Numerical Simulation of the Effects of Horizontal and Vertical EMBr on Jet Flow and Mold Level Fluctuation in Continuous Casting

Transcription

1 Numerical Simulation of the Effects of Horizontal and Vertical EMBr on Jet Flow and Mold Level Fluctuation in Continuous Casting LIN XU, ENGANG WANG, CHRISTIAN KARCHER, ANYUAN DENG, and XIUJIE XU In this article, a new type of electromagnetic braking (EMBr), named vertical EMBr (V-EMBr) was introduced in the continuous casting process. In order to investigate its capability and applicability, the impacts of horizontal and vertical EMBrs on the flow pattern in a continuous casting mold were simulated by means of an implemented Reynolds-averaged Navier Stokes (RANS) SST k x turbulence model. The characteristics of electromagnetic field and flow field inside a 1450 mm mm mold with Ruler-EMBr and V-EMBr have been compared. The numerical simulation results indicate that the static magnetic field generated by Ruler-EMBr can cover the main part of the discharging jet flow, which has a better control of the flow pattern in lower part of the mold. The static magnetic field generated by V-EMBr can cover both the vicinity of the mold narrow faces and the impingement region of the jet flow, which can effectively control the liquid steel flow in the upper recirculation zone. The parametric study also shows that the large vortices beneath the jet flow can be almost completely eliminated at an optimized magnetic flux density with Ruler-EMBr. In addition, the surface velocity and steel/ slag interface fluctuation can be suppressed with the application of V-EMBr to acceptable values even with a wide variation of SEN port angles. It is estimated that to reach the same level of braking effect on the upper recirculation flow, a magnetic flux density of 0.1 T is sufficient for V-EMBr, while 0.2 T is needed for Ruler-EMBr. Based on the results, a second-generation V-EMBr has been developed, which combines both of the merits of Ruler-EMBr and V-EMBr. Ó The Minerals, Metals & Materials Society and ASM International 2018 I. INTRODUCTION IN the continuous casting process, especially under the condition of high casting speed, increased flow rate of the liquid steel at the outlet of submerged entry nozzle (SEN) can easily cause disturbances at the steel/slag interface at the top of the mold. This phenomenon may cause mold flux entrapment and result in entrainment of inclusions and bubbles into the liquid steel, which are entrapped in the newly formed steel shell, thus affecting the slab quality. [1,2] Therefore, effectively controlling LIN XU, ENGANG WANG, ANYUAN DEN, and XIUJIE XU are with the Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, No. 3-11, Wenhua Road, Shenyang , P.R. China and also with the School of Metallurgy, Northeastern University, Shenyang , P.R. China. Contact egwang@mail.neu.edu.cn CHRISTIAN KARCHER is with the Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, P.O. Box , Ilmenau 98684, Germany. Manuscript submitted December 15, level fluctuations in the mold is key to producing high quality steel slabs. Equipment which controls fluid flow in the mold through the application of static magnetic fields is referred to as an electromagnetic brake (EMBr). The design of EMBrs is continuously being improved, and they have been demonstrated to be effective in reducing the potential for liquid steel breakouts from the strand shell, and decreasing slab and final product surface defects. [3 6] Up to now it has been developed into three typical types: Local EMBr, [3,4] Ruler-EMBr [5 9] and flow control mold (FC-Mold) EMBr. [10] Local EMBr has a characteristic that two separate magnets are located near the SEN ports, which is mainly used to suppress molten steel velocity from the nozzle and prevent mold flux entrapment. Ruler-EMBr utilizes one pair of magnets, which covers the entire wide faces of the mold, with the aim to stabilize the meniscus velocity and prevent mold flux entrapment. To better control meniscus fluctuations and molten steel flow behavior in the mold, a third-generation electromagnetic brake (FC-Mold EMBr) was proposed. FC-Mold EMBr

