6 Process Simulation of S-EMS and Its Application in Slab Continuous Casting

Process Simulation of S-EMS and Its Application in Slab Continuous Casting

JEN-HSIN CHEN, SHENG-YANG LIN and MUH-JUNG LU Iron & Steel Research & Development Department

China Steel Corporation

A mathematical model was developed to simulate the electromagnetic field and the flow and temperature fields for the different operation conditions of S-EMS in slab casting. The influence of the stirrers on the melt steel velocity was investigated for cases with one-stage stirrers placed face-to-face on both sides of the strand or with two-stage stirrers placed side-by-side just on the inner side of the caster. The simulation result showed that face-to-face arrangement could provide a stronger stirring intensity. However, due to the easy accumula-tion of slag on the outside radius, an S-EMS with double-stage stirrers placed closer to the strand between the rolls on the inside radius was developed to meet the demands of internal quality for high silicon steels. The newly-developed S-EMS proved to be a very effective device for creating an extended equiaxed zone for silicon steel, and an average of above 45% was normally achieved to significantly improve the ridging index.

1. INTRODUCTION

The electromagnetic processing of materials (EPM) is widely used in the steel industry to improve and upgrade steel products. In the continuous casting of steels, the electromagnetic stirring of the liquid steel in a mold and strand has been developed for many years, and has achieved a superior quality of blooms or slabs. A Mold Electro-Magnetic Stirrer (M-EMS) is mainly applied to improve the surface quality, especially to avoid surface cracks and to ensure the skin cleanness of the slab. A Strand Electro-Magnetic Stirrer (S-EMS) is applied to enhance the internal quality of the slab. Nowadays three types of S-EMS are used in the slab continuous casting of steels, i.e. between-roll type (NSC), in-roll type (Rotelec), and box type (ABB)(1). The merits of the S-EMS are to reduce the center segregation and/or porosity, to increase the equiaxed zone, and to decrease the susceptibility to internal cracking. As a result, the center quality of plate and the ridging defects of cold rolled sheet can be prevented.

An investigation of the electromagnetic stirring effect is usually rather complex and complicated during development in a laboratory. Thus, how to establish a simulation technique simultaneously for the electro-magnetic field, temperature field and fluid flow be-comes a fundamental technology for this particular steel process. Along with this electromagnetic stirring technology, there have been many reports on numerical analysis, especially on the M-EMS(2). However, very

few papers have reported on the simulation of S-EMS in slab casting, especially regarding the influence of the stirrer’s position and the operational variables on fluid flow and temperature fields.

In this paper, a modified NSC-type S-EMS was investigated and simulated according to the particular requirements in China Steel Corporation (CSC). Firstly, the coupled models of the electromagnetic field, fluid flow, and the temperature field were formulated and analyzed by computer. The stirring forces were calcu-lated and compared among the various cases. The effects of stirrer’s location, stirring pattern, slab width, electric current on the flow and temperature fields were analyzed. Two indexes, the maximum velocity at the solidification front and the superheat diminution in the upper zone of strand were stressed especially. Then, taking into account the shell thickness and location, the electromagnetic force and velocity in the stirring volume were integrated to evaluate an optimal location of the S-EMS installation.

2. MATHEMATICAL MODEL

The complex calculation domains in the S-EMS system were pre-processed by the SolidworkR software for the three fields. The magneto hydrodynamic (MHD) calculation then was performed by the COMSOL Mul-tiphysicsR to evaluate the stirring effect of the S-EMS. The stirrer could be located in the upper or lower seg-ment of the strand, ranging from about 3~8m from the meniscus, at which the total shell thickness was about

China Steel Technical Report, No. 23, pp. 6－13, (2010)

7 Jen-Hsin Chen, Sheng-Yang Lin and Muh-Jung Lu

30~60% of the slab thickness. The thickness of the solidifying shell was calculated from the existing cooling pattern for high silicon steel of 50A470. Then, the whole calculated domain of solid shell and liquid core was determined and sketched by the SolidworkR based on the calculated results of solidifying shell. The boundary between the solid shell and liquid core was determined at a solid fraction of 0.8. The total length of strand for simulation was 12 meters from the meniscus, including the submerged nozzle in the mold, to reveal the stirring effects of the S-EMS on the liquid flow and the temperature distribution, as shown in Fig. 1. The main specifications of the caster and the S-EMS are listed in Table 1. The formulation of the electromag-netic, fluid flow, and temperature fields are described in the following sections.

