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Numerical simulation of low and heat transfer

of continous cast steel slab under traveling

magnetic ield

*Gong Haijun

Male, born in 1978, doctoral candidate. Research interest: numerical simulation of casting process.

E-mail: 331ghj@163.com

Received: 2012-02-19 Accepted: 2012-10-06

*Gong Haijun, Li Xinzhong, Fan Xueyi, Qie Juhong, Xu Daming and Guo Jingjie

School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China

C

o n t i n u o u s c a s t i n g ( C C ) o f a l l o y s i s a p h a s e transformation process from liquid to solid (L-S), and thus the quality of the inal products mainly rests with this process. Owing to the heavy melt pours rapidly from the submerged entry nozzle (SEN), strong convection and meniscus oscillations would occur in the mold inevitably. An improper molten steel low in CC-mold would result in slab surface and internal defects, such as slag entrapment, inclusions, and pinholes [1-4]. Electromagnetic ields (EMF)

can exert great inluences on the transport process through Lorentz force and Joule heat [5]. Moreover, exerting static

magnetic ield [6-8] and travelling magnetic ield (TMF) [9, 10]

on molten steel low in CC-process are now recognized valid measures. Transverse static magnetic ields (TSMF) are used suppressing the melt convection [11], while it may

not be effective enough for a CC-process of slab with large thickness. TMFs are usually proposed to control the

molten metal low and proved to be effective [9, 10]

. The low behaviors in CC-mold are very complicated

Abstract:

A uniied numerical model for simulating solidiication transport phenomena (STP) of steel slab

in electromagnetic continuous casting (EMCC) process was developed. In order to solve the multi-physics ields coupled problem conveniently, the complicated bidirectional coupled process between EM and STP was simpliied as a unidirectional one, and a FEM/FVM-combined numerical simulation technique was adopted. The traveling magnetic ields (TMFs) applied to the EMCC process were calculated using the ANSYS11.0 software, and then the EM-data output by ANSYS were converted to FVM-format using a data-format conversion program developed previously. Thereafter, the governing equations were solved using a pressure-based Direct-SIMPLE algorithm. The simulation results of the STP in CC-process show that, due to the inluences of Lorentz force and Joule heat, the two strong circulating lows and the temperature ield can be obviously damped and changed once TMF with one pair of poles (1-POPs) or 2-POPs is applied, which would accordingly improve the quality of casting. It was found in the present research that the integrated actions of 2-POPs TMF are superior to 1-POPs. All the computations indicate that the present numerical model of EM-STP as well as the FEM/ FVM-combined technique is successful.

Key words:

continuous casting; low ield; electromagnetic ield; ANSYS; Direct-SIMPLE algorithm; FEM/FVM CLC numbers: TG142/TP391.9 Document code: A Article ID: 1672-6421(2013)02-092-07

due to the strong coupling among temperature, momentum and pressure fields. When an additional EM-field is applied to the CC-system, the coupling correlations turned even more complicated. Research on the flow behaviors and the influences of TMFs on the CC-process of steel slab can predict potential defects, consequently improve the quality of slab and reduce cost. The aim of the present paper is to establish an EM-STP-coupled model for EMCC process of steel slabs using a FEM/FVM-combined method and to investigate the low behaviors in CC-mold as well as the effectiveness of the convection controls of the applied TMFs by numerical simulation.

1 Modeling and computational

procedures

In the present multi-physics-ield computer modeling, the STP in the EMCC process was simulated using

a FVM-based Direct-SIMPLE algorithm [12], while

the EM-fields were calculated using ANSYS-FEM

software [13]

.

(2)

quasi-binary Fe-C alloy is shown in Fig. 1. The SEN is located at the center of the mold, and the upper edge of the SEN exit port is 156 mm below the free surface with 15° inclination angle. Due to the symmetry of the two dimensional (2-D) EMCC system, one half of the system (right half) was chosen as the computational domain for the solidiication transport process.

where cP is the speciic heat, and the EM-inducted Joule heat

(qJ) is given by

(3)

where J is the induced current density vector, E is the electric

ield intensity vector and g is the gravitational acceleration vector.

Mass conservation:

(4)

where V0 is the casting velocity, ρ is the density, m means the

mixture of liquid and solid.

The mushy zone is regarded as a porous medium with isotropic permeability, i.e. the flow in the mushy zone is

governed by the Darcy law, and the permeability, K, is a

function of the liquid volume fraction (fL), which is modeled

using the Kozeny-Karman relationship given by Formula (5).