2 consists of two pairs of magnets across each wide face. One is located on the meniscus of the mold, and the other is located below the SEN port. Currently, there are two widely used EMBr devices: Ruler-EMBr and FC-Mold EMBr. [11,12] It was found that, in the slab continuous casting process, the braking effects of Ruler-EMBr on the surface velocity and level fluctuation are not significant and usually Ruler-EMBr was u nable to suppress mold flux entrapment effectively. [6] Compared to Ruler-EMBr, FC-mold is good at controlling meniscus velocity and level fluctuation. However, it s not applicable for the continuous casting of thin slabs due to large volume, heavy weight and complicated structure. Therefore, on the basis of understanding the characteristics of the existing EMBr, a new type of EMBr, named vertical electromagnetic brake (V-EMBr) was proposed by our research group in previous publications. [13 16] Two pairs of magnetic poles are installed vertically on the mold wide sides close to the narrow faces for V-EMBr while a pair of magnetic poles is mounted on the mold wide sides horizontally for the Ruler-EMBr as shown in Figure 1. The special characteristic of V-EMBr device lies in the fact that the static magnetic field covers both the vicinity area of the narrow faces of the mold and the impingement region of liquidmetal jet from the SEN. Hence, it shows the potential to suppress the upper recirculation flow and control the fluctuation of meniscus. From the perspective of investigating the fluctuation behavior of the surface flow, most previous research focused on the numerical simulation in which the deformed interface was simplified as a plane. [17] For example, Hwang et al. [18] utilized a finite volume method to analyze the influence of EMBr on the flow of liquid steel in the mold with different operation parameters, and the shape of liquid surface was calculated by the pressure distribution on the free surface. Harada et al. [19] simplified the deformed interface to a flat surface, and compared the damping effect of the local magnetic field with the level magnetic field. In recent years, the researchers improved the simulation method of the deformed interface, and the simulation results showed that the fluctuation behavior of the surface flow were more practical. For instance, Anagnostopoulos et al. [20] showed a volume tracking method to simulate the behavior of three-dimensional (3D) water oil interface fluctuation in continuous casting mold. Yu et al. [21] utilized a volume of fluid (VOF) model to investigate the effects of the casting speed and the shape of nozzle on the fluctuation behavior of steel/slag in the mold under the condition of argon blowing. In comparison, the VOF method is more applicable to the numerical simulation of two-phase turbulent flows. [22 25] Another aspect addressed in the present study is the turbulence modeling. Until now, three approaches have been commonly employed to predict the effects of turbulence, i.e., direct numerical simulation (DNS), large eddy simulation (LES), and Reynolds-averaged Navier Stokes (RANS). DNS is a direct approach of solving the Navier Stokes equations for turbulent flows which is a powerful research tool for investigating simple turbulent flows at moderate Reynolds numbers. Nevertheless, due to the high computational cost, it is inapplicable to practical engineering systems with complex geometry or flow configurations. [26] In the LES approach, larger-scale vortices are separated from smaller-scale ones using low-pass filtered Navier Stokes equations. Subsequently, the larger unsteady turbulent motions are directly represented, whereas the smaller-scale motions are modeled. Obviously, it can capture the instantaneous turbulence characteristics, Fig. 1 Schematics of (a) Ruler-EMBr and (b) V-EMBr.

