Powder Injection Effect on Hot Metal Desulfurization Behavior in the Kanbara Reactor: a Transient 3D Coupled Numerical Model

Abstract

The increasing demand and stringent requirements for high-quality steels necessitate their desulfurization efficiency enhancement and its robust substantiation. In this study, the Kanbara Reactor (KR) hot metal desulfurization process was simulated by a transient 3D coupled numerical model of two-phase flow, heat transfer, and desulfurizing agent (DA) particles. The multiple reference frame method was used to simulate the stirring blade rotation, and a desulfurization kinetic model was introduced to analyze the mass transfer rate of sulfur. The effect of addition of DA particles on the desulfurization efficiency was quantitatively evaluated under different conditions. The calculated average particle size was consistent with that reported by other researchers. The increased gas flow rate promoted the hot metal penetration of the DA, and the gas flow rate of 180 m/s corresponded to the desulfurization rate of 95.27%. When the lance was shifted further from the stirring shaft, higher desulfurization rates were obtained. However, an increased angle between the lance and the vortex liquid surface would induce the detrimental hot metal splashing phenomenon.

1. Introduction

In recent years, the demand for high-quality steel continuously increases, promoting the development of new high-performance steel products. Since excessive sulfur content in steels promotes their anisotropy and corrosion, its reduction to 0.001% or even less by steel desulfurization became very topical for improving steel quality. In general, hot metal pretreatment is an integral part of the state-of-the-art steel production process. At present, there are two desulfurization methods in the pretreatment stage of hot metal: (i) the composite injection method, and (ii) the Kanbara reactor (KR) method. The latter is a hot metal desulfurization technology proposed by the Nippon Steel Co. in the 1960s,¹⁾ which ensured of stable desulfurization, low desulfurization agent consumption, rapid treatment, and low cost of deep desulfurization, due to its good desulfurization kinetic conditions. Currently, the KR desulfurization became the preferred deep desulfurization process of hot metal in the global steelmaking industry.²⁾ The KR method has been explored by physical analog models and numerical simulations, which revealed its fluid flow patterns and particle motion behavior.^{3,4,5,6,7,8,9,10,11)} The dispersion of desulfurizing agent (DA) particles in the hot metal directly affects desulfurization efficiency.^11,12) To reduce the DA amount used per ton of hot metal, it is necessary to enhance the DA reaction efficiency.

At present, most steelmaking companies still adopt the method of adding DA particles in batches for desulfurization, whereas all DA particles are added to the hot metal ladle within 1–2 min and aggregated before reacting with sulfur. Thus, some DA particles placed into hot metal are wrapped into a dense CaS coating with a large amount of calcium oxide, which inhibits their participation in the desulfurization reaction.

Study has shown that after using the batch method for desulfurization, calcium oxide content in the desulfurization residue accounted for about 90%.¹³⁾ On the one hand, the smaller the diameter of the DA particles, the higher their dispersion in the hot metal, and the stronger the desulfurization effect. On the other hand, the reaction efficiency of DA particles grows with a decrease in the initial diameter of the DA particles because of the larger specific surface area.¹⁴⁾ Enhancing the degree of particle dispersion and avoiding particle aggregation is vital for improving the desulfurization efficiency. However, the decreased DA particle size increases the degree of particle escape. Nakai et al. proposed a dynamic way of injecting DA particles directly into the hot metal by a carrier gas to overcome the surface tension of the hot metal, thereby increasing the degree of DA particles before coagulation reaction, effectively reducing their aggregation and improving desulfurization efficiency.^15,16)

