CFD Predictions for Mixing Times in an Elliptical Ladle Using Single-and Dual-Plug Conﬁgurations

: Argon bottom stirring is commonly practiced in secondary steelmaking processes due to its positive effects on achieving uniform temperatures and chemical compositions throughout a steel melt. It can also be used to facilitate slag metal reﬁning reactions. The inter-mixing phenomena associated with argon gas injection through porous plugs set in the bottom and its stirring efﬁciency can be summarized by evaluations of 95% mixing times. This study focuses on investigating the impact of different plug positions and ratios of argon ﬂow rates from two plugs on mixing behavior within a 110-tonne, elliptical-shaped industrial ladle. A quasi-single-phase modeling technique was employed for this purpose. The CFD ﬁndings revealed that the optimal position of the second plug is to be placed diametrically opposite the existing one at an equal mid-radius distance (R/2). An equal distribution of argon ﬂow rates yielded the best results in terms of refractory erosion. A comparative study was conducted between single-and dual-plug-conﬁgured ladles based on ﬂow behavior and wall shear stresses using this method. Furthermore, a transient multiphase model was developed to examine the formation of slag open eyes (SOE) for both single-and dual-plug conﬁgurations using a volume of ﬂuid (VOF) model. The results indicated that the dual-plug conﬁguration outperformed the current single-plug conﬁguration.