(5)

where C denotes morphology constant which depends on the

morphology of the solidifying alloy, the value of 1.0×107 was

adopted in this paper.

Momentum transfer for interdendritic liquid low:

(6)

where F is the force vector, η is dynamic viscosity.

It can be seen from the above that each of the transport

equations is provided with the additional V

0-related terms

respectively, due to the action of drive rolls lower in the machine continuously withdrawing the shell from the mold at a steady rate (casting speed). For the present model, the body force term induced by external ields includes the gravity and Lorentz force, i.e.

(7)

Once the current distribution and the vector potential are known, the Lorentz force raised by EM-ield can be expressed as follows (2-D):

(8)

where B stands for magnetic lux density vector, and j, k are

serial numbers specifying the position of a control volume of (j, k).

For small magnetic Reynolds numbers, the induced magnetic ield can be neglected and, hence, the magnetic ield

is uncoupled from the velocity ield [15], magnetic lux density

equation (Eq. 1) turns to be independent of STP equations, i.e., (9) Therefore, the coupling relations between EM-ield and STP become mono-directional, and the applied EM-field can be separately analyzed prior to the STP computations.

Fig. 1: Proile of 2-D EMCC system

W 136

H 2400 HN 156 HW 12 H1 505 H2 82 WN 32

WW 8

HJ 24 HI 120 H3 1015 H4 798

1.2 Mathematical model and assumptions

The mathematical model of EMF in ANSYS is described by the Maxwell’s equations. Neglecting displacement current in Ampere’s currents law equation and then submitting the simpliied Ampere’s law to Ohm’s law equation, the magnetic

lux density (B) equation can be deduced as follows:

(1)

where V is velocity vector, vm = (μσ)

-1, σ is electric conductivity

of casting materials.

The model for the STP of heat energy and momentum of liquid low under any EM-ield is extended from a previously proposed continuum model [14]. To develop the governing

equations, the assumptions listed below were made:

(1) The external forces exerted on the solidifying system are only gravity and Lorentz force;

(2) No pores occur, i.e. the geometric continuity, fL+fS =1 (fL

and fS are the liquid and solid volume fraction);

(3) The solid phase is rigid and macroscopically static during solidiication;

( 4 ) L o c a l t h e r m o d y n a m i c e q u i l i b r i u m h o l d s a t t h e microscopic solid-liquid interfaces;

(5) Fluid is considered to be Newtonian and incompressible laminar low.

The model can be expressed by the formulations of Eqs. (2) to (8).

Heat energy transfer:

(2)

L L L

L L L S S S

S

V

L LV V

·

L

L

L L

L L L L

L L

L

L L

L L L

L

L

L L

L L

L

(3)

q +

k = h(Tslab-Twater)

-k = eσ[(Tslab+273.15)

4-(T

air+273.15) 4]

(13)

(2) Cold mold (H1)

(14)

(3) Air cooling region (H2, H4)

(15)

(4) Water cooling region (H3)

(16)

where, the air gap thicknesses, LA is a constant,

and its value is 0.01 mm in the present modeling. The thermo-physical parameters and the initial conditions are shown in Table 1

To achieve a stable solution of the STP, the time step for the calculation must be limited. The

maximum time step ∆t i+1 was determined by the

following equation [14]:

(17)

Based on the same staggered grids and discretization style illustrated in reference [14], momentum conservation equations were directly discretized with the following forms.

Component of mass-low in y direction:

(10)

Component of mass-low in z direction:

(11)

where, the signiications of various symbols as well as the details of the numerical treatment for the correlation of temperature,

fS and velocity-pressure were described in Ref. [12, 14]. Based

on the momentum transport and mass conservation equation, a corresponding discrete equation for solving pressure in a time step can be given as formula (12), and, mass residuum

RES[12] was limited to less than 2×10-5 as the convergence

criterion in the present computational study.

(12)

where α is coeficient of pressure equation and b is source item.

