wang_et_al_isij_2007
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wang_et_al_isij_2007

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1. Introduction

Centrifugal flow tundish, in which the molten steel is
horizontally rotated by electromagnetic force, has been de-
veloped to produce high quality steel with high productiv-
ity. The effect of the rotating electromagnetic force on in-
clusions separation in a batch system1) and a pilot plant ex-
periment using a 500 kg capacity tundish2) have been re-
ported. Industrial plant test3) carried out at Chiba works
showed that the amount of inclusions was reduced to half
and defects of hot-rolled coils were reduced to 60%. The
swirling flow in the rotation chamber is crucial for the ef-
fectiveness of centrifugal flow tundish. Therefore, it is ben-
eficial to understand the flow structure of centrifugal flow
tundish.

Models of turbulent flow can be classified into the
Reynolds-averaged approach, large eddy simulation and di-
rect numerical simulation. Because of its computational
cost, the Reynolds-averaged approach, typically with the
two-equation (k–e) turbulence model,4,5) has been exten-
sively adopted in previous studies and has produced valu-
able insights about the flows in tundish. However, this ap-
proach is not suited for studying the time evolution of un-
steady flow structures. The direct numerical solution is to
solve directly the Navier–Stokes (NS) equations with high
computational cost. A midway choice between two-equa-
tion turbulence models and direct numerical simulation is
the employment of a computational technique known as

Large Eddy Simulation where the NS equations are filtered.
The filtered equations are then simulated and the left small-
est eddies are modeled.6–10)

The objective of the present work is to understand the
flow structure in centrifugal flow tundish by using the large
eddy simulation (LES), and analyze the effect of electro-
magnetic force and bending nozzle on the swirling flow. It
is an innovative technique to enhance the swirling flow in
rotation chamber using bending nozzle.

2. Mathematical Model

Flow field in the 1/12 low melting point alloy model is
solved using LES. The computational domain is shown in
Fig. 1. The size of tundish model is 0.42 m�0.128 m�
0.12 m. The diameter of rotation chamber is 0.128 m, the
size of the outlet gate of rotation chamber is 0.032 m�
0.04 m (length�height) the angle and diameter of the bend-
ing nozzle is 90 degree and 0.02 m. The depth of the bend-
ing nozzle is 0.01 m below the level of fluid. The casing
speed is 0.95 m/min. It also shows the coordinate directions
of x, y and z. The horizontal velocity component U, V and
the vertical component W are in x, y and z direction, respec-
tively.

2.1. Filtering Operation

In order to separate out the large eddies from the small-
scale motions, a filtering operations11) is applied to the

568© 2007 ISIJ

Large Eddy Simulation on Flow Structure in Centrifugal Flow
Tundish

Fang WANG,1) Baokuan LI1) and Fumitaka TSUKIHASHI2)

1) School of Materials and Metallurgy, Northeastern University, Wenhua road 3-11, Heping District, Shenyang, 110004, China.
2) Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5,
Kashiwanoha, Kashiwa, Chiba 277-8561 Japan.

(Received on August 4, 2006; accepted on January 5, 2007 )

Centrifugal flow tundish which the molten steel is horizontally rotated by electromagnetic force has been
developed to produce high quality steel with high productivity. Because the swirling flow in the rotation
chamber is crucial for the effectiveness of centrifugal flow tundish, it is beneficial to search the way to en-
hance the swirling flow and understand the flow structure in centrifugal flow tundish. Large Eddy Simula-
tion (LES) technique is developed to simulate the complicated flows. LES is computationally much more in-
tensive than k–e and cost less than direct numerical simulation (DNS), but offers a new level of insight into
transient phenomena. In the present works, flow structures in three cases are simulated and analyzed, i.e.
the swirling flow is produced by (a) electromagnetic force with the direct nozzle, (b) bending nozzle using
height potential energy of molten steel, (c) combination of electromagnetic force and bending nozzle. The
swirling flow and vortices are clearly displayed. The effectiveness of bending nozzle is validated by 17% in-
crement of maximum swirling velocity in rotation chamber.

KEY WORDS: large eddy simulation; centrifugal flow tundish; swirling flow; bending nozzle; electromag-
netic force.

ISIJ International, Vol. 47 (2007), No. 4, pp. 568–573

Navier–Stokes equation. A filterer variable, denoted by an
overbar, is defined as

......................(1)

Where G is the filter function, and the integral is extended
to the entire domain D. The filter employed here is the box
type in real space:

....................(2)

This procedure splits the problem into two parts: the first
one consists of solving the filterer NS equations without the
cumbersome task of evaluating the Reynolds stresses, and
the second one consists of using relatively simple models to
evaluate turbulent viscosity and the subgrid residual
stresses (small eddies). The instantaneous velocity is the
sum of the filtered velocity and of the residual velocity as
given by

u�u¯�u’....................................(3)

2.2. Governing Equations

The application of the filtering operation to the continu-
ity and the Navier–Stokes equations gives the resolved
Navier–Stokes equations, which, in incompressible flow,
are

...........................................(4)

where

m eff�m0�m t .................................(5)

The symbols p and ui in Eq. (4) represent the pressure and
filtered velocities. The subscripts i and j represent the three
Cartesian coordinate directions and repeated subscripts
imply summation. We choose the basic Smagorinsky SGS
model12) to study the present flow problem.

m t�(CsD)2|S¯| ................................(6)

D�(DxDyDz)1/3 ..............................(7)

Cs is Smagorinsky’s constant, Cs�0.1. Dx, Dy and Dz are
the size of each cell in the Cartesian computational grid. |S

–
|

is the magnitude of the strain-rate tensor, given by

...............................(8)

where

........................(9)

2.3. Electromagnetic Force

Electromagnetic force can be calculated using the
Maxwell’s equation and Ohm’s law.

Faraday law:

............................(10)

Ampere’s law:

��B�m J ................................(11)

∇ ∂∂� ��E
B

t

S
u

x

u

xij
i

j

j

i

� �
1

2

∂
∂

∂
∂







| |S S Sij ij� 2

∂
∂
∂
∂

∂
∂

∂
∂

∂
∂

∂
∂

∂
∂







u

x

u

t x
u u

p

x x

u

x

u

x

i

i

i

j
i j

i j

i

j

j

i

�

� �� � �

0

1
( )

ρ
µeff

G X
X

X

( )
, | |

,

�
�

�

1

2

0
2

∆
∆

∆

if

if | |








f f x G x x dx
D

� � � � �( ) ( )∫

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

569 © 2007 ISIJ

Fig. 1. Schematic of the physical model (all dimensions are in mm).

Continuity of the magnetic field is written as:

� ·B�0...................................(12)

Moreover, the induced current is expressed by ohm’s law:

J�s(E�V�B) ............................(13)

Here, E: electric field intensity, B: magnetic flux density, J:
current density, m : ermeability, s : conductivity, V: velocity.
Lorentz’s law is used to calculate electromagnetic force.

f�J�B ..................................(14)

where the 500 A electric current, 6 poles and 5 Hz fre-
quency with 5 mm inner copper wall of stirrer are used in
the present calculation. Figure 2 shows the calculated in-
stantaneous magnetic field and averaged electromagnetic
force in half cylindrical space using the commercial soft-
ware of ANSYS 8.0, these are used to calculate flow field
in centrifugal flow tundish.

2.4. Boundary Conditions for Flow Field

(1) At the outlet of blending nozzle: the velocity Vin is
specified by the casting speed.

(2) At the free surface of tundish: If the swirling flow
in the rotation chamber is enough strong, the surface defor-
mation occurs. In order to simplify