Mathematical Modeling on Transient Multiphase Flow and Slag Entrainment in Continuously Casting Mold with Double-ruler EMBr through LES+VOF+DPM Method

Abstract

To investigate the transient multiphase flow, slag entrainment and exposed slag eye in the mold with EMBr and argon injection, a transient multiphase LES model was constructed. In the model, the multiphase (steel-slag-air) flow was simulated through VOF method, argon bubbles were tracked using DPM method. The model was validated by previous experimental measurements through the particle image velocimetry. The results indicated that argon injection weakened the upper recirculation flow, and reduced the molten steel jet downward angle. Moreover, the turbulent flow in the mold was suppressed by EMBr. The slag entrainment mechanisms are different under different conditions. In the case without argon injection and EMBr, three slag entrainment mechanisms were found: shear flow, Von Kármán vortex, and level fluctuation. Nevertheless, when argon was injected, in addition to the above mechanisms, one extra mechanism was predicted that was bubble interaction. Additionally, bubble interaction was the unique slag entrainment mechanism in the case with argon injection and EMBr. The impact of argon bubbles on the steel-slag interface resulted in exposed slag eye. In the case without EMBr, the exposed slag eye phenomenon was intermittent. However, the phenomenon was persistent when EMBr was applied.

1. Introduction

During continuous casting (CC), mold flux is added periodically to the mold top surface, and a liquid slag layer is formed on the top surface as a result of mold powder melting. The functions of the liquid slag are following: lubrication of the initial solidified shell, making heat transfer between the shell and the mold more uniform, reducing re-oxidation and freezing of molten steel at the meniscus, absorbing inclusions.^1,2) Hence, a sufficiently thick slag layer is of great necessity. Furthermore, an idealized condition that slag layer is calm and evenly distributed on the free surface of steel, can promote the mold slag to best fulfill all its functions. However, it is well known that molten steel flow in mold is turbulent and unbalanced.³⁾ When the turbulent flow is strong enough at the steel-slag interface, abnormal level fluctuations and slag entrainment may occur, causing serious surface defects.^4,5) If the slag layer is extremely thin, the steel-slag interface exposes an open area of molten steel to the atmosphere, termed the “exposed slag eye”, leading to oxygen and nitrogen pickup. Argon injection (AI) is often adopted to prevent clogging of the nozzle and remove inclusions during CC.^6,7,8) After entering the submerged entry nozzle (SEN), argon bubbles are carried by the turbulent flow into the mold region, where they affect the flow pattern, level fluctuations, and slag entrainment. In addition, AI may cause the slag layer thin near the SEN, even form exposed slag eye.^9,10,11) Hence, for the improvement of molten steel cleanliness and slab surface quality, research on the hydrodynamics and the associated transport phenomena of the above regions are of great practical significance.

To optimize the transient flow, control the level fluctuation and alleviate the slag entrainment in the mold, electromagnetic braking (EMBr) systems have been extensively applied,^12,13,14,15) especially at high casting speed.^16,17) In industrial production, static magnetic fields are applied in EMBr systems, including local,^15,18,19,20) single-ruler,^21,22,23,24) and double-ruler systems.^13,25,26,27) The flow of the electrically-conductive molten steel in the magnetic fields generates an electromagnetic force opposing the motion, thus should be self-stabilizing and maintain a stable “double-roll” flow pattern. Local EMBr slows down jet flow as it passes through a circular-shaped field region through the mold thickness.¹⁵⁾ Single ruler EMBr produces a horizontal rectangular-shaped field across the entire mold width, which can slow down surface flow, lessen surface turbulence²⁸⁾ and deflect the jet upwards to accelerate surface flow.^22,29) Double ruler EMBr, also called Flow Control Mold (FC-Mold),²⁵⁾ generates two horizontal static fields across the mold width, one above and one below the SEN ports. Adjusting the relative strengths of the upper and lower fields can efficiently control of the flow field.