3 e.g. the coherent structure within the turbulent boundary layer. [27,28] However, the computational cost of LES is still high which hinders its extensive use in turbulent flow modeling. The approach of RANS is widely utilized in various turbulence flows, in which Spalart-Allmaras model, k e model, and k x model are developed to close the RANS equations. The k e model is the most widely used complete turbulence model. [26] Many efforts have been made to use the k e model to reveal the influence of a static direct current (DC) magnetic field on the mean flow and the turbulent fluctuation in the mold. For example, Tian et al. [29] utilized a low-reynolds-numbered k e model to study the influence of EMBr on the liquid steel flow in a funnel mold. Based on the realizable k e model, Liu et al. [30] described the behavior of liquid steel flow and heat transfer in the compact strip production (CSP) and flexible thin slab casting (FTSC) funnel molds under a static magnetic field, respectively. However, the k e model is quite inaccurate for complex flows due to inaccuracies in the turbulent-viscosity hypothesis. Another commonly used two-equation model is the k x model which has a distinct advantage in the treatment of the viscous near-wall region. [26] In order to predict the Reynolds stress, Menter [31] proposed the SST k x model on the basis of k x model which combines the merits of the k e model and the k x model. Asad et al. [32] utilized the SST k x model to simulate the transient-free surface behavior in a continuous casting mold. Miao et al. [7] performed numerical calculations on the fluid flow in the continuous casting process under a DC magnetic field using the SST k x model, which displayed a good agreement with the measurement results of turbulent flow in a facility termed as Liquid Metal Model for Continuous Casting (LIMMCAST). [33] The previous studies demonstrated that the SST k x model can successfully describe the liquid metal flow exposed to a DC magnetic field. In this study, the SST k x model was utilized to describe the transient flow in a continuous casting slab mold, and the VOF model was applied for the treatment of the two-phase surface flow. A grid independence test was first performed to determine an appropriate grid density to ensure computational efficiency and accuracy. On this basis, the numerical simulations were carried out to examine the braking effect of V-EMBr in comparison with the Ruler-EMBr. The current study focuses on the effect of a static magnetic field on the fluctuation of steel/slag interface and the flow pattern in the mold, without considering the impacts of solidification and heat transfer on the liquid metal flow. In addition, the influences of the magnetic flux density and the nozzle port angle on the braking effect were analyzed. II. DESCRIPTION OF HORIZONTAL AND VERTICAL EMBR In the continuous casting process, the electromagnetic brake device is installed on the mold, which can affect fluid flow and consequently temperature distribution in the mold. Reasonable electromagnetic parameters and the installation position of electromagnetic brake device have an important influence on the effectiveness of EMBr on the slab quality improvement in industrial production. Schematics of two types of electromagnetic brake (Ruler-EMBr and V-EMBr) are illustrated in Figure 1. The cross section of the mold is 1450 mm mm, with a height of 800 mm. The Ruler-EMBr device consists of two sets of electrified coils, which covers the entire wide faces of the mold, as shown in Figure 1(a). For Ruler-EMBr device, the distance between the upper surface of the magnetic pole and the free surface is 290 mm, and the height of the magnetic pole is 200 mm. Different from the Ruler- EMBr device, the V-EMBr device has two pairs of magnetic poles with a height of 600 mm which are arranged vertically near the mold narrow face, as shown in Figure 1(b). [13,14] It could cover the impact region of the metal jet out from the SEN and could control the free surface of liquid steel flow. III. MATHEMATICAL MODEL AND NUMERICAL METHOD A. Mathematical Formulation In order to better describe liquid steel flow in the slab continuous casting mold under the influence of EMBr, and on the premise of making the simulation results reasonable, the following assumptions were made. The flow of liquid steel and mold flux in the mold was assumed to be unsteady, and their physical properties constant. The liquid steel and mold flux were considered to be homogeneous, viscous, and Newtonian incompressible fluids. The influence of oscillation and negative taper of the mold was not taken into account. Heat transfer in the mold and the presence of the solidified shell were ignored. In the process of continuous casting, mold flux was assumed to infiltrate into the mold flux channel between the mold wall and solidified shell to reduce withdrawal force. Therefore, for the calculation of the electromagnetic field, the mold wall was assumed to be electrically insulated. Finally, the electromagnetic characteristics of liquid steel were homogeneous and isotropic. Under these assumptions the time-averaged governing equations read as þrðqu/þ ¼rðC / r/þþs / ½1Š where / stands for various time-averaged variables, i.e., turbulence kinetic energy and turbulence dissipation rate; C / and S / represent the diffusion coefficient of the variable / and the source term for various transport equations, respectively. More details for the time-averaged governing equations are given in Appendix. 1. Turbulence model In this paper, the Reynolds-averaged Navier Stokes (RANS) SST k x model was utilized to simulate the mean flow characteristics of liquid steel and the steel/

