DYNAMICS OF TWO-PHASE DOWNWARD FLOWS IN SUBMERGED
ENTRY NOZZLES AND THEIR INFLUENCE ON THE TWO-PHASE FLOW
IN THE MOLD
R. SANCHEZ-PEREZ1 & R.D. MORALES2
1
Graduate student at Instituto Politecnico Nacional-ESIQIE, Department of Metallurgy and
Materials Engineering, Apdo. Postal 75-874, Mexico D.F., CP 07300. e-mail:
[email protected], [email protected]
2
Professor at Instituto Politecnico Nacional-ESIQIE, Department of Metallurgy and Materials,
Apdo. Postal 75-874, México D.F., CP 07300 and President of K&E Technologies S.A. de C.V.
e-mails: [email protected], [email protected]
ABSTRACT
Gas-liquid flows inside the submerged entry nozzle (SEN) of a slab mold and their influence
on the flow field in the mold were studied using video recording, mathematical simulations
and Digital Particle Image Velocimetry (DPIV) approaches. Coalescence-breakup phenomena
of bubbles in liquid steel flowing through a slab mold were studied using a water model. At
low gas loads (ratio of mass flow rates of gas and liquid in the submerged entry nozzle)
bubble dynamics consist of coalescence-breakup and dragged processes from the SEN until
close to the narrow wall. At high gas loads, bubbles are accumulated close to the narrow
wall where they coalesce, break and ascend toward the bath surface forming bubble swarms
or descend along the narrow wall by dragging forces exerted by liquid phase on the surfaces
of the bubbles. These swarms consist of coalescing bubbles and agglomerating groups of
bubbles. The presence of bubbles in the flow decreases the magnitudes of vorticity values in
the flow field of mono-phase flows. Thus, to increase the casting speed, the injection of
argon should be adjusted to an appropriate level to avoid an excess of liquid entrainment to
the flux phase. Bubbly and annular flows in the SEN yield structurally-uncoupled and
structurally coupled flows in the mold, respectively. High gas loads at high casting rates
lead to increases of bubble population and bubbles sizes due to coalescence processes
whose rate exceeds that of their breakup. The presence of gas bubbles or gas layers inside
the SEN lead to periodical twisting of the liquid flow that induces biased flows through both
ports yielding uneven flows in the mold. A multiphase mathematical model predicts
acceptably well the flow dynamics of two-phase flows inside the SEN.
Keywords: Mold, continuous casting, flux, liquid entrainment, DPIV, vorticity, two-phase
flow, SEN.
DINÁMICA DEL FLUJO BIFÁSICO EN BUZAS SUMERGIDAS Y SU INFLUENCIA SOBRE
EL FLUJO BIFÁSICO EN EL MOLDE.
RESUMEN
El flujo gas-liquido dentro de la buza sumergida de un molde de planchon y su influencia en
el campo de flujo se estudio usando grabaciones de video, simulaciones matemáticas y
velocimetría de partículas. El fenómeno de coalescencia-rompimiento de burbujas en acero
líquido fluyendo a través de un molde de planchon se estudio por medio de un modelo de
agua. A bajas cargas de gas, la dinámica de burbujas consiste de procesos de
coalescenciarompimiento y arrastre de procesos desde la buza hasta las proximidades de la
pared estrecha del molde. A altas cargas de gas las burbujas se acumulan cerca de la pared
estrecha donde coalescen, se rompen y ascienden hacia la superficie del baño formando
cortinas de burbujas o bien, descienden a lo largo de la pared estrecha debido a las fuerzas
de arrastre de la fase líquida ejercidas sobre la superficie de las burbujas. Estas cortinas
están formadas de grupos de burbujas que coalescen y se aglomeran. La presencia de
burbujas disminuye las magnitudes de los valores de vorticidad en el campo de flujo de
flujos monofásicos. Así, para incrementar la velocidad de colada la inyección de argon
debería ser ajustada a niveles adecuados para evitar el exceso de arrastre de liquido. Los
flujos burbujeante y anular en la buza provocan flujos estructuralmente desacoplados y
acoplados respectivamente en el molde. Altas cargas de gas con altas velocidades de colada
tienen un aumento en la población y tamaño de burbujas como una consecuencia de los
procesos de coalescencia cuyas velocidades exceden a las de rompimiento. La presencia de
burbujas o la fase gas provoca arremolinamientos repetitivos del flujo líquido lo que lleva a
un flujo dividido en la salida de los puertos observándose un flujo desigual en el molde. Un
modelo matemático multifásico predijo adecuadamente la dinámica del flujo bifásico dentro
de la buza.