In recent years, extensive research have been conducted on the phenomena of level fluctuation,^{3,30,31,32,33,34)} slag entrapment^{5,10,35,36,37,38)} and exposed slag eye^9,39) in the mold, through physical modeling and mathematical simulation. However, these phenomena are difficult to measure or to accurately simulate using a physical model, especially for the mold with a magnetic field. For the purpose of optimizing flow field and reducing slag entrainment, many studies about multiphase flow in the CC mold have been carried out by method of numerical simulation. Among these studies, two main approaches, the Euler–Lagrange and Euler–Euler approach, are widely adopted. Z. Liu et al.⁹⁾ investigated the multiphase (argon-steel-slag-air) flow in the CC mold through a hybrid Euler–Lagrange model. In the model, argon bubbles were tracked through the discrete particle model (DPM). The effect of AI on the flow pattern and exposed slag eye has been studied. The results indicated that varying gas flow rates had a large effect on the steel flow pattern in the upper recirculation zone. Moreover, the size of exposed slag eye increased with increasing the argon gas flow rate. In another work, Z. Liu et al.³⁹⁾ constructed an Euler–Euler model to study the exposed slag eye phenomenon. Through the model, two main locations of the exposed slag eye were found: adjacent to the SEN and the mold’s mid-section. P. Zhao et al.^37,38) developed a large eddy simulation (LES) model to study the two-phase (steel and slag) flow, level fluctuations and slag entrainment in the mold. The two-phase flow in the model was calculated through the volume of fluid (VOF) model. The influences of the casting speed, SEN immersion depth and slag thickness on slag entrainment and entrained droplet size were revealed. It was found that the casting speed and SEN immersion depth significantly affected the number, and the size distribution of entrained droplets. Nevertheless, the effect of the slag thickness on those was insignificant. X. Li et al.¹⁰⁾ researched multiphase flow and slag entrainment in a bubbly CC mold through a LES+VOF+DPM model. Three main slag entrapment mechanisms were predicted: vortex formation, shear-layer instability, and meniscus fluctuation.

With reference to EMBr, researchers mainly paid attention to the effects of the applied magnetic fields on the molten steel flow pattern in the mold.^{21,22,23,29,40,41,42,43,44,45)} Several works^46,47,48) investigated the influences of EMBr on the level fluctuation during CC process. At present, research about level fluctuation, slag entrainment and exposed slag eye in CC mold with EMBr and AI has not been reported.

The scope of the current work was to investigate the transient multiphase flow, slag entrainment, level fluctuation and exposed slag eye during CC through a transient multiphase LES model. Moreover, the effects of AI and EMBr on the transient flow pattern and steel-slag interface behaviors have also been studied. Additionally, the mathematical model was validated using the experimental data of W. Chen et al.,⁴⁹⁾ obtained from a water model experiment.

2. Numerical Methodology

The numerical model involves three parts: the electromagnetic force model, the multiphase flow model and the bubble transport model. The current work calculated the Lorentz force by the electric potential method. The multiphase flow in the present work is simulated through VOF+LES method. The VOF model is used to track the free surfaces by solving a single set of momentum equations and tracking the volume fraction of each fluid. The LES turbulence model is taken to describe the turbulence in the system. The sub-grid scale (SGS) modeling is based on the Wall-Adapting Local Eddy (WALE) kernel. The argon bubbles are tracked using the DPM, and the buoyancy, drag force, virtual mass force, lift force and pressure gradient force are included.

2.1. Assumptions

In order to simplify the numerical model, the present work includes the following assumptions:

1) the molten steel is considered to be homogeneous incompressible Newtonian fluid;

2) the discrete bubbles generally take the shape of a sphere. The breakage and coalescence of bubbles and the interactions between them are neglected. The bubbles have no expansion;

3) the caster is perfectly vertical with respect to the gravitational field while the curvature of the strand is ignored;

4) only the liquid slag layer is considered, other state slag layers are ignored;

5) the influence of the solidified shell is ignored;.

6) the influence of mold oscillation and mold taper is ignored.