The available experimental techniques fail to grasp the interaction between hot metal and DA particles in the KR desulfurization process. Therefore, this study elaborated a three-dimensional transient numerical model to study the effect of DA particles sprayed by powder injection on the desulfurization behavior, particle motion, and mass transfer of hot metal. The agitation caused by the impeller rotation is described by applying the multiple reference frame (MRF) model, while the volume of fluid (VOF) method captures the interface between the air and hot metal. The trajectory of DA particles is obtained by the two-way coupling Eulerian-Lagrangian method. Besides, a desulfurization kinetic model is introduced to evaluate the sulfur mass transfer rate. According to this model, the influence of particle aggregation and temperature distribution of hot metal on the diffusion behavior of sulfur in hot metal is considered. The effects of particle coagulation, reduction of the specific surface area of DA particles, and formation of the CaS layer on the particle surface hindering the reaction of CaO on the reaction rate of CaO and [S] are analyzed and discussed in detail. Finally, the proposed model is used to study the effects of different horizontal and vertical positions of the lance and gas flow rates on the desulfurization efficiency.

2. Mathematical Method

2.1. Assumptions

This study used the following assumptions:

(1) The air and hot metal in the ladle were treated as Newtonian fluids with constant physical properties, the formation of slag in the ladle was ignored.⁸⁾

(2) The effect of sulfur content on the interfacial tension was ignored; the constant coefficient of the hot metal-air and molten metal-DA particles interfacial tension was assumed.¹⁷⁾

(3) The DA particle was treated as an inert solid sphere.

2.2. Multiple Reference Frame Model

The rotating coordinate system is suitable for the simulation of rotating machinery, agitators and other related equipment. Owing to the periodic movement of the stirring paddle, in the absence of a stator, the flow becomes a steady flow relative to the rotating parts, and the analysis of the flow can be greatly simplified. Due to the existence of the rotating impeller, the computational domain was subdivided into (i) moving and (ii) stationary regions, separated by the interface boundary. The impeller was located in the moving region and a moving coordinate system was given to simulate the rotation of the impeller. The moving reference frame equations described the moving region containing the rotating impeller, while the stationary region was defined by the equations of the stationary reference frame.^{18,19,20,21,22)}

2.3. Continuity, Momentum and Energy Equations used in the Stationary Reference Frame

In the present work, a realizable k–ε turbulence model was adopted, which provided an accurate prediction of the divergence ratio of the cylindrical jet and had a good performance for rotating flows, boundary layer flows with strong counterpressure gradient, flow separation, and secondary flow.²³⁾

The continuity, momentum, and energy equations used in the stationary reference frame were as follows:   

$$\frac{\partial \alpha }{\partial t}+\nabla \cdot \left(\alpha \overrightarrow{v}\right)=0$$(1)

  

$$\begin{array}{c}\frac{\partial \left(\overline{\rho }\overrightarrow{v}\right)}{\partial t}+\nabla \cdot \left(\overline{\rho }\overrightarrow{v}\overrightarrow{v}\right)=-\nabla P+\nabla \cdot \left[\overline{\mu }\left(\nabla \overrightarrow{v}+\nabla {\overrightarrow{v}}^{\text{T}}\right)\right]+\overline{\rho }\overrightarrow{g}\\ +{\overrightarrow{F}}_{\text{st}}+{\overrightarrow{S}}_{\text{mp}}\end{array}$$(2)

  

$$\frac{\partial \left(\overline{\rho }\overline{E}\right)}{\partial t}+\nabla \cdot \left(\overline{\rho }\overrightarrow{v}\overline{E}\right)=\nabla \cdot \left(k_{\text{eff}}\nabla T\right)$$(3)

  

$$\overline{E}=\overline{h}-\frac{p}{\overline{\rho }}+\frac{{\overrightarrow{v}}^2}{2}\mathrm{\hspace{0.17em} } \mathrm{a}\mathrm{n}\mathrm{d}\mathrm{\hspace{0.17em} } \overline{h}={\int }_{T_{\text{ref}}}^T{\overline{c}}_{\text{p}}\text{d}T$$(4)