Palabras clave: Molde, colada continua, flux, arrastre de líquido, DPIV, vorticidad, flujo
bifásico, buza sumergida.
Recibido: Septiembre de 2004
Recibido en forma final revisado: Abril de 2005
INTRODUCTION
The highest casting speed in conventional thick slab casters, so far reported in the open
literature, is 2 m/min attained by the company NKK [1] and theoretical considerations
indicate that is possible to increase this speed reasonably up to 4 m/min [2]. If such a high
speed would be obtained thus conventional slab casters would be able to match and surpass
the productivity of thin slab casters. Since the number of conventional thick slab casters in
the world exceeds very much the number of thin slab casters the productivity of the
steelmaking world would be very much improved if such high casting speeds are obtained.
However, to reach that goal many problems have to be solved like heat transfer
optimization, design of new casting fluxes, design of cooling systems of molds and control of
the fluid turbulence in the mold cavity. To deal with most of these obstacles feasible
solutions have been proposed [3] with the exception of the last one because so far fluid flow
remains as a key problem of a difficult solution since increases of casting speeds enlarge the
amplitude of the standing waves of the bath surface. Moreover, an unstable bath surface
leads to the entrainment of flux particles which disintegrate in the mold and that may not
float totally out of the molten metal becoming into macro inclusions in the solidified slab.
These conditions can be aggravated by the flow of argon through the Submerged Entry
Nozzle (SEN) because high casting speeds increase the inertial and drag forces that
transport argon bubbles to the solid-liquid interface to become into pinholes and slivers
defects in slab.
Since two-phase flows are very important in continuous casting of steel the authors started
a research program aimed at the understanding flow dynamics in a conventional slab mold
as a first step to look for other alternatives to control fluid flow turbulence. Jet angles at the
SEN’ s ports and the main body of the jet were measured as functions of the gas load (ratio
of mass flow rate of gas and flow rate of liquid in the SEN) [4, 5]. In these works it was also
reported that increases of casting speeds raise almost exponentially the volume of liquid
entrainment by gas bubbles and would intensify the instability of the bath surface. Through
video images it was also observed that gas bubbles suffer coalescencebreakup processes
and the corresponding kinetics depends strongly on the gas-load.
The authors classified, on basis of measured maps of streamlines of both phases, what is
called structurallyuncoupled and structurally-coupled flows [5]. A structurally-coupled flow is
that where the streamlines of the liquid and gas phases observe high similarities. The
transition between structurally uncoupled and structurally coupled flows depends on the
relationship between the dimensionless parameters of the mass flux ratio or gas load and
the pi-momentum given by the expression (see the list of symbols at the end of this paper),
where v is the time response of the dispersed phase (gas bubbles) to the signals coming
from the continuous phase (water) and is given by:
the gas load is defined in this work as,
and
are the fraction volume-averaged densities of the gas and liquid phases,
respectively,
This parameter mom in Equation (1) is the ratio between the drag momentum transfer
exerted by the liquid on the bubbles surfaces and the inertial momentum transfer of fluid.
When this parameter, plotted against the gas load in Fig. 1, exceeds the value of 1.6 X 105, approximately, the flow enters into a transition zone and when it exceeds the value of
3.5X10-5 the flow becomes into a structurally-coupled one. In structurally-coupled flows the
orientations of velocity vectors of both phases are similar and this implies high turbulent
flows in the bath surface. Consequently, most of the casters operate in the transition zone
or in the structurally-uncoupled zone presented in Fig. 1
In the present work the coalescence-breakup phenomena of gas bubbles in two-phase flows
in a slab mold are studied. Also we emphasize the importance of the twophase flow regime
in the SEN as well as its important influence on the fluid flow patterns inside the mold.
Furthermore, the unsteady nature of the fluid flow and the distribution of the volume
fractions of both phases, which are not considered in previous works, are also analyzed. The
final aim is to contribute with additional knowledge to the complex and important flow in
continuous casting systems.
