Numerical Study on Interfacial Structure and Mixing Characteristics in Converter Based on CLSVOF Method

Abstract

The blowing flow is a key factor in molten bath stirring to affects the steel-bath interface fluctuation and chemical reaction in the top-bottom-blowing converter. The Volume of Fluid (VOF) method is widely used to capture the gas-liquid interface. However, some limitations exist in dealing with the interface curvature and normal vectors of the complex deformed slag-bath interface. The Coupled Level-Set and Volume of Fluid (CLSVOF) method uses the VOF function to achieve mass conservation and capture interface smoothly by computing the curvature and normal vector using the Level-Set function to overcome the limitations in the VOF model. In the present work, a three-dimensional (3D) transient mathematical model coupled CLSVOF method has been developed to analyze the mixing process under different injection flow rates and bottom-blowing positions. The results show that when the bottom-blowing flow rate increases from 0.252 kg/s to 0.379 kg/s, the mixing time in the molten bath gradually decreases from 74 s to 66 s. When the bottom-blowing flow rate is 0.252 kg/s, it is recommended to distribute the outer bottom-blowing position on concentric circles with D_tuy,₂/D₂ = 0.33.

1. Introduction

The converter is one of the important stages in steel production. The gas-liquid two-phase flow of the molten bath in the converter is of critical importance for both the productivity and quality of the process. In the steelmaking process, the effectiveness of the top-bottom-blowing converter depends on the mixing characteristics of the molten bath. Sufficient stirring of the molten bath is beneficial for the mixing of steel slag, which in turn promotes the carbon-oxygen reaction at the slag-steel interface. This reduces the iron content in the slag, achieves the goal of purifying the steel, and ultimately reduces costs. The circulation flow and mixing behavior of the molten bath are crucial in accomplishing efficient dephosphorization, decarburization, and composition homogenization throughout the steelmaking process [1]. A crucial prerequisite for investigating the behavior of the gas-liquid two-phase flow interface is precise interface capture. A common research area is the study of the flow, interface fluctuation, and mixing features of the molten bath in converters.

Recent studies on gas-liquid two-phase flow and the mixing behavior of molten bath flow in top-bottom combined blowing processes have made extensive use of physical and numerical simulation approaches. Some academics [2,3,4,5,6,7,8,9] have used physical and numerical simulations to research the bottom-blowing process optimization. Choudhary et al. [3] conducted experiments using a water model to optimize the configuration of the bottom tuyere. Their results showed that the eight-tuyere symmetrical non-equiangular arrangement resulted in the shortest mixing time. However, Lai et al. [2] observed that the asymmetrical and concentrated structures were more conducive to mixing in the molten bath. Olivares [4] and Ajmani [5] conducted water model experiments and discovered that an increase in the number of bottom-blowing tuyeres resulted in a decrease in mixing time. However, Li et al. [6] showed that the number of bottom-blowing tuyeres is different, and the mixing time is also inconsistent. The mixing time increases with the number of bottom-blowing tuyeres. Odenthal et al. [7] studied the variation of mixing time with bottom-blowing parameters, weld pool shape, and other factors. Numerical simulation and theoretical analysis led them to recognize that the mixing time would decrease initially, followed by an increase, and then a subsequent decrease as the number of bottom tuyeres increased. Luomala et al. [8] observed that enhancing the impact of the jet on the slag layer resulted in a more uniform radial velocity distribution of molten steel in the molten bath. They conducted physical modeling experiments and found that increasing the number of bottom air holes led to an increase in the number of splitting surfaces with low exchange rates, which in turn increased the mixing duration. However, once the mass of the molten metal reached a constant value, further increasing the number of bottom air outlets only prolonged the mixing time without any significant effect on the mass of the molten metal. Sun et al. [9] carried out water model experiments and numerical simulations to investigate the effect of the bottom blow pattern on the flow and mixing characteristics of the melt pool and arrived at an optimum bottom blow arrangement. It was also shown that the bottom-blowing mode significantly influences the local flow field, velocity interval distribution, and turbulent kinetic energy in the inner ring of the bottom-blowing air outlet.