where α is the volume fraction of hot metal, $\overrightarrow{v}$ is the absolute velocity (m/s), $\overline{\rho }$ is the density of mixture phase (kg/m³), $\overline{\mu }$ is viscosity on mixture phase (Pa·s), $\overrightarrow{g}$ is gravity, ${\overrightarrow{F}}_{\text{st}}$ is interfacial tension (N/m³), ${\overrightarrow{S}}_{\text{mp}}$ is the source term describing the momentum exchange between the hot metal and DA particles, $\overline{E}$ is the internal energy of the mixture phase (J/m³), k_eff is the effective thermal conductivity (W/(m·K)), $\overline{h}$ is the sensible enthalpy of mixture phase (J/kg), T is the temperature (K), T_ref is the reference temperature, and ${\overline{c}}_{\text{p}}$ is the specific heat of mixture phase at constant pressure (J/(kg·K)).

2.4. Continuity, Momentum, and Energy Equations used in the Moving Reference Frame

For the moving frame, the respective equations take the following form:   

$$\frac{\partial \alpha }{\partial t}+\nabla \cdot \left(\alpha {\overrightarrow{v}}_{\text{r}}\right)=0$$(5)

  

$$\begin{array}{l}\frac{\partial \left(\overline{\rho }\overrightarrow{v}\right)}{\partial t}+\nabla \cdot \left(\overline{\rho }{\overrightarrow{v}}_{\text{r}}\overrightarrow{v}\right)+\overline{\rho }\left[\overrightarrow{\omega }\times \left(\overrightarrow{v}-{\overrightarrow{v}}_{\text{t}}\right)\right]\\ =-\nabla P+\nabla \cdot \left[\mu \left(\nabla \overrightarrow{v}+\nabla {\overrightarrow{v}}^{\text{T}}\right)\right]+\overline{\rho }\overrightarrow{g}+{\overrightarrow{F}}_{\text{st}}+{\overrightarrow{S}}_{\text{mp}}\end{array}$$(6)

  

$$\frac{\partial (\overline{\rho }\overline{E})}{\partial t}+\nabla \cdot \left(\overline{\rho }{\overrightarrow{v}}_{\text{r}}\overline{H}+\overline{\rho }{\overline{u}}_{\text{r}}\right)=\nabla \cdot \left(k_{\text{eff}}\nabla T+\left[\overline{\mu }\left(\nabla \overrightarrow{v}+\nabla {\overrightarrow{v}}^{\text{T}}\right)\right]\cdot \overrightarrow{v}\right)$$(7)

  

$$\overline{H}={\overline{h}}_{\text{ref}}+{\int }_{T_{\text{ref}}}^T{\overline{c}}_{\text{p}}\text{d}T$$(8)

where ${\overrightarrow{v}}_{\text{r}}$, $\overrightarrow{\omega }$, ${\overrightarrow{v}}_{\text{t}}$ are relative, angular, and translational frame velocities, respectively; H is the enthalpy of mixture phase (J/kg), h_ref is the sensible reference enthalpy of mixture phase (J/kg), ${\overrightarrow{u}}_{\text{r}}$ is the velocity of the moving reference frame relative to the stationary reference frame, which is derived as follows:   

$${\overrightarrow{v}}_{\text{r}}=\overrightarrow{v}-{\overrightarrow{u}}_{\text{r}}\mathrm{\hspace{0.17em} } \mathrm{a}\mathrm{n}\mathrm{d}\mathrm{\hspace{0.17em} } {\overrightarrow{u}}_{\text{r}}=\overrightarrow{\omega }\times \overrightarrow{r}$$(9)

2.5. VOF Method

The volume of fraction (VOF) method was used to track the motion of the interface between air and hot metal. Hot metal and air shared a set of momentum equations described above, and the phase volume fraction α, representing the phase A-to-grid phase volume ratio, was introduced to track the interface between phases in the cell. The physical properties of the mixed phase, such as density, viscosity, and thermal conductivity, were related to the volume fraction of each phase as follows:   

$$\overline{\varphi }={\varphi }_{\text{m}}\alpha +{\varphi }_{\text{g}}\left(1-\alpha \right)$$(10)

where φ, φ_m, φ_g are the physical property of mixture phase, air, and hot metal, respectively. The entire computational domain was used to solve the continuity, momentum, and energy equations and the two phases’ volume fraction was updated on real-time scale. The two phases shared the temperature and velocity distributions.