2.2. The Electromagnetic Force Model

The molten steel flowing through the magnetic field generates an electric current, $\overrightarrow{J}$, which flows through the entire domain to produce the Lorentz force ${\overrightarrow{F}}_{Lorentz}$, and is given as follows:   

$$\overrightarrow{J}=\sigma (\overrightarrow{E}+\overrightarrow{u}\times {\overrightarrow{B}}_0)=\sigma (-\nabla \varphi +\overrightarrow{u}\times {\overrightarrow{B}}_0),$$(1)

This equation neglects the induced magnetic field, which is small compared with the applied magnetic field by the EMBr. The charge conservation condition, $\nabla \cdot \overrightarrow{J}=0$, is then used to find the potential ϕ as follows:   

$$\nabla \cdot (\nabla \varphi )=\nabla \cdot (\overrightarrow{u}\times {\overrightarrow{B}}_0),$$(2)

The Lorentz force ${\overrightarrow{F}}_{Lorentz}$ is given by   

$${\overrightarrow{F}}_{Lorentz}=\overrightarrow{J}\times {\overrightarrow{B}}_0,$$(3)

where σ is electrical conductivity, $\overrightarrow{E}$ is the induced electrical field, ϕ is electric potential, ${\overrightarrow{B}}_0$ is the applied magnetic field.

2.3. The Multiphase Flow Model

2.3.1. The VOF Model

The VOF model can model two or more immiscible fluids, and it is used in the current work for tracking the free surfaces among the liquid steel, slag layer, and air. The tracking of the interfaces between phases is accomplished by the solution of a continuity equation for the volume fraction. For the i_th phase, the continuity equation is described in the following form:   

$$\frac{1}{{\rho }_i}\left[\frac{\partial }{\partial t}\left({\rho }_i{\alpha }_i\right)+\nabla \cdot \left({\rho }_i\overrightarrow{u}{\alpha }_i\right)\right]=0,$$(4)

where α_i is the volume fraction of the i_th phase, ρ_i is the density of the i_th phase, and $\overrightarrow{u}$ is the fluid velocity solved in Eq. (6). The volume fraction equation will not be solved for the primary phase. The volume fraction of the primary phase is solved by the following constraint.   

$$\sum _{i=1}^n{\alpha }_i=1,$$(5)

When the VOF model is used, it is assumed that the velocity field is shared among the phases and a single momentum equation is solved throughout the domain. The momentum equation is as follows:   

$$\begin{array}{l}\frac{\partial }{\partial t}\left(\rho \overrightarrow{u}\right)+\nabla \cdot \left(\rho \overrightarrow{u}\overrightarrow{u}\right)=\\ -\nabla p+\nabla \cdot \left[\mu \left(\nabla \overrightarrow{u}+\nabla {\overrightarrow{u}}^T\right)\right]+\rho \overrightarrow{g}+{\overrightarrow{F}}_{bubble}+{\overrightarrow{F}}_{\sigma }+{\overrightarrow{F}}_{Lorentz},\end{array}$$(6)

where p is pressure, $\overrightarrow{g}$ is gravitational acceleration, ${\overrightarrow{F}}_{bubble}$ is the momentum transfer term exerted by the discrete bubbles, ${\overrightarrow{F}}_{\sigma }$ is the surface tension at the interface. The density ρ and viscosity μ in each grid are determined by the mixture properties, and calculated as follows:   

$$\rho =\sum _{i=1}^n{\rho }_i{\alpha }_i,\mu =\sum _{i=1}^n{\mu }_i{\alpha }_i,$$(7)

2.3.2. The LES Model

The turbulent viscosity, μ_t, are modeled with the WALE SGS viscosity model.⁵⁰⁾ This model captures the expected variation of eddy viscosity with the cube of distance close to the wall without any expensive or complicated dynamic procedure or need of Van-driest damping as a function of y+, which is difficult in a complex geometry. In the WALE SGS model, μ_t is calculated as follows:   

$${\mu }_t\text{=}{\rho }_{\text{l}}{\nu }_t={\rho }_{\text{l}}{L}_s^2\frac{{(S_{ij}^d{S}_{ij}^d)}^{2/3}}{{(S_{ij}{S}_{ij})}^{\text{5/2}}+{(S_{ij}^d{S}_{ij}^d)}^{4/5}},$$(8)

where $S_{ij}\text{=}\frac{\text{1}}{\text{2}}\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)$, $S_{ij}^d\text{=}\frac{\text{1}}{\text{2}}\left(g_{ij}^2+g_{ji}^2\right)-\frac{1}{3}{\delta }_{ij}{g}_{kk}^2$, $g_{ij}^2$=g_ikg_kj, g_ij = $\frac{\partial u_i}{\partial x_j}$, δ_ij = 1, if i = j, else δ_ij = 0, and Δ = (ΔxΔyΔz)^1/3, Δx, Δy, Δz are the grid spacing in x, y and z directions. The length scale is defied as L_s = C_wΔ, $C_w^2=10.6C_s^2$ and C_s = 0.18.