2.1 Formulation of Electromagnetic Field

The basic equation of the electromagnetic field is known as Maxwell’s equation. The electromagnetic force generated by the S-EMS was first simulated by a 3-D flux software of COMSOL MultiphysicsR. There were four parts in the calculation, namely stirrer (core and coil), solid shell, liquid core of slab and the infinite box, as shown in Fig. 1. The governing equation is expressed as:

()-j( r2 ×∇+εεωωσ A0 0r

1µµ eJ) =×∇ A

in which σ, εr and µr are electrical conductivity (S/m), relative permittivity and permeability in each domain, respectively. ε0 and µ0 are the permittivity and perme-ability of a vacuum. Je is current density (A/m2), and A is the vector potential. In addition, the skin depth δ is also an important parameter which can be expressed as:

ωµσ=δ /2

where ω is frequency. In general, the higher the frequency, the higher the permeability and the higher the electric conductivity, the smaller skin depth is. There are only six exterior boundary conditions in this simulation model, which are assumed to be mag-netic insulation with the following governing equation,

▽×A = 0

while the inner boundary of the system is assumed to be continuously magnetic. The calculated domain of the stirrer merely consists of the core and coils, while the housing, cooling pipe, non-magnetic rolls, and copper buses are neglected because their effects on the electromagnetic field are relatively small. The S-EMS is designed as a three-phase, two-pole induction motor.

Fig. 1. Physical and electromagnetic field domain for simulation.

In the S-EMS system, the solution domain can be

assumed as free space. In the calculation zone of the strand, the solidifying shell has finite thickness. How-ever, it is reasonable to assume that the liquid core and the solidifying shell are electro-conductive, but not magneto-conductive, due to their temperatures being higher than the Curie temperature during casting. At temperatures under 200°C, the resistance of the iron increases as the temperature increases. However, as the metal is heated to extremely high temperatures, for example 1000°C, the expected resistance from the temperature coefficients is no longer applicable. Accord-ing to the literature(3), the Pauling electro negativity (i.e., Pauling Index) can be expressed as the ratio of elec-trical conductivity at room temperature to that at the molten temperature, from the viewpoint of the mole-cule.

In this study, the electrical conductivity of the liquid core is determined from literature as 4.91×106. Assuming the electro negativity of the solidifying shell is 1.8, the electrical conductivity of the solid shell can be deter-mined as 5.72×106. Furthermore, the iron core in the stirrer is packed by hundreds of insulated electric

Table 1 Specifications of the caster and the S-EMS Caster S-EMS

Caster radius 12500 mm Distance to slab 25 mm Slab size 250×950~1680mm No. of phases 3 No. of segment 17 No. of poles 2 Steel grade 50CS600~50CS290 Pole pitch 483 mm Casting speed 1.0 m/min Electric current 0~700 A Specific water 1.2 ℓ/kg Frequency 0~15Hz

8 Process Simulation of S-EMS and Its Application in Slab Continuous Casting

sheets. Therefore, the core can be considered as having high relative permeability and low electrical conductivity. Table 2 lists the assumed material properties of each part of the S-EMS model.

2.2 Formulation of Flow Field

The flow field of the liquid core in the slab was also calculated by a 3-D software model. Figure 2 shows the domain and the boundary conditions for the fluid flow calculation, including the liquid core and the submerged nozzle. The solid shell was not considered due to the viscosity coefficient of the solidifying shell (fs≧0.8) being much larger than that of molten steel. In order to simplify the physical model and easily achieve the convergence to save the computation time, the mushy zone was also not considered. In other words, the whole physical model was considered as a single liquid phase. The governing equation of the flow with a k-ε turbulence model is expressed as Navier-Stokes equation:

▽‧u = 0

iixju

jxiu

tixP

ixP

jiix Fuu +⎥⎦⎤

⎢⎣⎡

⎟⎠⎞

⎜⎝⎛ +µ+µ+−=ρ ∂

∂

∂∂

∂∂

∂∂

∂∂ )()(

Fig. 2. Domain and the boundary conditions for flow field calculation.