Introduction
Due to the rising need for high-quality steel products, ladle metallurgy, a secondary steelmaking process, has attracted a lot of attention over time. Ladle metallurgy is practiced by adjusting a steel's composition, cleanliness, and temperature over wide ranges to meet diverse plant and customer requirements. The technique involves a series of different steps after tapping liquid steel into a teeming ladle and before sending it to the caster. These steps include de-oxidation, composition adjustment, temperature control, degassing, cleanliness adjustments, etc. Depending upon the final grade of steel, the steelmaking professional must select different operations wisely. However, all secondary steelmaking operations have one thing in common: the injection of inert gas into the steel melt using one or more porous plugs installed in the bottom brickwork of a ladle. Since argon (Ar) gas has zero solubility in steel and is inert by nature, it is frequently used for purging a melt to ensure temperature and composition homogeneity as well as to encourage reactions that lead to the refining of the steel through slag-metal interactions. Many studies have also confirmed that argon gas injection can aid in inclusion removal.
The rate of injection of argon gas varies, depending upon end requirements, i.e., inclusion removal, floating out the non-metallic inclusions, or desulphurization of steel. The argon gas bubbles become the carrying agents, taking the non-metallic inclusions toward the slag surface. For homogenization or alloy additions, an intermediate flow rate needed. The dissipation of the buoyant energy of the injected gas primarily cau homogenization of bath temperature and composition via gas bubbling. On the hand, a relatively high argon flow rate is used for desulphurization or reoxidati which intense mixing conditions are desired. In Figure 1, a schematic of ladle purg a Ladle Refining Furnace (LRF) is shown [1]. The gas rising through the melt induces a turbulent re-circulatory motion in mass transfer-controlled processes (such as the melting of deoxidizer and alloying tions as well as their dissolution and dispersion) take place. Furthermore, as the in gas escapes to the surroundings, the redirected bulk flow from the spout region ( eye) pushes the slag layer radially outwards, exposing the melt surface to the am atmosphere. The uncovered area of the melt thus created is typically referred to as a or the "slag open eye". Note that the slag eye is a potential site for reoxidation, ni pick up, and slag entrainment/entrapment phenomena and hence can profoundly ence the quality of steel. Therefore, during the final stage of ladle refining and im ately before continuous casting, it is customary to practice gentle stirring (com termed in the industry as 'argon rinsing') to ensure a small "Slag Open Eye" (SOE) Numerical studies of this gas-liquid flow phenomena in a ladle can be categ into four methods: (a) Quasi-single-phase model, (b) Volume of Fluid (VOF) mo Eulerian multiphase (E-E) model, and (d) Eulerian-Lagrangian (E-L) model. Two review papers [2,3] have discussed all these methods in detail. In this present wo quasi-single-phase method was used for the optimization study of the porous plu tion at the bo om of the ladle. This current research opted for quasi-single-phase m ing to compare mixing times in a steel ladle with a dual-plug configuration at di plug locations and flow rates, which is a less computationally expensive metho multiphase modeling. In quasi-single-phase modeling, the gas-liquid two-phase re considered a homogenous liquid with a slightly reduced density compared to th rounding bulk liquid. This allows for a single set of equations of motion to be u represent the flow in the liquid phase, where the buoyant forces resulting from ga The gas rising through the melt induces a turbulent re-circulatory motion in which mass transfer-controlled processes (such as the melting of deoxidizer and alloying additions as well as their dissolution and dispersion) take place. Furthermore, as the injected gas escapes to the surroundings, the redirected bulk flow from the spout region (plume eye) pushes the slag layer radially outwards, exposing the melt surface to the ambient atmosphere. The uncovered area of the melt thus created is typically referred to as an SOE or the "slag open eye". Note that the slag eye is a potential site for reoxidation, nitrogen pick up, and slag entrainment/entrapment phenomena and hence can profoundly influence the quality of steel. Therefore, during the final stage of ladle refining and immediately before continuous casting, it is customary to practice gentle stirring (commonly termed in the industry as 'argon rinsing') to ensure a small "Slag Open Eye" (SOE) area.
Numerical studies of this gas-liquid flow phenomena in a ladle can be categorized into four methods: (a) Quasi-single-phase model, (b) Volume of Fluid (VOF) model, (c) Eulerian multiphase (E-E) model, and (d) Eulerian-Lagrangian (E-L) model. Two good review papers [2,3] have discussed all these methods in detail. In this present work, the quasi-single-phase method was used for the optimization study of the porous plug position at the bottom of the ladle. This current research opted for quasi-single-phase modeling to compare mixing times in a steel ladle with a dual-plug configuration at different plug locations and flow rates, which is a less computationally expensive method than multiphase modeling. In quasi-single-phase modeling, the gas-liquid two-phase region is considered a homogenous liquid with a slightly reduced density compared to the surrounding bulk liquid. This allows for a single set of equations of motion to be used to represent the flow in the liquid phase, where the buoyant forces resulting from gas injection are included in the momentum conservation equation in the axial or vertical direction. To understand the state of stirring or agitation efficiency in a ladle, the concept of mixing time has been commonly used. Some previous works [4,5] have successfully validated numerically calculated mixing time using the quasi-single-phase method with their corresponding physical model. Several mathematical studies [4][5][6][7][8][9] have used mixing time in the ladle to identify the positions best suited for porous plugs to ensure rapid mixing. Several works [10][11][12] have been conducted to study the effect of differential gas flow rates from a dual plug. Luis et al. [10] showed that the 3:1 ratio of gas flow rate from a porous plug gives a reduced (i.e., better) mixing time compared to a 1:1 ratio of gas flow rate from the two porous plugs. In this dual-plug design, the net gas flow rate is divided into two regions, resulting in two weakened plumes compared to a single-plug system.
In addition, previous studies have explored the formation of slag open eyes using multiphase modeling techniques [13][14][15][16][17][18][19]. Ramasetti et al. [13] investigated the impact of top layer thickness and density on open-eye formation in a gas-stirred ladle. Mantripragada et al. [14] used the Coupled Level Set Volume of Fluid (CLSVOF) model to investigate inlet-gas-purging rate, melt height, slag layer thickness, and angular and radial positions of gas inlets affecting slag opening area. Liu et al. [15] simulated a four-phase flow consisting of bubble-steel-slag-top gas in a bottom-blown argon-stirred ladle. Results showed that at low gas flow rates, small open eyes formed and collapsed alternately, while at high gas flow rates, the size of the slag eye increased and its shape changed from circular to oval.
Apart from those studies, Liu et al. [7] have shown that a ladle with a dual-plug configuration can perform better in reducing wear on refractory linings compared to a single-plug system for an equal net flow rate of argon gas injection. The two plugs can reduce the values of interfacial velocity, reducing the potential for slag entrainment and erosion of the upper sections of the refractory wall. Similar observations are reported in some other literature [20,21].
While numerous studies have focused on simulating steel flow fields and optimizing the positions of porous plugs, these investigations have customarily been limited to cylindrical ladles. In contrast, this study aims to analyze and simulate mixing behavior within an elliptical ladle. The primary objective is to conduct a numerical investigation to determine how the arrangement of plugs and their varying flow rates would affect the mixing times in the ladle. To achieve this, a quasi-single-phase modeling approach is employed. Furthermore, this study compares the mixing behavior between a single-plug configuration and a dual-plug configuration in an argon-stirred ladle using a single-phase modeling technique for computational efficiency. Additionally, a transient multiphase model incorporating a volume of fluid (VOF) model was developed to simulate the formation of slag open eyes (SOE) in the single-and dual-plug ladle configurations.