2.4. The Bubble Transport Model

The movement of the particles is governed by the particle force balance equation defined as follows:   

$${\rho }_p\frac{\pi }{6}{d}_p^3\frac{d{\overrightarrow{u}}_p}{dt}={\overrightarrow{F}}_D+{\overrightarrow{F}}_p+{\overrightarrow{F}}_b+{\overrightarrow{F}}_{VM}+{\overrightarrow{F}}_l,$$(9)

where ρ_p is inclusion density, d_p is particle diameter, ${\overrightarrow{u}}_p$ is particle velocity, ${\overrightarrow{F}}_D$ is particle drag force, ${\overrightarrow{F}}_p$ is pressure gradient force, ${\overrightarrow{F}}_b$ is buoyancy force, ${\overrightarrow{F}}_{VM}$ is virtual mass force, ${\overrightarrow{F}}_l$ is lift force. Details of these forces can be seen in previous work.^51,52)

2.5. Boundary Condition and Numerical Details

As is shown in Fig. 1(a), a full scale geometry model for a real caster was established, including the submerged entry nozzle (SEN) and the mold. The height of the computational domain was 3000 mm and the slag layer between the molten steel and the air layer was 40 mm. Moreover, the thickness of the air layer was 50 mm. As Fig. 1(b) shows, to capture the flow characteristics in detail, the mesh size is refined near the two interfaces (slag–steel interface and air–slag interface). The structured grid was employed in all of the domain. The total number of grids was approximately 2×10⁶. Figure 1(c) shows the locations of velocity probes. The mold dimensions and operating parameters used in numerical simulation are summarized in Table 1. During the calculations, expansion⁵⁾ was considered for the argon gas flow rate which was in hot condition (1830 K).

Fig. 1.

Schematic diagrams of computational domain and mesh structures: a) geometry; b) local mesh distribution; c) velocity probe locations. (Online version in color.)

Table 1. The mold dimensions and operating parameters used in numerical simulation.

Parameters	Values	Parameters	Values
SEN submergence depth, mm	150	Slag density, kg·m−3	3000
SEN inner diameter, mm	78	Air density, kg·m−3	1.78
SEN out port angle, °	−15	Steel viscosity, kg·s−1·m−1	0.0055
SEN out port size, mm × mm	70×90	Slag viscosity, kg·s−1·m−1	0.14
Mold section size, mm × mm	1055×247	Air viscosity, kg·s−1·m−1	1.78×10−5
Casting speed, m·min−1	1.8	Steel-slag interfacial tension, N·m−1	1.4
Argon injection rate, L·min−1	20	Steel-air interfacial tension, N·m−1	1.6
Argon density, kg·m−3	0.5	Slag-air interfacial tension, N·m−1	0.38
Steel density, kg·m−3	7020	Steel electrical conductivity, S·m−1	714000

A fixed velocity is applied at the SEN inlet based on the casting speed. Boundary conditions for momentum transfer at all solid surfaces including the mold faces and the SEN walls are specified with no slip boundary condition. For the mold and nozzle walls, the standard wall function is adopted in the simulations. The mold top surface is modeled as an opening boundary condition. The opening boundary condition is realized through the combination of pressureInletOutletVelocity (for velocity) and totalPressure (for pressure) boundary conditions in OpenFOAM. Furthermore, the inletOutlet boundary condition is adopted for α_i at the mold top surface. The discrete argon bubbles are injected from the inlet of the SEN. The initial locations are uniformly distributed at the inlet surface. According to the work of K. Jin and B.G. Thomas et al.,⁵³⁾ a Rosin–Rammler size distribution (25 μm to 5 mm range) is set for the injected argon bubble. It is assumed that argon bubbles are reflected once touching the walls, and leave the system once entering the outlet of the domain. It should be noted that the escape position of the argon bubbles is generally below the air-slag interface. Moreover, the influence of bubbles on the top air layer is ignored. Therefore, the argon bubbles which arrived at the position that the volume fraction of air is larger than 0.5, are deleted during the calculation. The gradients of all electromagnetic variables are equal to zero and are assumed stationary.