4 slag interface behavior in the mold. Different from the other two-equation eddy-viscosity turbulence models, the SST k x model computes the anisotropic turbulent flow field and considers the effect of Reynolds stress. Moreover, in the near wall region, where the SST k x model is superior to the other two-equation models, an automatic wall function is utilized. [31] 2. Electromagnetic force equations The magnetic induction method [34] was utilized to calculate the induced current and electromagnetic force, which is derived from Ohm s law and Maxwell s equations. The induced current density can be deduced from the following equation: J ¼ 1 l rb; where the magnetic flux density B consists of the applied DC magnetic field B 0 and the secondary field b induced by the mold flow. Hence, we have B = B 0 + b. The induced field b can be calculated from the magnetic þ ðu rþb ¼ 1 lr r2 b þ ðb rþu ðurþb 0 Finally, the Lorentz force is given by F mag ¼ J B 3. VOF model equation The method of volume of fluid (VOF) was utilized to build two-phase turbulent transient flow model, which could track the shape of fluctuating steel/slag interface in the slab continuous casting mold. A characteristic of VOF model is that it utilizes a moving steel/slag interface to define the fraction of fluid volume in a space lattice. For an incompressible fluid, assuming that the densities of liquid steel and mold flux are constant, so the volume fraction of liquid steel should satisfy the following equation. ½2Š ½3Š ½4Š þrðu st U st Þ ¼ 0; ½5Š where u st = 1 represents the liquid steel, u st =0 stands for the mold flux, and 0 < u st < 1 represents the steel/slag interface. 4. Boundary conditions The inlet velocity was positioned at the exit of the side aperture of the nozzle, which was calculated from the specific casting speed to maintain flow equilibrium. The top surface of the mold was set as a free surface, and its boundary condition was the same as symmetry boundary condition, where the velocity components perpendicular to the free surface and normal gradients of other variables were set to zero. For the mold wall, an automatic near wall treatment was adopted by the SST k x model. Normal component of the induced current and normal gradients of other variables were set to zero. At the exit of computational domain, fully developed flow was assumed, and normal gradients of all variables were set to zero. At the boundary, the induced magnetic field b can be represented by [36] : b ¼ fb n b t1 b t2 g T ; ½6Š where b n represents normal component, b t1 and b t2 are tangential components. In this paper, an electrically insulating boundary condition was assumed (j n = 0). Therefore, according to Ampere s law, b t1 and b t2 at the boundary should satisfy the following condition. b t1 ¼ b t2 ¼ 0 ½7Š 5. Computational domain In this study, we mainly discuss the influence of the Ruler-EMBr and V-EMBr on the behavior of the liquid metal jet from the submerged entry nozzle (SEN) ports and steel/slag interface fluctuation in the mold. In order to better observe the flow distribution and expansion of the liquid metal jet, we define a mid-plane at the nozzle port as a-plane, whose angle relative to the horizontal plane equals to the nozzle port angle a as shown in Figure 2(a).The geometry of the computational domain is shown in Figure 2(b). Due to the fact that the model is symmetrical, in order to reduce the calculation time and improve the computational efficiency, one half of the mold geometry was considered. Hexahedral unstructured meshing was adopted in which a local mesh refinement method was used in the region near the mold wall and the steel/slag interface. The operating parameters and physical properties of the mold are shown in Table I. B. Numerical Method For the first stage of the numerical calculation, the 3D external magnetic field B 0 in the mold was solved by the commercial software ANSYS (version ), which was then imported into the FLUENT software as the calculated load of 3D flow field. More specifically, the magnetic field data was imported to the activated magnetohydrodynamic (MHD) module in order to couple the flow field. Afterwards, the FLUENT flow modeling software package was utilized to simulate the interfacial fluctuation behavior of steel/slag and fluid flow patterns of the liquid metal jet from the SEN port under a static direct current (DC) magnetic field. In addition, the computation of the effect of the DC magnetic field on the flow field was based on a 3D finite-volume method. Finally, the governing equations were discretized in the FLUENT software using the pressure implicit with splitting of operators (PISO) algorithm for pressure velocity coupling. The computations were performed on an AMD OPTERON 6134 CPU with a frequency of 2.3 GHz. A grid independence test was performed to minimize the effect of grid density on the computational results. The operating parameters are as follows: a casting speed of 1.6 m/min, a SEN port angle of downward 15 deg,

5 Fig. 2 Schematic and mesh to be based on the geometry of the mold: (a) schematic of the mold and (b) geometry of the mold. and a magnetic flux density of 0 T. Calculations were carried out for three grid sizes as listed in Table II. The relative errors d p and d t correspond to the calculated results at the peak and trough of the steel/slag interface, respectively. The results showed that even the node number was increased to 1.5 times of the node number in the mesh M 1, the relative errors of the height were less than 5 pct. Therefore, considering the balance between computational cost and accuracy, M 1 was selected for the present computations. IV. RESULTS AND DISCUSSION A. Magnetic Field Figure 3 shows distributions of magnetic flux density of two types of EMBr in one half volume of the mold under a magnetomotive force (MMF) of ampere-turns (At). [37] Irrespective of the EMBr type (Ruler- EMBr or V-EMBr), the distribution of magnetic flux density within the coverage area of the magnetic pole is uniform. At the central cross section of the mold, the maximum magnetic flux density (B max ) is 0.2 T. The static magnetic field generated by the Ruler-EMBr can cover the entire wide faces of the mold. In contrast, for V-EMBr, the magnetic field can not only cover the free surface, but also the impact region of the liquid metal jet from the SEN. In order to show the details about the differences in the magnetic flux density between the Ruler-EMBr and V-EMBr, the distributions of magnetic flux density along three lines (the lines AB, CD, and EF in Figures 3(a) and (b)) were extracted at the mold central cross section along the direction of width, height, and thickness of the mold, respectively. Figure 4 represents the magnetic flux density distribution with two types of magnets along three typical lines (the lines AB, CD and EF). With the Ruler-EMBr, the curvature of the magnetic flux density forms a plateau along the width direction, and it descends slightly near the narrow face of the mold due to magnetic flux leakage as shown in Figure 4(a 1 ). On the contrary, when the V-EMBr is applied, the magnetic flux density along the width direction is considerably stronger in the vicinity of mold narrow face while it is distinctly smaller within the central zone, which forms a saddle shape as shown in Figure 4(b 1 ). Figures 4(a 2 ) and (b 2 ) indicate that the magnetic flux density along the mold height direction is higher within the magnet zone, and gradually decreases along both sides of the mold for the case of Ruler-EMBr and V-EMBr. As shown in Figures 4(a 3 ) and (b 3 ), the magnitude of magnetic flux density along the mold thickness direction with the Ruler-EMBr is almost the same as that with the V-EMBr under the same magnetomotive force (MMF).

