Effects of Angle of Rotation of Submerged Entry Nozzle on Fluid Flows in a Square Billet Casting Mold
Effects of Angle of Rotation of Submerged Entry Nozzle on Fluid Flows in a Square Billet Casting Mold
MAHDI M. ABOUTALEBI 0
FRANCIS LAPOINTE 0
JULIEN D'AMOURS 0
MIHAIELA M. ISAC 0
RODERICK I.L. GUTHRIE 0
0 1.-McGill Metals Processing Center (MMPC), Faculty of Engineering, McGill University , 3610 University Street, Montreal, QC H3A 0C5 , Canada. 2.-Rio Tinto Iron & Titanium, Sorel-Tracy, QC J3R 1M6 , Canada. 3.-
Having knowledge of fluid flows within the mold region of a billet continuous caster is of paramount importance to reduce a product's internal and external defects. In this regard, a three-dimensional numerical model was developed to simulate the influence of the orientation of a five-port submerged entry nozzle (SEN) on the flow field of liquid steel within the mold region of a curved, square billet, continuous caster. The realizable k- turbulence model, together with the volume of fluid multiphase model, was used to simulate the effects of turbulence on these fluid flows, and their impact on the liquefied mold powder layer sitting on top of the liquid steel within the mold. The behavior of flows generated in the mold cavity was validated against previous experimental work. The numerical results showed that the modified SEN's horizontal angle of rotation can significantly change the flow pattern within the billet mold. These changes can stabilize the liquid steel meniscus, which is expected to improve the quality of continuously cast products by decreasing mold powder entrainment.
The World Steel Association reported that, in
2016, more than 95% of steel solidified worldwide
was produced by conventional continuous casting
processes.1 Nonetheless, these processes remain
subject to inherent processing defects, resulting in
an ongoing battle to increase the quality of
continuously cast products, but not at the expense of
productivity. One of the key factors for enhancing
cast products and reducing, or even eliminating,
casting defects, is to develop and maintain uniform
fluid flow within the mold region.2,3
One of the most influential and trusted ways to
modify liquid steel flows within a continuous
caster’s mold is nozzle design, which itself includes
various factors that can be altered and dramatically
impact on the resulting liquid steel flow. These
include the number of exit ports, their angle, shape,
and size, or the insertion of flow modifiers within
the submerged entry nozzle (SEN) tube itself, as
well as the vertical location of the SEN within the
A number of studies have revealed that a proper
multiport SEN can have a positive influence on
liquid steel flows within the mold. Sun et al.5
developed a mathematical model for a newly
designed quadfurcated SEN that could produce
strong swirling flow within the mold region. This
reduced the depth of impingement of the molten
steel jet and accelerated inclusion flotation
processes. In another study, Capurro et al.6
investigated the effect of a new SEN with six lateral ports
on the distribution of inclusions in finished cast
products. They reported that lower density of
inclusions was found in products cast with the newly
designed SEN in comparison with a straight,
singleport nozzle. In recent years, Morales et al.6–9
developed a fluid flow model to study the effect of new
SEN designs on mold powder entrainment (MPE)
for both round and square billet casting processes.
Based on their numerical and physical modeling
results, their proposed curved ported SEN could
reduce the risk of MPE, due to swirling flows
created in the mold cavity.
Based on these assumptions, the time-averaged
governing equations used in this study are listed
Continuity and Navier–Stokes Equations
þ qgi þ Si;
where q, ui, P, gi, leff , and Si, are density, velocity
component, pressure, gravitational acceleration,
effective viscosity, and momentum source/sink
Turbulence Governing Equations
In several studies by Yokoya et al.,10–14 and
Kholmatov et al.,15,16 the impact of the ‘‘fixed swirl
blade’’ system as a swirl flow generator was studied
on fluid flows within the SEN and within mold
cavities. In those articles, a positive effect of the flow
modifier on reduction of inclusions in final products
was reported, together with creation of a stable
liquid steel meniscus, and the distribution of bubbles
within the mold cavity. However, due to erosion
caused by constant impingement of liquid steel, it is
extremely difficult, if not impossible, to maintain
the shape and integrity of the swirl blade system.
The objective of this study is to develop a numerical
model to quantify the effect of an existing industrial
SEN’s position on flow patterns generated within a
vertically curved, square billet mold. Previous
physical modeling results for a similar case were used to
demonstrate the accuracy of the predicted fluid flows
calculated by the present numerical simulations.
In this numerical model, the averaged continuity
and Navier–Stokes equations in three-dimensional
Cartesian coordinates were solved. The realizable
k– turbulence model was fully coupled with the
volume of fluid (VOF) multiphase model to simulate
the effect of turbulent flows on the behavior of the
slag layer within the billet mold.