Mathematical Modeling
Mathematical modeling was carried out using the Computational Fluid Dynamics (CFD) software ANSYS Fluent. In this present work, the simulation process was performed in two parts. In the first part, a quasi-single phase, isothermal, three-dimensional, incompressible, turbulent flow model was developed to simulate and understand flow dynamics inside an elliptical ladle and to calculate its mixing times numerically. In this case, slag and air phases in the ladle were ignored. Only the effects of argon bubbling into the ladle were considered. In the quasi-single-phase modeling, the gas-liquid two-phase region is treated as a homogeneous liquid with a slightly reduced density compared to the surrounding bulk liquid. This modeling approach ignores the interactions and exchanges between different phases and assumes constant fluid properties, such as density and viscosity, throughout the entire domain. Consequently, it fails to capture the complexity and dynamics of multiphase flows accurately, including interfacial phenomena. The objective was to numerically investigate the fluid flow behavior and mixing phenomena between a single-plug configuration and a dual-plug configuration in the argon-stirred ladle. Additionally, the effect of the different positional arrangements of an additional plug along with the existing plug is Processes 2023, 11, 1665 4 of 17 studied in terms of mixing times. Additionally, the effect of differential gas flow rates through the two plugs was studied. As such, the relevant governing equations used in the simulation are as follows.

Governing Equations
In Equation (1), terms ρ and v i denote density (kg/m 3 ) and velocity (m/s), respectively at a point x j .

Momentum Conservation Equation
In Equation (2), the term P represents pressure (Pa), g is acceleration due to gravity (m·s −2 ), and µ e f f is the effective viscosity, representing the summation of molecular viscosity and turbulent viscosity (µ + µ t ).

Transport Equations for k and ε in the k-ε Model
The kinetic energy of turbulence, k, is given as follows: The rate of dissipation of kinetic energy, ε is given as follows: where C 1 , C 2 , σ k , and σ ε are empirical constants, whose values are 1.38, 1.92, 1.0, and 1.3, respectively. Moreover, G represents the generation of kinetic energy of turbulence due to mean velocity gradients.

Species Transport Equation
Once the flow fields have converged during simulation, the transient state is switched on for the species transport equation to visualize mass flow rate within the domain.

∂(ρC) ∂t
In Equation (5), Γ e f f is the effective mass diffusion coefficient given by Γ e f f = µ S c + µ t S c,t . S c and S c,t are the laminar and turbulent Schmidt numbers, respectively.
In the second part of the simulation, a transient, isothermal, multiphase phase (steel-slag-argon-air) model was developed. The volume of fluid (VOF) modeling technique was used to investigate slag open eye (SOE) formation. To conduct this simulation, the mass and momentum equations were solved as shown in Equations (1) and (2), respectively. Additionally, the k-ε model was used to incorporate turbulence phenomena, as shown in Equations (3) and (4). It is important to note that the transient term was added to all four equations to account for the system's transient behavior.