6 Table I. Geometrical Parameters and Physical Properties Parameter Value Mold Size (mm) Mold Length (mm) 800 Computational Domain (mm) Casting Speed (m min 1 ) 1.6 The Height of Liquid Mold Flux (mm) 35 Angle of Nozzle Port (deg) 10, 15, 20 Depth of SEN (mm) 225 Total Height of SEN Outlet (mm) 80 Magnetomotive Force (A t) 0, 15750, Liquid Steel Density (kg m 3 ) 7020 Mold Flux Density (kg m 3 ) 3500 Steel Viscosity (kg m 1 s 1 ) Mold Flux Viscosity (kg m 1 s 1 ) Interface Tension Coefficient (N m 1 ) 1.2 Steel Electric Conductivity (S m 1 ) Magnetic Permeability (H m 1 ) Reynolds Number (Re ¼ qud=l; Based On Nozzle Diameter) Reynolds Number (Re ¼ qul=l; Based on Magnetic Pole Width) Hartmann Number p (Ha ¼ B 0 L ffiffiffiffiffiffiffiffi r=l ; Based on Magnetic Pole Width) Stuart Number (N ¼ B 2 0 Lr=qU; Based on Magnetic Pole Width) Ruler-EMBr V-EMBr Depth of SEN is the distance from the top of port to the mold level. The Hartmann number can be obtained by imposing the magnetic flux density of 0.2 T. Table II. Statistic Results of the Error with Different Grid Node Numbers Mesh M 1 M 2 M 3 Total Node Number d p ¼ jh Mi H M1 j=h M pct pct d t ¼ jh Mi h M1 j=h M pct pct H: distance from the level of steel/slag interface (z = m) to the peak of the fluctuating interface. h: distance from the level of static steel/slag interface (z = m) to the trough of the fluctuating interface. B. Electromagnetic Field Using the same operating parameters described earlier, Figures 5 and 6 show the contour of magnetic flux density, vectors of current density and Lorentz force at half thickness in the mold with Ruler-EMBr and V-EMBr, respectively. The black dashed lines in the plots indicate the EMBr position. Figure 5(a) shows that the distribution of magnetic field with Ruler-EMBr is almost uniformly focused on the mold wide face, which can cover the main part of the discharging jet flow. Figure 5(b) shows that the path of the induced current is concentrated in the vicinity of the nozzle exit. The vortices of induced current are formed at the region where the jet flow splits into an upward flow and a downward flow. Figure 5(c) shows that the Lorentz force acts to the direction of the nozzle port, which produces a braking effect directly on the initial segment of the jet. Figure 6(a) shows that the magnetic field with V-EMBr is concentrated in the region which is close to the narrow face of the mold, and it decays significantly moving toward the SEN. Figure 6(b) shows that the induced current flows clockwise from the region where the front of the jet flow interacts with the higher magnetic field. As a consequence, the Lorentz force produces a braking effect on the upward flow and downward flow as shown in Figure 6(c). C. The Effect of EMBr on the Flow Pattern and Mold Level Fluctuation Figure 7 presents the velocity distribution in the mid-plane at the mold wide face with two types of magnets under different magnetic flux densities. In case when no EMBr is applied, a typical double-roll flow pattern is predicted as shown in Figure 7(a). Note that the liquid metal jet discharged from the SEN shows the tendency of tilting upward at the main body section. It splits into an upward and a downward flow pattern after impacting on the narrow face of the mold. The liquid steel flows upward along the mold narrow face, approaches to the steel/slag interface and then flows back to the center of the mold to form an anticlockwise vortex. The downward liquid steel flow penetrates deeply into the molten pool and generates a big clockwise vortex. Figures 7(b) and (c) show that the jet impingement upon the narrow face of the mold is suppressed by Ruler-EMBr. In the lower recirculation zone, the core of the vortex is shifted downward by the magnetic field which is in agreement with the results of Reference 7. In addition, extra small vortices are generated below the jet stream when the magnetic flux density reaches to 0.2 T. However, in the upper recirculation zone, the braking effect is not significant. Figures 7(d) and (e) show that the tendency of tilting of the jet flow is weakened by V-EMBr, which is beneficial for the stabilization of the mold level. In addition, the lower recirculation zone is pushed away by the Lorentz force from the narrow face of mold, which could promote the uniformity of the initial solidified shell on the narrow side of the mold. However, at a higher magnetic field, an extra vortex is formed below the jet flow which may have an adverse effect on the flotation of bubbles and nonmetallic inclusions. Figure 8 shows the streamlines and velocity distribution of jet stream in a-plane with different magnets. The jet stream from the SEN has an obvious expansion characteristic. In case when the EMBr is absent, the jet stream in a-plane is irregular and divergent. Figures 8(b) through (c) illustrate that in the case of Ruler-EMBr, the extent of expansion of the jet stream increases with the increase of magnetic flux density. The vortex in the vicinity of the nozzle disappears when magnetic flux density is increased to 0.2 T. Figures 8(d) through (e) show that in the case of V-EMBr, the discharging jet flow is stretched by the gradient of the magnetic field. This stretching effect is enhanced by the increase of