In the current work, the first step of the simulation was to calculation the applied magnetic field, which was performed using a finite-element analysis implemented in ANSYS (Version 16.0). The following step was to conduct the coupling multiphase simulation using the open-source computational fluid dynamics library OpenFOAM (Version 4.1) under Ubuntu 16.04 operating system. The numerical model was implemented into an improved version of the OpenFOAM solver multiphaseInterFoam. The Courant number, Co, at the interface is significant in multiphase simulations. In the current work, the max Co was set as 0.25. During the simulations, the variation of the time step was determined by the prescribed Co at the interface. The total calculation time of the coupling simulation was 100 s. Approximately 30 days were required to perform a fully-coupled simulation case on a workstation with 16 CPUs (AMD Ryzen Threadripper 2990WX 3.0 GHz) in parallel.

3. Results and Discussion

3.1. Model Validiation and the Applied Magnetic Field Calculation

To validate the mathematical model, the current work conducted a numerical calculation, whose geometry, material properties and boundary conditions were set corresponding to the water model of W. Chen et al.⁴⁹⁾ As is presented in Fig. 2, the predicted velocity magnitude of the meniscus centerline was compared with the measured results by the particle image velocimetry (PIV). The maximum velocity magnitude appeared at 1/4 of mold width in both the calculated and measured results. Good agreement could be found between the measured and the predicted results, which indicated the accuracy of the mathematical model used in the current study.

Fig. 2.

Comparison of the velocity magnitude of the meniscus centerline between predicted results and measured results in Ref.⁴⁹⁾. (Online version in color.)

The current in both upper and lower coils of the EMBr was 665 A. The applied magnetic field is mainly perpendicular to the wide face of mold wall (B_y). The applied magnetic field intensity in the width direction (B_x) and the vertical direction (B_z) is far lower than the maximum magnetic field intensity of B_y. Hence, in order to simplify the calculation, the components of B_x and B_z were ignored and only the component of B_y was considered in the current coupling calculation. Figure 3 shows a contour plot of the applied magnetic field (B_y) on the center plane and the comparison of its variation at the center line in the casting direction between the measurement⁵⁴⁾ and the calculation. The variation trend of the predicted magnetic field intensity agrees well with the measurement. It can be observed that the maximum value of B_y on the center plane is about 0.33 T.

Fig. 3.

Contour plot of the applied magnetic field on the center plane (a); comparison of magnetic field intensity between the calculation⁵⁴⁾ and the measurement (b). (Online version in color.)

3.2. Characteristics of MultiPhase Flow under Different Conditions

The transient molten steel flow patterns inside the mold obtained from the LES model are shown in Fig. 4. In the case without AI and EMBr, the LES results reveal that the flow field is obviously asymmetric and unsteady, with multiple vortexes inside the slab mold. The molten steel flowing out of the SEN port forms two big vortexes, showing a typical “double roll” flow pattern in the slab mold. An intense and turbulent flow can be observed in the mold region, especially in the upper recirculation zone. When argon bubbles are injected into the mold through the SEN, the flow pattern in the mold changes. The flow in the upper recirculation zone is weakened, resulting from the turbulent dispersion by the argon bubbles. Moreover, due to the buoyancy effect generated by the argon bubbles, the molten steel jet downward angle reduces. In the case with AI and EMBr, a distinctive flow pattern can be observed. The turbulent flow in the mold region can be suppressed by the magnetic field, and it tends to be steady and symmetric relatively. The suppression effect by the magnetic field is more significant in the lower recirculation zone. The molten steel jet downward angle is smaller than that in the case with AI but without EMBr.

Fig. 4.

Instantaneous flow patterns under different conditions. (Online version in color.)

Figure 5 shows the computed time history of the fluctuating velocity component U_z (in the casting direction) at four points P1, P1^*, P2 and P2^*, shown in Fig. 1(c). P1 and P1^*, which are near the narrow face of the mold, locate at the lower recirculation zone. Similarly, two points (P2 and P2^*) locating at the upper circulation zone are selected. Asymmetric flow pattern can be found when the EMBr is not applied. Moreover, it can be observed that the velocity component dramatically fluctuates when the magnetic field is not applied. The asymmetric flow characteristic is more significant in the case without AI and EMBr. When argon bubbles are injected into the mold, argon bubbles weaken the flow in the upper recirculation zone. As a result, the velocity component U_z at P2 and P2^* decreases. Consequently, more molten steel flows into the lower region, and the velocity component U_z at P1 and P1^* slightly increases. In the case with AI and EMBr, velocity component is efficiently damped by the magnetic field.