1.3 Initial conditions and boundary conditions

The same fundamental assumptions and similar boundary conditions of the mathematical model on EM-field have been explained in detail in Ref. [10, 16], and the main boundary conditions of the heat energy transfer for the continuous cast steel slab with the coniguration shown in Fig. 1 can be written as

(1) Free surface

TMF-loads were imposed at the beginning of EMCC simulation, and the temperature of liquid phase (TP) was assumed

to be uniform initially. The downwards withdrawal velocity of slab

was assumed to be constant with V0 = 2.5 mm·s

-1, while outlet

low velocity rested with the casting speed and derived from following formula:

(18)

1.4 ANSYS TMF-computations

As previously mentioned, the FEM/FVM-combined numerical simulation of EM-STP may be divided into EM-field and transport process calculations, and therefore, the EM-field can be analyzed separately prior to the STP-computations. To obtaining 1-POPs/2-POPs TMFs using in the EM-STP numerical simulation, the coils were fed a low frequency (10 Hz) alternating current (AC) load with different phase positions. The EM-parameters of the medium in the model are given in Table 2. Δ

Δ

Δ

Δ Δ

Δ Δ

Δ

--

--

-αj,k ·Δ(fLP)j,k = αj-1/2,k·Δ(fLP)j-1,k + αj+1/2,k ·Δ(fLP)j+1,k +

αj,k +1/2·Δ(fLP)j,k+1 + αj,k-1/2·Δ(fLP)j,k-1 + bj,k

(j,k = 1,2,3...)

n+1 n+1 n+1 n+1 n+1 n+1

n+1 n+1 n+1 n+1

= Conve Radia

T

q y

∂ ∂

=

xx w

T

(

)

A

A

T - T L

= λ Cooler

x T ∂ ∂

=w

x T

y

·

( )

Table 1: Thermo-physical parameters and initial conditions

Parameter Value

Thermal conductivity of S-phase kS = 0.060 (W·mm-1 ·℃-1

)

Thermal conductivity of L-phase kL = 0.030 (W·mm

-1 ·℃-1

)

Speciic heat (S) cpS = 0.672 (J·g-1 ·℃-1

)

Speciic heat (L) cpL = 0.781 (J·g-1 ·℃-1

)

Density (S) ρS = 7.34×10

-3 (g ·cm-3)

Density (L) ρL = 9.265-1.45×10

-3T (g ·cm-3)

Latent heat ∆H = 237 (J·g-1)

Coeficient of heat transfer 0.025 (W·mm-2·K-1)

Boltzmann constant (K) 5.67×10-8

J·(m2·k4·s)-1

Blackness coeficient of slab (ε) 0.8 Temperature of air 35 ℃ Temperature of water 30 ℃ Temperature of melt 1,650 ℃

W ·ρS ·Vo

VJ =

HJ·ρL ·cos15°

Table 2: EM-parameters and element types used in ANSYS

Medium Elem. Type Materials

Nozzle PLANE13 Al2O3 1.0 1.0 × 10 8

Crystallizer PLANE13 Pure Cu 1.0 1.673 × 10-8

Coils PLANE13 Pure Cu 1.0 1.673 × 10-8

Core PLANE13 Si-steel 2,500 4.4 × 10-7

Free space PLANE13 Air 1.0 Far space Inf110 Air 1.0

Relative magnetic permeability

Electrical resistivity (W·m)

Slab PLANE53 Steel 1.0 0.143 × 10-5

In this paper, the calculations of 1-POPs and 2-POPs TMF take the same

load, i.e. at a frequency of 10 Hz and with electric current of 106

(4)

a process of data-format conversion from FEM to FVM was performed using the method of data-conversion proposed previously [17]. As time goes on, the 24 converted instant-result files of TMFs were then periodically called acting as TMF-loads during the whole EM-STP numerical simulation process.

2 Inluences of TMF on luid low in

EMCC

When the molten steel is poured from the SEN at a high velocity, the mould powder and some oxide inclusions could be involved or entrapped during the process of solidiication. When a larger casting speed is needed, the velocity of molten metal coming from the SEN has to increase accordingly. The faster and more abundant molten metal feeding would bring stronger density of kinetic energy in the continuous caster mold. The increase in kinetic energy tends to cause non-uniform growth of the solidiied shell in the mold and promote entrapment of non-metallic inclusions into the molten steel, and sometimes even

result in melting of the mold. Due to the large length-width ratio of the casting, the casting was evenly divided into four segments from top to bottom for conveniently displaying the results of melt low. Figures 2(a) and (b) present the low and the contour of solidiication interface without TMF load at 199.9 s and 601.4 s, respectively. Two circulatory lows formed when the spraying low struck on the wall of mold. As illustrated in Fig. 2, one (low) descends along the side wall of the mold, and then turns around clockwise when it encounters the front of solidiication interface; and the other ascends to the free surface of molten metal in a counter-clockwise direction, which are well in agreement with the research result by ZHANG and et al. [18] (Fig. 2(c)). It can

be found from Fig. 2(a) that a thick skull (see segments 2, 3 and 4 of the casting) has formed at 199.9 s due to the elimination of heat from the mold and the action of cooling water sprayed on steel casting, but it has not yet reached a steady state. When it comes to 601.4 s, the solid phase increase is obviously more than that at 199.9 s, and at this time there is little liquid metal remaining in the fourth segment of the mold.

