exit, the flow becomes practically 
motionless. 
The incoming jet's velocity through the ladle shroud 
was 1.13 m/s , while local velocities in the tundish 
varied from 3 to 100 mm/s. The average flow veloc- 
ity in this full-scale tundish was computed to be only 
22 mm/s. Figure 8 also provides a view of flow char- 
acteristics within the tundish. The incoming jet generates 
a back-mix flow (recirculating flow) region and a flow 
toward the exit nozzle which has plug-flow characteristics. 
Weir and dam combinations were next introduced into 
the tundish in order to obtain flows that were potentially 
more conducive to inclusion float-out. The length of weir 
chosen penetrated to 0.8 m below the free surface, while 
the height of dam chosen was 0.45 m from the bottom. 
The separation distance between the weir and dam was 
0.3 m. These weir and dam combinations were used at 
1/3Lr 1/2Lc, and 2/3Lc so that their optimum place- 
ment could be determined. (Lc represents the distance 
between inlet and outlet nozzles, 3.37 m.) 
Figures 9(a) and (b) show the velocity fields given a 
1/2Lc placement of the weir and dam arrangement. The 
METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--761 
- -~ >O. 5M/S " - " >O. 1M/5 -" =0.05M/5 
= : . : . . : . ; . . . . . . . . . 
141 " , r ' - J vu" f . . . . . nn, , . . . . . . . . . . . . . . . . - 
I f 5_" I~ , ' , ' , ' " , IF ~' . . . . . . . . . . . . . . . / 
I 9 - '~11td r o ; o ltp ]~ . . . . . . . . " . . . . . . I 
" - I - R) CENTER l 
.ow"NG""~176176176176 : 00o, m, , , ~---..-,,-,~--------.rr r-~--- ------------------.I 
F .M.D. : 112 I_( we i r /da . . . . ang . . . . t ~j0##00 . . . . ; l i t . . . . . . . . . . . . . . . . / 
/ , ,~ , ! . . . . . . . . . . . . . . . . 
~ . . . . . . . / 
B) SIDE HRLL 
ii,:dk:,il .,ttln;th;l 
~,'ll|ll4;/ I~,, , .~(l 
i! e C::, ) MIDDLE 
,'. 
(a) 
~l l i *uoHgO 
BI~I I I I I I 
i~mo~me 
i~ Ooe 
I 
.~=. : . . ! . , . -~ z=== . . . . . . . . 
F) SURFRCE 
GI BOTTOM 
(b) 
Fig. 9 - - (a) An isometric view of flow fields predicted in the longitudinally bisected single-strand water model tundish of slab casting with weir/ 
dam arrangement placed at 1/2 Lc. (b) Predicted flow fields in some (A) and (B) selected longitudinal planes, (C) through (E) transverse planes, 
and (F) and (G) horizontal planes for the single-strand water model tundish with weir/dam arrangement placed at 1/2L,,. 
flow pattern predicted for the region of the entering jet 
was similar to that for no flow controls. As seen, once 
liquid reaches the weir, part of it generates an ascending 
flow up the weir's vertical face, swirling backward to 
the inlet jet. Some of the liquid flows underneath the 
weir and then vertically upward toward the free surface 
between the weir and the dam. This flow then moves 
downstream toward the exit nozzle. The flow down- 
stream of the dam/weir arrangements tends to exhibit 
more stable plug flow characteristics vis-a-vis the no flow 
control flows. 
Computations were also carried out for a tundish set 
up for twin bloom casting. The geometry and boundary 
conditions were taken to be exactly the same as those 
for single slab casting, but at a volumetric flow rate of 
0.005 m3/s vs 0.0069 m3/s. 
Figure 10 provides isometric views of the flows de- 
veloped within a full-scale water model tundish for no 
flow control and flow control, respectively. The flow 
patterns within the tundish are similar to those for the 
single-ported slab casting arrangement, except that ef- 
fluent occurs at two outlet nozzles. It can be seen that 
the flows will be weaker than those for their slab casting 
operations, owing to the smaller volumetric flow rate at 
the inlet nozzle. 
B. Particle Dispersion and Separation 
The entrainment rate of inclusion particles into the mold 
through the outlet nozzle of the tundish can be repre- 
sented by the residual ratio of particles defined as 
Nout 
R = [201 
Ni. 