Fig. 5.

Time variation of components of the fluctuating velocity. (Online version in color.)

3.3. Slag Entrainment Mechanisms under Different Conditions

AI and EMBr can change the flow pattern in the mold region. Hence, it is inevitable that AI and EMBr influence the slag entrainment mechanisms in the mold region. To reveal the slag entrainment in the mold region, transient 0.05 iso-surfaces of slag volume fraction inside the mold at arbitrary time points have been obtained. As Figs. 6, 7, 8 show, three slag entrainment mechanisms have been found in the case without AI and EMBr.

Fig. 6.

Slag entrainment caused by the shear flow in the case without AI and EMBr. (Online version in color.)

Fig. 7.

Slag entrainment caused by the Von Kármán vortex in the case without AI and EMBr. (Online version in color.)

Fig. 8.

Slag entrainment caused by the level fluctuation in the case without AI and EMBr. (Online version in color.)

In the case without AI and EMBr, the upper recirculation flow is strong, and the shear stress at the steel-slag interface is intense. Hence, at the steel-slag interface, slag may be entrained into the molten steel resulting from the shear flow. Figure 6 shows the process of slag entrainment caused by the shear flow at the steel-slag interface. This phenomenon mainly experiences three steps: firstly, due to the shear stress at the steel-slag interface, the liquid slag is carried by the molten steel and is accumulated at quarter region of the mold (51.2–51.4 s); secondly, when this accumulation reaches the breaking point, the slag droplets are separated from the liquid slag layer (51.6 s); thirdly, the separated slag droplets are transported in the molten steel (51.8 s). Some of the entrained slag droplets can float up and enter into the slag layer again. Whereas, some of them are carried deep into the mold and captured by the solidified shell, causing serious slab surface defects.

As a result of flow asymmetry, near the cylindrical obstacle different-velocity streams shears each other, causing a flow deflection, forcing a rotational flow, at last forming the Von Kármán vortex. Under the condition that argon bubbles are not injected and the EMBr is off, flow between two halves of mold is obviously asymmetric and unbalanced. Consequently, the Von Kármán vortexes in the top area of mold can be formed. These vortexes always cause slag entrainment. Figure 7 shows another slag entrainment process resulting from the Von Kármán vortex. This phenomenon may experience three stages: firstly, a rotational flow forms the vortex at the steel-slag interface near the SEN (97.9 s); secondly, the vortex is further developed and draws down slag to molten steel (98–98.1 s); thirdly, the slag droplet is separated from the liquid slag layer and motions in the molten steel (98.2 s). Slag droplets in the molten steel caused by this mechanism occur near the SEN, and are always very close to the solidified shell. Therefore, these slag droplets are extremely easily entrapped by the solidified shell.

Due to the unbalanced flow in the mold, the transient steel-slag interface at an arbitrary position, especially near the narrow face of the mold, may dramatically fluctuate. Figure 8 illustrates the third slag entrainment mechanism, level fluctuation, in the case without AI and EMBr. This slag entrainment process mainly experiences three steps: firstly, the steel-slag interface is suddenly risen and the slag layer is thinned at one position (80.3–80.4 s); secondly, the steel-slag interface falls back and the slag droplet forms (80.5 s); thirdly, the slag droplet moves in the molten steel (80.6 s). This slag entrainment phenomenon mainly occurs beside the narrow face of the mold. Hence, slag droplets formed by this pattern can be immediately captured by the solidified shell once they are formed, which may deteriorate the steel surface quality.

As Figs. 9, 10, 11 present, four slag entrainment mechanisms have been observed in the case with AI but without EMBr. Figure 9 shows two slag entrainment mechanisms, level fluctuation and Von Kármán vortex, which are similar to the case without AI and EMBr. Figure 10 illustrates the slag entrainment phenomenon resulting from the shear flow, whose process is similar to that shown in Fig. 7. However, the forming position of this slag entrainment phenomenon diverges from the quarter of the mold and is close to the mold narrow face. This is due to the weakened flow in the upper recirculation zone resulting from the turbulent dispersion by the argon bubbles.