The studies mentioned above demonstrate that the bottom-blowing mode can significantly alter fluid flow during the steelmaking process. In general, modifying the bottom-blowing mode is a cost-effective and practical way to enhance the dynamics of the molten bath in real-time steel production.

There are some methods for the study of gas-liquid interfaces. The van der Waals bulk equation had been generalized by Guillermo et al. [10] for a fluid contained within an inert nanopore. The equations anticipate equilibria between liquid and vapor as well as a shift in the critical point relative to the value obtained from the van der Waals bulk equation. A novel equation of state for actual gases is proposed by Christian [11] within the context of Bader’s Theory and tested on a variety of gases (monoatomic, diatomic, and triatomic). This new equation results from the substitution of van der Walls dumping parameters. The new equation’s best compatibility with the van der Waals equation was demonstrated by the different atomic partition and interaction energy acquired by ab initio calculations.

Numerical simulations have been widely used by scholars to study gas-liquid flows in top-bottom compound blowing converters, with the Volume of Fluid (VOF) method being the most commonly employed approach [12,13]. For instance, Odenthal et al. [12] used CFD technology to investigate the transport behavior of multiphase flows in a top-bottom-blowing converter. Their study focused on the interaction between supersonic oxygen jets and metal phases, with the VOF model used to describe the time-related impact crater. The authors found that bottom-blowing has a direct impact on the depth of the impact cavity shape. Zhang et al. [13] used the Eulerian-multifluid VOF mathematical of top-blow impact on the melt pool and bottom-blow mixing to analyze the effect of interphase forces on the impact cavity and molten pool mixing.

However, it is important to note that there are still some conflicting issues when using the VOF method to describe the multiphase flow of the top-bottom-blowing converter. Specifically, the VOF method can result in errors [13,14,15,16] when calculating complex deformation interfaces.

Hirt and Nichols [17] proposed a surface tracking method under a fixed Eulerian grid, introducing the concept of a fluid volume function expressed as the phase fraction. However, most current reconstruction methods cannot guarantee continuous derivability of the interface, leading to significant errors when dealing with complex deformation interfaces [18,19]. To overcome this issue, Osher and Sethian [20] proposed the Level Set method to express the phase interface as a continuous function. This method ensures that the interface is continuously derivable, and the curvature and the normal vector of the interface can be obtained at any position. However, the Level Set method was later found to cause volume non-conservation, leading to the proposal of the coupled Level Set and Volume of Fluid (CLSVOF) method by Olsson et al. [21,22]. The CLSVOF method is capable of accurately calculating interfacial curvature and achieving good mass conservation [23,24,25]. Moreover, its application range is continually expanding. The research on this method is still limited to classic cases such as sloshing [26], friction stirring [27] wave breaking [28], dam break [29], bubble lifting in liquid [30], and spray [31] (droplet) wall collision phenomena. However, this approach is very limited in the study of gas-liquid two-phase flow in converters.

Accurate interface capture and prediction have a certain influence on the mixing time. In order to capture the shape of the gas-liquid interface accurately, based on the CLSVOF method, a 3D mathematical model of the gas-liquid two-phase flow in a 335 t converter has been established to analyze the mixing process under different injection flow rates and bottom-blowing positions. This paper discusses the accuracy of a mathematical prediction model and analyzes the laws governing the effects of operating parameters on interfacial structure and mixing characteristics.

2. Materials and Methods

2.1. Geometric Models

As depicted in Figure 1, a geometric model of the 335 t top-bottom combined blowing converter has been developed. The model is established by combining the six-hole top spray lance with 14 bottom nozzles distributed in two dimensionless interval circles. To reduce resource pressure and shorten the calculation time, only the lower part of the converter is simulated, that is the fluid domain containing the spray lance outlet to the bottom of the molten bath.