Volume of Fluid Model
The VOF method is widely used for simulating multiphase flows. It assumes incompressible fluid phases with no mass transfer between them. The VOF method tracks the interface between phases with a sharp boundary assumption, facilitating clear interface location tracking during the simulation. However, this assumption can lead to inaccuracies in capturing small-scale features or sharp gradients at the interface. In this work, it was used to track the liquid steel/slag/air interface behavior. The finite volume equation of the VOF model can be written in the following form: where . m pq and m qp represent the mass transfer from phase p to phase q and q to p, respectively, in unit time and volume; α q is the volume fraction of phase q; ρ q is the density of phase q; S αq is a source term (=0). When the volume fractions are summed, the following equation must be satisfied:

Characteristics of Gas-Liquid Plume
In quasi-single-phase modeling, the gas-liquid mixture is modeled as a homogeneous fluid. This region is referred to as a plume; the volume fraction of gas inside the plume and the dimension of the plume region play a significant role in modeling. They are predicted with experimental results or equations available in the literature. The volume fraction of gas is estimated from the principle of volume continuity using the average rise velocity of the gas-liquid mixture and plume dimensions. Assuming a no-slip condition for this current study average gas volume fraction is given as follows: where r av,p is the average velocity of plume, and U p is plume rising velocity; Sahai and Guthrie [22] provided the following equation to calculate plume rising velocity: Using gas volume fraction value, density of the plume can be estimated as follows: Similarly, Goldschmit and Owen [23] have estimated top surface radius of plume for a ladle with height, H containing liquid steel as r p = 1.5 b, where b is radius of plume in which gas fraction is half of centerline gas fraction, given by the following: where value of H o is given by the following: where Q 0 is equivalent to gas flow rate a bottom (z = 0) at steel melting temperature. It is expressed as follows: and Q 1 is the equivalent gas flow rate a top (z = H) at steel melting temperature.

Geometry and Mesh Setup
The geometry of an elliptical ladle operating in an industrial set-up was developed using ANSYS SpaceClaim software. Figure 2 shows the three-dimensional geometry of the elliptical ladle. For the quasi-single-phase simulation, the air region and slag layer were ignored, and the gas-liquid plume region was introduced to incorporate the effect of argon bubbling. Plume dimension calculations are discussed in the previous section. The constructed geometry was then exported to the ANSYS Meshing tool, in which a tetrahedral mesh was generated. Figure 2a presents the geometry created for the ladle with a single plug, and Figure 2b presents a dual-plug configuration. The generated mesh for the ladle with a single plug contained 217,812 nodes and 136,267 elements. Similarly, the mesh of a ladle with a dual plug had 589,903 nodes and 363,293 elements. The geometrical parameters of the ladle for the quasi-single-phase modeling are shown in Table 1.  Table 1.  For the VOF multiphase model, all four phases (liquid steel, slag, argon, and air) were considered. The same geometries and meshes were used, as shown in Figure 2, after ignoring the plume region. The height of the air region was considered as 609 mm, and the slag layer thickness was kept at 106 mm as per the industrial setup. The details of material properties used in the mathematical model are shown in Table 2. To replicate the actual plant process, the density of argon gas is taken, corresponding to a temperature around 1100 °C [24].   For the VOF multiphase model, all four phases (liquid steel, slag, argon, and air) were considered. The same geometries and meshes were used, as shown in Figure 2, after ignoring the plume region. The height of the air region was considered as 609 mm, and the slag layer thickness was kept at 106 mm as per the industrial setup. The details of material properties used in the mathematical model are shown in Table 2. To replicate the actual plant process, the density of argon gas is taken, corresponding to a temperature around 1100 • C [24].