The effective viscosity was taken as the sum of laminar viscosity, µ, and turbulent viscosity, µt. The turbulent viscosity was expresses as μt =ρCμ(k2/ε); Cμ = 0.09. The principle of S-EMS was based on the linear motor with alternative current to produce the induced current in the liquid steel, which was coupled with the moving magnetic field and exerted a so-called Lorenz force. This time-variable electromagnetic force

could drive the liquid steel. If the time-variable force was input directly into the external force term of the Navier-Stokes equation during the analysis of the fluid flow, the computation time would be extremely tedious for a single set of process parameters. To reduce the computing time, the time-average electromagnetic force was usually used as input into the force term. Electromagnetic force at current phase angle of 0° and 90° was averaged as an input in Argonne National Laboratory(4). However, the maximum value or the root-mean-square value of the electromagnetic force at every time angle were chosen as the input in the Nippon Steel calculation(5). In this study, an average of the electromagnetic force at phase angle of 0° and 90° was used in the calculation.

The shaded area in Fig. 2 shows the domain for electromagnetic calculation, which is also the domain for the flow field calculation. Because the grid systems of the three fields were generated in the same software of COMSOL MultiphysicsR, the resultant time average electromagnetic force from electromagnetic field could be passed easily to the flow field for calculation. The whole physical domain should be calculated due to the asymmetrical nature of the flow field under the effect of electromagnetic stirring. The mold level was assumed as the symmetry boundary. That means all the gradients of the variables at the normal direction of the mold surface are set to zero. The outer surface of the liquid core was assumed as the logarithmic wall function. The boundary conditions at the outlet of liquid core was assumed to be zero pressure, P0 = 0, with no viscous stress. The boundary condition at the inlet of sub-merged nozzle was set as(6);

2)(5.1 IUk ××= , l

kC5.1

75.0 ×= µε

where I = 0.16×Re-1/8 l = 0.07×L U : inlet velocity I : turbulent intensity Cµ : 0.09 (from the turbulence model) k : turbulent kinetic energy l : turbulent mixing length Re : Reynolds number L : characteristic length

Table 2 Material properties of each domain in S-EMS system

Domain Relative permeability,µr

Electrical conductivity,σ

Relative permittivity,εr

Solution box (air) 1 0 1 Solid shell Steel 1 5.72×106 1 Liquid core Steel 1 4.91×106 1

Core 4000 100 1 Stirrer Coil 1 1 1

9 Jen-Hsin Chen, Sheng-Yang Lin and Muh-Jung Lu

2.3 Formulation of Temperature Field

The temperature field of the liquid core in the slab was simulated by a 3-D software model. Figure 3 shows the calculation domain of the liquid core only for the temperature simulation. The submerged nozzle and the solid shell were not considered. Because the flow field and the temperature field were built in the same domain of COMSOL MultiphysicsR, the calcu-lated velocity field of the liquid core can be easily transferred to the temperature field for further calcula-tion. The governing equation of the temperature with a k-ε turbulence model is expressed as:

Fig. 3. Domain and the boundary conditions for temperature field calculation.

The effective thermal conductivity was the sum of

the laminar thermal conductivity, κ, and the turbulent thermal conductivity, κt. Turbulent thermal conductivity was expressed as κt = Cpµt /σt, σt=0.9. The interface of the solidifying shell and liquid core was determined at a solidification fraction of 0.8. Thus, the boundary con-dition of temperature of liquid core was set at the temperature of 0.8 solid fraction of the cast steel(7). An insulation condition was set at the interface of the submerged nozzle and the liquid steel, and at the meniscus. The boundary at the ports of the submerged nozzle was assumed to be the casting temperature. The boundary condition at the outlet of the strand was set as convective flux ( ) 0n Tκ⋅ − ∇ = .