In the present simulation, the unstructured grids are used in the regions of molten steel and top splash lance, while the hexahedral structured grids are in the remaining region. At the same time, the grids have been locally refined at the oxygen outlet and the bottom-blowing argon inlet. The total number of grids is 800,000, which meets the requirements met by the calculation. Detailed geometric parameters of the converter and fluid characteristics are shown in

Table 1. Geometrical conditions of the model.

Geometric Parameters of the Converter	Unit	Numerical Value
BOF nominal capacity(m)	t	335
cavity (V)	m3	48.3
computational domain height (H)	m	3.954
average furnace diameter (D1)	m	7.41
average bottom diameter (D2)	m	5.32
lance height (Htl)	m	1.00
molten depth (Hm)	m	1.65
slag layer thickness (Hsl)	m	0.26

and

Table 2. Fluid properties in converter [7].

Physical Parameters	Unit	Argon	Molten Steel	Slag
density (ρ)	kg/m3	1.6228	6940	3490
dynamic viscosity (μ)	kg/(m∙s)	2.125 × 10−5	5.100 × 10−3	1.000 × 10−1
surface tension coefficient (σ)	N/m	-	1.54	1.54
thermal conductivity (λ)	W/(m∙k)	0.016	40	1.7

.

2.2. Control Equations and Boundary Conditions

To maintain a reasonable computational time and study the multiphase flow field clearly in the converter, some hypotheses are proposed:

(1)

Oxygen and argon are the constant physical incompressible Newtonian fluid.

(2)

Temperature and chemical reactions in the molten bath are not considered.

(3)

The standard wall function is adopted for the near-wall treatment in the turbulence model with a no-slip wall boundary.

2.2.1. Basic Governing Equations

The mass conservation equation is satisfied for the i-phase fluid in the converter [31]:

$$\frac{\partial }{\partial t}({\alpha }_i{\rho }_i)+\nabla \cdot ({\alpha }_i{\rho }_i\stackrel{\rightharpoonup }{u})=0$$

(1)

However, the volume fraction of the initial phase in the multiphase flow is limited by the law of conservation of mass and is obtained by Formula (2), so as to ensure that the sum of the phase fraction of each phase is 1 [32].

$${\displaystyle \sum _{i=1}^n{\alpha }_i}=1$$

(2)

The zero-value surface of the Level Set phase function represents the moving interface of the multiphase flow. In the coupling model, the solution of the interface depends on the Level Set model. The curvature of the moving interface can be well estimated by Formula (3), and the surface tension involved in the momentum conservation equation can be obtained by Formula (4).

$$\kappa (\varphi )=\nabla \cdot {\frac{\nabla \varphi }{\left|\nabla \varphi \right|}|}_{\varphi =0},$$

(3)

$$\stackrel{\rightharpoonup }{F}=\sigma \kappa (\varphi )\nabla \varphi {\delta }_{\epsilon }(\varphi )$$

(4)

Here, it is assumed that the phase interface can be regarded as a thin fluid region with a thickness of δ, and the function δ_ε is smooth in the thin fluid region, which can be expressed as:

$${\delta }_{\epsilon }(\varphi )=\{\begin{array}{ll}\frac{1}{2\epsilon }(1+\cos (\frac{\mathsf{\pi }\varphi }{\epsilon }))\hfill & \left|\varphi \right|<\epsilon \hfill \\ 0\hfill & others\hfill \end{array},$$

(5)

in the formula, ε is taken as 1.5 times the grid spacing.

In this paper, the CLSVOF coupling model [26] is used to capture and track the moving interface between gas-liquid two-phase flow in the converter. The physical parameters used in the multiphase flow control equation in the converter depend on the physical parameters of each phase and the phase fraction of each phase. According to the main idea of model coupling, the value of physical parameters in the momentum equation adopts the calculation theory of physical parameters in the Level Set model, that is, to establish a relationship with gas and liquid two-phase fluids through Formulas (6) and (7):

$$\rho ={\rho }_g+({\rho }_l-{\rho }_g)H_{\epsilon }(\varphi ),$$

(6)

$$\mu ={\mu }_g+({\mu }_l-{\mu }_g)H_{\epsilon }(\varphi )$$

(7)