7 Fig. 3 Contour plot of magnetic flux density in the mold with (a) Ruler-EMBr and (b) V-EMBr. Fig. 4 Distribution of magnetic flux density in different directions with (a) Ruler-EMBr and (b) V-EMBr. magnetic flux density, in which the velocity of liquid steel close to the mold wall is further decreased. Moreover, the jet stream flows regularly towards the narrow face of the mold which presents a fan-shape. As a consequence, the impingement of the jet stream on the mold wall should be controlled by V-EMBr which reduces the potential for breakout of liquid steel from the solidified shell.

8 Fig. 5 Distribution of magnetic flux density, induced current density, and Lorentz force in the central plane with Ruler-EMBr: (a) B0 = 0.2 T, (b) induced current density, and (c) Lorentz force. Fig. 6 Distribution of magnetic flux density, induced current density, and Lorentz force in the central plane with V-EMBr: (a) B0 = 0.2 T, (b) induced current density, and (c) Lorentz force. Figure 9 illustrates the 3D steel/slag interface profiles with different EMBrs. The results show that the deformation of the steel/slag interface with V-EMBr is much smaller than that with Ruler-EMBr. Furthermore, this phenomenon is more apparent under a higher magnetic field. The quantitative analysis of the steel/slag interface fluctuation is shown in Figure 10. On the condition of no EMBr, the fluctuation height is up to 16.2 mm. In the case of Ruler-EMBr, the fluctuation height is reduced to 15.0 and 11.9 mm with a magnetic flux density of 0.1 and 0.2 T, respectively. With the application of V-EMBr, the fluctuation height is remarkably reduced from 11.2 to 6.0 mm when the magnetic flux density is increased from 0.1 to 0.2 T. Figure 11 shows the velocity distribution along the centerline in x-y cross section (z = 35 mm) with different magnetic flux densities under Ruler-EMBr and V-EMBr. With the absence of EMBr, the maximum surface velocity is 0.24 m/s. When the Ruler-EMBr is applied, the surface velocity is reduced to 0.23 and 0.22 m/s with a magnetic flux density of 0.1 and 0.2 T, respectively. In the case of V-EMBr, when the magnetic flux density is increased from 0.1 to 0.2 T, the maximum

9 Fig. 7 Velocity distribution under two types of magnets in the central plane: (a) B = 0 T, no EMBr; (b) B = 0.1 T, and (c) B = 0.2 T, with Ruler-EMBr; (d) B = 0.1 T, and (e) B = 0.2 T, with V-EMBr. Fig. 8 Streamlines and velocity distribution under Ruler-EMBr and V-EMBr in the a-plane: (a) B = 0 T, no EMBr; (b) B = 0.1 T, and (c) B = 0.2 T, with Ruler-EMBr; (d) B = 0.1 T, and (e) B = 0.2 T, with V-EMBr.

10 Fig. 9 Steel/slag interface profiles under two types of magnets with different magnetic flux densities: (a) B = 0 T, no EMBr; (b) B = 0.1 T, and (c) B = 0.2 T, with Ruler-EMBr; (d) B = 0.1 T, and (e) B = 0.2 T, with V-EMBr. Fig. 10 Profile of fluctuating steel/slag interface with various magnetic flux densities. surface velocity is significantly reduced from 0.20 to 0.15 m/s. It can be summarized from above that to reach the same level of braking effect on the surface flow and steel/slag interface fluctuation, a magnetic flux density of 0.1 T is sufficient for V-EMBr, while 0.2 T is needed for Ruler-EMBr. D. The Effect of Nozzle Port Angle on the Braking Effect Figure 12 describes the velocity distribution in the mid-plane of the mold wide face with different nozzle port angles. It can be seen from Figures 12(a) through (c), when the Ruler-EMBr is applied, the penetration depth in the lower part of the mold and the range of the Fig. 11 Distribution of horizontal component of velocity on the centerline in the mold width direction 35 mm deep from the free surface. upper recirculation zone are increased with increased port angles. Furthermore, extra vortices below the jet stream are restrained especially when the port angle is increased to downward 20 deg. Obviously, the flow pattern in the lower recirculation zone is more strongly influenced by the nozzle port angle than that in the upper recirculation zone with the fixed location of Ruler-EMBr. With the application of V-EMBr, Figure 12(d) shows that the front jet stream is rejected by the magnetic field and extra small vortices are formed below the jet stream. When the downward port angle increases, the front jet stream is deflected rather than rejected by the magnetic field as show in Figures 12(e) and (f). Additionally, the vortex core in the upper