3. RESULTS AND DISCUSSION

The main purpose of the S-EMS installation was to stir the liquid core during continuous casting to increase the equiaxed zone of slab to avoid the ridging defect of cold rolled electric sheet. In general, there are three groups of slab widths in CSC. The width of the stirrer

core is designed to less than 1000mm, since most of the slab widths of electric steels are smaller than 1270mm. The electromagnetic stirrer could be installed as a pair in segments 1 or 2 of the strand, which are about 4.5m and 6.5m from the meniscus, respectively.

There are three cases in the calculations for two layouts of S-EMS, as shown in Fig. 4. Two stirrers were set face-to-face in the segment in layout I, while in layout II the stirrers were set side-by-side only on the inner side of the strand. Three cases were analyzed in the process simulation for these two layouts, according to the stirring direction. There is only parallel stirring in case 1 of layout I. However, there are two stirring pat-terns from the layout II of S-EMS, i.e., parallel stirring in case 2 and opposite stirring in case 3.

Fig. 4. Two layouts and three cases in the S-EMS analysis.

3.1 Calculation of Electromagnetic, Flow and Temperature Fields

Figure 5 shows a typical example of the calculated electromagnetic field (force) for the three cases with 1270mm slab width. The calculated force field is more localized between the stirrers in case 1 than that in cases 2 and 3. Thus, the electromagnetic force in case 1 as expected is the highest among all cases. The calcu-lated results also show that the electromagnetic force near the slab narrow sides is smaller in the case of 1575mm slab than that of 1270mm. The electromag-netic field in case 2 is more distributed and diffused than that in case 3, as shown in Fig. 5.

Fig. 5. Electromagnetic fields of the three cases with 1270mm slab.

10 Process Simulation of S-EMS and Its Application in Slab Continuous Casting

Figure 6 shows the calculated flow field and tem-perature field without S-EMS for three widths of slabs. The temperature is apparently un-uniformly distributed at each transverse section of slab along the casting direction, due to the hot steel pouring from the bifur-cated submerged nozzle. This un-uniform (high tem-perature gradient) temperature distribution is definitely not good for the equiaxed grain formation.

Fig. 6. Flow field and temperature field without S-EMS for three slab widths.

In general, the flow field in the slab is determined

by the discharged stream from submerged nozzle and the liquid stream stirred by the S-EMS. Figure 7 shows that in case 1 the liquid flow driven by the electromag-netic force predominately horizontally hits to the narrow side of the slab. Then, two big loops of recirculation flows are formed at the upper and lower sides of the stirrer. However, for the low current of 250A, the lower recirculation flow is very weak. As a result, the tem-perature uniformity of 650A is much better than that of 250A, especially in the upper zone of strand.

Fig. 7. Flow and temperature fields of 1575mm slab for three cases with 250, 650A.

There are three main loops formed in case 3 where the stirring mode is opposite, as shown in Fig. 7. After hitting narrow side of slab, the flow forms anti-clockwise

loop above the upper stirrer. Similarly the flow forms a clockwise loop below the lower stirrer. The third loop was formed clockwise in the zone between the two stirrers. However, the circulation of these loops is not as strong as in case 1.

Only two recirculation loops were formed in case 2 where the stirring mode is parallel. One loop is located at the upper zone of upper stirrer. The other loop is located at the lower zone of lower stirrer. These two loops were similar to those in case 3. However, there is no pre-dictable flow pattern that can be predicted due to the complex flow pattern between the two stirrers. How-ever, the mixed zone seems larger due to the parallel stirring of the liquid steel. In all cases, the temperature uniformity becomes worse as the current decreases, as shown from the temperature field. The superheat at the upper zone of strand was significantly reduced and the temperature uniformity was improved due to the elec-tromagnetic stirring, from the comparison of Figs. 6 and 7. This superheat diminished and the uniform tem-perature reduced the temperature gradient of the mushy zone, and enhanced the formation of an equiaxed zone during solidification. Therefore, the effectiveness of the S-EMS can be summarized as; Superheat diminution at upper strand: Face-to-Face, parallel stirring > Side-by-Side, parallel stirring > Side-by-Side, opposite stirring Increase in the temperature uniformity of strand (except upper zone): Face-to-Face, parallel stirring > Side-by-Side, opposite stirring > Side-by-Side, parallel stirring