2.6. Dispersed Phase Dynamics

Newton’s second law is known to govern the motion of a discrete phase DA particle, that is:⁸⁾   

$${\text{m}}_{\text{p}}\frac{d{v}_{\text{d}}}{dt}={\overrightarrow{F}}_{\text{g}}+{\overrightarrow{F}}_{\text{b}}+{\overrightarrow{F}}_{\text{d}}+{\overrightarrow{F}}_{\text{l}}+{\overrightarrow{F}}_{\text{vm}}+{\overrightarrow{F}}_{\text{p}}$$(11)

where: ${\overrightarrow{F}}_{\text{g}}$, ${\overrightarrow{F}}_{\text{b}}$, ${\overrightarrow{F}}_{\text{d}}$, ${\overrightarrow{F}}_{\text{l}}$, ${\overrightarrow{F}}_{\text{vm}}$ and ${\overrightarrow{F}}_{\text{p}}$ are the gravity, buoyancy, drag, lift, virtual mass, and pressure gradient forces, respectively. When Newton’s second law was transformed into a rotating reference frame, the centrifugal and Coriolis accelerations appeared;²⁶⁾   

$${\text{m}}_{\text{p}}\frac{d{v}_{\text{d}}}{dt}={\overrightarrow{F}}_{\text{d}}+{\overrightarrow{F}}_{\text{g}}+{\overrightarrow{F}}_{\text{b}}+{\overrightarrow{F}}_1+{\overrightarrow{F}}_{\text{vm}}+{\overrightarrow{F}}_{\text{p}}+{\overrightarrow{F}}_{\text{centri}}+{\overrightarrow{F}}_{\text{Coriolis}}$$(12)

where: ${\overrightarrow{F}}_{\text{centri}}$ and ${\overrightarrow{F}}_{\text{Coriolis}}$ are the centrifugal and Coriolis forces, respectively. These two forces allowed Newton’s laws to be applied to a rotating system since they involved the object motion in an inertial reference frame.

2.7. Desulfurization Model

In the pretreatment of hot metal by the KR method, the DA particles reacted with the sulfur element in the hot metal to absorb the sulfur in the hot metal. In addition, the convection and diffusion of sulfur in the hot metal also affected the desulfurization rate of the DA particles. The above phenomenon was taken into account in this study by establishing the desulfurization mass transfer control equations:^27,28,29,30)   

$$\frac{\partial \left(\overline{\rho }c\right)}{\partial t}+\nabla \cdot \left(\overline{\rho }\overrightarrow{v}c\right)=\nabla \cdot \left(\overline{\rho }{D}_{\text{S}}\nabla c\right)+S_{\text{des}}$$(13)

where c is the concentration of sulfur in hot metal, and D_S is the diffusion coefficient of sulfur in hot metal, which positively correlates with temperature.   

$$D_{\mathrm{S}}=\text{6}\text{.45}\times {10}^{-4}\cdot exp\left(\frac{\left(3.11T/T_0-116\right)\times {10}^{-5}}{R}T\right)$$(14)

where T₀ is the initial molten iron temperature, R is the ideal gas constant. Our approach was based on the simplified surface area method proposed by Oeters et al.²⁹⁾ The reaction rate constant for a single particle size level can be written as:   

$$S_{\text{des}}=\frac{dw\left[S\right]}{dt}=-\overline{\rho }\frac{6}{\pi }\frac{{\beta }_{\text{[S]}}}{\delta }\frac{T}{298}c$$(15)