1. EXPERIMENTAL PROCEDURE
A ½ scale model of IMEXSA Steel mold was built using 20 mm thick transparent plastic
sheets; the geometric dimensions are shown in Fig. 2a. Water is delivered through a SEN
with a conventional design, which is shown in Fig. 2b. At this step the effects of the slide
gate opening or its orientation are not considered. Flow rate of water into the mold model is
controlled by globe valves and flow meters and is drained through a honeycomb type plate
located in the bottom. The outer water is sent back to a storage tank to be re-circulated into
the mold. Injection of air, from a compressor, into the SEN is performed using a connection
and a gas flow meter to feed, accurately, different flow rates of this gas. Fluid dynamics
under different operating conditions was characterized through Digital Particle Image
Velocimetry (DPIV) technology using equipment from Dantec Systems. A green frequency
double pulsed Nd:YAG laser with a wavelength of 532 nm was employed. In order to obtain
short bursts of light energy, the lasing cavity is Q-switched so that the energy is emitted in
6-10 ns bursts with pulses of 250 µs, which is the duration of the exciting lamp in the laser
cavity. Output energy from the laser is 20 mJ of Nd:YAG crystal from the fiber bundle. This
energy is increased with light guides that can transmit 500 mJ of pulsed radiation with an
optical transmission that is greater than 90% at 532 nm. Interrogation areas of 1X1 mm in
the flow were scanned with a resolution of 32X32 or 64X64 pixels.
The laser sheet is 0.001 m thick with length X height dimensions of 0.432X0.261 m. It was
positioned at half the mold thickness by means of a computer-controlled frame-holder
system with 3-D motions; this plane includes from the SEN axis to one of the narrow faces
assuming that a similar fluid flow pattern is formed in the other side of this mold. In order
to follow the fluid flow the fluid was previously seeded with 20 µm polyamide particles with
a density of 1030 kg/m3, which were injected in the SEN. A cross-correlation procedure
using Fast Fourier Transforms allowed processing the recorded signals and a Gaussian
distribution function was used to determine the location of the maximum of the peak
displacement with subpixel accuracy[5,6,7]. The signals were recorded by a Dantec coupled
charged device (CCD) with 90 mm Nikon lenses and the recordings were processed using
commercial Flow Map software in a Pentium-IV PC in order to obtain the vector-velocity
fields. To record the flow fields of air in the bubbles two CCD´s were mounted in a twin
holder fixed to the frame-holder system. The first CCD captured the images from the laser
sheet and transferred it to the other parallel CCD through a prism. In the second CCD there
is a red filter to avoid the passage of green light. This filter allowed the detection and
recording of airflow velocity fields by masking the vectors of the liquid phase. Fig. 3 is a
scheme of the experimental set-up.
One hundred images for each experiment and for each phase flow fields were analyzed
using this procedure. Vorticity fields of the flow patterns were derived from the velocity
fields, as determined by the DPIV measurements, using a finite center difference scheme
[7],
Bubble sizes were calculated from the video images captured by the CCD´s, which were
recorded in a PC, calculation of bubble sizes and their population was performed using
commercial IMAQ software [8]. This is an image analyzer program which uses mathematical
filters and combinations of contrast, brightness and zooms which make possible the
resolution, definition and identification of individual bubbles or groups of agglomerated
bubbles in mist type flows. From the 100 images for each case, 35 were randomly chosen
for bubble analysis; this means that in the case of the highest and lowest mass loads (mass
flow rate of gas /mass flow rate of liquid) about 300 000 and 75 000 bubbles were analyzed,
respectively. The informationstored for all these experiments totalized about 20 Gigabytes.
The experimental program is shown in Table I where SI and more conventional units are
shown; the casting speed was employed as the scaling up criterion, and thus the same
casting speeds used in the plant were employed in the model because this procedure allows
an intermediate criterion between full scale Reynolds and Froude criteria. The main
experimental variables include casting speed and gas flow rate or gas-load.
Table 1.
Parameter
Value
5
3
Gas flow rate x10 , m /s
0.83, 2.0, 4.17, 8.33, 16.7
Gas flow rate, l/min
0.5, 1.2, 2.5, 5.0,10.0
Casting speed, m/min
0.8, 1.2, 1.8
Water flow rate, l/min
80, 120, 160
Experimental conditions for model experiments
2. RESULTS AND DISCUSSION
2.1. DESCRIPTION OF THE TWO-PHASE FLOW
The jetting characteristics in the ports vary according to the gas load inside the SEN. With
high gas loads the two-phase flow inside the SEN is slug or annular type and air exits
through the ports by intermittent torrents together with a continuous flow of water.
