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Content
ISIJ International, Vol. 55 (2015), No. 4, pp. 791–798
Transport Phenomena in a Beam-Blank Continuous Casting Mold
with Two Types of Submerged Entry Nozzle
Mianguang XU and Miaoyong ZHU*
School of Materials and Metallurgy, Northeastern University, No. 3 Wenhua Road, Heping District, Shenyang, 110819 P.R. China.
(Received on September 18, 2014; accepted on December 22, 2014)
A three-dimensional full-coupled mathematical model is established to study the fluid flow, heat transfer
and solidification in a 450 mm × 350 mm × 90 mm beam-blank mold with two different types of submerged
entry nozzle (SEN), namely single-port straight SEN and three-port radial flow SEN. Water modeling experiments, industrial trials and public results available in literature are performed to validate the numerical
results. The results show that, with the straight SEN which has been widely applied in beam-blank continuous casting, there is a very inactive top free surface in the mold which level fluctuation magnitude is less
than 1 mm and velocity magnitude is far from a reasonable interval, and the shell thickness distribution at
the mold exit is very uneven, thick at the web but thin at the fillet. Moreover, there exists a “wavy contour” at the flange due to the washing effect of the off-center molten steel jet. While with the new
designed radial flow SEN, a suitable meniscus status and a more uniform shell thickness at the mold exit
can be obtained, which is helpful to avoid the breakouts caused by the rupture of thin fillet and the flange
depression. The “self-braking” effect caused by two radial flow SENs provides good flow stability at the
web center.
KEY WORDS: beam-blank; continuous casting; submerged entry nozzle; transport phenomena; numerical
simulation.
posed to meet the demand for higher quality.
Mathematical modeling is very convenient for investigating
the suitable structure of SEN and has had a wide application
as a powerful tool in the analysis of the transport phenomena
in the mold. Unfortunately, most of mathematical models
about beam-blank continuous casting are based on the mold
thermal-mechanical analysis,2–4) mold water channel design5,6)
and secondary cooling strategy,7,8) a few literatures found
are mainly on the straight SEN.4,9) With such SEN, two
major problems engineers encountering in steelworks are
the inactive meniscus status and the non-uniform shell
thickness distribution at the mold exit, which can seriously
affect the function of the mold flux and the uniform distri-
1. Introduction
Recently, as a near-net-shape continuous casting technique, the need of beam-blank steel has been experiencing
a dramatic rapid increase and more than ten beam-blank
continuous casting machines have been put into production
in China due to its special usage, economic advantages and
outstanding mechanical properties. However, there is a common problem that the producers have to face, that is the
quality of continuously cast beam-blank, especially the
crack of the strand. As it is known, most of defects affecting
steel quality in the continuous casting process are associated
with fluid flow in the mold which is largely determined by
the SEN structure.1) SEN structure can strongly affect the
transport phenomena in mold, including meniscus status,
superheat dissipation, solidified shell growth and inclusion
removal. However, the complicated mold geometry shape
creates great difficulties for the design of a suitable SEN.
Although the beam-blank caster was installed at Maanshan
Steel in China in 1998, the simple straight SEN is still widely used. With this nozzle, molten steel is directly open
poured into two ceramic funnels, which are located in the
central flange regions, as shown in Fig. 1. Such pouring
method can give rise to serious problems on the quality of
final products, especially in the production of some new
steel grade, so new types of SEN are necessary to be pro-
Fig. 1.
* Corresponding author: E-mail: [email protected]
DOI: http://dx.doi.org/10.2355/isijinternational.55.791
791
Molten steel open poured into ceramic funnels: (a) industrial trial, two nozzles per mold are used for uniform steel
feeding; (b) schematic of upper nozzle and SEN.
© 2015 ISIJ
ISIJ International, Vol. 55 (2015), No. 4
bution of the stress and ultimately lead to a bad quality.
In the current study, a mathematical model based on the
enthalpy-porosity approach in a single-framework has been
developed for the prediction of three-dimensional transport
phenomena including fluid flow, heat transfer and solidification in a beam-blank slab casting process. With the understanding of shortcomings of the straight SEN and previous
studies, a new designed three-port radial flow SEN geometry and proper relevant casting parameters are presented for
the purpose of overcoming two major problems, and the
effects of port angle, casting speed and “self-braking”
induced by two radial flow SENs are discussed.
2.2.
Geometrical Model, Boundary and Initial Conditions
The research object of present work is a five-strand
bloom/beam-blank continuous casting machine with the
length about 37 m and the mold is not instrumented with
thermo-couples. The single-port straight SEN used in steelworks is shown in Fig. 2(a) and the new designed three-port
radial flow SEN is shown in Fig. 2(b).
The aspect ratio of thickness to height for the port of radial flow SEN is selected to be 0.83 in order to improve the
effectiveness of the SEN having a better direction of molten
steel flow to ensure its “self-braking” in the mold. The
geometry for the port of radial flow SEN is shown in Fig.
2(b), and the total area of these three ports is 32 pct larger
than that of the original straight SEN to enhance the inclusion removal ratio.15) The present simulations are performed
for port angles varying from –15 to +15 degree (downward
and upward port angles are denoted with + and – sign,
respectively).
At all the refractory walls of SEN, the zero-slip boundary
condition is applied16) and the thermal insulation is assumed.
The inlet velocity is computed by using the mass conservation between the inlet and outlet according to casting
speed.17) The values of turbulent kinetic energy k and its
dissipation rate ε at the inlet of SEN are based on the semiempirical expressions.18) The meniscus is specified as a
zero-shear condition.14)
In the mold region, the heat flux from the surface of
strand to the mold is assumed to be a function of the casting
speed and the distance below the meniscus, as suggested by
Lee et al.4) and Luo et al.7) With the straight SEN, the mea-
2. Mathematical Models
2.1. Mathematical Formulations
The general assumptions applied in the present solidification of beam-blank continuous casting can be found
elsewhere.11) There are seven partial equations in the threedimensional mathematical model which are solved by the
algorithm of SIMPLE, including one mass equation, three
momentum equations, two standard k-ε turbulence
equations12) and one energy equation.13) When the residual
for energy is smaller than 10–6 and others are smaller than
10–4, the converged solution is obtained. The general form
of all the partial equations can be written as the form of Eq.
(1).
∂
∂
∂φ
( ρ uiφ ) = ⎛⎜ Γ φ ⎞⎟ + Sφ ................. (1)
∂xi
∂xi ⎝
∂xi ⎠
where ρ is the steel density, ui is the speed in i direction, ϕ
is the variables including velocities at three directions, temperature, enthalpy, turbulence energy and its dissipation
rate, xi is the direction, Γϕ is the coefficient of diffusion and
Sϕ is the source term.
To accountant for the macro-solidification process, additional source terms SDarcy10) are added to momentum equations and turbulence equations, as shown in Eqs. (2) and (3),
respectively.