where S_des is the desulfurization rate (kg/s), d_p is the equivalent diameter of the DA particles, The DA particles will form a thicker reaction layer in the hot metal. During the desulfurization process, the CaS reaction layer will surround the surface of the lime particles. Sulfur slowly diffuses into the lime particles through the growing layer of CaS reaction products. This kind of solid-phase diffusion is the “stumbling block” of the desulfurization reaction. Based on this, the parameters of the desulfurization model were adjusted and optimized by comparing with the results of literature data to make them more consistent with the final desulfurization results.³¹⁾ δ is the thickness of CaS outer layer of DA particles. Finally, β_[S] represents the sulfur from the hot metal to the rate of motion of the particle boundaries. The rate of the affected particle size, velocity and local sulfur concentration can be expressed as:³⁰⁾   

$$Sh=\frac{{\beta }_{[\text{S}]}{\text{d}}_{\text{p}}}{D_{\text{S}}}=\text{2}+\text{0}\text{.6}R{e}^{\frac{\text{1}}{\text{2}}}S{c}^{\frac{\text{1}}{\text{3}}}$$(16)

where Sh is the Sherwood number, which represents the ratio of convective mass transfer to diffusion mass transfer rate; Re and S_C are local Reynolds number and Schmidt number respectively. The formation rate and thickness growth rate of the CaS outer layer of the DA particles were derived as follows:   

$$\left(\text{CaO}\right)+\left[\text{S}\right]=\left(\text{CaS}\right)+\left[\text{O}\right]$$(17)

  

$$\frac{dw\left(\text{CaS}\right)}{dt}=\frac{M_{\text{CaS}}}{M_{\text{S}}}\frac{dw\left[S\right]}{dt}={\rho }_{\text{CaS}}\frac{\pi }{6}\left[d_{\text{p}}{}^3-{\left(d_{\text{p}}-2\delta \right)}^3\right]$$(18)

where M_CaS and M_S are the relative molar masses of CaS and S, respectively, and ρ_CaS is the density of CaS.

3. Boundary Conditions

As shown in Fig. 1(a), the horizontal position of the lance was the radial distance d between the lance center and the ladle axis, and its vertical position was the distance h between the lance and the initial liquid level. The red area was molten iron, and the initial depth was L, the radius of the calculation domain was R, and the yellow area was the rotating area. The lance positions h and d were treated as dimensionless parameters normalized by L and R, respectively. The specific grid structure is shown in Fig. 1(b). The mesh below the lance was refined. This processing method improved the solution accuracy of the entire system, reduced the total number of nodes, and could capture the shape of the liquid surface under the lance.

Fig. 1.

Computational domain and numerical grid. (Online version in color.)

The stirring impeller rotated clockwise with constant rotation speed and the initial hot metal level L=3621 mm. Assuming that the top surface was an atmospheric pressure outlet, a constant temperature of 373 K was assumed. Initially, the mass fraction of sulfur was set to 0.03% and the hot metal temperature to 1573 K. The sulfur flux of the top surface, shaft, and impeller were considered to be zero. The wall and bottom of the ladle were treated as stationary no-slip walls; the convection heat transfer coefficients applied to the lateral wall and bottom were 55 and 35 W/(m²/K), respectively. Since DA particles were continuously poured into the container from the lance, their initial speed and temperature were assumed to be fixed, and their initial particle size obeyed the Rosin-Lammer logarithmic distribution. The particle size ranges from 0.1 mm–1 mm, with an average particle size of 0.35 mm and a spread parameter of 3.5. For the DA particles, the reflection coefficient of the top surface of the ladle and all walls was 0.5. Usage of this assumption made the prediction results closer to the actual situation and helped one to understand particle motion better. In addition, during the stirring process, the particles escaped from the hot metal through the air-metal-hot metal interface for 5 s and then were removed.

4. Numerical Procedure

The ANSYS 19.2 commercial software was used for the numerical simulation. A user-defined scalar indicating the mass fraction of sulfur was set in the hot metal. In addition, the discrete phase scalar was also introduced to indicate the mass fraction of CaO in the desulfurization slag. The code developed by the author was used to numerically run the desulfurization kinetic model and CaO consumption rate, which were integrated into the software program.