To predict swirling flows and vortices inside the
mold cavity, the realizable k– turbulence model
was used. This model has better capability for
predicting vortexing flows, by solving a modified
transport equation for the rate of dissipation of the
kinetic energy of turbulence .17
The VOF model was employed to track the
interfaces of a system with three immiscible fluids.
One set of momentum equations is solved
throughout the calculation domain, and the resulting
velocity field is shared among phases within each control
volume. To account for surface tension effects
between the three phases, an additional source/sink
term was applied in the Navier–Stokes equations.18
To develop the relevant governing equations, the
following assumptions were incorporated:
1. The liquid steel was considered to be
incompressible and isothermal, and behave as a
Newtonian fluid. Heat transfer and
solidification were ignored.
2. The physical properties of phases were
considered to be constant.
3. Mold oscillation was neglected in this study.
l þ r
where k, , rk, r , C1, and C2 represent the kinetic
energy of turbulence, the turbulent dissipation rate,
the turbulent Prandtl numbers for k and , and two
model parameters C1 and C2, respectively. The term
S is a function of the shearing deformation
component, and Gk represents the local rate of production
of kinetic energy of turbulence due to local mean
The turbulent viscosity is then determined by the
where unlike the standard k– turbulence model,
the Cl value is no longer constant but is a function
of different parameters such as the local shearing
and rotational deformation rates, as well as k and .
Volume of Fluid Equation
Tracking the interface between phases is done by
solving the continuity equation for the volume
fractions of each of the secondary phases; in this
case study, this equation was solved for air, liquid
slag, and vegetable oil. The continuity equation for
the qth phase is as follows:18
m_ qp ;
where aq, m_ pq, and m_ qp represent the volume
fraction of phase q, mass transfers of phase p to q,
and mass transfer of phase q to p, respectively. Saq
is the source term, indicating creation or
destruction of phases.
The above governing equations with appropriate
boundary conditions were discretized and solved
numerically, using the commercial finite volume
method (FVM)-based software ANSYS-Fluent 14.5.
The computational mesh constructed had around 1
million cells, and mesh construction was carried out
using third-party software, GAMBIT.
Geometrical Model and Boundary Conditions
The calculation domain in this study is a square
billet mold with cross section of 165 mm 9 165 mm
and longitudinal radius of curvature of 10 m. A
fiveport SEN was selected as the feeding system in this
paper, and three different nozzle lateral angles of
rotation were considered, as shown in Fig. 1. As
seen from Fig. 1a, the selected SEN consisted of four
downward angle exit ports, along with an exit port
oriented vertically downwards. For the SEN with
fixed 0 angle of rotation (case 1), the four inclined
ports face towards the corners of the mold. For cases
2 and 3, the SEN was rotated 15 around the central
Z axis, clockwise and counterclockwise,
The physical properties of all the fluids with the
operational conditions used in this study are given
in Table I.
The inlet velocity was linked to the casting speed
by equating the inlet volume flow rate and the
outlet volume flow rate, to maintain mass
conservation within the mold cavity.
The value for the inlet kinetic energy of
turbulence and its dissipation rate were taken from
semiempirical correlations reported in
literature.21,22 These relations are as follows:
kin ¼ 0:01ui2n;
in ¼ 2:35 ki3n=2 ;
where Din, represents the inner diameter of the
SEN’s inflow tube.
For the single-phase model, the steel meniscus
was specified as being equivalent to a flat surface
with zero-shear stress boundary condition. All walls
were subjected to no-slip boundary conditions.
RESULTS AND DISCUSSION
To verify the computed results, the behavior of
the slag layer predicted by the present model was
compared with the experimental results in Fig. 2, in
which Fig. 2b was first reported by Morales et al.7
The phases involved in this model are water as
primary phase, together with vegetable oil and air.
The initial thickness of the vegetable oil in both the
experiment and numerical model was set to 15 mm.
According to this figure, the computed results are in
very good agreement with the experimental
observations, and in both the experimental and
computational results, the flow field near the top region of
the mold drives the slag layer towards the center of
the mold walls.
Comparison between the velocity fields at the
horizontal cross-sectional plane 20 mm below the
meniscus and at the vertical diagonal plane for the
three different cases is shown in Fig. 3. The
resultant velocity field in these planes shows that, for
case 1 (0 ), multiple vortexes are being formed near
the meniscus region. Moreover, the flow pattern at
the diagonal plane for this case shows
semistagnation points at the corners of the mold. These points
are the results of direct impingement of liquid steel
towards the mold corners, which significantly
transforms the shear flows to normal flows. Conversely,
the velocity field created by rotating the
nozzle ± 15 with respect to the mold corners shows
that the multiple vortexes were removed.