SDarcy_mom = − A
fs2
(1 − fs )
SDarcy_tur = − A
3
+ 0.001
( ui − us,i )
fs2
(1 − fs )
3
+ 0.001
........ (2)
ϕ tur .............. (3)
where A is the mushy zone constant and its value is set to
be 5×10–6, fs is the solid fraction which is assumed to vary
linearly between the liquidus temperature and solidus temperature, us,i is the moving speed of the solidified shell, and
ϕtur represents the turbulence quantity.
The top free surface profile in the beam-blank mold is
expressed in Eq. (4) by the liquid displacement estimated
from a simple potential energy balance.14)
Δz = −
p − pmean
( ρ − ρflux ) g
.......................... (4)
where Δz is the top free surface height, p is the static
pressure of the top free surface, pmean is the area-weighted
average value of the static pressure over the entire top free
surface, and ρflux is the flux density.
© 2015 ISIJ
Fig. 2.
792
Schematic drawing of beam-blank mold and SEN vertical
section: (a) beam-blank mold with an original single-port
straight SEN; (b) beam-blank mold with a new design of
radial flow SEN.
ISIJ International, Vol. 55 (2015), No. 4
surement of the mold water volume and water temperature
differences between the inflow and the outflow of cooling
water is employed, and the value of constant b obtained in
the Savage and Prichard’s relation q=a–b⋅t1/2 is 0.336.19)
The typical kinds of computation domains are presented
in Fig. 3, and the hexahedral mesh system is adopted to
improve calculation precision. The full-coupled simulation
starts from a previously converged flow-field solution and
the temperature of the pool region at the initial time is set
to be 1 828 K. The geometry, casting conditions, material
properties and computational conditions are summarized in
Table 1, and SEN submergence depth is defined as the dis-
tance of SEN bottom from meniscus. In order to minimize
the end effect of fluid flow at the outlet boundary, the
computational domain has a distance longer than the effective length of the mold along the casting direction, the
calculation domain is cut off 700 mm below the mold exit,
so the secondary cooling zone I (0.66 m, water flow rate 260
L/min) is completely included and secondary cooling zone
II (1.6 m, water flow rate 70 L/min) is partly included. In
the regions of secondary cooling spray, the heat transfer is
defined as the Robin boundary condition as shown in Eq. (5)
and the spray cooling heat-transfer coefficient hspray is calculated by using Eq. (6).20) By calculating Eq. (6), hspary in
Eq. (5) is 1 004.5 W/m2/K in the secondary cooling zone I
and 768.2 W/m2/K in the secondary cooling zone II , respectively.
q = hspray ( Tslab − Tspray ) ........................ (5)
hspray =
1.57 × W 0.55 × (1.0 − 0.0075 × Tspray )
....... (6)
α
where q is the heat flux, W is the water flow rate, Tslab is the
temperature of the slab surface, Tspray is the temperature of
the spray cooling water, and α is a machine-dependent
calibration factor.
3. Results and Discussion
Fig. 3.
3.1. Top Free Surface Characteristics
A number of studies have shed light on the important
aspects of top free surface characteristics in slab, billet and
bloom continuous casting molds,1) but few studies are related to the beam-blank continuous casting.
Figure 4 shows the predicted level fluctuation, maximum
velocity magnitude and temperature distribution on the top
free surface. Using the straight SEN, the level fluctuation is
less than 1 mm and the velocity magnitude is far from a reasonable interval. One of the reasons for the weak and calm
top free surface characteristics is that the use of two nozzles
per mold for uniform steel feeding which can reduce the
impact caused by molten steel injection, and meanwhile a
few publications9,21) have suggested that the flow near the
meniscus is characterized by a low turbulence.
Using the radial flow SEN, the “self-braking” effect
caused by two radial flow SENs provides good flow stability at the web region, as shown in Fig. 4(a). When the radial
flow SEN is adopted, the level fluctuation, velocities and
temperature at the top free surface of the mold increase
effectively when the SEN port angle changes upward. With
the radial flow SEN, the maximum velocity and temperature
distribution at the top free surface is obviously larger than
that of using the straight SEN. Considering that low temperature and inactive meniscus status induced by the straight
SEN are bad for the function of mold flux, which could give
rise to bad strand quality and it implies the radial flow SEN
has a better performance than that of using the straight SEN.
Also, due to that the flow structures inside the mold have a
significant influence on the meniscus,22) though there is a
high horizontal velocity magnitude near the fillet using the
radial flow SEN as Fig. 4(b) shows, the fluctuation is not
obvious.
However, the wave crest near the flange tip as shown in
Geometrical model and mesh systems: (a) mold with the
single-port straight SEN; (b) mold with the new designed
three-port radial flow SEN.
Table 1.
Properties and conditions of the simulations.
Items
Values
Geometry
Mold Length, m
0.8
Effective mold length, m
0.7
Casting parameter
Casting speed, m/min
0.6, 1.0
Superheat, K
20
Straight SEN submergence depth, mm
60–100
Radial flow SEN submergence depth, mm
115
Thermo-physical properties of steel
Liquids temperature, K
1 791
Solidus temperature, K
1 753
Specific heat of steel, J/kg/K
Latent heat of solidification of steel, J/kg
700
272 000
Thermal conductivity of steel, W/m/K
32
3
Density of steel, kg/m
7 020
3
Density of flux, kg/m
3 000
Viscosity of steel, kg/m/s
0.0062
Steel composition (Provided by some plant for specific conditions)
Steel chemistry in mass %: C=0.17, Si=0.19, Mn=0.51, P=0.017, S=0.016.
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© 2015 ISIJ
ISIJ International, Vol. 55 (2015), No. 4
Fig. 4.
Top free surface characteristics: (a) level fluctuation, calculate by using Eq. (4); (b) velocity magnitude, which is
defined as ux2 + uy2 , where ux and uy are the velocities in x direction and in y direction, respectively; (c) temperature distribution.
Fig. 4(a) which generates the thinnest liquid flux layer may
prevent the mold powder from penetrating into the gap
between the mold and the solidifying shell, which is not
favorable for the mold lubrication, and the maximum temperature of the top free surface appears at the web center as
shown in Fig. 4(c), and the mold flux at high temperature
locations may be burned, thus, more reoxidation will occur
due to the reaction with air, and therefore reduce the steel
cleanliness. For a suitable meniscus status, the radial flow
SEN with a positive angle should use a submergence depth
deeper than 115 mm and the radial flow SEN with a negative angle could be used at a faster casting speed.
Fig. 5.
3.2. Fluid Flow in the Mold
To verify acceptable accuracy of the present mathematical
model, the predictions are compared with experiments conducted using a transparent plastic water model of the system, as shown in Fig. 5. In order to observe the flow pattern
in the mold, a small quantity of visible tracer ink is injected
into the water after steady-state conditions are achieved. The
computed results for the velocity fields are found to be in a
© 2015 ISIJ
Schematic depiction of the full-scale geometry water model
experiment.
reasonably good agreement with the results of water model
both for the single-port straight SEN and the radial flow
SEN.