762--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B 
0 o 
i ~ . DOUBLE PORT WATER MODEL TUNDISH 
~'~\ FlowRate : 0.005 m3/s 
~"~-~'~'~ ~"~,~ " LIs- I mm/s 
0.8 
~--~.::- ,:.,',:q .,-..~ ~% ~-~"-' , ' , " - ' . :- '~ ." .. o Us-2mm/s 
a 0.6 
"='~"~: ~Z=~ "~ : " " " "" "% ~ 
i i!i -"%. 04 ~- ' - : -~ ~~: : : . : - ' - . . . . 
=.'-.,.~'~,~,~,'~-.~-..,~'~, ...,.....-.. .. 
"% ~ ~ : : : : ' ~ L . . . . . . . . . . . , . . . . . 03 
'%'Co " " "'q ,~""b'" ":" ' : ' : , : - , " 
. ,9~ �9 , ,~, /,,.'54 ,.~'.,",,',,?, ".,:'.,',.:',. 
Tlnw(mln) 
- . : . . ,x :, .~ " " :: ~:~ (a ) no f low cont ro l 
�9 ,:- ~ M ~. - : .. Us - l .~Vs 
~'~' , :.:" ~ . ~ , " , t . ~ : / 
"% ' : ' : :- < ' : ' : ":":~ "~":b. ' U~=2mm/s 
-.-. , "%.% 
" ":::' "~"~ 0.4 
Fig. 10 - -An isometric view of flow fields predicted for a half vol- 
ume of the water model tundish set up for twin bloom casting with 
(a) no flow control and (b) flow control. 
O 
O 
& :, 
Q: ~ u O 
02 
0.0 
0 
where N~. and No.t denote the number density of inclu- 
sions at the inlet and outlet nozzles, respectively. 
A comparison of inclusion residual ratios (i.e., those 
inclusions still present in the effluent stream expressed 
as a fraction of those entering) with experiments in the 
water model is provided in Figure 11. As seen, good 
agreement was achieved between predicted and mea- 
sured R values. It is emphasized that these data refer to 
quasi steady-state conditions, following the continuous 
injection of inclusions into the tundish. This is typically 
achieved after about three mean residence times and cor- 
responds to those conditions where inclusions within the 
recirculating flow zones have accumulated to steady lev- 
els while those in stagnant zones continue to accumulate. 
This slow approach to steady state does not seem to have 
been recognized in early work on tundishes (e.g., 
References 1, 2, and 4). 
Corresponding particle/inclusion separation curves at 
quasi steady state (30 minutes after feeding) for the dam 
and weir arrangements set up for the water model are 
shown in Figure 12. As seen, the residual ratio of very 
small inclusions is unity at all dam/weir combinations 
and zero for all large inclusions. This is to be expected, 
since very small particles will have minimal Stokes ris- 
ing velocities and are therefore unable to separate, while 
inclusions with rising velocities on the order of 5 to 
6 mm/s will have an adequate opportunity to accumulate 
i i 
10 ~ 313 40 50 
Tlme(raln) 
(b ) f low cont ro l . 
Fig. 11 - -Compar ison of experimentally measured and predicted par- 
ticle separation ratio vs time of casting for the single-strand water 
model tundish with (a) no flow control and (b) flow control. 
Inclusion Diameter (]am) 
20 40 60 80 1 O0 120 140 
1.0 ~ , ~ . . . . 
.s 0.e ~ o o . 
m 0.6 
n. 
r " ~ ","r-Of 
.'9_ 0.4 ~ 
0.2 
0.0 ' 
0 I ~ 3 4 5 6 Stokes Velocity (ram/s) 
Fig. 12--Relat ionship between the residual ratios of inclusion par- 
ticles and Stokes rising velocities predicted for a full-scale water model 
of slab casting tundish. 
METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--763 
1.0 
0.8 
o 
o.6 
n,. 
i o.4 
o 
0.2 
0.( 
0 
f 
0 0 0 
A A 
0 
: i ~ 
10 ~ ~ 
T l~(min) 
Lls-lmm/s 
L~2mrv'e 
I.~3mm/s 
50 
(a) the inside port 
1.0 
0.8 
o 
, 0 .8 
~ 13.4 
O.Z 
Us- 1 mm/s 
~Eb~n/6 
TlnmCmim) 
60 
0~ i 
0 I0 20 30 40 50 60 
(b) the far port 
Fig. 13- -Compar ison of experimentally measured and predicted par- 
ticle separation ratio vs time of casting at (a) the inside port (nozzle 
A) and (b) the far port (nozzle B) of a full-scale water model tundish 
for twin bloom casting arrangement with flow control. 
in the top regions of the tundish. The data show that the 
optimum placement for a dam and weir is at 1/3Lc and 
the difference between that and no flow controls would 
be significant for inclusions ranging between about 40 
and 120-/zm diameter. Beyond these limits, no signifi- 
cant difference would be observed. 