11 Fig. 12 Velocity vectors in the central plane under two types of magnets with different SEN port angles: (a) 10, (b) 15, and (c) 20 deg, with Ruler-EMBr; (d) 10, (e) 15, and (f) 20 deg, with V-EMBr.

12 recirculation zone is shifted downward with the increase of SEN port angle, which results in a more stable steel/ slag interface. Figure 13 shows the streamlines and velocity distribution of jet stream in the a-plane with various nozzle port angles. From Figures 13(a) through (c), it can be seen that when the Ruler-EMBr is applied, the expansion of the jet stream is slightly restrained with the increase of SEN port angles. However, the impingement velocity of the jet stream on the mold narrow face is obviously weakened. In contrast, a fan-shaped jet stream is produced by V-EMBr, regardless of the variations of the nozzle port angle as shown in Figures 13(d) through (f). Note that both the expansion and the impingement of the jet stream on the mold narrow face are significantly restrained, which decreases the impact strength against the mold faces. Figure 14 shows the fluctuation of steel/slag interface with various port angles under Ruler-EMBr and V-EMBr. With Ruler-EMBr, the fluctuation height is reduced to 12.6, 11.9 and 11.3 mm when the port angle is 10, 15 and 20 deg, respectively. In addition, with V-EMBr, the fluctuation height is remarkably reduced to 8.7, 6.0 and 3.8 mm, when the corresponding to the downward port angle is 10, 15 and 20 deg, respectively. The velocity distribution along the centerline in x-y cross section (z = 35 mm) with different port angles under Ruler-EMBr and V-EMBr is illustrated in Figure 15. The velocity of the backflow under the free surface is decreased with the increase of port angle for both Ruler-EMBr and V-EMBr. When the Ruler-EMBr is applied, the braking effect on the upper recirculation is not obvious. The maximum velocity is reduced to 0.22, 0.22 and 0.21 m/s in turn when the downward port angle is 10, 15 and 20 deg, respectively. In comparison, the surface velocity is significantly reduced by V-EMBr. The maximum velocity is reduced to 0.19, 0.16 and 0.13 m/s, when the corresponding to the downward port angle is 10, 15 and 20 deg. From Figures 12 through 15, it can be seen that Ruler-EMBr and V-EMBr have their own characteristics in terms of the braking effect. Ruler-EMBr has a better control of the flow pattern in the lower part of the mold, while V-EMBr has a better suppression on the surface flow. Moreover, with V-EMBr the surface Fig. 14 Profile of fluctuating steel/slag interface with different port angles. Fig. 13 Streamlines and velocity distribution contour under Ruler-EMBr and V-EMBr in the a-plane with different SEN port angles: (a) 10, (b) 15, and (c) 20 deg, with Ruler-EMBr; (d) 10, (e) 15, and (f) 20 deg, with V-EMBr.