Figure 6 shows the flow patterns in a water model of the
beam-blank continuous casting mold with different SENs at
the same casting speed 1.0 m/min. It can be seen that using
the radial flow SEN, with the port angles varying from –15
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ISIJ International, Vol. 55 (2015), No. 4
Fig. 6.
Flow patterns obtained with different nozzles in the mold at casting speed 1.0 m/min: (a) straight SEN: (b) radial
flow SEN, port angle –15 degree; (c) radial flow SEN, port angle 0 degree; (d) radial flow SEN, port angle +15
degree.
Fig. 7.
Flow pattern in the beam-blank mold: (a) characteristics of straight SEN, locating in an off-center position; (b)
flow field obtained with straight SEN, wide face center-plane, the velocity higher than 0.2 m/s is blanked for a
more clearly visual effect; (c) flow field obtained with straight SEN, three-dimensional arrangement; (d) flow field
obtained with radial flow SEN with port angle –15 degree at casting speed 1.0 m/min.
to +15 degree, the active region obviously moves upward to
the meniscus. Zhang and his coworkers first proposed the
“self-braking” for a single SEN with four ports,23) and in the
present study, a clear “self-braking” effect as Fig. 6 shows has
been achieved in the web region by two radial flow SENs.
In the beam-blank mold, the SEN is closer to the flange
as Fig. 7(a) indicates, so the “reverse flow” will not appear
near the flange and there is a “washing zone”. In Fig. 7(b),
on the wide face center-plane of the mold, two swirl centers
at the same height can be found, which is a typical single-roll
flow pattern and not favorable for the mold metallurgical
behavior.24,25) Fig. 7(c) shows the three-dimensional pattern of
fluid flow in the vertical sections of the strand at casting
speed 1.0 m/min with submergence depth 80 mm. Fig. 7(d)
shows the “self-braking” effect we obtained by two radial
flow SENs and after the fluid leaves the SEN and enters the
mold, the flow out from two SENs’ ports will occur in the
web center. After collision of the two streams, a stream will
flow upward, another downward. The upward stream will
help to obtain an active meniscus, and both of the upward
and downward stream will augment the temperature of the
meniscus and inside the mold.
Fig. 8.
Predicted shell surface temperature distribution in the
beam-blank mold.
3.3. Temperature Distribution and Solidification
Figure 8 shows the temperature distribution along the
mold surface with two different type SENs. It can be clearly
seen that both SEN structure and casting speed strongly
affect the temperature distribution on the surface of the
strand. Using the radial flow SEN, molten steel jet first
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© 2015 ISIJ
ISIJ International, Vol. 55 (2015), No. 4
Fig. 9.
Fig. 10.
Temperature distribution along the strand surface in the beam-blank mold and the legend could be found in Fig.
10: (a) flange tip center; (b) web center.
Shell thickness distribution along Z direction, the liquid fraction was set to be 0.2, which stands for a full solidified shell: (a) flange tip center; (b) web center.
impinges on the flange tip. The “self-braking” also creates
impingement near the “self-braking” zone. These impingements produce a local maximum in superheat extraction at
this location, so a disproportionately large amount of the
superheat is delivered to the flange tip and the web center,
which increases the risk of breakouts and defects.
Details of the calculated surface temperature of the shell
surface in the two parts of the beam-blank are shown in Fig.
9. At the initial stage of the solidification, the temperature
at the outer strand surface is largely determined by the SEN
structure. Lower the SEN port angle or casting speed could
significantly decrease the local highest temperature. Considering that the maximum heat flux from superheat dissipation
is always centered about the point where the jet impinges
upon the inside of the solidified shell,26) the local temperature should be lower than that of the simulation results. At
the flange center, the SEN port angle could not obviously
change the temperature. Also, at the same casting speed,
SEN structure cannot change obviously the temperature at
these positions. The radial flow SEN can increase the web
temperature at the lower part of the mold, as shown in Fig.
9(b).
The corresponding distribution of shell thickness in the
flange center and web center of the beam-blank are shown
in Fig. 10 and it can be seen that, using the radial flow SEN,
at the initial stage of the solidification, too much superheat
is delivered to these regions because of the directly impingement or “self-braking” effect which confines superheat to a
© 2015 ISIJ
Fig. 11.
Solidified shell profile and isothermal-surfaces using the
three-port radial flow SEN at casting speed 1.0 m/min.
narrow region as Fig. 11 shows. Shell growth significantly
slows down or even reverses locally in these regions and it
is likely to increase the incidence of breakouts and could
have an important effect on other quality problems as well.
At the mold exit, the cross secion temperature distribution
is presented in Fig. 12. Using the straight SEN, it can be
seen that there is a high temperature gradient. Using the
radial flow SEN, the temperature distribution at the mold
exit is more uniform and may be helpful to avoid serious
center looseness caused by using the straight SEN or unsuitable secondary cooling strategy, as shown in Fig. 13.
Figure 14 shows the solidified shell profile at the mold
exit, from which it can be clearly seen that there are many
differences. With the straight SEN, the shell thickness is
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ISIJ International, Vol. 55 (2015), No. 4
thinner at the fillet but thicker at the web. The thin solidified
shell thickness of the fillet could be validated by Fig. 15.
According to the experience in a few steelworks, the break-
Fig. 12.
outs usually occur at the fillet, which further confirms the
present calculation results. The radial flow SEN could
decrease the risk of breakouts caused by rupture of skin at
Contours of temperature field and velocity vectors at the
beam-blank mold exit at casting speed 1.0 m/min, straight
SEN with submergence depth 60 mm and radial flow SEN
with port angle 0 degree.
Fig. 13.
Macroetch of a transverse section of beam-blank.
Fig. 14.
Comparison of solidified shell thickness at the mold exit: (a) single-port straight SEN with submergence depth 80
mm at casting speed 1.0 m/min; (b) radial flow SEN with port angle –15 degree.
Fig. 15.
Photographs of solidified shell: (a) obtained by adding radioactive tracer to the liquid pool;27) (b) obtained by a
breakout.2)
Fig. 16.
Solidified shell profile: (a) flange depression, from some steelworks in China; (b) calculated shell profile, an
average value of solid fraction 0.5 is chosen in order to have a better view; (c) calculated shell thickness distribution of the flange at the mold exit at casting speed 1.0 m/min.
797
© 2015 ISIJ
ISIJ International, Vol. 55 (2015), No. 4
the fillet. With the radial flow SEN, the shell thickness is
thinner at the web center, as shown in Fig. 14(b), and it
should be mentioned that the molten steel jet angle largely
determined by the port angle could influence the heat flux
at the interface of mold cooper and solidified shell,26) so the
shell thickness at the web center as Fig. 14(b) shows should
be treated critically.