Figure 13 presents comparisons of the prediction and 
the experimental measurement of particle entrainment at 
the inside port (nozzle A) and at the far port (nozzle B) 
of the double bloom casting tundish. There, a weir/dam 
arrangement was used for flow modification. As seen, 
good agreement was achieved between predicted and 
measured values. 
Similarly, Figure 14 illustrates the relationship be- 
tween the inclusion residual ratios vs Stokes rising ve- 
locity at both outlet nozzles with and without flow controls 
under isothermal conditions. Since the outlet ports of this 
tundish are serially arranged, it is supposed that the 
particle concentration exiting the inside port should be 
0 
to z., 
"0 
q~ 
t~" 
1.0 
0.8 
0.8 
0.4 
O.Z 
0.0 
0 
Inclusion diameter (pm) 
20 40 60 80 100 120 140 
t f ! 
I 2 3 4 5 8 7 
Stokes velocity (mm/s) 
(a) no flow control 
I nc lus ion d iameter (pm) 
20 40 60 80 100 120 140 
1.0 r , , , i , t 
~ O.eo.B "x,,,.,.,...... 
1 2 3 4 5 8 
Stokes velocity (mm/s) 
(b) flow control 
Fig. 14--Relat ionship between the residual ratios of inclusions and 
Stokes rising velocities at exit nozzles of the tundish set for twin bloom 
casting with (a) no flow control and (b) flow control. 
denser than that exiting the far port, there being less time 
for float out with no flow control. Figure 14(a) illustrates 
this point, while particle entrainment amounts at both 
outlet ports become approximately identical when a weir/ 
dam arrangement is employed, as seen in Figure 14(b). 
1. 
. 
V. CONCLUSIONS 
A general purpose computer code, METFLO 3D, has 
been developed. Using this code, one can predict 3-D 
fluid flows, heat transfer, inclusion behavior, and their 
population distributions within steelmaking tundishes. 
A novel technique for the on-line measurement of 
particle concentrations in aqueous systems has been 
developed, which allows local concentrations of 
"inclusions" (hollow glass microspheres) to be 
764--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B 
. 
. 
monitored on-line in full-scale water models of met- 
allurgical flow systems. 
It is shown that a fully 3-D description of the flow 
field and of buoyant particle dispersion and separa- 
tion was capable of matching corresponding experi- 
mental data. No "tuning" coefficients were required. 
Both experiments and predictions show that concen- 
tration transients of small particles within tundishes 
reached pseudo-steady-state level at about three nom- 
inal holding times. 
C 
ch 
d 
G 
g 
k 
k(T) 
Lc 
Ni. 
Nout 
P 
O 
R 
Rnozzle 
T 
t 
Us 
Fe 
/'/'eft 
/xt 
P 
Ap 
Crc 
~r 
O't, C 
a't, ~ 
NOMENCLATURE 
mass fraction of inclusions 
channel number on multichannel amplifier 
inclusion/particle diameter 
generation of turbulence kinetic energy 
gravity acceleration constant 
turbulent kinetic energy 
a resistance constant 
distance between inlet and outlet nozzles 
number density of inclusions at the inlet 
nozzle 
number density of particles at the outlet 
nozzle 
pressure 
volumetric flow rate of fluid 
residual ratio of inclusion particles 
radius of inlet nozzle 
temperature 
time 
Stokes rising velocity of particles/inclusions 
dissipation rate of turbulent kinetic energy 
effective diffusivity 
laminar viscosity 
effective turbulent viscosity 
turbulent viscosity 
density of fluid (water/molten steel) 
density difference between fluid and particle 
laminar Schmidt number 
laminar Prandtl number 
turbulent Schmidt number 
turbulent Prandtl number 
ACKNOWLEDGMENTS 
This work was carried out in collaboration with Stelco 
Inc. (L. Dumitru and D.J. Harris), under the auspices 
of a CRD grant from the Natural Science and Engineering 
Research Council of Canada. The authors are deeply in- 
debted to NSERC for such funding, as well as to Stelco 
colleagues for their unfailing cooperation in providing 
access to their full-scale water model tundishes. 
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METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--765