Inclusion could be caught by the solidifying shell during solidification if the relative velocity of inclusion is slow, especially at the quarter thickness of slab. Therefore, the maximum liquid velocity near the solidi-fication front was evaluated for different S-EMS layouts. Figure 8 shows the calculated maximum velocity at the interface of a 1270mm slab for three cases with different currents. Case 1 always has the highest maximum velocity due to the concentrated electromagnetic force. The velocity at the interface of case 3 is also always larger than that of case 2. In the same conditions of S-EMS operation, the wider the slab is, the higher the maximum velocity. However, the difference becomes smaller as the slab width increases. As a result, Maximum velocity along the interface: Face-to-Face, parallel stirring > Side-by-Side, opposite stirring > Side-by-Side, parallel stirring Slab width 1575mm＞1270mm＞950mm

From the above discussion, cases 1 and 3, face-to- face layout with parallel stirring and side-by-side lay-out with opposite stirring, are further investigated for operational guidance. Figure 9 shows the flow field and temperature field of two cases with three different currents for a 1270mm slab. The stirred length is larger

11 Jen-Hsin Chen, Sheng-Yang Lin and Muh-Jung Lu

when the current is higher. Also the intensity of the circulation loop becomes stronger. As a result, the diminution of superheat in the upper strand and the temperature uniformity in the other parts are better as the current is increased.

Fig. 8. Maximum velocity at interface of 1270 mm slab for different currents of three cases.

Fig. 9. Flow and temperature fields of cases 1 and 3 with three currents for 1270mm slab.

Figure 10 shows the flow field and temperature

field of two cases with three slab widths for 650A. The flow field shows that the wider the slab, the longer the mixed zone length. Thus, the superheat diminution and the temperature uniformity are better. In summary, the following conclusions can be obtained. Superheat diminution: Current 650A＞450A＞250A Slab width 1575mm＞1270mm＞950mm

Temperature uniformity: Current 650A＞450A＞250A Slab width 1575mm＞1270mm＞950mm

Fig. 10. Flow and temperature fields of cases 1 and 3 with three slab widths for 650A.

All the above calculations and discussion are based

on the installation of S-EMS in segment 1. However, segment 2 installation is also an option to avoid the damage risk due to breakout during casting. The fol-lowing section discusses the calculated results of the electromagnetic field and flow field for different seg-ments, considering the different shell thicknesses. Table 3 lists the location of S-EMS, shell thickness, and liquid core size for the calculation of side-by-side layout. The electromagnetic force was calculated first for certain casting conditions. Then, the flow field was calculated for the whole strand.

Figure 11 shows the electromagnetic field and flow field of side-by-side layout with parallel stirring for S-EMS installed in segments 1 and 2 with a current of 650A. Since the magnetic flux in the solid shell cannot induce fluid flow to the liquid core, the total electro-magnetic force applied to the liquid core can be obtained by the integration of electromagnetic force in the volume of stirring zone. Table 4 shows the comparison of elec-tromagnetic force in the liquid core for different slab widths for different S-EMS installations. A higher elec-tromagnetic force can be obtained as the slab width is increased, due to the larger liquid core, no matter in segments 1 or 2. However, the calculated results show that the total electromagnetic force in segment 2 is about 0.72 times that in segment 1.

12 Process Simulation of S-EMS and Its Application in Slab Continuous Casting

Fig. 11. Electromagnetic and flow fields of case 2 for S-EMS installed in segments 1 and 2 with current of 650A.

As mentioned previously, the flow field in slab is determined by the discharged stream from the sub-merged nozzle and the liquid stream stirred by the

S-EMS. The calculated results show that the stirring force is smaller and far from the meniscus when S-EMS is installed in segment 2. Therefore, the stirring stream is less influential in the upper zone of strand. The superheat diminution becomes small, as does the effectiveness of equiaxed zone formation. Table 5 shows the comparison of integration of velocity in liquid core for different slab widths at different S-EMS installations. The calculated results show that the inte-gration of velocity in segment 2 is about 0.77 times that in segment 1. In other words, the stirring energy is much larger in segment 1 than in segment 2.