Using the single-port straight SEN, the depression sometimes occurs at the flange, as shown in Fig. 16(a). This
defect should be caused by the structure of straight SEN.
The characteristics of this nozzle locating in an off-center
position have been introduced in Fig. 7(a), and the washing
effect results in shell erosion in local thin spots and cause a
“wavy contour” as shown in Figs. 14(a) and 15(b). The
flange depression indicates that the “wavy contour” shell
could be unable to withstand the stress of solidified shell
shrinkage process and could be pushed back by the mold
inner surface or the retaining rolls in the secondary cooling
zone.
The simulated shell profile in the beam-blank mold is
shown in Fig. 16(b), and how the impinging molten steel jet
pouring from the straight SEN affects the shell distribution
of the flange can be found. Fig. 16(c) clearly shows that the
shell thickness of the flange at the mold exit is very nonuniform. Using the radial flow SEN, the shell thickness at
the flange is more uniform and thicker, and may avoid the
flange depression. In addition, shell thickness is the minimum in the position which is about 0.03 m away from the
flange center in Fig. 16(c), this may be induced by the
reverse flow from the web region, as shown in Figs. 7(b)
and 12, because the reverse flow can push the molten steel
jet and change its shape slightly.
of the single-port straight SEN in a beam-blank mold locating in an off-center position are illustrated and the flange
depression is possibly caused by the off-center molten steel
jet washing effect.
(2) The new designed three-port radial flow SEN has
the advantage to obtain an active meniscus status and a uniform shell thickness distribution except the web center. This
type nozzle could decrease the risk of breakouts caused by
the rupture of skin at the fillet and reduce the probability of
flange depression, center looseness and the crack of strand.
(3) The “self-braking” effect caused by two radial flow
SENs provides a good stability of flow at the meniscus, but
this braking effect could confine a large amount of superheat
to a small region and a further improvement is necessary in
future.
Acknowledgements
The authors would like to thank the financial support
from the Fundamental Research Funds for the Central
Universities No. N130602005.
REFERENCES
1) B. G. Thomas and L. F. Zhang: ISIJ Int., 41 (2001), 1181.
2) L. C. Hibbeler, S. Koric, K. Xu, B. G. Thomas and C. Spangler: Iron
Steel Tech., 6 (2009), 60.
3) W. Chen, Y. Z. Zhang, C. J. Zhang, L. G. Zhu, B. X. Wang, W. G.
Lu and J. H. Ma: Acta Metall. Sin., 20 (2007), 241.
4) J.-E. Lee, T.-J. Yeo, K. H. Oh, J.-K. Yoon and U.-S. Yoon: Metall.
Mater. Trans. A, 31A (2000), 225.
5) H. L. Xu, G. H. Wen, W. Sun, K. Z. Wang, B. Yan and W. Luo: Ironmaking Steelmaking, 37 (2010), 380.
6) W. Luo, B. Yan, X. Lu and G. H. Wen: Ironmaking Steelmaking, 40
(2013), 582.
7) W. Luo, B. Yan, Y. X. Xiong, G. H. Wen and H. L. Xu: Ironmaking
Steelmaking, 39 (2012), 125.
8) Y. Zhao, D. F. Chen, M. J. Long, J. L. Shen and R. S. Qin: Ironmaking Steelmaking, 41 (2014), 377.
9) J.-E. Lee, J.-K. Yoon and H. N. Han: ISIJ Int., 38 (1998), 132.
10) D. R. Poirier: Metall. Trans. B, 18B (1987), 245.
11) H. L. Yang, L. G. Zhao, X. Z. Zhang, K. W. Deng, W. C. Li and Y.
Gan: Metall. Mater. Trans. B, 29B (1998), 1345.
12) D. E. Hershey, B. G. Thomas and F. M. Najjar: Int. J. Numer. Meth.
Fluids, 17 (1993), 23.
13) V. R. Voller and C. Prakash: Int. J. Heat Mass Transfer, 30 (1989),
1709.
14) H. P. Liu, M. G. Xu, S. T. Qiu and H. Zhang: Metall. Mater. Trans.
B, 43B (2012), 1657.
15) F. M. Najiar, B. G. Thomas and D. E. Hershey: Metall. Mater. Trans.
B, 26B (1995), 749.
16) M. Kamal and Y. Sahai: Steel Res. Int., 76 (2005), 44.
17) H. Nam, H.-S. Park and J. K. Yoon: ISIJ Int., 40 (2000), 886.
18) B. G. Thomas, L. J. Mika and F. M. Najiar: Metall. Trans. B, 21B
(1990), 387.
19) J. Savage and W. H. Pritchard: J. Iron Steel Inst., 178 (1954), 268.
20) T. Nozaki, J. L. Matsuno, K. Murata, H. Ooi and M. Kodama: Trans.
Iron Steel Inst. Jpn., 18 (1978), 330.
21) E. Torres-Alonso, R. D. Morales, S. Hernandez-Garcia and J.
Palafox-Ramos: Metall. Mater. Trans. B, 39B (2008), 840.
22) Y. J. Jeon, H. J. Sung and S. Lee: Metall. Mater. Trans. B, 41B
(2010), 121.
23) Y. F. Chen, L. F. Zhang, S. F. Yang and J. S. Li: JOM, 64 (2012),
1080.
24) B. G. Thomas: Fluid Flow in the Mold, Vol. 5, ed. by A. Cramb,
AISE Steel Foundation, Pittsburgh, PA, (2003), 9.
25) L. C. Hibbeler and B. G. Thomas: AIST 2010 Steelmaking Conf.
Proc., AIST, Warrendale, PA, (2010).
26) X. Huang, B. G. Thomas and F. M. Najjar: Metall. Mater. Trans. B,
23B (1992), 339.
27) J.-E. Lait, J. K. Brimacombe, F. Weinberg and F. C. Muttitt: Open
Hearth Conf. Proc., Vol. 56, ISS, Warrendale, PA, (1973), 259.
4. Conclusions
Since there are a number of quality problems in beamblank casting using the straight SEN, such as the weak and
calm meniscus status, non-uniform shell thickness distribution at the mold exit, flange depression and breakouts
induced by the rupture of the fillet, mathematical modeling
has been used to investigate the suitable structure of SEN by
the analysis of the transport phenomena in the mold. In
order to facilitate the comparison and analysis, in all the
simulations, the same thermal boundary is assumed. Though
the Savage and Prichard’s relation could provide a reasonable tendency to describe the heat flux profile along the
height of the mold, there are unavoidable partial difference
in solidification, especially when the radial flow SEN is
used and the results of solidification should be treated critically.