Effect of Plug Position on Mixing Behavior
To investigate the impact of plug position on mixing behavior, six distinct cases were identified. To create these scenarios, it was necessary to determine the location of the second plug with reference to the existing one. However, because the geometry was elliptical, direct calculation of the second position using Cartesian coordinates was not feasible. To overcome this issue, the positions were first converted to polar form (r, θ) with the following equation: In Equation (14), r represents the radial distance, and θ represents the angle formed with the major axis. The major and minor axes are denoted by a and b, respectively. Based on calculations, the existing plug was located at an angle of 38.2 degrees, at a half radius from the center of the ellipse. Using this as a reference point, six additional positions were identified at angles of 60, 120, and 180 degrees from the reference point and at distances of 0.5 and 0.75 times the radius from the center. The calculated positions are summarized in Table 3, while the locations of the plugs at the bottom of the ladle are illustrated in Figure 3. In Figure 3, Point 0 represents the location of the existing plug and Points 1-6 denote different proposed positions for the second plug. The corresponding cases selected for questioning are presented in Table 4.     Mixing times were numerically calculated for these six proposed cases to identify the best-suited position for the second plug with respect to the existing one. For this current study, mixing time was defined as the time required for all elements of the fluid to attain a 95% degree of homogenization in molten steel. To simulate alloy additions to liquid steel, the tracer (potassium chloride) is released at the point located in a straight line with the existing purging plug 0.1 m below the surface. The concentration of the tracer is checked with time at six different locations. The tracer injection point and tracker positions to calculate the mixing time in the ladle are shown in Figure 4, and their corresponding locations are given in Table 5. steel, the tracer (potassium chloride) is released at the point located in a straight lin the existing purging plug 0.1 m below the surface. The concentration of the tr checked with time at six different locations. The tracer injection point and tracker po to calculate the mixing time in the ladle are shown in Figure 4, and their correspo locations are given in Table 5.    Figure 5 shows the tracer concentration curves at various monitoring points for all the cases studied: Cases 1, 2, 3, 4, 5, and 6 are shown. Additionally, Figure 6 shows the overall mixing times for each case. It was determined that Case 3 (i.e., dual-plug configuration with plugs placed diametrically opposite each other, at half radius) provided the shortest mixing time, although Case 2 was a very close second. Figure 7 shows tracer iso-concentration and colored contours at different times for Case 3. The colored contours are plotted on a vertical plane passing through the center of a ladle and both purging plugs (plane A, Figure 8). As shown in Figure 4, the tracer is injected at point 7, at the top surface slightly to the left of the plume (let us say plume 1). Figure 7 shows the tracer patterns at different instants of time: initially, the tracer flows around plume 1 following a recirculatory flow pattern. With increasing time, the tracer diffuses, spreading out between plume 1 and the ladle sidewall, while the tracer concentration begins to develop around the second plume. At t = 124 s, the ladle is predicted to have reached the 95% mixing criteria along the vertical plane A. It can be observed that the tracer mixing patterns follow recirculatory trends before achieving this well-mixed condition along plane A. Figure 5 shows the tracer concentration curves at various monitoring points for all the cases studied: Cases 1, 2, 3, 4, 5, and 6 are shown. Additionally, Figure 6 shows the overall mixing times for each case. It was determined that Case 3 (i.e., dual-plug configuration with plugs placed diametrically opposite each other, at half radius) provided the shortest mixing time, although Case 2 was a very close second.  overall mixing times for each case. It was determined that Case 3 (i.e., dual-plug configuration with plugs placed diametrically opposite each other, at half radius) provided the shortest mixing time, although Case 2 was a very close second.   Figure 7 shows the tracer pa erns at different instants of time: initially, the tracer flows around plume 1 following a recirculatory flow pa ern. With increasing time, the tracer diffuses, spreading out between plume 1 and the ladle sidewall, while the tracer concentration begins to develop around the second plume. At t = 124 s, the ladle is predicted to have reached the 95% mixing criteria along the vertical plane A. It can be observed that the tracer mixing pa erns follow recirculatory trends before achieving this well-mixed condition along plane A.