The smooth Heaviside function H_ε (ϕ) can be expressed as:

$$H_{\epsilon }(\varphi )=\{\begin{array}{ll}0\hfill & \varphi <-\epsilon \hfill \\ \frac{(\varphi +\epsilon )}{(2\epsilon )}+\frac{1}{(2\mathsf{\pi })}\sin (\frac{\mathsf{\pi }\varphi }{\epsilon })\hfill & \left|\varphi \right|\le \epsilon \hfill \\ 1\hfill & \varphi >\epsilon \hfill \end{array},$$

(8)

In order to make the turbulence simulation in the numerical calculation closer to the fluid turbulence phenomenon in the real converter, this study uses the Realizable k-ε two-equation model to simulate the turbulent motion [33]. The two-equation can be expressed as follows:

$$\frac{\partial }{\partial t}(\rho k)+\frac{\partial }{\partial x_j}(\rho k{u}_j)=\frac{\partial }{\partial x_j}\left[(\mu +\frac{{\mu }_t}{{\mathsf{\sigma }}_{\mathrm{k}}})\frac{\partial k}{\partial x_j}\right]+G_k+G_b-\rho \epsilon -Y_M$$

(9)

$$\begin{array}{l}\frac{\partial }{\partial t}(\rho \epsilon )+\frac{\partial }{\partial x_j}(\rho \epsilon u_j)\\ =\frac{\partial }{\partial x_j}\left[(\mu +\frac{{\mu }_t}{{\mathsf{\sigma }}_{\mathsf{\epsilon }}})\frac{\partial \epsilon }{\partial x_j}\right]+\rho C_{1}S\epsilon -\rho {\mathrm{C}}_2\frac{{\epsilon }^2}{k+\sqrt{\nu \epsilon }}{\mathrm{C}}_{1\mathsf{\epsilon }}\frac{\epsilon }{k}{C}_{3\epsilon }{G}_b\end{array}$$

(10)

of which:

$$C_1=\max \left[0.43,\frac{\eta }{\eta +5}\right],$$

(11)

$$\eta =S\frac{\epsilon }{k}$$

(12)

$$S=\sqrt{2S_{ij}{S}_{ij}}$$

(13)

In the formula, the meanings of k and $\epsilon$ are turbulent pulsating kinetic energy and its dissipation rate, respectively. $G_k$ and $G_b$ refer to the generation terms of turbulent kinetic energy due to average velocity gradient and buoyancy, respectively. According to the assumptions, the bath is incompressible fluid, so $Y_M=0$. The turbulent Prandtl number ${\sigma }_{\epsilon }$ of ${\mathrm{C}}_{1\mathsf{\epsilon }}$, ${\mathrm{C}}_2$, $\epsilon$ and the turbulent Prandtl number ${\sigma }_k$ of k are constants, which are 1.44, 1.9, 1.2, and 1.0, respectively.

In order to investigate the mixing characteristics of the melt pool, this paper adds UDS (user-defined scalar) [34] to the steel solution, which satisfies the following equation:

$$\frac{\partial {\alpha }_{\mathrm{s}}{\rho }_{\mathrm{s}}\chi }{\partial t}+\nabla \cdot \left({\alpha }_{\mathrm{s}}{\rho }_{\mathrm{s}}{u}_{\mathrm{s}}\chi -{\alpha }_{\mathrm{s}}{\mathrm{\Gamma }}_{\mathrm{s}}\nabla \chi \right)=0,$$

(14)

Among them, ${\alpha }_s$ represents the volume fraction of molten steel, ${\rho }_s$ represents the density of molten steel, $u_s$ represents the velocity of molten steel, ${\mathrm{\Gamma }}_{\mathrm{s}}$ represents the diffusion coefficient of scalar in molten steel, and $\chi$ represents the value of UDS.