Fig. 2: Flow and solidiication of melt in the mold without TMF at different moments: t = 199.9 s (a); t = 601.4 s (b); luid low pattern in the mold region [18]

(c) Vl

max

= 0.86930E+01,

Vmmax

= 0.23635E+01 (mm

·s

-1)

Vlmax

= 0.88574E+01,

Vmmax

= 0.24108E+01 (mm

·s

-1)

Height (mm)

0

-200

-400

-600

Height (mm)

-600

-800

-1000

-1200

Height (mm)

-1200

-1400

-1600

-1800

-1800

-2000

-2200

-2400

Height (mm)

Width (mm) Width (mm) Width (mm) Width (mm) Width (mm) Width (mm) Width (mm) Width (mm)

Height (mm)

0

-200

-400

-600

Height (mm)

-600

-800

-1000

-1200

Height (mm)

-1200

-1400

-1600

-1800

-1800

-2000

-2200

-2400

Height (mm)

0.5 m·s-1

0 68 136 0 68 136 0 68 136 0 68 136 0 68 136 0 68 136 0 68 136 0 68 136

(a) (b) (c)

In a practical casting process, the downward circulation would bring inclusions into the solidiication front of the CC-casting, and thus result in solidification defects. In addition, such a great velocity of back-flow could also make the meniscus unstable, and then involve protection residues into the liquid metal phase. Therefore, controlling molten steel low in the mold is an important technical aspect to prevent luctuation, entrapment, etc. In the present research, the influences of TMF on STP in the CC-process were investigated. Some of

the magnetic lux density (B) results at different phase angles

are shown in Fig. 3. It can be seen that the wavelike Bs are a

list of moving magnetic ields with the velocity of v, where v

= 2τf, and τ is the span of one pair of poles. There are several differences in the distribution of B. It is obvious that just one peak exists in the travelling direction of 1-POPs TMF, while two humps appear in the 2-POPs TMF. Moreover, the maximal value of B (|B

max|=8.62×10

-1T) and its induction depth in

1-POPs system are stronger and deeper than that in 2-POPs system (|B

max|=8.59×10

-1T). Because too strong EM force

may bring detrimental effects, a suitable electric current load is signiicant for controlling the low of molten steel. Thus, a

decay coeficient (1.0×10-3

) is introduced for B here.

The low ields of EMCC-process with 1-POPs and 2-POPs TMF are shown in Fig. 4. Comparing Fig. 4 with Figs. 2(a) and 2(b), it can be found that after the upward moving TMFs are applied, the directions of spraying flow are changed obviously in both 1-POPs and 2-POPs systems, which greatly decreases heat impact on the side wall of the mold. More importantly, the counter-clockwise circulatory low upon the SEN is damped, easing the fluctuation of free-surface and stabilizing the low conditions. Synchronously, the clockwise circulatory flow along the side wall of the mold is inversed due to the change of jet flow, which provides enough time for inclusions to escape. As shown in Fig. 4, the maximal velocity (Vmax) under the influence of 1-POPs or 2-POPs

system is greater than that without TMF-load, and especially, the maximal velocity in the mushy zone (Vmmax) increases

(5)

the surface lows of the castings are impacted the most. This effect leads to an undulate motion which models worm-like motion. Generally speaking, the flow pattern becomes more symmetric than that without magnetic ield, especially in casting surface layer; the 1-POPs and 2-POPs TMFs are effective to stabilize the low pattern in the mold, and it may be concluded that the 2-POPs TMF acts more remarkably than 1-POPs in the present research.