13 Fig. 15 Distribution of horizontal component of velocity on the centerline in the mold width direction 35 mm deep from the free surface. velocity and fluctuation can be suppressed to a desirable extent even with a wide variation of nozzle port angles, which can be influenced by inclusion buildup in the SEN port during casting. Last but not least, it s necessary to mention that these findings are based on computations that experimental data are needed to verify these predictions. V. CONCLUSIONS In this study, the Reynolds-averaged Navier Stokes (RANS) SST k x model was utilized to investigate the influence of EMBr on the steel/slag interface fluctuation and liquid metal jet flow. A horizontal EMBr (Ruler- EMBr) and a vertical EMBr (V-EMBr) were considered and compared in the present study. Two important parameters including magnetic flux density and nozzle port angle were taken into account to analyze the braking effects of Ruler-EMBr and V-EMBr, with the following findings. 1. The characteristics of electromagnetic field inside a 1450 mm mm mold with Ruler-EMBr and V-EMBr have been compared. In the model simulations with Ruler-EMBr configuration, the effective area of influence can cover the mold wide face, which produces a braking effect directly on the main part of discharging jet flow. However, the effective area that the V-EMBr influences can not only cover the front jet stream, but also the free surface, which produces a braking effect to maintain a favorable double-roll flow pattern in the mold and stabilize the mold level surface. 2. When the Ruler-EMBr is applied, the lower recirculation flow can be effectively controlled with an increase of magnetic flux density. However, the influence of the Ruler-EMBr is insufficient to control the upper recirculation flow due to the significant magnetic field decay in the upper part of the mold. When the magnetic field from a V-EMBr is imposed, both the expansion and the velocity of jet flow are significantly restrained, which suppresses the impingement of the liquid steel on the mold narrow face. In addition, the upward deflection of jet flow near the mold narrow face is further suppressed as the magnetic field is strengthened, and the braking effect on the surface flow and steel/slag interface fluctuation are more effective. To reach the same level of braking effect on the upper recirculation flow, a magnetic flux density of 0.1 T is sufficient for V-EMBr, while 0.2 T is needed for Ruler-EMBr. 3. An increase of the nozzle port angle results in a downward movement of the liquid metal jet stream. When the nozzle port angle is increased to match the installation position of the Ruler-EMBr, the large vortices beneath the jet flow is almost completely eliminated. On the condition with V-EMBr, the front jet stream is deflected rather than rejected by the magnetic field with the increasing port angles. However, the surface velocity and steel/slag interface fluctuation can be suppressed to acceptable values even with a wide variation of nozzle port angles. In the current study, the focus is mainly on the influence of Ruler-EMBr and V-EMBr on the behavior of steel/slag interface fluctuation and metal jet flow in the continuous casting mold. The effects of the second-generation V-EMBr device, which combines the merits of the Ruler-EMBr and V-EMBr on the flow of liquid steel, solidification. and heat transfer in the continuous casting mold will be the subject of ongoing studies.

14 ACKNOWLEDGMENTS This study was financially supported by the National Nature Science Foundation of China (Grant No , Grant No and Grant No. U ), the Program of Introducing Talents of Discipline to Universities (The 111 Project of China, Grant No. B07015), and the Fundamental Research Funds for the Central Universities (Grant No. N ). Computer resources were provided by the computing center at the Technische Universita t Ilmenau, Germany. The authors are also grateful to Deutsche Forschungsgemeinschaft (DFG) for the financial support in the framework of Research Training Group Lorentz Force Velocimetry and Lorentz Force Eddy Current Testing (GRK 1567). APPENDIX: GOVERNING EQUATIONS FOR FLUID FLOW Continuity Equation: rðquþ ¼ 0; ½A1Š where q ¼ q st u st þ q sl ð1 u st Þ Momentum ðquþ þr½qðuuþš ¼ rp l eff ru þru T þ qg þ f þ F mag Turbulence ðqkþ þ U j l þ l þ G j r ðqxþ þ j l þ l t r þ a 3q l t G j þ 21 ð F 1 ; xr j where r k, r x are the turbulent Prandtl numbers 1 r k ¼ F 1 rk;1þ ð1 F 1 Þ r k;2 ½A2Š ½A3Š ½A4Š " pffiffiffi! # k arg 1 ¼ min max 0:09xy ; 500l 4qk qy 2 ; x r x;2 CD kx y 2 : where CD kx : the positive portion of the cross-diffusion term CD kx ¼ max 2q ; ; r x;2 j where l eff : effective viscosity l eff ¼ l þ l t l ¼ l st u st þ l sl ð1 u st Þ; where l t : turbulent viscosity qa 1 k l t ¼ maxða 1 x; SF 2 Þ ; where S: strain rate magnitude p S ¼ ffiffiffiffiffiffiffiffiffiffiffiffi 2S ij S ij ; S ij ¼ 1 j i ; where F 2 : a blending function is similar to F 1 F 2 ¼ tanh arg 2 2 pffiffiffi! k arg 2 ¼ max 2 0:09xy ; 500l qy 2 ; x where a 3 : a linear combination of the corresponding coefficients a 3 ¼ a 1 F 1 þ a 2 ð1 F 1 Þ; where G k : generation of turbulence kinetic energy ( 2 G k ¼ l t @x @x ) Turbulence model constants: a 1 = 0.56, a 2 = 0.44, r k,1 = 1.176, r x,1 =2,r k,2 =1, r x,2 = r x ¼ F 1 rx;1þ ð1 F 1 Þ ; r x;2 where F 1 : a function of the wall distance; y: the distance to the nearest wall F 1 ¼ tanh arg 4 1 t d p U U st U in NOMENCLATURE Time (s) Nozzle diameter (m) Pressure (Pa) Average mixture velocity vector (m/s) Velocity vector of the steel (m/s) Normal velocity of inlet (m/s)

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