2.2.2. Boundary Conditions

In the setting of boundary conditions, the velocity-inlet boundary condition is used at the top lance exit. The bottom-blowing argon inlet is set to the mass-flow-inlet boundary condition. This condition can be used whether the fluid is compressible or not. For an incompressible fluid with a constant density, the determination of its flow velocity depends on the mass flow rate. The top outlet of the converter is set as the pressure-outlet boundary condition, and the external surface pressure of the converter outlet is −1000 Pa, which is beneficial to control the flow direction of oxygen at the converter outlet. The reflux volume fraction of oxygen is set to 1, that is, only oxygen is allowed to reflux at the converter outlet. The boundary conditions between different computational domains are defined as interfaces so that the computational data of different computational domains at such boundaries can be transmitted. A standard wall function adjusts the wall surface [35], and the wall surface has no slip. This method does not solve the viscous region near the wall but uses the semi-empirical method of wall function to calculate the region. It is critical to change the turbulence model from the near-wall model to realize the connection between the fully developed area and the viscous influence area near the wall.

The fixed bottom-blowing port positions distributed on two concentric circles of D_tuy,1/D₂ = 0.19 (n = 4), D_tuy,2/D₂ = 0.50 (n = 10) are selected to study the influence of bottom-blowing argon flow rate on the flow field. The bottom-blowing flow rates are set to 0.252 kg/s, 0.347 kg/s, and 0.379 kg/s respectively.

2.2.3. Solution Method

The present study employs the finite volume method to solve the developed mathematical model, with the aim of (state the goal of the study). To ensure the accuracy of the results, the pressure-velocity coupling is rectified using the SIMPLE approach. To balance the requirements of computational efficiency and accuracy when using the CLSVOF model to track the interface and reinitializing the Level Set function with high accuracy, the first-order upwind scheme for the difference scheme is adopted and the Courant number is set to 0.5, and then the CLSVOF model is solved by the Euler explicit equation.

The convergence criteria for velocity, Level Set function, turbulent kinetic energy, and dissipation rate are set to 0.001. Limited by the global Courant number, which is not greater than 250, the fixed time step is 0.0002 s.

3. Results and Discussion

3.1. Model Validation

The CLSVOF mathematical model is validated using the water model experiment data in reference. This method greatly improves the accuracy of interface capture. In order to verify the accuracy of this method, we choose the experiment [36] of measuring the impact cavity size. In this experiment, water and air are used to represent liquid steel and nitrogen, respectively. The model has a geometric ratio of 1:10 with respect to the 210 t converter prototype. It is made of organic glass and includes a bottom-blowing device with an aperture and an aqueous solution. Air is forced into the molten bath from both the top oxygen lance and the bottom-blowing device at a specified flow rate. This paper investigates the impact cavity diameter under varying top-blowing flow, bottom-blowing flow, oxygen lance height, and oxygen lance inclination when the injection process is stable. The impact cavity diameter simulation outcomes are contrasted with experimental data that is most precisely predicted using an optimized CLSVOF. Experimental conditions are shown in

Table 3. Three scenarios of experimental conditions [36].

	Bottom Tuyeres Layout	Top Gas Flowrate (m3/h)	Bottom Gas Flowrate (m3/h)	Lance Height (mm)	Nozzle Angle (°)
case 1	0.51 D	77.15	0.209	104	15
case 2	0.51 D	80.52	0.261	133	15
case 3	0.65 D	70.45	0.157	104	15

. The results are shown in Figure 2.

3.2. Subsection

In the present work, the bottom-blowing port distributed on two concentric circles of D_tuy,1/D₂ = 0.19 (n = 4), D_tuy,2/D₂ = 0.50 (n = 10) is selected to solve the gas-liquid interface fluctuation using the VOF and CLSVOF models with the same mesh in a bottom-blowing flow rate of 0.252 kg/s. Figure 3 shows the phase fraction of different models at the same time, in which red represents molten steel. Figure 4 shows the free surface curve of molten steel at this time.