Preferential region of gas exit through the ports involve the full orifice area or regions close
to the lower edges of these ports independently of the gas load, changing from one region
to another without any apparent pattern. However, air exits mostly close to the inferior
edges with large angles (measured with respect to the horizontal axis). This description is
illustrated in Figs. 4a-b for a high gas load, in the first one air exits through the full port
area while in the second air stream is mostly exiting close to the lower edge of the port.
Close to the port very small bubbles suffer coalescence growing to some dynamic
equilibrium size and ascend immediately through the water column as indicated by number
1 in Fig. 4b. Other bubbles are driven by drag and inertial forces further into the liquid bulk
where additional coalescence-agglomerating phenomena take place and the grown bubbles,
traveling further in the liquid, float toward the bath free surface as is indicated by numbers
2 and 3, respectively. After the ascending column there is another zone of bubbling
coalescence, marked with number 4 followed by another ascending zone, number 5, to
repeat the cycle as marked by number 6; some bubbles are dragged downward along the
narrow wall. The disturbed free bath surface, shows the formation of a spout, which is close
to the SEN because the buoyancy forces are larger than inertial ones making the flows of
gas and liquid to be directed upwards. Large bubbles ascend through a two-phase layer with
a thickness of 0.04-0.06 m, close to the bath free surface, with defined identities and
without apparent further coalescence neither breakup.
As the casting rate increases, for a given flow rate of gas, these cycles of bubble breaking,
coalescence, agglomeration, dragging and ascending phenomena continue taking place. At
low gas loads the two-phase flow inside the SEN should be closer to a bubbling condition
than to a slug or annular flow and the jet in the port adopts a continuous structure as is
seen in Figs. 4cd for gas exiting through the whole orifice area of the port and for gas
exiting through the lower port edge with large angles, respectively. Just in front of the port
the two-phase jet yields a mist type structure with very small bubbles that coalesce and
grow in zones marked with numbers 1 and 2 in Fig. 4d. Once that the bubbles have grown
they ascend through the water column, marked with number 3 and the rest of the bubbles,
zone 4, are dragged close to the narrow wall where they are accumulated, zone 5, forming a
large bubble swarm. This behavior is because the leaving velocities of ascending bubbles are
not large enough to compensate the supply of bubbles dragged by the two-phase jet to zone
5. Many bubbles descend downward, driven by inertial and drag forces, further along the
narrow wall. Figs. 5a-b show zooms of filtered images corresponding to Figs. 4a-b
respectively. Looking carefully at Figs. 5ab, the description of bubbles behaviors, presented
above, is corroborated. Is also interesting to see that some bubbles are agglomerated but
do not coalesce into larger ones and in other cases there are coalescence phenomena.
Nevertheless, in the present work the term coalescence is applied to both cases, i.e., that
where bubbles coalesce and grow and that where they agglomerate.
Low gas loads produce sparse bubbles immersed in the liquid maintaining their individual
identity, as is seen in Figs. 6a-c for casting speed of 0.8, 1.2 and 1.8 m/min with a flow rate
of gas of 1.2 l/min. When the gas load increases coalescence phenomena of bubbles, in the
sense defined above, and bubbles breakup phenomena are more frequent as is shown in
Figs. 7a-c for casting speeds of 0.8, 1.2 and 1.8 m/min with a gas flow rate of 10 l/min,
respectively.
2.2. TWO-PHASE FLOWS IN THE SEN
Figures 8a-8f show video images of the two phase flow at 0.1, 0.2, 0.4, 0.7, 0.9 and 1.1
seconds respectively under a flow of 80 l/minute of liquid and 0.5 l/minute of gas.
A large bubble is formed at the injection point of air which elongates as the time passes on.
After 0.9 seconds the bubble is so large that is not able to sustain the inertial forces of the
liquid and is disintegrated forming smaller bubbles that flow downwards through the SEN
length. At longer times, larger than 1.1-1.4 seconds, a new bubble is formed and the cycle
repeats the process described. The effects of bubble formation and its further disintegration
has profound effects on liquid flow as is seen through the simulated velocity fields in the
symmetrical plane which is perpendicular to the SEN’ s exit ports as is shown in Figures 9a9f for the same times of 0.1, 0.2, 0.4, 0.7, 0.9 and 1.1 seconds, respectively. At the
beginning the flow seems to be symmetrical, plug flow type and balanced regarding both
exit ports, in the well the fluid observes small velocities. However, as the time passes on,
after 0.7 seconds in Figure 9d, flow leaves the plug flow becoming biased. Biasness starts
just a time when the first bubbles, from a disintegrating bubble, reach the lower part of the
SEN as is seen in Figure 8d. In the well of the SEN the fluid observes larger motions, as is
seen in Figures 9g-9j when bubbles are in contact with this containment. At end of the
disintegration process of a large bubble the flow is clearly biased as is seen in Figure 9j
where is seen that the two-phase jet has a downward angle in the left port and a near
horizontal jet in the right port.
