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# wang_et_al_isij_2007

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```calculation, the defor-

mation of the surface is neglected since the effect of the
surface deformation on the flow structure in the whole
tundish is not big. The normal gradient of all variables is
equal to zero except from the normal velocity is zero.

(3) At the solid wall: Velocities at the solid wall are
zero. To estimate the velocity near a wall, it often uses a
Van Driest damping function13,14) modification to reduce the
eddy viscosity in the near-wall region:

ls�CsD[1�exp(�y�/26)] ....................(15)

Where y� is the dimensionless distance from the wall, D is
a length scale, and A� is a constant, here A��26.

(4) At the exit of the tundish: the velocity gradient is
zero.

2.5. Solution Method

The magnetic field and the electromagnetic force is
firstly calculated using the commercial software of ANSYS
8.0. Electromagnetic force is included in the NS equation.
The electromagnetic forces are obtained by interpolation
into the momentum equation. A finite volume method has
been chosen for this calculation of complicated system, and
the computer code in FORTRAN language for solution of
flow field is self-developed. The domain is discretized with
200, 68, and 68 points along the long, wide and height axes
respectively. It means a 0.92 million node computational
grid. The time step (D t) is set to 0.003 s. The filtered non-
linear simultaneous equations are solved by using SIM-
PLEC algorithm. A combination of Alternating-Direction-
semi-Implicit iteration scheme (ADI) and block correction
is used to solve the discrete algebraic equations.

3. Numerical Results

Numerical simulations are conducted on the flow field in
centrifugal flow tundish for the three cases, i.e. (a) electro-
magnetic force with the direct nozzle, (b) bending nozzle
using height potential energy of molten steel and (c) combi-
nation of electromagnetic force and bending nozzle.

3.1. Effect of Electromagnetic Force

Figures 3–5 show the calculated flow field of centrifugal
flow tundish, the electromagnetic force field in Fig. 2 is
used as the driven force of swirling flow in rotation cham-
ber. Molten steel is poured by using the direct nozzle. It can
be observed that flow field of rotation chamber is composed
of a toroidal vortex in the central zone and two small vor-
tices at the top and bottom respectively as shown in Fig. 3.
Figures 4(a)–4(c) show the flow patterns in horizontal sec-
tion of centrifugal flow tundish at three locations with
z�0.1 m, z�0.06 m and z�0.02 m. In Figs. 4(a) and 4(b)
show that there is a strong swirling flow in the rotation
chamber and a flow crack in the tundish. The crack is a re-
sult from bifurcation the upward flow at the upper of the
distribution chamber of tundish. Moreover, it can be ob-
served in Fig. 4(c) that there is a swirling flow compared
with Figs. 4(a) and 4(b), two asymmetrical vortices in the
inlet of the distribution chamber and a sink in the outlet of
the tundish. The center of swirling flow is accord with geo-
metrical center of rotation chamber, as shown in Fig. 5.

ISIJ International, Vol. 47 (2007), No. 4

Fig. 2. Calculated (a) instantaneous magnetic flux density and
(b) averaged electromagnetic force in cylindrical end of
tundish.

3.2. Effect of the Bending Nozzle

Figures 6–8 show the calculated flow field while the
bending nozzle is applied in centrifugal flow tundish. Flow
pattern in main section as shown in Fig. 6 is significantly
different from that of electromagnetic force with the direct
nozzle. The vortices pattern in rotation chamber is simple.
Figures 7(a)–7(c) show the flow patterns in horizontal sec-
tion of centrifugal flow tundish at three locations with
z�0.1 m, z�0.06 m and z�0.02 m. From Figs. 7(a) and
7(b), ones can see the jet flow discharged from bending
nozzle impinges toward the chamber wall, and then the

swirling flow can be formed. Figure 7(c) shows the outflow
from rotation chamber impinging on the sidewall of tundish
at an angle, and vortices are formed near corner and outlet
of tundish. The cores of swirling flow at different heights in
rotation chamber are not in a line and not accord with the
centerline of chamber. This is because the driven force of
swirling flow is not uniform in rotation chamber.

3.3. Effect of the Bending Nozzle and Electromagnetic
Force

Figures 9 and 10 show the calculated flow field in case
that the bending nozzle and electromagnetic force are used

ISIJ International, Vol. 47 (2007), No. 4

Fig. 3. Flow patterns in main section of centrifugal flow tundish
using the electromagnetic force.

Fig. 4. Flow patterns in horizontal section of centrifugal flow
tundish (a) through the upper plane (z�0.1 m), (b)
through the center plane of rotation chamber (z�0.06 m)
and (c) through outlet of rotation chamber (z�0.02 m).

Fig. 5. Instantaneous velocity field near the bottom of tundish
through outlet of rotation chamber (z�0.02 m).

Fig. 6. Flow patterns in main section of centrifugal flow tundish
using the bending nozzle.

Fig. 7. Flow patterns in horizontal section using the bending
nozzle (a) through bending nozzle (z�0.1 m), (b) through
the center plane of rotation chamber (z�0.06m) and (c)
through outlet of rotation chamber (z�0.02 m).

Fig. 8. Instantaneous velocity field in horizontal section using
the bending nozzle through outlet of rotation chamber
(z�0.02 m).

together. The flow patterns are complex compared with
those of above. The values of velocity component at hori-
zontal and vertical direction are in same order in rotation
chamber. There are two vortices in main section of the rota-
tion chamber and two big vortices in the distribution cham-
ber, which can be observed in Fig. 9. Figures 10(a)–10(c)
show the flow patterns in horizontal section of centrifugal
flow tundish at three locations with z�0.1 m, z�0.06 m and
z�0.02 m. Figures 10(a)–10(c) illustrate that a strong
swirling flow is formed in rotation chamber and the com-
plex vortices patterns in the distribution chamber. The in-
tensity of swirling flow in rotation chamber is remarkably
strengthened.

Figure 11 shows the transient fluctuation of the averaged
velocities at three heights with x�0.0315 m, y�0.0282 m,
the vertical distances, z�0.1 m, z�0.06 m and z�0.02 m,
respectively. It can be concluded that when the time is more
than 250 s, transient velocities at three locations are not
variational with time, which indicated that the fluctuation of
the velocity is steady. If the bending nozzle is applied, in-
crement of maximum velocity which is only produced by
magnetic field exceeds 0.2 m/s or 17% of the original ve-

locity observed in Fig. 12. The effectiveness of the bending
nozzle, which is an innovative technique, has been con-
firmed in the present study.

4. Conclusions

Three-dimensional turbulent flow fields in centrifugal
flow tundish have been studied using LES method. It is
concluded that:

(1) When the rotating magnetic field with the direct
nozzle is applied, the flow field of rotation chamber in-
cludes two strong recirculation flows and two small vortices
in vertical section. When the bending nozzle is only ap-
plied, the swirling flow in horizontal section is strong, but
small in vertical section. If the rotating magnetic field and
the bending nozzle are applied together, the swirling flow in
horizontal section is significantly enhanced, and flow struc-
ture become complex.

(2) Transient velocities in flow field are steady while
the operation time is more than 250 s.

(3) When the bending nozzle is applied, increment of
maximum swirling velocity exceeds 17% of the original
velocity, which is produced by rotating magnetic field with
the direct nozzle.

ISIJ International, Vol. 47 (2007), No. 4