The momentum, turbulent kinetic energy, specific dissipation rate, energy, and user-defined scalar equations were discretized using a second-order upwind scheme for higher accuracy. A PISO scheme was utilized for the pressure-velocity coupling. The modified high-resolution interface capturing method was adopted as a discretization scheme for the volume fraction analysis. The convergence criteria for the continuity, momentum, turbulent kinetic energy, specific dissipation rate, user-defined scalar, and volume fraction equations were set at 10⁻³, while that for the energy equation was 10⁻⁶.

After the grid-independent test, the average size of the six-sided grid was set to 25 mm. Due to the possible fluctuation of the liquid level under the lance, the area was encrypted. The total number of nodes was about 500000, achieving a reasonable balance between computational cost and accuracy. Table 1 lists other physical properties, geometric parameters, and operating conditions of the fluids used in this study.^{27,28,29,30,32,33)} A typical simulation scenario required about 800 CPU hours with a 0.0005 s time step, using a AMD Ryzen 93900x 12 cores processor.

Table 1. Geometric, physical, and technological parameters adopted in the numerical simulation.

Parameter	Value
Physical properties of hot metal
Hot metal density (kg·m−3)	7036
Hot metal viscosity (Pa·s)	0.0075
Thermal conductivity (W/(m·K))	36.3
Specific heat (J/(kg·K))	1.6
Surface tension (N/m)	1.7
Diffusion coefficient of sulfur (m2/s)	0.68×10−4·exp(0.005T/R)
Physical properties of DA particle
DA particle diameter (mm)	1.5
DA particle density (kg·m−3)	3000
Thermal conductivity of DA particles (W/(m·K))	3.5
Geometry and operating conditions
Ladle diameter (mm)	3856
Ladle height (mm)	4700
SM interface diameter (mm)	2000
Initial bath depth (mm)	3731
Impeller immersion depth (mm)	1833
Impeller rotation rate (rpm)	80
Gas flow rate (m/s)	100–180
Distance between the lance axis and the ladle center	0.53–0.84
Distance between the lance and the initial liquid level	0.11–0.22

5. Model Validation

To verify the current mathematical model, the same conditions were used as in the water model, as shown in Table 2. The water model’s vortex surface and particle distribution and those predicted by the numerical simulation at 140 rpm are depicted in Fig. 2. It can be seen that the surface shape of the vortex predicted by the model was consistent with the height of the water model. If the vortex did not reach the impeller bottom, most of the particles were already floating in the vortex. The simulation results of the vortex depth and height at different rotation speeds were the same as those measured in the water model, as shown in Fig. 3. The trend of the simulation results on vortex depth was consistent with the measured one: the maximum errors of ΔH₁ and ΔH₂ did not exceed 28 and 4.7 mm, respectively.

Table 2. Experimental conditions of the water model.

Parameter	Value
Vessel height (mm)	670
Vessel diameter (mm)	540
Water depth (mm)	500
Rotation speed (rpm)	60–260
Impeller height (mm)	141
Impeller diameter (mm)	206
Impeller width (mm)	65
Impeller immersion depth (mm)	250
Particle diameter (mm)	3
Particle density (g/cm3)	0.03

Fig. 2.

Comparison of vortex surface and particle distribution between the water model (a) and numerical simulation (b) predictions. (Online version in color.)

Fig. 3.

Comparison of simulated vortex depth and height with those measured in the water model. (Online version in color.)

Diagrams of vortex depth and height under different immersion depths are plotted in Fig. 3. It can be seen that the simulation results were consistent with the water model measurement results, and the maximum error was 5%. Therefore, the validity of the proposed mathematical model was proved.