Fig. 9.

Slag entrainment caused by the level fluctuation (a) and Von Kármán vortex (b) in the case with AI but without EMBr. (Online version in color.)

Fig. 10.

Slag entrainment caused by the shear flow in the case with AI but without EMBr. (Online version in color.)

.

Fig. 11.

Slag entrainment caused by bubble interaction in the case with AI but without EMBr. (Online version in color.)

Figure 11 illustrates the steel-slag interface and the distribution of bubbles in the mold at 88.5 s and 96.4 s, which presents a new slag entrainment mode resulted from bubble interaction. The color spheres represent the argon bubbles. Because of strong buoyancy, most of the argon bubbles in the molten steel float upward and enter into the liquid slag layer during the time that the liquid jet takes to travel from the SEN port to the narrow face wall. A number of small argon bubbles disperse in the upper mold zone, few argon bubbles with smaller diameters can be transported into the lower part of the mold. The escape region of many argon bubbles is close to the SEN, especially for the large argon bubbles. The argon bubbles closed to the SEN, accumulate at some regions of the steel-slag interface and interact with the steel-slag interface. As a result, the steel-slag interface at these regions fluctuates seriously, which induces slag entrainment

Figure 12 shows the unique slag entrainment mechanism, bubble interaction, under the condition that argon bubbles are injected and the EMBr is applied. The magnetic field can suppress the turbulent and unbalanced flow in the mold region, and the flow tends to be steady and symmetric relatively. As a result, the transient deformation of the steel-slag interface changes to be gentle. Hence, the shear stress instability, Von Kármán vortex and level fluctuation generated by the asymmetric and unbalanced flow can be efficiently alleviated. In addition, due to the suppressing effect of the magnetic field on the flow, most argon bubbles are constrained in the region closed to the SEN. Consequently, the interaction between argon bubbles and steel-slag interface is more intense than that in the case without EMBr, and causes significant slag entrainment. It should be mentioned that many slag droplets in molten steel formed by the bubble interaction can float up, enter into the slag layer and hardly be entrapped by the solidified shell. Therefore, EMBr can efficiently reduce slag entrainment in the mold.

Fig. 12.

Slag entrainment caused by bubble interaction in the case with AI and EMBr. (Online version in color.)

In order to quantitatively recognize the level fluctuations of steel–slag interface, a new parameter, H, is marked, where H is the level value of steel–slag interface. H = 0 is the initial interface between slag and steel. The positive value of H represents that the direction of level fluctuation is upward. In contrast, negative value represents that the direction of level fluctuation is downward. The history of H at different positions along the centerline of the mold is investigated in Fig. 13, where the time signal of the computed H is plotted. In the case without AI and EMBr, the level fluctuation at the points near the SEN is the very pacific. At the positions near the mold narrow face, larger level fluctuations can be observed, and lead to the slag entrainment shown in Fig. 8. At the quarter of the mold, slag droplets are frequently entrained into the molten steel by the shear flow. Hence, at the quarter of the mold thickness centerline, the level fluctuation is the most dramatic among the three positions (near the SEN, quarter of the mold, near the narrow face), especially for the downward level fluctuation. In the case with AI but without EMBr, the most obvious level fluctuation can be found at the points near the SEN, resulting from the impact of argon bubbles on the steel-slag interface. Additionally, the level fluctuation at the quarter of the mold is the most gentle among the three positions, which is due to the weakened flow in the upper recirculation zone resulting from the turbulent dispersion by the argon bubbles. Therefore, slag entrainment formed by the shear flow was not found at this positions. When EMBr is applied, the level fluctuations can be efficiently controlled at the points near the quarter and narrow face of the mold. Hence, at these positions, slag would not be entrained into the molten steel. Due to the interaction between argon bubbles and steel-slag interface, the level fluctuation is larger at the points near the SEN. In addition, because the interaction is more intense, the frequency of the level fluctuation is larger than that in the case with AI but without EMBr. However, due to the restrain by the magnetic field, the amplitude of the level fluctuation is lower than that in the case with AI but without EMBr.

Fig. 13.

Time series of the steel–slag interface fluctuations. (Online version in color.)