Additionally, by changing the orientation of the inclined
ports of the SEN, the normal flows could be
drastically decreased compared with the normal
flows shown in case 1 (0 ).
Figure 4 shows the velocity profile at 0.02 m,
0.3 m, 0.5 m, and 0.7 m below the mold top, to
quantify the magnitude of the swirling flows in
these case studies. For these velocity profiles, the
velocity components in the X axis, U, were probed
through the width of the billet along the Y axis, at
the mid-vertical cross-sectional plane of the billet.
As shown in Fig. 4a, at Z = 0.02 m, the swirling
flows created for cases 2 and 3 are almost equal but
with opposite rotational directions. According to
Fig. 4b, the swirling flows also appear below the
immersion depth of the SEN for these two cases.
However, in the mid-region of the velocity profiles
for these cases, the U velocities do not show
consistent swirling flows. This can be explained by
the effect of the turbulent flows within this region
and the influence of the flow issuing from the
vertical bottom port of the SEN. Based on a
comparison of the velocity profiles in Fig. 4b and c,
the strength of the swirling flows starts to decay as
one moves away from the top region of the mold. At
Z = 0.5 m, the magnitude of the swirling flows
decreased by a factor of two compared with the
values predicted at Z = 0.02 m and Z = 0.3 m.
Comparison of Fig. 4c and d demonstrates that the
changes in the velocity profile for all three cases, at
Z = 0.5 m and Z = 0.7 m, are negligible.
Effect of SEN Angle of Rotation on Behavior of Molten Slag Layer
Figure 5 shows the contours of the volume
fraction of slag across the vertical diagonal plane,
together with the predicted shape of the liquid
steel menisci. It is known that the shape of the
meniscus is a critical parameter for the lubrication
procedure for continuous casting processes.
According to Fig. 5, the fluid flow in the top
region of the mold for case 1 (0 ) creates strong
upward flows towards the corners of the meniscus.
Due to the curvature of the square billet mold, the
strength of the upward flows is not uniform and
similar near different walls of the mold. These
flows create discontinuities in the slag layer at the
corners of the mold. Based on the behavior of the
slag layer for case 1 (0 ), upward flows increase
the risk of exposure of the liquid steel to air and
should lead to a growing number of inclusions in
the solidified billets. Moreover, the meniscus
shape in this case confirms that the upward flows
create differences in steel meniscus levels at all
four corners of the mold. With this liquid steel
meniscus shape, final products are susceptible to
Fig. 4. U velocity profiles in mid-plane at different positions down the meniscus for different SEN angles of rotation: (a) Z = 0.02 m, (b)
0.3 m, (c) 0.5 m, and (d) 0.7 m.
deep oscillation marks at the corners of
continuously cast products, as well as longitudinal corner
cracks, due to insufficient lubricant being pumped
into the corners of the mold. However, the
proposed port orientations for the SEN can create a
uniform distribution of liquid slag across the
entire meniscus and a stable meniscus in the top
region of the mold. This new liquid steel meniscus
shape is expected to have a positive influence on
uniform pumping of liquid mold powder into the
mold, to lubricate the solidified steel shell passing
down the water-cooled copper mold. Therefore, for
such a meniscus shape, different types of surface
defects can be minimized.
Based on the current computational results, the
following conclusions can be drawn:
1. The commonly used location of the SEN (0
angle of rotation) inside the mold cavity
produces normal flows towards the upper surface
meniscus. These flows can dramatically
destabilize the liquid steel meniscus and promote the
risk of MPE, insufficient feeding of liquid mold
powder, and in severe cases, exposure of liquid
steel to air.
2. Changing the SEN’s angle of rotation to either
+ 15 (case 3) or 15 (case 2) is a key factor for
activating swirling flow within the mold cavity
of a square billet continuous caster. These
swirling flows can form a stable meniscus.
3. It has been noticed that, for ± 15 SEN angles of
rotation, the shape of the meniscus is almost
flat. Therefore, the advantages of swirling flows
are not dependent on the direction of rotation.
4. Based on the velocity profiles produced for case 2
) and case 3 (+ 15 ), the strength of the
swirling flows decays as one moves away from the
meniscus, down towards the mid-section of the mold.
The authors would like to acknowledge financial
and/or technical support received from ANSYS Inc.,
the Rio Tinto Fer et Titane (RTFT) steel plant (located
at Sorel, Tracy, Quebec, Canada), and the McGill
Metals Processing Centre’s member companies.
This article is distributed under the terms of the
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source, provide a link to the Creative Commons
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