(1) Using the single-port straight SEN, the major shortcomings are inactive top free surface and non-uniform shell
thickness distribution at the mold exit. It’s hard to obtain a
suitable meniscus status by simply changing the SEN submergence depth. Center looseness of a transverse section of
the beam-blank is related with large temperature gradient
caused by molten steel jet from this nozzle. Characteristics
© 2015 ISIJ
798
Transport Phenomena in a Beam-Blank Continuous Casting Mold
with Two Types of Submerged Entry Nozzle
Mianguang XU and Miaoyong ZHU*
School of Materials and Metallurgy, Northeastern University, No. 3 Wenhua Road, Heping District, Shenyang, 110819 P.R. China.
(Received on September 18, 2014; accepted on December 22, 2014)
A three-dimensional full-coupled mathematical model is established to study the fluid flow, heat transfer
and solidification in a 450 mm × 350 mm × 90 mm beam-blank mold with two different types of submerged
entry nozzle (SEN), namely single-port straight SEN and three-port radial flow SEN. Water modeling experiments, industrial trials and public results available in literature are performed to validate the numerical
results. The results show that, with the straight SEN which has been widely applied in beam-blank continuous casting, there is a very inactive top free surface in the mold which level fluctuation magnitude is less
than 1 mm and velocity magnitude is far from a reasonable interval, and the shell thickness distribution at
the mold exit is very uneven, thick at the web but thin at the fillet. Moreover, there exists a “wavy contour” at the flange due to the washing effect of the off-center molten steel jet. While with the new
designed radial flow SEN, a suitable meniscus status and a more uniform shell thickness at the mold exit
can be obtained, which is helpful to avoid the breakouts caused by the rupture of thin fillet and the flange
depression. The “self-braking” effect caused by two radial flow SENs provides good flow stability at the
web center.
KEY WORDS: beam-blank; continuous casting; submerged entry nozzle; transport phenomena; numerical
simulation.
posed to meet the demand for higher quality.
Mathematical modeling is very convenient for investigating
the suitable structure of SEN and has had a wide application
as a powerful tool in the analysis of the transport phenomena
in the mold. Unfortunately, most of mathematical models
about beam-blank continuous casting are based on the mold
thermal-mechanical analysis,2–4) mold water channel design5,6)
and secondary cooling strategy,7,8) a few literatures found
are mainly on the straight SEN.4,9) With such SEN, two
major problems engineers encountering in steelworks are
the inactive meniscus status and the non-uniform shell
thickness distribution at the mold exit, which can seriously
affect the function of the mold flux and the uniform distri-
1. Introduction
Recently, as a near-net-shape continuous casting technique, the need of beam-blank steel has been experiencing
a dramatic rapid increase and more than ten beam-blank
continuous casting machines have been put into production
in China due to its special usage, economic advantages and
outstanding mechanical properties. However, there is a common problem that the producers have to face, that is the
quality of continuously cast beam-blank, especially the
crack of the strand. As it is known, most of defects affecting
steel quality in the continuous casting process are associated
with fluid flow in the mold which is largely determined by
the SEN structure.1) SEN structure can strongly affect the
transport phenomena in mold, including meniscus status,
superheat dissipation, solidified shell growth and inclusion
removal. However, the complicated mold geometry shape
creates great difficulties for the design of a suitable SEN.
Although the beam-blank caster was installed at Maanshan
Steel in China in 1998, the simple straight SEN is still widely used. With this nozzle, molten steel is directly open
poured into two ceramic funnels, which are located in the
central flange regions, as shown in Fig. 1. Such pouring
method can give rise to serious problems on the quality of
final products, especially in the production of some new
steel grade, so new types of SEN are necessary to be pro-
Fig. 1.
* Corresponding author: E-mail: [email protected]
DOI: http://dx.doi.org/10.2355/isijinternational.55.791
791
Molten steel open poured into ceramic funnels: (a) industrial trial, two nozzles per mold are used for uniform steel
feeding; (b) schematic of upper nozzle and SEN.
© 2015 ISIJ
ISIJ International, Vol. 55 (2015), No. 4
bution of the stress and ultimately lead to a bad quality.
In the current study, a mathematical model based on the
enthalpy-porosity approach in a single-framework has been
developed for the prediction of three-dimensional transport
phenomena including fluid flow, heat transfer and solidification in a beam-blank slab casting process. With the understanding of shortcomings of the straight SEN and previous
studies, a new designed three-port radial flow SEN geometry and proper relevant casting parameters are presented for
the purpose of overcoming two major problems, and the
effects of port angle, casting speed and “self-braking”
induced by two radial flow SENs are discussed.
2.2.
Geometrical Model, Boundary and Initial Conditions
The research object of present work is a five-strand
bloom/beam-blank continuous casting machine with the
length about 37 m and the mold is not instrumented with
thermo-couples. The single-port straight SEN used in steelworks is shown in Fig. 2(a) and the new designed three-port
radial flow SEN is shown in Fig. 2(b).
The aspect ratio of thickness to height for the port of radial flow SEN is selected to be 0.83 in order to improve the
effectiveness of the SEN having a better direction of molten
steel flow to ensure its “self-braking” in the mold. The
geometry for the port of radial flow SEN is shown in Fig.
2(b), and the total area of these three ports is 32 pct larger
than that of the original straight SEN to enhance the inclusion removal ratio.15) The present simulations are performed
for port angles varying from –15 to +15 degree (downward
and upward port angles are denoted with + and – sign,
respectively).
At all the refractory walls of SEN, the zero-slip boundary
condition is applied16) and the thermal insulation is assumed.
The inlet velocity is computed by using the mass conservation between the inlet and outlet according to casting
speed.17) The values of turbulent kinetic energy k and its
dissipation rate ε at the inlet of SEN are based on the semiempirical expressions.18) The meniscus is specified as a
zero-shear condition.14)
In the mold region, the heat flux from the surface of
strand to the mold is assumed to be a function of the casting
speed and the distance below the meniscus, as suggested by
Lee et al.4) and Luo et al.7) With the straight SEN, the mea-
2. Mathematical Models
2.1. Mathematical Formulations
The general assumptions applied in the present solidification of beam-blank continuous casting can be found
elsewhere.11) There are seven partial equations in the threedimensional mathematical model which are solved by the
algorithm of SIMPLE, including one mass equation, three
momentum equations, two standard k-ε turbulence
equations12) and one energy equation.13) When the residual
for energy is smaller than 10–6 and others are smaller than
10–4, the converged solution is obtained. The general form
of all the partial equations can be written as the form of Eq.
(1).
∂
∂
∂φ
( ρ uiφ ) = ⎛⎜ Γ φ ⎞⎟ + Sφ ................. (1)
∂xi
∂xi ⎝
∂xi ⎠
where ρ is the steel density, ui is the speed in i direction, ϕ
is the variables including velocities at three directions, temperature, enthalpy, turbulence energy and its dissipation
rate, xi is the direction, Γϕ is the coefficient of diffusion and
Sϕ is the source term.
To accountant for the macro-solidification process, additional source terms SDarcy10) are added to momentum equations and turbulence equations, as shown in Eqs. (2) and (3),
respectively.