6. Results and Discussion

6.1. Characterization of Flow Field

The velocity vector and temperature distribution cloud diagram of the hot metal at 500 s are depicted in Fig. 4. The state of the hot metal flow at 100 rpm of the stirring impeller was stable. Recently, Wang et al.¹⁴⁾ reported that the lance effect shifted the positions of the upper and lower vortex boundaries downward, and changed the flow field in the area below the lance; the hot metal temperature distribution in the container also changed, except for the bottom. In addition to the lower hot metal temperature, due to the downward shift of the eddy current boundary, the heat loss near the impact point increased, and the temperature dropped.

Fig. 4.

Flow pattern and temperature profile in the KR vessel at 500 s. (Online version in color.)

With increased distance between the lance and the hot metal surface, the hot metal fluctuated more intensively. At the same time, the larger angles between the gas incident direction and the hot metal surface induced the hot metal splashing phenomenon. As shown in Fig. 5, when the lance was located at the (0.84R; 0.11L) position, which corresponded to the minimal distance from the melt iron surface, and the carrier gas flow rate was 120 m/s, the hot metal fluctuated greatly at this position, and a large amount of gas overflew from the side.

Fig. 5.

The wave shape distribution of hot metal surface and velocity vector directly under the lance. (Online version in color.)

6.2. Distribution and Motion of DA Particles

The distributions of the mass fraction of sulfur in the hot metal and the mass fraction of CaO in the DA particles at 500 s are depicted in Fig. 6, with a tenfold magnification of DA particles. It can be seen that the reaction of sulfur in the hot metal with CaO in the DA particles caused the mass fraction of CaO to decrease gradually. A lower sulfur content was observed around the stirring blade was due to a large number of particles located here, while the presence of a cone-shaped desulfurization passivation zone was due to the low particle content at the bottom of the ladle. In addition, there were some rising bubbles.

Fig. 6.

Numerical simulation of DA particle distribution and sulfur content distribution diagram. (Online version in color.)

The particles moved from the lance with the carrier gas to the interface between the hot metal and the air, rushed into the hot metal for a short period, and rotated with the hot metal to the vortex depth. When the particles reached the bottom of the hot metal ladle, their path differed from that of directly injected particles: the latter mostly floated on the interface between the air and the hot metal, while the former either sank or floated with the hot metal upon reaching the vortex bottom.¹⁷⁾

6.3. Carrier Gas Flow Rate Effect

The gas injection was aimed at accelerating the DA particles, in order to overcome the surface tension and directly penetrate the hot metal surface. According to the findings of Nakai et al.,¹³⁾ the relationship between Da particle diameter and the critical velocity of penetration into the molten metal was considered. The acceleration effects of the carrier gas on the DA particles of different diameters at different lance positions varied, resulting in different DA velocities, as shown in Fig. 7. This led to different amounts of DA particles below the liquid level, which affected the final desulfurization effect. The changes in sulfur content in the four monitoring points are illustrated in Fig. 8. In the initial stage of desulfurization, the sulfur content in the bottom area decreased slowly. This shows that there was a small amount of DA in the bottom area, but the difference in sulfur content in different monitoring points gradually decreased with time.

Fig. 7.

The relationship between the DA particle diameter and the critical CaO velocity of hot metal penetration at a 140 m/s gas flow rate. (Online version in color.)

Fig. 8.

The evolution of sulfur content in four monitoring points with time. (Online version in color.)

To compare the final desulfurization effect under different operating conditions, the S content at 500 s was used to calculate the desulfurization rate and the ratio between the number of DA particles immersed in the hot metal at this time to the total number of DA particles. These ratios at different injection velocities are depicted in Fig. 9. The distance between the lance and the initial liquid level was 0.11L, and the distance from the ladle axis was 0.53R. With an increase in the carrier gas flow rate, the share of DA particles immersed in the hot metal gradually increased from the lowest value of 86.5 to 89%. A 10 m/s growth in the carrier gas flow rate increased the share of DA particles below the liquid level by 0.5%. Thereby, the content of DA participating in the desulfurization reaction was increased. The desulfurization rate trend, as shown in Fig. 9, shows that as the carrier gas flow increased, the desulfurization rate grew from 90 to 95%. Therefore, a larger carrier gas flow was more conducive to desulfurization. Compared with the study,¹²⁾ with the same particle physical properties and particle injection mass flow values, the desulfurization effect was stronger, and the desulfurization rate at 500 s was increased by about 4.65%.

