Abstract: A three-dimensional numerical model coupling the electromagnetic field, fluid flow and level fluctuation has been developed to investigate the flow behavior of molten steel in a slab continuous casting mold for interstitial-free (IF) steel. According to the industrial and modeling results, the swirls are generated on the cross section due to the electromagnetic force (EMF) and its number relies on the magnetic pole pairs of electromagnetic fields. With the increase in current frequency, the EMF reaches the maximum at the current frequency of 4.5 Hz and then gradually decreases. When the current intensity increases from 0A to 600A, the rate of slag entrapment related to the billet defects is decreased from 7.46% to 1.09%, but it increases to 6.09% when the current intensity reaches 650A. The study suggests that the optimized current intensity of mold-electromagnetic stirring (M-EMS) can effectively prevent surface or subsurface defects for clean steel production.

Keywords: Interstitial-free Steel; Electromagnetic field; Fluid flow; Current intensity; Rate of slag entrapment. 

1 Introduction

With the development of clean steel production, the quality requirements for continuous casting products are becoming increasingly strict ^[1]. For interstitial free (IF) steel production, which is widely used in the automobile industry due to its excellent deep-drawing property, the surface defects such as slivers and pencil blisters are the most frequent problems leading to rejections and downgrading of their final sheet products ^[2]. It is especially important to control the mold liquid level fluctuation during casting, and to avoid the subsurface inclusions collection related to the hook shell characteristic of the steels at the meniscus. A new M-EMS has been introduced which can produce swirling stirring to clean the popular hook collected inclusions, coupled magnetohydrodynamics model has been developed to analyze the characteristics of the three-dimensional electromagnetic field, fluid flow and level fluctuation phenomena in the 0.23m×1.6m slab mold. The relationships between the EMF and the current intensity or frequency have been analyzed in detail. The influence of stirring current and stirrer position on the level fluctuation of molten steel is also studied. Finally, the various M-EMS parameters of coil current intensity are compared through a combined analysis to the mold flow behavior and the feedback from industrial plant trials.

2 Model description

2.1 Three-dimensional geometrical model of M-EMS

Fig. 1 Geometry model and Finite element mesh:(a) electromagnetic simulation; (b) flow simulation

The geometry model and finite element mesh in a slab strand with a traveling-wave electromagnetic stirrer is shown in Figure 1. The model of M-EMS mainly includes molten steel, copper mold, stainless backboard, iron core, stirring coil, and air (not shown).

3 Results and discussion

3.1 Validity of developed model

To ensure the validity of the mathematical model, the computed results for the magnetic flux density along Y=0.1m line at the mid-plane of the stirrer were compared with the measured data in a plant, which is shown in Figure 2. The measured data was obtained by the Hunan Zhongke Electric Co., Ltd through a Lake Shore 475 DSP Gauss meter. From this figure, the tendencies of the magnetic flux density are centrally symmetrical distribution. The calculated results are in good agreement with the measured data， which indicates that the developed mathematic model is reasonable for this stirring system and the calculated results could be used to provide theoretical guidance for optimizing stirring operation parameters in actual production. Besides, the measured magnetic flux density is a little lower than that calculated, owing to the magnetic field leakage and measured or computed error. However, this error is small and can be neglected. 

Fig. 2 Comparison between the calculated and measured values of magnetic flux intensity

3.2 Magnetic flux density

Fig.3 The magnetic flux density (BF, BL, BO). (a) with stainless backboard; (b) without stainless backboard

Figure 3 shows the magnetic flux density along lines for Y= -0.1m (BF), Y=0.1m (BL), Y=0m (B0) at the mid-plane of the stirrer with and without stainless backboard. It can be observed that the BF is almost equal to BL. For the case with the stainless backboard in Fig. 3a, its magnetic flux density is more uniform and smaller than that without stainless backboard, which plays a role of electromagnetic shield from the coils. The average values of BF are respectively 61.92 mT and 122.26 mT for with and without stainless backboard, so it is not accurate to ignore stainless backboard in the M-EMS geometry model.

Fig. 4 Distribution of magnetic flux density on the stirrer mid-plane (Z = −0.12 m). (a) Vector; (b) contour

Figure 4 shows the vector and contour plots of magnetic flux density at the mid-plane of the stirrer (Z = −0.12 m). It is seen that the vector and contour of magnetic flux density of the initial phase distribute centrosymmetric. The magnetic flux density is larger at the edge of wide face, and it decreases gradually from the exterior to the interior. The maximums are located in the vicinity of the mold wide edge (Y=0.125m or Y= -0.125m).