SDarcy_mom = − A
fs2
(1 − fs )
SDarcy_tur = − A
3
+ 0.001
( ui − us,i )
fs2
(1 − fs )
3
+ 0.001
........ (2)
ϕ tur .............. (3)
where A is the mushy zone constant and its value is set to
be 5×10–6, fs is the solid fraction which is assumed to vary
linearly between the liquidus temperature and solidus temperature, us,i is the moving speed of the solidified shell, and
ϕtur represents the turbulence quantity.
The top free surface profile in the beam-blank mold is
expressed in Eq. (4) by the liquid displacement estimated
from a simple potential energy balance.14)
Δz = −
p − pmean
( ρ − ρflux ) g
.......................... (4)
where Δz is the top free surface height, p is the static
pressure of the top free surface, pmean is the area-weighted
average value of the static pressure over the entire top free
surface, and ρflux is the flux density.
© 2015 ISIJ
Fig. 2.
792
Schematic drawing of beam-blank mold and SEN vertical
section: (a) beam-blank mold with an original single-port
straight SEN; (b) beam-blank mold with a new design of
radial flow SEN.
ISIJ International, Vol. 55 (2015), No. 4
surement of the mold water volume and water temperature
differences between the inflow and the outflow of cooling
water is employed, and the value of constant b obtained in
the Savage and Prichard’s relation q=a–b⋅t1/2 is 0.336.19)
The typical kinds of computation domains are presented
in Fig. 3, and the hexahedral mesh system is adopted to
improve calculation precision. The full-coupled simulation
starts from a previously converged flow-field solution and
the temperature of the pool region at the initial time is set
to be 1 828 K. The geometry, casting conditions, material
properties and computational conditions are summarized in
Table 1, and SEN submergence depth is defined as the dis-
tance of SEN bottom from meniscus. In order to minimize
the end effect of fluid flow at the outlet boundary, the
computational domain has a distance longer than the effective length of the mold along the casting direction, the
calculation domain is cut off 700 mm below the mold exit,
so the secondary cooling zone I (0.66 m, water flow rate 260
L/min) is completely included and secondary cooling zone
II (1.6 m, water flow rate 70 L/min) is partly included. In
the regions of secondary cooling spray, the heat transfer is
defined as the Robin boundary condition as shown in Eq. (5)
and the spray cooling heat-transfer coefficient hspray is calculated by using Eq. (6).20) By calculating Eq. (6), hspary in
Eq. (5) is 1 004.5 W/m2/K in the secondary cooling zone I
and 768.2 W/m2/K in the secondary cooling zone II , respectively.
q = hspray ( Tslab − Tspray ) ........................ (5)
hspray =
1.57 × W 0.55 × (1.0 − 0.0075 × Tspray )
....... (6)
α
where q is the heat flux, W is the water flow rate, Tslab is the
temperature of the slab surface, Tspray is the temperature of
the spray cooling water, and α is a machine-dependent
calibration factor.
3. Results and Discussion
Fig. 3.
3.1. Top Free Surface Characteristics
A number of studies have shed light on the important
aspects of top free surface characteristics in slab, billet and
bloom continuous casting molds,1) but few studies are related to the beam-blank continuous casting.
Figure 4 shows the predicted level fluctuation, maximum
velocity magnitude and temperature distribution on the top
free surface. Using the straight SEN, the level fluctuation is
less than 1 mm and the velocity magnitude is far from a reasonable interval. One of the reasons for the weak and calm
top free surface characteristics is that the use of two nozzles
per mold for uniform steel feeding which can reduce the
impact caused by molten steel injection, and meanwhile a
few publications9,21) have suggested that the flow near the
meniscus is characterized by a low turbulence.
Using the radial flow SEN, the “self-braking” effect
caused by two radial flow SENs provides good flow stability at the web region, as shown in Fig. 4(a). When the radial
flow SEN is adopted, the level fluctuation, velocities and
temperature at the top free surface of the mold increase
effectively when the SEN port angle changes upward. With
the radial flow SEN, the maximum velocity and temperature
distribution at the top free surface is obviously larger than
that of using the straight SEN. Considering that low temperature and inactive meniscus status induced by the straight
SEN are bad for the function of mold flux, which could give
rise to bad strand quality and it implies the radial flow SEN
has a better performance than that of using the straight SEN.
Also, due to that the flow structures inside the mold have a
significant influence on the meniscus,22) though there is a
high horizontal velocity magnitude near the fillet using the
radial flow SEN as Fig. 4(b) shows, the fluctuation is not
obvious.
However, the wave crest near the flange tip as shown in
Geometrical model and mesh systems: (a) mold with the
single-port straight SEN; (b) mold with the new designed
three-port radial flow SEN.
Table 1.
Properties and conditions of the simulations.
Items
Values
Geometry
Mold Length, m
0.8
Effective mold length, m
0.7
Casting parameter
Casting speed, m/min
0.6, 1.0
Superheat, K
20
Straight SEN submergence depth, mm
60–100
Radial flow SEN submergence depth, mm
115
Thermo-physical properties of steel
Liquids temperature, K
1 791
Solidus temperature, K
1 753
Specific heat of steel, J/kg/K
Latent heat of solidification of steel, J/kg
700
272 000
Thermal conductivity of steel, W/m/K
32
3
Density of steel, kg/m
7 020
3
Density of flux, kg/m
3 000
Viscosity of steel, kg/m/s
0.0062
Steel composition (Provided by some plant for specific conditions)
Steel chemistry in mass %: C=0.17, Si=0.19, Mn=0.51, P=0.017, S=0.016.
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ISIJ International, Vol. 55 (2015), No. 4
Fig. 4.
Top free surface characteristics: (a) level fluctuation, calculate by using Eq. (4); (b) velocity magnitude, which is
defined as ux2 + uy2 , where ux and uy are the velocities in x direction and in y direction, respectively; (c) temperature distribution.
Fig. 4(a) which generates the thinnest liquid flux layer may
prevent the mold powder from penetrating into the gap
between the mold and the solidifying shell, which is not
favorable for the mold lubrication, and the maximum temperature of the top free surface appears at the web center as
shown in Fig. 4(c), and the mold flux at high temperature
locations may be burned, thus, more reoxidation will occur
due to the reaction with air, and therefore reduce the steel
cleanliness. For a suitable meniscus status, the radial flow
SEN with a positive angle should use a submergence depth
deeper than 115 mm and the radial flow SEN with a negative angle could be used at a faster casting speed.
Fig. 5.
3.2. Fluid Flow in the Mold
To verify acceptable accuracy of the present mathematical
model, the predictions are compared with experiments conducted using a transparent plastic water model of the system, as shown in Fig. 5. In order to observe the flow pattern
in the mold, a small quantity of visible tracer ink is injected
into the water after steady-state conditions are achieved. The
computed results for the velocity fields are found to be in a
© 2015 ISIJ
Schematic depiction of the full-scale geometry water model
experiment.
reasonably good agreement with the results of water model
both for the single-port straight SEN and the radial flow
SEN.