It is well known that with solidiication progresses, micro-segregation of alloying elements occurs among the dendrites as they grow. The rejected solutes would lower the local solidification temperature, i.e. bring constitutional

super-cooling, leaving a thin layer of liquid steel along the grain boundaries, which may later form embrittling precipitates. When liquid feeding could not compensate for the shrinkage due to solidiication, thermal contraction, phase transformation and mechanical forces, tensile stresses may be generated. When the tensile stresses are high enough to nucleate an interface from the dissolved gases, then a crack would form. In an actual CC-process, the instantaneous velocity of melt rests with the combined effect of Lorentz force, gravity and other factors acting on molten steel, and the low inluences the quality of castings in succession. The specific coupling relations between EM-ield and STP are shown in Fig. 5.

(a) (b) (c) (d)

(e) (f)

v1

v2

SEP 24 2011 21:58:07 PLOT NO. 1 VECTOR STEP=1 SUB =1 FREQ=10 IMAGINARY B ELEM=8485 MIN=.001433 MAX=.808989 ZV =1 *DIST=.324936

*XF =-.119814

*YF =-.232599

Z-BUFFER EDGE .001433 .091162 .18089 .270618 .360347 .450075 .539804 .629532 .719261 .808989

SEP 24 2011 22:04:21 PLOT NO. 1 VECTOR STEP=1 SUB =1 FREQ=10 IMAGINARY B ELEM=8457 MIN=.807E-03 MAX=.845353 ZV =1 *DIST=.324936

*XF =-.119814

*YF =-.232599

Z-BUFFER EDGE .807E-03 .094645 .188484 .282322 .376161 .469999 .563837 .657676 .751514 .845353

SEP 24 2011 22:10:48 PLOT NO. 1 VECTOR STEP=1 SUB =1 FREQ=10 IMAGINARY B ELEM=8498 MIN=.331E-03 MAX=.802409 ZV =1 *DIST=.324936

*XF =-.119814

*YF =-.232599

Z-BUFFER EDGE .331E-03 .089451 .17857 .26769 .35681 .44593 .535049 .624169 .713289 .802409

SEP 24 2011 15:29:05 PLOT NO. 1 VECTOR STEP=1 SUB =1 FREQ=10 IMAGINARY B ELEM=8501 MIN=.891E-03 MAX=.802496 ZV =1 *DIST=.300248

*XF =-.089025

*YF =-.200283

Z-BUFFER EDGE .891E-03 .089959 .179026 .268093 .35716 .446227 .535295 .624362 .713429 .802496

SEP 24 2011 15:44:50 PLOT NO. 1 VECTOR STEP=1 SUB =1 FREQ=10 IMAGINARY B ELEM=8462 MIN=.769E-03 MAX=.82812 ZV =1 *DIST=.300248

*XF =-.089025

*YF =-.200283

Z-BUFFER EDGE .769E-03 .092697 .184625 .276553 .368481 .460409 .552336 .644264 .736192 .82812

SEP 24 2011 15:58:18 PLOT NO. 1 VECTOR STEP=1 SUB =1 FREQ=10 IMAGINARY B ELEM=8470 MIN=.104E-03 MAX=.83844 ZV =1 *DIST=.300248

*XF =-.089025

*YF =-.200283

Z-BUFFER EDGE .104E-03 .093252 .186401 .279549 .372697 .465846 .558994 .652143 .745291 .83844

Fig. 3: Magnetic lux density results at phase

angle φ=2π/3, 4π/3 and 2π with 10 Hz,

1.0 × 106 At current load: 1-POPs (a), (b), (c); 2-POPs (d), (e), (f)

Fig. 4: Liquid phase low ields in CC-process with TMF at t = 400.0 s: 1-POPs TMF (|Bmax| = 8.62×10-4T) (a),

2-POPs TMF (|Bmax| = 8.59×10-4T) (b)

Vlmax

= 0.30300E+02,

Vmmax

= 0.40857E+02 (mm

·s -1) Height (mm) 0 -200 -400 -600 Height (mm) -600 -800 -1000 -1200 Height (mm) -1200 -1400 -1600 -1800 -1800 -2000 -2200 -2400 Height (mm)

Width (mm) Width (mm) Width (mm) Width (mm) Width (mm) Width (mm) Width (mm) Width (mm)

0 68 136 0 68 136 0 68 136 0 68 136 0 68 136 0 68 136 0 68 136 0 68 136

Vlmax

= 0.15690E+02,

Vmmax

= 0.20734E+02 (mm

(6)