Effects of disintegration of gas bubbles is particularly more evident in the vertical-symmetric
plane which is parallel to both ports as is observed in Figures 10a-10j for times of 0.1, 0.2,
0.4, 0.7, 0.9, 1.1, 1.3, 1.5 1.6 and 2 seconds, respectively. At short times, Figures 10a-10c,
a planar front of velocity vectors reaches the bottom pf the SEN. Many velocity vectors, in
the lower part of the SEN, are represented by dots because the fluid is coming out from a
plane parallel to this sheet, toward the port exit. Again, after 0.7 seconds in Figure 10d, the
flow is twisted and a strong recirculating flow in the well is rapidly formed and developed
through the time as is seen in Figures 10e-10j. These changes of flow patterns are
responsible of the biased outflow through both ports of the SEN and they are originated by
the presence of bubbles in the well.
Two-phase flow dynamics can be also visualized through the distribution of gas volume
fractions inside the SEN, Figures 11a-11f show those distributions for times of 0.1, 0.2, 0.4,
0.7, 0.9, and 1.1 seconds, respectively.
At times, such as 0.2-0.9 seconds, the large bubble is disintegrated, as is indicated by the
volume fractions of the gas phase, until it disappears completely at the time of 1.1 seconds
to start a new cycle. This is in complete agreement with the images presented in Figures 8a8f. Is also noteworthy to mention that gas distribution inside the SEN is not symmetrical and
this is another reason of the existence of biased flows through both ports of the SEN. When
the gas load increases the cycles of the two phase flow described above increase in
frequency and the full column is filled with bubbles under disintegrations processes. Is clear
here that gas fraction in the injection level has increased considerably and that is
permanently high as long as the experiment stands. Other differences are that bubbles fill
the full SEN length and in the well approximately 1/3 of the volume is gas permanently.
Thus gas is working as a cushion of the liquid impacting in the well producing a large
amount of bubbles exiting toward the mold together with liquid. At still higher gas loads a
well defined annular flow is developed with a permanent gas layer along the SEN length.
Although not determined quantitatively, through visual observations, the bubblyannular flow
transition was estimated approximately at a gas load of 3X10-5. Naturally this transition
changes radically the flow pattern in the mold, as will be discussed in the following section.
3. CONCLUSIONS
Gas bubble coalescence-breakup phenomena of twophase flows in a continuous casting
mold and submerged entry nozzle is modeled through a slab water model using a Digital
Particle Image Velocimetry technology and video recording and mathematical simulations
and the conclusions derived are as follows:
1.- At low gas loads (ratio of mass flow rates of gas and liquid) bubbles coalesce after
leaving the submerged entry nozzle (SEN) to suffer later, coalescence-breakup phenomena
followed by an ascending motion to the bath surface. These cycles repeat until the bubbles
reach the narrow wall of the mold.
2.- At high gas loads the number of cycles described above decrease to only one or two
forming swarms of bubbles close to the narrow face where coalescence are observed. Most
of the bubbles ascend toward the bath surface and others are dragged along the narrow
wall.
3.- Bubbly and annular flows in the SEN are directly related with structurally-uncoupled and
structurally coupled-flows in the mold, respectively.
4.- Under bubbling conditions in the SEN the presence of bubbles promote periodical
twisting motions of liquid stream inside the column and consequently liquid flow is biased
through both exit ports.
5.- Mathematical simulations of two-phase, bubbly flows, predict
experimental observations made through a video recording technique.
acceptably
well
ACKNOWLEDGEMENTS
RSP give the thanks to CoNaCyT for a granted scholarship to carry out graduate studies at
IPN. RDM thank to the institutions SNI, CoNaCyT and IPN for the financial support to this
work.
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NOMENCLATURE
ML: Gas load
L : Length
u: Liquid velocity.
v: Gas velocity.
Db: Bubble diameter.
Eob: Eotvos number.
ui: Fluid velocity in direction x
uJ: Fluid Velocity in direction y