Effect of Different Flow Rates from Plugs on Mixing Behavior
To evaluate the impact of different plug flow rates on mixing behavior, three separate cases were devised by distributing argon in varying ratios while maintaining the same total flow rate of argon. As depicted in Table 6, for Case 7, the argon flow rate was evenly divided between both inlets, resulting in a flow rate of 5 m 3 /h from each inlet. For Case 8,

Effect of Different Flow Rates from Plugs on Mixing Behavior
To evaluate the impact of different plug flow rates on mixing behavior, three separate cases were devised by distributing argon in varying ratios while maintaining the same total flow rate of argon. As depicted in Table 6, for Case 7, the argon flow rate was evenly divided between both inlets, resulting in a flow rate of 5 m 3 /h from each inlet. For Case 8, the argon flow rate was distributed in a 3:1 ratio, with a flow rate of 7.5 m 3 /h from inlet 1 and 2.5 m 3 /h from inlet 2, resulting in a total flow rate of 10 m 3 /h. Similarly, for Case 9, the flow rate was distributed in a 2:1 ratio, with flow rates of 6.7 and 3.3 m 3 /h, respectively. Based on these flow rates, plume radius and density were calculated, and mixing time was determined using the method described in the previous sections. The calculated mixing times for all cases are presented in Table 6, below. There, it is important to note that the position of the second plug was situated diametrically opposite to the existing plug at an equal radial distance. The results of this exercise showed that Case 8 (3:1) had the shortest mixing time of the three studied. However, it is crucial to also consider other significant variables, such as the lining life in the inevitable presence of refractory lining wear. In this regard, Figure 9 illustrates a comparative plot of hydrodynamic wall shear stresses generated for the three cases. It can be observed that for the same total argon injection rate, Case 7 has a much lower detrimental effect on the wall's erosion than the other two cases.  Figure 10 depicts the flow pa erns for the single-plug and dual-plug systems, with the velocity vector plo ed on a vertical plane passing through the center of the plug and the center of the ladle (plane A in Figure 8). In the case of a single-plug configuration, two typical recirculation fluid flow pa erns can be observed between the plume region and  Figure 10 depicts the flow patterns for the single-plug and dual-plug systems, with the velocity vector plotted on a vertical plane passing through the center of the plug and the center of the ladle (plane A in Figure 8). In the case of a single-plug configuration, two typical recirculation fluid flow patterns can be observed between the plume region and the ladle wall generated by argon injection. The size of the recirculation loop depends on the radial distance between the plug and the ladle sidewall. The recirculation flow can be characterized by an upward flow driven by injected gas, which then turns horizontally towards the sidewall in the vicinity of the free surface and, finally, into a downward flow along the sidewall. It should be noted that the plume shape is not strictly vertical conical; it is slightly tilted towards the nearest wall with increasing height in the ladle. In contrast, the flow profile for a dual-plug arrangement exhibits an additional recirculation loop between two plumes, along with two large recirculations between the plume and ladle wall. Since the gas flow rate is the same in both plugs, the flow pattern is nearly symmetrical. These figures show that the predicted results align well with the theoretical understanding of plume formation during argon injection into a ladle [7]. Due to gas injection, the gas-liquid region of both plumes expands laterally with increasing liquid height, causing the plume to split into two primary streams. Additionally, both plume shapes are slightly tilted toward the nearest ladle wall. In addition to flow pa erns, mixing times were also compared for the two cases. For the single-plug system, the calculated mixing time was 136 s, whereas, for the dual-plug configuration (Case 3), the mixing time was 128 s. Figure 11 shows a comparative plot of the hydrodynamic wall shear stress generated by a single-plug system with those for a dual-plug configuration (Case 3). It can be observed that the dual-plug system has a significantly lower detrimental effect on the wall's erosion compared to the single-plug system, despite having the same total argon injection rate. The maximum intensity of wall shear stress in the dual-plug system is approximately two-thirds of that observed in the single-plug system. In a single-plug configuration, higher wall shear stress can lead to accelerated erosion of the refractory material, resulting in reduced service life of the lining and increased maintenance costs. In addition to flow patterns, mixing times were also compared for the two cases. For the single-plug system, the calculated mixing time was 136 s, whereas, for the dual-plug configuration (Case 3), the mixing time was 128 s. Figure 11 shows a comparative plot of the hydrodynamic wall shear stress generated by a single-plug system with those for a dual-plug configuration (Case 3). It can be observed that the dual-plug system has a significantly lower detrimental effect on the wall's erosion compared to the single-plug system, despite having the same total argon injection rate. The maximum intensity of wall shear stress in the dual-plug system is approximately two-thirds of that observed in the single-plug system. In a single-plug configuration, higher wall shear stress can lead to accelerated erosion of the refractory material, resulting in reduced service life of the lining and increased maintenance costs.