Figure 6 presents the results of current density, Joule heat and Lorentz force fields in 1-POPs and 2-POPs systems, which are the output by the ANSYS and EM-STP program. By comparing Figs. 6(a) to (c) with Figs. 6(d) to (f), it can be seen that the values as well as their effective depths in 1-POPs are bigger and deeper than that in 2-POPs,

coinciding with the distribution of B in Fig. 3. Because

of the action of opposite direction Lorentz force, the low velocity of molten steel would be slowed down, which is Fig. 5: Coupling relations between EM-ield and STP

Lorentz

force Flow field Induced

magnetic field

Joule heat Induced

current

Gravity field Heat transfer Mass transfer

Drawing movement EM induction

Quality of casting

Fig. 6: Distribution of current density, Joule heat and Lorentz force in the melt with 1-POPs and 2-POPs near the SEN: 1-POPs (a), (b), (c); 2-POPs (d), (e), (f)

(a) (b) (c)

(d) (e) (f)

PLOT NO. 1 ELEMENT SOLUTION STEP=1

SUB =1

FREQ=10 IMAGINARY JHEM SMN =.43673 SMX =.642E+07 ZV =1 *DIST=.277436 *XF =-.129784

*YF =-.242771

Z-BUFFER

.043673 713811 .143E+07 .214E+07 .286E+07 .357E+07 .428E+07 .500E+07 .571E+07 .642E+07

PLOT NO. 1 ELEMENT SOLUTION STEP=1

SUB =1

FREQ=10 IMAGINARY JTSUM SMN =-.264E+07

SMX =.199E+07 ZV =1

*DIST=.277436 *XF =-.130616

*YF =-.246517

Z-BUFFER

-.264E+07 -.213E+07 -.161E+07 -.110E+07 -585801 -71222.7 443355 957933 .147E+07 .199E+07

PLOT NO. 1 ELEMENT SOLUTION STEP=1

SUB =1

FREQ=10 IMAGINARY JTSUM SMN =-.187E+07

SMX =.158E+07 ZV =1

*DIST=.256356 *XF =-.111069

*YF =-.226602

Z-BUFFER

-.187E+07 -.148E+07 -.110E+07 -718945 -335963 -47018.5 440000 812982 .120E+07 .158E+07

PLOT NO. 1 ELEMENT SOLUTION STEP=1

SUB =1

FREQ=10 IMAGINARY

JHEA

SMN =.020508 SMX =.272E+07 ZV =1 *DIST=.256356 *XF =-.111069

*YF =-.226602

Z-BUFFER

.020508 301902 603804 905706 .121E+07 .151E+07 .181E+07 .211E+07 .242E+07 .272E+07

The FEM/FVM-combined numerical simulation in EMCC-process was performed successfully, which is a simple and feasible numerical simulation approach to researching multi-physical ields coupled issues.

(2) Upwards moving 1-POPs and 2-POPs TMF can remarkably change the convection patterns of melt, and thus achieve a desirable controlling effect on melt convections, consequently reduce the amplitude of luctuation and decrease the occurrence frequency of casting defects.

(3) The values and the effect depth in 1-POPs system are bigger and deeper than that in 2-POPs, whereas the 2-POPs system can provide a more uniform TMF than the 1-POPs, and the braking effect as well as stirring action of the 2-POPs TMF is superior to the 1-POPs in the present research.

References

[1] Jun Kubota, Noriko Kubo, Toshio Ishii, et al. Steel low control in continuous slab caster mold by traveling magnetic ield. NKK

Technical Review, 2001, 85: 1-9.

[2] Zhang Lifeng, Yang Subo, Cai Kaike, et al. Investigation of luid flow and steel cleanliness in the continuous casting strand.

Metallurgical and Materials Transactions B, 2007, 38(1): 63-83.

[3] Thomas B G. Modeling of continuous casting defects related to

mold luid low. Iron & Steel Technology, 2006, 3(5): 2-17.

[4] Wang Hongming, Li Guirong. Effect of induction heat on initial solidification during electromagnetic continuous casting of steel. Journal of Iron and Steel Research International, 2010,

17(7): 13-18.

[5] Li K, Hu W R. Magnetic ield design for loating zone crystal growth. Journal of Crystal Growth, 2001, 230: 125-134.

essential for reducing the velocity of molten metal low jet and the surface velocity of the melt in the mold so as to decrease the occurrence frequency of the defects. In addition, whether 1-POPs or 2-POPs TMF, according to Formula (3), would generate Joule heat, as shown in Figs. 6(b) and (e). However, the melt temperature in the first segment of the casting with the action of TMF is lower than that without TMF (see Fig. 7), while the temperature of the third segment of the casting with 1-POPs or 2-POPs TMF is higher than that without TMF, as shown in Fig. 7(d). All of these are attributed to the influence of upwards moving TMF, which is propitious to stirring the melt, feeding the mushy-zone, controlling eddies, and consequently, making inclusions emerge, loat and escape.