3.2 Plant Application

From the above analysis and discussion, a newly developed S-EMS was tested in the steelmaking plant of CSC. Figure 12 shows the photo of the S-EMS in segment 1 of the bending type caster. The equiaxed zone ratios of the produced slabs where the S-EMS is installed in segments 1 and 2 are 40~50% and 30~40%, respectively. The plant trials were in agreement with the model calculations in term of electromagnetic force and stirring energy for different installations. Figure 13 shows the equiaxed zone of 50A350 slab which the S-EMS was set in side-by-side layout and operated in opposite stirring with 650A, 15 Hz.

Table 3 Comparison of shell thickness, liquid core size at different S-EMS locations Slab width (mm) Shell thickness

(mm) Liquid core size (mm×mm) Location Stirrer

U: upper L: lower

Distance from

meniscus (m) Narrow Wide 950 1270 1575 U stirrer 4.07 61.8 65.3 134.1×819.4 134.1×1139.4 134.1×1444.4

Segment 1 L stirrer 4.91 65.6 68.8 125.9×812.4 125.9×1132.4 125.9×1437.4U stirrer 6.10 70.9 73.7 114.4×802.5 114.4×1122.5 114.4×1427.5

Segment 2 L stirrer 6.94 74.7 77.3 106.2×795.5 106.2×1115.5 106.2×1420.5

Table 4 Comparison of electromagnetic force with S-EMS installed in segments 1 and 2

Slab Width 950mm 1270mm 1575mm Segment No. Seg.1 Seg.2 Seg.1 Seg.2 Seg.1 Seg.2

EM force of stirred zone, F (N) 464.6 332.6 524.0 380.9 537.5 392.0 Fseg2/Fseg1 0.716 0.727 0.729

Table 5 Comparison of integral velocity with S-EMS set in segments 1 and 2

Slab width 950mm 1270mm 1575mm Segment No. Seg.1 Seg.2 Seg.1 Seg.2 Seg.1 Seg.2

Integral velocity of stirred zone U (m4/s) 0.0804 0.0635 0.1330 0.1010 0.1661 0.1273 Useg2/Useg1 0.789 0.760 0.767

13 Jen-Hsin Chen, Sheng-Yang Lin and Muh-Jung Lu

Fig. 12. The photos of S-EMS in segment 1.

Fig. 13. The macroetch of 50A350 silicon slab.

4. CONCLUSION

A mathematical formulation for the complex S-EMS system was established and applied to the steelmaking plant in CSC. The formulation involved the Maxwell equations to determine the induced force field and the turbulent Navier-Stokes equations to calculate the velocity field in the liquid core of the strand. The temperature field was further analyzed by computer modeling to find its effects on the equiaxed ratio of slab. A parametric study was performed with different S-EMS layouts, locations, and stirring modes for process optimization. The following conclusions were obtained. (1) The liquid steel driven horizontally by S-EMS hit

the narrow face of the slab. Two big loops of recir-culation flow were formed at the upper and lower sides of the stirrers. The superheat at the upper zone of strand was significantly reduced; meanwhile, the temperature evenness of other parts was improved due to liquid stirring. As a result, the temperature gradient of the mushy zone was reduced and the equiaxed ratio was increased.

(2) The parametric study of the simulation obtained the following results; Maximum velocity along the interface: Face-to-Face, parallel stirring > Side-by-Side, Opposite stirring > Side-by-Side, parallel stirring Slab width 1575mm＞1270mm＞950mm Superheat diminution at upper strand: Face-to-Face, parallel stirring > Side-by-Side, parallel stirring > Side-by-Side, opposite stirring Temperature uniformity: Current 650A＞450A＞250A Slab width 1575mm＞1270mm＞950mm

(3) As to the S-EMS installation, the electromagnetic force and velocity integral in segment 2 was about 0.72 and 0.77 times that in segment 1, respectively. The stirring effect on the upper zone of stand was small when the S-EMS was installed in segment 2. As a result, the equiaxed ratio was not as effective as in the segment 1.

(4) The simulation process was verified by a newly- developed S-EMS, and the S-EMS was optimized by the computer simulation. An average of >45% equiaxed zone was normally achieved.

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