Comparing Figure 3 and Figure 4, it can be seen that the VOF method does not capture enough details of the interface fluctuation during the phase interface tracking process. The VOF method exhibits an evident, intermittent discontinuity in the gas column, whereas the CLSVOF method not only maintains a continuous gas column but also generates delicate droplets that can be vividly visualized. Moreover, the fluctuation caused by the splashed droplets falling onto the free surface is well characterized. The unsmooth morphology of the impact cavity is also revealed clearly.

3.3. Criteria of Mixing Time

As the control variable, the tracer position is below the liquid steel level and fixed at the converter axis. At the same time, the diffusion coefficient of the tracer in each phase fluid remains unchanged, and three representative concentration monitoring points are set up in the converter. The coordinates are point A (−3500 mm, 900 mm, and 0 mm), point B (0 mm, 900 mm, and −3500 mm), and point C (0 mm, −450 mm, and 0 mm), as shown in Figure 5.

Figure 6 shows the tracer concentration of the three monitoring points in the molten bath with time when the bottom-blowing flow rate is 0.252 kg/s. Because the initial tracer patch area is near point C and the fluid flows downward, the concentration at monitoring point C increases abruptly at the start. With the diffusion of the tracer, monitoring point C declines while points A and B grow after extended stirring. The tracer concentration of the three monitoring points eventually converges and stabilizes at the end of stirring due to the tracer concentration difference and molten turbulent motion. In industrial reality, when the ratio of the concentration of the three-monitoring points Ci to the theoretical equilibrium concentration of the tracer Cm in the molten bath is, the pool is regarded as entirely mixed, and the time taken is τ.

3.4. Effect of Bottom-Blowing Flow on Mixing Behavior

Figure 7 shows the flow deflects downward along the converter wall, it returns to the center, gradually forming a relatively regular and complete annular molten vortex mode in the molten bath. The maximum velocity of the molten bath occurs in the center of the bottom-blowing column. As the bottom-blowing flow rate increases from 0.252 kg/s to 0.379 kg/s, the maximum velocity steadily increases, and the distribution becomes more uniform. The highest velocity of 2.763 m/s in the molten bath was recorded when the blowing rate from the bottom was 0.379 kg/s. This leads to further expansion of the gas-liquid two-phase flow, resulting in more uniform molten baths and minimized low-velocity areas. Furthermore, as the flow rate increases gradually, the gas column carries a greater amount of metal liquid, causing it to float in the gas column. The gas column in the metal liquid becomes stable and is not prone to tilt distortion due to extrusion. The argon-metal liquid two-phase flow region is further extended with extrusion.

Figure 8 and Figure 9 show the velocity counters at Z and Y sections, respectively. the buoyancy effect of the gas column becomes more significant as the bottom-blowing flow rate increases. A large bottom-blowing flow rate can decrease the low-velocity circulation regions near the converter wall and increase the metal velocity in the converter bottom. Additionally, the velocity distribution of the axial or radial molten becomes more uniform. As a result, increasing the flow rate of bottom-blowing is an effective method for eliminating the dead zone in the flow and improving the mixing efficiency of the molten bath. This is because more areas of molten are created, and the vortex forms an annular shape.

Figure 10 illustrates the mixing time of the molten bath as the bottom-blowing flow rate varies. The mixing time decreases from 73.5 s to 66.5 s when the bottom-blowing flow rate increases from 0.252 kg/s to 0.379 kg/s. The molten bath dead zone decreases as the bottom blow flow rate increases. A large bottom-blowing flow rate can increase the holding force of the gas column, hence the molten bath is absorbed into the vortex, leading to strengthening the mixing of the molten bath. These findings suggest that controlling the bottom-blowing flow rate can significantly impact the mixing efficiency of the molten bath. By selecting an appropriate bottom-blowing flow rate, the mixing time of the molten bath can be optimized, which can improve the overall performance of the converter.

3.5. Effect of Bottom-Blowing Mode on Mixing Behavior

Figure 11 illustrates the 14 bottom-blowing modes arranged in the order caseA: D_tuy,1/D₂ = 0.19, D_tuy,2/D₂ = 0.33; caseB: D_tuy,1/D₂ = 0.19, D_tuy,2/D₂ = 0.5; caseC: D_tuy,1/D₂ = 0.19, D_tuy,2/D₂ = 0.75 under the bottom-blowing flow rate of 0.252 kg/s.