3 Conclusions

(7)

This project was supported by the National Natural Science Foundation of China (Grant Nos. 50801019 and 51071062), the State Key Lab of Advanced Metals Materials (Grant No. 2009ZD-06) and the National Key Basic Research and Development Program (973) of China (Grant No. 2011CB605504).

[6] Amnon J M, Paul G. Schmidt, Sayavur I. Bakhtiyarov, Ruel A. Overfelt. Numerical simulation of steady liquid-metal flow in the presence of a static magnetic ield. Journal of Applied

Mechanics, 2004, 71: 786-795.

[7] Lei Hong, Zhang Hongwei, He Jicheng. Flow, solidification, and solute transport in a continuous casting mold with electromagnetic brake. 2009 WILEY-VCH Verlag GmbH & Co.

KGaA, Weinheim, 2009, 32(6): 991-1002.

[8] Aboutalebi M R, Guthrie R I L, Seyedein S H. Mathematical modeling of coupled turbulent low and solidiication in a single belt caster with electromagnetic brake. Applied Mathematical

Modelling, 2007, 31: 1671-1689.

[9] Su Yanqing, Xu Yanjin, Zhao Lei, et al. Effect of electromagnetic force on melt induced by traveling magnetic ield, Transactions

of Nonferrous Metals Society of China, 2010, 20: 662-667.

[10] Wang Hongdan, Zhu Miaoyong, Yu Haiqi. Numerical analysis of electromagnetic field and flow field in high casting speed slab continuous casting mold with traveling magnetic field. Journal of Iron and Steel Research International, 2010, 17( 9): 25-30.

[11] Tian X Y, Li B W, He J C. Numerical analysis of inluences of casting speeds on luid low in funnel shape mould with new type EMBr. International Journal of Cast Metals Research

2010, 23(2): 73-80

[12] Xu Daming, Bai Yunfeng, Guo Jingjie, Fu Hengzhi. Numerical simulation of heat, mass and momentum transport behaviors

in directionally solidifying alloy castings under electromagnetic ields using an extended direct-simple scheme. Int J Numerical

Methods in Fluids, 2004, 46(7): 767-791.

[13] Bai Yunfeng, Xu Daming, Mao Lihe, et al. FEM/FDM-Joint simulation for transport phenomena in directionally solidifying TiAl casting under electromagnetic field. ISIJ International,

2004, 44(7): 1173-1179.

[14] Xu Daming, Li Qingchun. Gravity and solidiication shrinkage induced liquid flow in a horizontally solidified alloy ingot.

Numerical Heat Transfer A, 1991, 20: 203-221.

[15] Hughes M, Pericleous K A, Cross M, The numerical modelling of DC electromagnetic pump and brake flow. Appl. Math.

Modelling, 1995, 19: 713-723

[16] Xu Daming, Bai Yunfeng, Fu Hengzhi, Guo Jingjie. Heat, mass and momentum transport behaviors in directionally solidifying bade-like castings in different electromagnetic ields described using a continuum model. International Journal of Heat and

Mass Transfer, 2005, 48: 2219-2232.

[17] Gong Haijun, Xu Daming, Fu Hengzhi. An FEM FDM data conversion algorithm for three-dimensional electromagnetic

ields. Journal of Harbin Institute of Technology, 2010, 9:1418

-1423. (in Chinese)

[18] Zhang Lifeng, Wang Yufeng, Zuo Xiangjun. Flow transport and inclusion motion in steel continuous-casting mold under submerged entry nozzle clogging condition. Metallurgical and

Materials Transactions B, 2008, 39: 534-550.

Fig. 7: Temperature ields of casting: (a) without TMF; (b) with 1-POPs TMF; (c) with 2-POPs TMF; (d) the temperature of casting at x = 12.0

Width (mm) Width (mm) Width (mm) Width (mm) Width (mm) Width (mm) Width (mm) Width (mm)

Width (mm) Width (mm) Width (mm) Width (mm)

Temperature (

)

Temperature (

)

Temperature (

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

Height (

mm

)

(a) (b)

Referências

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