Figure 6 shows the flow patterns in a water model of the
beam-blank continuous casting mold with different SENs at
the same casting speed 1.0 m/min. It can be seen that using
the radial flow SEN, with the port angles varying from –15
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ISIJ International, Vol. 55 (2015), No. 4
Fig. 6.
Flow patterns obtained with different nozzles in the mold at casting speed 1.0 m/min: (a) straight SEN: (b) radial
flow SEN, port angle –15 degree; (c) radial flow SEN, port angle 0 degree; (d) radial flow SEN, port angle +15
degree.
Fig. 7.
Flow pattern in the beam-blank mold: (a) characteristics of straight SEN, locating in an off-center position; (b)
flow field obtained with straight SEN, wide face center-plane, the velocity higher than 0.2 m/s is blanked for a
more clearly visual effect; (c) flow field obtained with straight SEN, three-dimensional arrangement; (d) flow field
obtained with radial flow SEN with port angle –15 degree at casting speed 1.0 m/min.
to +15 degree, the active region obviously moves upward to
the meniscus. Zhang and his coworkers first proposed the
“self-braking” for a single SEN with four ports,23) and in the
present study, a clear “self-braking” effect as Fig. 6 shows has
been achieved in the web region by two radial flow SENs.
In the beam-blank mold, the SEN is closer to the flange
as Fig. 7(a) indicates, so the “reverse flow” will not appear
near the flange and there is a “washing zone”. In Fig. 7(b),
on the wide face center-plane of the mold, two swirl centers
at the same height can be found, which is a typical single-roll
flow pattern and not favorable for the mold metallurgical
behavior.24,25) Fig. 7(c) shows the three-dimensional pattern of
fluid flow in the vertical sections of the strand at casting
speed 1.0 m/min with submergence depth 80 mm. Fig. 7(d)
shows the “self-braking” effect we obtained by two radial
flow SENs and after the fluid leaves the SEN and enters the
mold, the flow out from two SENs’ ports will occur in the
web center. After collision of the two streams, a stream will
flow upward, another downward. The upward stream will
help to obtain an active meniscus, and both of the upward
and downward stream will augment the temperature of the
meniscus and inside the mold.
Fig. 8.
Predicted shell surface temperature distribution in the
beam-blank mold.
3.3. Temperature Distribution and Solidification
Figure 8 shows the temperature distribution along the
mold surface with two different type SENs. It can be clearly
seen that both SEN structure and casting speed strongly
affect the temperature distribution on the surface of the
strand. Using the radial flow SEN, molten steel jet first
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ISIJ International, Vol. 55 (2015), No. 4
Fig. 9.
Fig. 10.
Temperature distribution along the strand surface in the beam-blank mold and the legend could be found in Fig.
10: (a) flange tip center; (b) web center.
Shell thickness distribution along Z direction, the liquid fraction was set to be 0.2, which stands for a full solidified shell: (a) flange tip center; (b) web center.
impinges on the flange tip. The “self-braking” also creates
impingement near the “self-braking” zone. These impingements produce a local maximum in superheat extraction at
this location, so a disproportionately large amount of the
superheat is delivered to the flange tip and the web center,
which increases the risk of breakouts and defects.
Details of the calculated surface temperature of the shell
surface in the two parts of the beam-blank are shown in Fig.
9. At the initial stage of the solidification, the temperature
at the outer strand surface is largely determined by the SEN
structure. Lower the SEN port angle or casting speed could
significantly decrease the local highest temperature. Considering that the maximum heat flux from superheat dissipation
is always centered about the point where the jet impinges
upon the inside of the solidified shell,26) the local temperature should be lower than that of the simulation results. At
the flange center, the SEN port angle could not obviously
change the temperature. Also, at the same casting speed,
SEN structure cannot change obviously the temperature at
these positions. The radial flow SEN can increase the web
temperature at the lower part of the mold, as shown in Fig.
9(b).
The corresponding distribution of shell thickness in the
flange center and web center of the beam-blank are shown
in Fig. 10 and it can be seen that, using the radial flow SEN,
at the initial stage of the solidification, too much superheat
is delivered to these regions because of the directly impingement or “self-braking” effect which confines superheat to a
© 2015 ISIJ
Fig. 11.
Solidified shell profile and isothermal-surfaces using the
three-port radial flow SEN at casting speed 1.0 m/min.
narrow region as Fig. 11 shows. Shell growth significantly
slows down or even reverses locally in these regions and it
is likely to increase the incidence of breakouts and could
have an important effect on other quality problems as well.
At the mold exit, the cross secion temperature distribution
is presented in Fig. 12. Using the straight SEN, it can be
seen that there is a high temperature gradient. Using the
radial flow SEN, the temperature distribution at the mold
exit is more uniform and may be helpful to avoid serious
center looseness caused by using the straight SEN or unsuitable secondary cooling strategy, as shown in Fig. 13.
Figure 14 shows the solidified shell profile at the mold
exit, from which it can be clearly seen that there are many
differences. With the straight SEN, the shell thickness is
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ISIJ International, Vol. 55 (2015), No. 4
thinner at the fillet but thicker at the web. The thin solidified
shell thickness of the fillet could be validated by Fig. 15.
According to the experience in a few steelworks, the break-
Fig. 12.
outs usually occur at the fillet, which further confirms the
present calculation results. The radial flow SEN could
decrease the risk of breakouts caused by rupture of skin at
Contours of temperature field and velocity vectors at the
beam-blank mold exit at casting speed 1.0 m/min, straight
SEN with submergence depth 60 mm and radial flow SEN
with port angle 0 degree.
Fig. 13.
Macroetch of a transverse section of beam-blank.
Fig. 14.
Comparison of solidified shell thickness at the mold exit: (a) single-port straight SEN with submergence depth 80
mm at casting speed 1.0 m/min; (b) radial flow SEN with port angle –15 degree.
Fig. 15.
Photographs of solidified shell: (a) obtained by adding radioactive tracer to the liquid pool;27) (b) obtained by a
breakout.2)
Fig. 16.
Solidified shell profile: (a) flange depression, from some steelworks in China; (b) calculated shell profile, an
average value of solid fraction 0.5 is chosen in order to have a better view; (c) calculated shell thickness distribution of the flange at the mold exit at casting speed 1.0 m/min.
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ISIJ International, Vol. 55 (2015), No. 4
the fillet. With the radial flow SEN, the shell thickness is
thinner at the web center, as shown in Fig. 14(b), and it
should be mentioned that the molten steel jet angle largely
determined by the port angle could influence the heat flux
at the interface of mold cooper and solidified shell,26) so the
shell thickness at the web center as Fig. 14(b) shows should
be treated critically.