Fig. 5 Vector and contour plots of time-averaged EMF on the stirrer mid-plane (Z=−0.12 m). (a) vector; (b) contour 

Figure 5 shows the vector and contour of the time averaged EMF on the stirrer mid-plane (Z= −0.12 m). It is seen that the distribution of EMF is centrosymmetric due to the centrosymmetric distribution of the magnetic flux density. The tangential components of the EMFs in the vicinity of the edges are greater than that in the inner part of the cross-section, and the tangential components of the EMFs at the two parallel edges of the wide face are equal in value with opposite direction. Four transverse swirls of the time-averaged EMF exist in the interior of cross-section. The maximum of the time-averaged EMF is 9000 N/m3, which appears at the points X=0.57m, Y=0.125m and X=-0.57m, Y=-0.125m. The minimum of the time-averaged EMF is lower than 1000 N/m3, which appears in the interior.

Figure 6a shows the distribution of magnetic flux density for different current at 4.5Hz. The magnetic flux density increases with the increasing current intensity, and they are in approximate proportional relationship. Figure 6b shows the distribution of tangential EMF for different current frequencies at 600 A. In the range of applied current frequencies for M-EMS (1.0–5.5 Hz) at 600 A, the tangential EMF increases with the increasing current frequency and reaches the maximum at the current frequency 4.5Hz and then decreases gradually. 

Fig. 6 Distribution of magnetic flux density and tangential EMF. (a) different currents; (b) different frequencies

Fig. 7 The comparison of three-dimensional level fluctuations: (a) M-EMS off; (b) with M-EMS, Z=-0.42m; (c) with M-EMS, Z=-0.27m; (d) with M-EMS, Z=-0.12m

Figure 7 shows the three-dimensional level fluctuations under different positions of stirrer mid-plane, in which the plane of steel volume fraction value 0.5 is chosen to express the status of level fluctuation. It can be intuitively seen that the steel/slag interface is nearly flat as the M-EMS off. The swirling flow from the effect of M-EMS increases the fluctuation of the free surface, and the highest-level fluctuations for M-EMS happen at four corners of the mold free surface. In the local regions, the maximum height of level fluctuation for M-EMS at Z=-0.42m, -0.27m, -0.12m are 1.0 mm, 2.4 mm and 2.9 mm, respectively. The height of the stirrer increases, which can easily induce the fluctuation of the free surface. The results indicate that as the height of the stirrer is increased, the level fluctuation is aggravated. The largest value of level fluctuation under M-EMS at Z= -0.12m is acceptable for the movement of slag, which the range of level fluctuation within ±4mm is acceptable for plant ^[15]. Therefore, the optimum stirrer position for the mid-plane of M-EMS is at Z= -0.12m below the meniscus.

Figure 8 indicates the effect of stirring current on the level fluctuation. With the increase of stirring current, the level fluctuation is intensified due to the obvious transversal swirling flow induced by the M-EMS, which may lead to slag entrapment. In the local regions. The maximum height of level fluctuation for current 500A, 550A, 600A, 650A are 2.1 mm, 2.8 mm, 3.6 mm, and 4.2mm, respectively. When the current is 650A, the level fluctuation exceeds ±4mm, the aggravation of the level fluctuation may lead to the slag entrapment.

Fig. 8 The comparison of three-dimensional level fluctuations: (a) 500A; (b) 550A; (c) 600A; (d) 650A

Fig. 9 Vector distribution at the center of EMS (a) 500A; (b) 550A; (c) 600A; (d) 650A

Figure 9 reveal the flow pattern on the mid-plane of M-EMS under various currents. The tangential velocity rises with the increasing current intensity. Four transverse swirls of the molten steel are symmetrically distributed, which almost coincide with the four magnetic pole pairs.

3.3 Quality of slab with different process parameters

Table 2 he blocking rate for slag entrapment with different current intensities

According to the simulation results above, four current intensities were chosen to test for a interstitial-free steel slab produced by a steel plant in China, the blocking rate of slag entrapment was counted in Table 2, which is one of the main sources of inclusions in the final product, and will greatly harm the clean steel production. When the M-EMS is powered on, the blocking rate of flux entrainment obvious decreases. At the current intensity 600A，the blocking rate of slag entrapment is only 1.09%, which is decreased by 85% compared with the situation M-EMS off. Therefore, the industrial results agree well with the calculated results, and thus verify the success of the present model.

4 Conclusions

Combined numerical simulation and plant trials, the effect of M-EMS on the electromagnetic field, fluid flow and level fluctuation were studied. The main conclusions are as follows:

(1) The magnetic flux density and the EMF distribute centrally symmetrical on the wide face of mold. The EMF generates the swirls on the cross-section and its number is corresponding to the magnetic pole pairs of electromagnetic field. With the increase in current frequency, the EMF reaches the maximum at the current frequency of 4.5 Hz and then gradually decreases. 

(2) With the increase in the height of the stirrer position, the level fluctuation aggravates, which may lead to the flux entrainment. When the mid-plane of M-EMS is at Z= -0.12m, the level fluctuation is ±4mm, which is accepted by the plant.

(3)  According to the statistical results of the entrainment blocking rate for different process parameters in industrial plant trials, the optimized current intensity is 600A, and at this current intensity, the blocking rate of slag entrapment is only 1.09%, far lower than the case with M-EMS off.

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