Fig. 9.

Share of DA particles in the hot metal at different gas flow rates. (Online version in color.)

6.4. Effect of Powder Blasting Position

The desulfurization efficiency and the share of DA particles immersed in the hot metal versus lance height are plotted in Fig. 10. The distance between the lance and the ladle axis was 0.53R, and the carrier gas flow rate was 120 m/s. The difference between the maximum and minimum desulfurization rates was only 0.5%. In comparison, the difference in the shares of DA particles in the hot metal was about 0.3%, and no obvious trend was observed. It may be caused by the small velocity difference of DA particles in the distance range.

Fig. 10.

The effect of the distance between the lance and the ladle axis on the share of DA particles in the hot metal and desulfurization efficiency. (Online version in color.)

The effect of the distance between the lance and the ladle axis on the desulfurization rate is depicted in Fig. 11. The carrier gas flow rate at the lance position was 120 m/s, and the distance from the initial liquid level was 0.11L. With the increased distance from the ladle axis, the desulfurization rate gradually dropped, while the share of DA particles in the hot metal exhibited an upward trend. At the same distance and the initial liquid level height of 0.11L, different horizontal positions also implied different distances from the vortex. Farther from the ladle center, the interface between the hot metal and the air got closer, forcing makes the DA particles to reach the liquid surface at higher velocities, thus yielding larger desulfurization rates. For the lance location at 0.84R, as compared to that at 0.68R, the percentage of DA particles in the hot metal was also slightly reduced. This may be because the lance was too close to the hot metal surface, and the splashing phenomenon slightly reduced the number of particles immersed in the hot metal. The total desulfurization rate difference between 0.53R and 0.86R locations was only 0.3%, and the lance position closer to the ladle axis effectively reduced the hot metal splashing. Since the interface between the upper surface of the blade and the hot metal surface also had a certain range, it could not be ignored. The distance was restricted, so the lance should be arranged within a 0.53R–0.68R range. As the share of DA particles in the hot metal was higher at 0.68R, it tends to have a better desulfurization effect near 0.68R.

Fig. 11.

The effect of different lance heights on the share of DA particles immersed in the hot metal and desulfurization efficiency. (Online version in color.)

7. Conclusions

A numerical 3D transient coupled model of the KR desulfurization method was designed and applied to study two-phase flow, heat transfer, and DA particle motion behavior. The results obtained can be summarized as follows:

(1) The numerical simulation results were consistent with the water model’s ones. The carrier gas flow accelerated the DA particles when they reached the liquid surface, promoting their immersion in the hot metal.

(2) With an increase in the carrier gas flow rate, the ratio between the number of DA particles in the hot metal to the total number of sprayed DA particles gradually increased, and the desulfurization rate also gradually grew.

(3) The lowest sulfur content in the hot metal was observed near the impeller, while the highest sulfur content was observed in the inactive area at the bottom of the vessel containing colder hot metal. The sulfur content varied greatly at the beginning of the desulfurization stage, and the difference between different positions was small at 500 s.

(4) Changes in the lance position had little effect on the total desulfurization rate. The difference in the total desulfurization rate between 0.53R and 0.86R locations was only 0.3%, and the lance position closer to the ladle axis could effectively reduce the hot metal splashing, so the lance should be arranged at a 0.68R distance from the ladle axis.

Acknowledgments

The authors appreciate the financial support of this study by the National Natural Science Foundation of China (Grant No. 51974211) and the Special Project of Central Government for Local Science and Technology Development of Hubei Province of China (Grant Nos. 2019ZYYD003 and 2019ZYYD076). We also thank the Baoshan Iron & Steel Co., Ltd. for providing the supporting data.

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