Figure 12 reveals that the inner and outer pitch circles are in close proximity. Consequently, the rising gas column gets compressed by the molten steel in the molten bath. On the other hand, air columns on various pitch circles result in more concentrated and powerful gas columns that aid in the circulation and homogenization of the molten metal. When the inner and outer nozzles are positioned close to each other, the bottom-blowing gas column generates a stronger lifting force, which prevents the formation of a flow dead zone.

The arrangement shown in Figure 13b divides the molten pool into several independent parts. The interaction between regions is difficult, and the cycle efficiency is significantly reduced. While effective mixing occurs on the outside of the chamber, poor mixing occurs on the inside, leading to difficulties in the interaction between these zones and a significant decrease in circulation efficiency. As a result, core circulation is restricted and problematic, but lateral circulation is vigorous. Unfortunately, this arrangement does not reduce the low-speed circulation area of the converter side wall, and it also expands the low-speed circulation area in the lower part of the molten bath as a whole. The arrangement shown in Figure 14a takes into account the problem of eliminating the flow dead zone and improving the radial flow uniformity of the melt. Undoubtedly, this method promotes better circulation and homogeneity within the molten bath than other methods.

The arrangement of bottom-blowing modes with D_tuy,1/D2 = 0.19 and D_tuy,2/D2 = 0.33 maximizes the lifting effect on the liquid metal due to the proximity of the gas columns, resulting in a clear annular vortex shape for optimizing stirring in the molten bath with a mixing time of 52.5 s in Figure 15. In general, the mixing time increases gradually as the distance between the inner and outer nozzles increases. When the outer nozzle element is positioned further away from the converter axis and closer to the wall surface, that is, D_tuy,2/D2 = 0.5, the gas column divides the molten bath into several regions and resulting in a mixing time of 73.5 s. However, when the outer gas column collides with the converter wall at an excessive distance, it causes energy loss, resulting in a reduced flow rate in the middle and lower parts of the molten bath. Additionally, there is a lack of stirring effect, which increases the mixing time by 80 s. Moreover, if the distance is too close, it will isolate the inner and outer molten regions and make it difficult to mix the molten bath. Conversely, when the distance is too long, the low-speed area in the middle and lower part of the molten bath becomes large, and the circulation flow is poor, leading to a prolonged mixing time.

4. Conclusions

In this study, we use the CLSVOF coupling model to accurately capture and track the interface of the gas-liquid two-phase flow in a steelmaking converter. To evaluate the mixing behavior, we track the tracer concentration at three designated points. We monitor the tracer concentration at three specified points to assess the mixing behavior of the molten metal. The tracer conversation equation solved by the UDF is applied to calculate the mixing time as a criterion for predicting the stirring efficiency. The results are summarized as follows:

(1)

The VOF and the CLSVOF methods are compared to track the gas-bath interface fluctuation with the same number and quality of grids. The CLSVOF method has a better tracking accuracy of the complex gas-bath interface morphology during the gas column rising process than the VOF method.

(2)

By increasing the bottom-blowing flow of argon from 0.252 kg/s to 0.379 kg/s, the maximum velocity in the molten bath gradually increases up to 2.763 m/s. Moreover, the mixing times are gradually shortened, with the mixing time reduced to just 66 s when the bottom-blowing flow rate rises to 0.379 kg/s.

(3)

The most optimal arrangement of bottom-blowing modes should be D_tuy,1/D₂ = 0.19, D_tuy,2/D₂ = 0.33. However, if the outer bottom element is too far away from the axis, defects and the overlap of gas columns will reduce the lifting force.

In summary, our findings indicate that managing the bottom-blowing flow rate is an essential aspect of optimizing converter performance. The productivity of the converter can be increased by minimizing the low-velocity zones and boosting the mixing efficiency of the molten bath, with proper bottom-blow modes for excellent molten bath circulation.