Using the single-port straight SEN, the depression sometimes occurs at the flange, as shown in Fig. 16(a). This
defect should be caused by the structure of straight SEN.
The characteristics of this nozzle locating in an off-center
position have been introduced in Fig. 7(a), and the washing
effect results in shell erosion in local thin spots and cause a
“wavy contour” as shown in Figs. 14(a) and 15(b). The
flange depression indicates that the “wavy contour” shell
could be unable to withstand the stress of solidified shell
shrinkage process and could be pushed back by the mold
inner surface or the retaining rolls in the secondary cooling
zone.
The simulated shell profile in the beam-blank mold is
shown in Fig. 16(b), and how the impinging molten steel jet
pouring from the straight SEN affects the shell distribution
of the flange can be found. Fig. 16(c) clearly shows that the
shell thickness of the flange at the mold exit is very nonuniform. Using the radial flow SEN, the shell thickness at
the flange is more uniform and thicker, and may avoid the
flange depression. In addition, shell thickness is the minimum in the position which is about 0.03 m away from the
flange center in Fig. 16(c), this may be induced by the
reverse flow from the web region, as shown in Figs. 7(b)
and 12, because the reverse flow can push the molten steel
jet and change its shape slightly.
of the single-port straight SEN in a beam-blank mold locating in an off-center position are illustrated and the flange
depression is possibly caused by the off-center molten steel
jet washing effect.
(2) The new designed three-port radial flow SEN has
the advantage to obtain an active meniscus status and a uniform shell thickness distribution except the web center. This
type nozzle could decrease the risk of breakouts caused by
the rupture of skin at the fillet and reduce the probability of
flange depression, center looseness and the crack of strand.
(3) The “self-braking” effect caused by two radial flow
SENs provides a good stability of flow at the meniscus, but
this braking effect could confine a large amount of superheat
to a small region and a further improvement is necessary in
future.
Acknowledgements
The authors would like to thank the financial support
from the Fundamental Research Funds for the Central
Universities No. N130602005.
REFERENCES
1) B. G. Thomas and L. F. Zhang: ISIJ Int., 41 (2001), 1181.
2) L. C. Hibbeler, S. Koric, K. Xu, B. G. Thomas and C. Spangler: Iron
Steel Tech., 6 (2009), 60.
3) W. Chen, Y. Z. Zhang, C. J. Zhang, L. G. Zhu, B. X. Wang, W. G.
Lu and J. H. Ma: Acta Metall. Sin., 20 (2007), 241.
4) J.-E. Lee, T.-J. Yeo, K. H. Oh, J.-K. Yoon and U.-S. Yoon: Metall.
Mater. Trans. A, 31A (2000), 225.
5) H. L. Xu, G. H. Wen, W. Sun, K. Z. Wang, B. Yan and W. Luo: Ironmaking Steelmaking, 37 (2010), 380.
6) W. Luo, B. Yan, X. Lu and G. H. Wen: Ironmaking Steelmaking, 40
(2013), 582.
7) W. Luo, B. Yan, Y. X. Xiong, G. H. Wen and H. L. Xu: Ironmaking
Steelmaking, 39 (2012), 125.
8) Y. Zhao, D. F. Chen, M. J. Long, J. L. Shen and R. S. Qin: Ironmaking Steelmaking, 41 (2014), 377.
9) J.-E. Lee, J.-K. Yoon and H. N. Han: ISIJ Int., 38 (1998), 132.
10) D. R. Poirier: Metall. Trans. B, 18B (1987), 245.
11) H. L. Yang, L. G. Zhao, X. Z. Zhang, K. W. Deng, W. C. Li and Y.
Gan: Metall. Mater. Trans. B, 29B (1998), 1345.
12) D. E. Hershey, B. G. Thomas and F. M. Najjar: Int. J. Numer. Meth.
Fluids, 17 (1993), 23.
13) V. R. Voller and C. Prakash: Int. J. Heat Mass Transfer, 30 (1989),
1709.
14) H. P. Liu, M. G. Xu, S. T. Qiu and H. Zhang: Metall. Mater. Trans.
B, 43B (2012), 1657.
15) F. M. Najiar, B. G. Thomas and D. E. Hershey: Metall. Mater. Trans.
B, 26B (1995), 749.
16) M. Kamal and Y. Sahai: Steel Res. Int., 76 (2005), 44.
17) H. Nam, H.-S. Park and J. K. Yoon: ISIJ Int., 40 (2000), 886.
18) B. G. Thomas, L. J. Mika and F. M. Najiar: Metall. Trans. B, 21B
(1990), 387.
19) J. Savage and W. H. Pritchard: J. Iron Steel Inst., 178 (1954), 268.
20) T. Nozaki, J. L. Matsuno, K. Murata, H. Ooi and M. Kodama: Trans.
Iron Steel Inst. Jpn., 18 (1978), 330.
21) E. Torres-Alonso, R. D. Morales, S. Hernandez-Garcia and J.
Palafox-Ramos: Metall. Mater. Trans. B, 39B (2008), 840.
22) Y. J. Jeon, H. J. Sung and S. Lee: Metall. Mater. Trans. B, 41B
(2010), 121.
23) Y. F. Chen, L. F. Zhang, S. F. Yang and J. S. Li: JOM, 64 (2012),
1080.
24) B. G. Thomas: Fluid Flow in the Mold, Vol. 5, ed. by A. Cramb,
AISE Steel Foundation, Pittsburgh, PA, (2003), 9.
25) L. C. Hibbeler and B. G. Thomas: AIST 2010 Steelmaking Conf.
Proc., AIST, Warrendale, PA, (2010).
26) X. Huang, B. G. Thomas and F. M. Najjar: Metall. Mater. Trans. B,
23B (1992), 339.
27) J.-E. Lait, J. K. Brimacombe, F. Weinberg and F. C. Muttitt: Open
Hearth Conf. Proc., Vol. 56, ISS, Warrendale, PA, (1973), 259.
4. Conclusions
Since there are a number of quality problems in beamblank casting using the straight SEN, such as the weak and
calm meniscus status, non-uniform shell thickness distribution at the mold exit, flange depression and breakouts
induced by the rupture of the fillet, mathematical modeling
has been used to investigate the suitable structure of SEN by
the analysis of the transport phenomena in the mold. In
order to facilitate the comparison and analysis, in all the
simulations, the same thermal boundary is assumed. Though
the Savage and Prichard’s relation could provide a reasonable tendency to describe the heat flux profile along the
height of the mold, there are unavoidable partial difference
in solidification, especially when the radial flow SEN is
used and the results of solidification should be treated critically.
(1) Using the single-port straight SEN, the major shortcomings are inactive top free surface and non-uniform shell
thickness distribution at the mold exit. It’s hard to obtain a
suitable meniscus status by simply changing the SEN submergence depth. Center looseness of a transverse section of
the beam-blank is related with large temperature gradient
caused by molten steel jet from this nozzle. Characteristics
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