Figure 14 shows the ratios of slag entrainment caused by different mechanisms under different conditions. In the case without AI and EMBr, the most frequent slag entrainment mechanism is the shear flow, followed by the Von Kármán vortex. Slag entrainment caused by the level fluctuation makes up a very small proportion, however, this phenomenon is extremely harmful to steel surface quality. In the case with AI but without EMBr, the most frequent slag entrainment mechanism is the bubble interaction, followed by the Von Kármán vortex. Slag entrainment formed by the shear flow and the level fluctuation occurs less frequent. Under the condition that AI and EMBr are applied, only bubble interaction can lead to slag entrainment.

Fig. 14.

The ratio of slag entrainment caused by different mechanisms. (Online version in color.)

3.4. Exposed Slag Eye near the SEN

AI in the mold can lead to level fluctuation near the SEN, then slag entrainment occurs because of the interaction between argon bubbles and the steel-slag interface. When plentiful of argon bubbles concentrate at the steel-slag interface near the SEN, the impact of argon bubbles on the interface is significant. As a result, the opening slag eye may be formed, and the molten steel is exposed to the air causing re-oxidation. Figure 15 illustrates the transient slag eye open and collapse processes in the mold. When EMBr is off, as Fig. 15(a) shows, the exposed slag eye phenomenon is intermittent. Argon is injected into the molten steel from the stopper rod and slide gate during CC, and many argon bubbles may reside inside the SEN. When the amount of these argon bubbles reaches a certain level, they would instantly motion into the liquid pool from the SEN port, float up directly and impact the steel-slag interface. As a result, an exposed slag eye is formed. As these argon bubbles enter into the ambient, the formed slag eye may collapse and disappear. After a period of absence, another exposed slag eye would be form again. In the case with EMBr, most argon bubbles are constrained in the region closed to the SEN, and the interaction between argon bubbles and steel-slag interface is more intense than that in the case without EMBr. Therefore, when EMBr is applied, the exposed slag eye phenomenon is persistent, and the areas of slag eyes are larger than those in the case without EMBr.

Fig. 15.

Transient slag eye open and collapse processes: (a) with AI but without EMBr; (b) with AI and EMBr. (Online version in color.)

4. Conclusions

In the current work, a transient multiphase LES has been developed. In the model, the flow of the continuous fluids (molten steel, liquid slag and air) were solved by the VOF method, the discrete argon bubbles were tracked by the DPM. Furthermore, the magnetic field was coupled into the model through the electric potential method. Through the constructed model, the effects of AI and EMBr on the transient multiphase flow, slag entrainment, level fluctuation and exposed slag eye have been investigated. The conclusions are as follows:

(1) AI and EMBr change the transient flow pattern in the mold. In the case without AI and EMBr, the flow field is obviously asymmetric and unsteady. An intense and turbulent flow can be observed in the mold region, especially in the upper recirculation zone. AI weakens the flow in the upper recirculation zone, and the molten steel jet downward angle reduces. In the case with AI and EMBr, the turbulent flow in the mold region can be suppressed, and it tends to be steady and symmetric relatively. The molten steel jet downward angle is the smallest among the three cases;

(2) The slag entrainment mechanisms are different under different conditions. In the case without AI and EMBr, three slag entrainment mechanisms have been found: shear flow, Von Kármán vortex, and level fluctuation. Slag entrainment caused by the shear flow mechanism is the most frequent. Nevertheless, when argon was injected, in addition to the above mechanisms, one extra mechanism was predicted that was bubble interaction. Moreover, bubble interaction is the main slag entrainment mechanism. In the case with AI and EMBr, bubble interaction is the unique slag entrainment mechanism;

(3) AI and EMBr influence the level fluctuations in the mold. In the case without AI and EMBr, at the quarter of the mold thickness centerline, the level fluctuation is the most dramatic. In the case with AI but without EMBr, the most obvious level fluctuation can be found at the points near the SEN. In the case with AI and EMBr, the level fluctuations can be efficiently controlled, especially at the points near the quarter and narrow face of the mold;

(4) The impact of argon bubbles on the steel-slag interface leads to the exposed slag eye. When EMBr is off, the exposed slag eye phenomenon is intermittent. In the case with EMBr, the exposed slag eye phenomenon is persistent, and the areas of slag eyes are larger than those in the case without EMBr.

Acknowledgments

The authors gratefully express their appreciation to the National Natural Science Foundation of China (51834002) for sponsoring this work.

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