Comparison of Dual-Plug with single-Plug Configuration
nificantly lower detrimental effect on the wall's erosion compared to the single-plug sy tem, despite having the same total argon injection rate. The maximum intensity of wa shear stress in the dual-plug system is approximately two-thirds of that observed in th single-plug system. In a single-plug configuration, higher wall shear stress can lead accelerated erosion of the refractory material, resulting in reduced service life of the linin and increased maintenance costs. The cleanliness of steel is significantly impacted by the size of the slag open eye (SO area, which determines the amount of liquid metal exposed to the surroundin The cleanliness of steel is significantly impacted by the size of the slag open eye (SOE) area, which determines the amount of liquid metal exposed to the surrounding atmosphere. This exposure can lead to increased oxidation and nitrogen absorption by the steel. Figure 12 compares the formation of SOE in single-plug-and dual-plug-configured ladles. The contour plot in Figure 12 depicts the volume fraction of liquid steel at the air/slag interface after the ladle purging process reaches a steady state. The red color represents the highest steel fraction. In the single-plug system, the argon flow rate was 10 m 3 /h, while in the dual-plug system, the total argon flow rate was equal to the singleplug system but equally distributed between both plugs. The SOE area was found to be larger in the single-plug configuration, indicating higher slag entrainment in liquid steel than in the dual-plug system, as the impact of upward liquid steel driven by rising bubbles breaking up the slag layer is more intensive for the single-plug system. atmosphere. This exposure can lead to increased oxidation and nitrogen absorption by the steel. Figure 12 compares the formation of SOE in single-plug-and dual-plug-configured ladles. The contour plot in Figure 12 depicts the volume fraction of liquid steel at the air/slag interface after the ladle purging process reaches a steady state. The red color represents the highest steel fraction. In the single-plug system, the argon flow rate was 10 m 3 /h, while in the dual-plug system, the total argon flow rate was equal to the single-plug system but equally distributed between both plugs. The SOE area was found to be larger in the single-plug configuration, indicating higher slag entrainment in liquid steel than in the dual-plug system, as the impact of upward liquid steel driven by rising bubbles breaking up the slag layer is more intensive for the single-plug system.  Figure 13 shows the liquid steel profile (with volume fraction, α = 0.7) at the air and slag region for both configurations. It should be noted that the steel surface is covered by a thin layer of slag, which is disrupted by argon gas bubbles intermi ently. This results in the formation of a standing wave at the interface of slag and steel. The upwelling flow in the gas plume causes the configuration of the molten steel surface to be displayed as a spout peak in Figure 13. The use of two plugs at symmetrical locations reduces the height of the spout peak. However, the interaction between the two rising plumes on the surface  Figure 13 shows the liquid steel profile (with volume fraction, α = 0.7) at the air and slag region for both configurations. It should be noted that the steel surface is covered by a thin layer of slag, which is disrupted by argon gas bubbles intermittently. This results in the area, is significantly reduced. The reduction in the SOE area has a profound impact on maintaining the quality of the liquid steel by minimizing re-oxidation.
Based on these findings, it is recommended to incorporate a second plug in the proposed diametrically opposite position to the existing plug, with equal flow rate distribution, to optimize the ladle's mixing efficiency, reduce refractory erosion, and minimize steel reoxidation. These insights provide valuable guidance for improving the plant configuration and enhancing the steelmaking process.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to a confidentiality agreement with our industrial partner.