Numerical Simulation of Powder Spraying at the Bottom of Converter Based on Gas-liquid-solid Coupling Model

Abstract

In this work, the powder injection process at the bottom of the converter was numerically simulated by establishing a coupled gas-liquid-solid mathematical model. The effects of powder injection speed, solid-gas ratio, particle size, and injection position on the trajectory and residence time of particles in the molten pool are studied. The discrete phase and continuous phase coupling solution method is used to analyze the change of the molten pool flow field after powder injection. It is found that increasing the spraying rate can reduce the particle concentration near the liquid surface from 2.3 kg/m³ to 1.18 kg/m³. Increasing the solid-gas ratio from 10 kg/m³ to 30 kg/m³ can increase the powder distribution ratio from 70.9% to 93.1%. The larger the size of the particles, the easier it is to stay near the liquid level, and the maximum can reach 2.13 kg/m³. Finally, it was also found that spraying powder at 0.7 R can make the powder more uniformly distributed in the molten pool.

1. Introduction

Nowadays the converter dephosphorization process mainly includes single-slag method, the dephosphorization furnace–decarburization converter duplex method, and double-slag method.^{1,2,3,4,5,6,7,8)} However, with the continuous improvement of the requirements for steel cleanliness, it is difficult for the current steelmaking process to control the phosphorus content below 50 ppm.^9,10) In order to develop steel grades for low temperature applications with a P content of only 20–30 ppm, it is still of great significance to continuously explore dephosphorization processes. Since the advent of converter bottom blowing limestone powder technology, it has attracted more and more attention in the industry for decades due to its metallurgical advantages such as high-efficiency dephosphorization, uniform molten pool stirring, and reduction of molten steel peroxidation.^11,12,13) In particular, Nuzaki¹³⁾ found that bottom blowing limestone powder mixed with fluorite in the Q-BOP process can make the dephosphorization rate reach 90%–95% in a short time. The main reason is that the removal of P occurs at the steel-slag interface, and the injection of limestone powder from the bottom can effectively increase the interface reaction area. And the limestone can absorb the excess heat in the converter and prolong the lower temperature state during the dephosphorization period, meanwhile greatly increase the stirring efficiency of the molten pool.^14,15,16,17)

Considering the complexity of limestone spraying at the bottom of the converter, some researchers have studied the movement characteristics of powder in the molten pool by means of physical simulation in recent years.^18,19,20) However, the approximate motion trajectory of the powder in the molten pool can be observed by means of physical simulation, but it is difficult to quantitatively analyze the distribution characteristics of particle concentration and the spatial distribution of particles of different sizes. In the numerical simulation of spray metallurgy, some scholars have studied in detail the influence of powder injection speed, particle size and spray gun structure on powder distribution.^21,22,23,24) However, the current research has only obtained the particle distribution and motion trajectories in the gas-solid two-phase state, and few reports have considered the effect of molten steel on powders. In the actual powder spraying, the solid particles will move in the molten pool under the simultaneous action of carrier gas and molten steel, and the whole process includes the interaction between the carrier gas and the molten steel in the continuous phase and the complex interaction between the continuous phase and the discrete particles.

Therefore, the current work aims to establish a gas-liquid-solid three-phase coupling model in the process of powder injection at the bottom of the converter through the method of numerical simulation, and analyzes the influence of powder spraying speed, solid-gas ratio, particle size and spraying position on the particle trajectory in the molten pool. Under different injection parameters, the residence time and concentration distribution of particles in the molten pool were discussed. Meanwhile, the effect of the spraying parameters on the flow field of the molten pool was revealed.

2. Mathematical Equations and Solutions

2.1. Assumption

For the three-phase interaction process of gas, liquid and solid in the molten pool, the following assumptions are made:

1. The molten steel is regarded as an incompressible liquid, and the bottom blowing gas is regarded as an ideal compressible gas;

2. The bubbles and particles in the molten pool are considered to be spherical, and the bubbles will not aggregate and break during the rising stage, and the particles will not collide and change the trajectory of motion;

3. The influence of the slag layer on the flow of molten steel and the movement of particles is ignored, and the liquid level is considered to be flat, and there will be no splashes of molten steel and particles;

4. The chemical reaction between the components of the molten steel and the particles is ignored, and only the movement and aggregation of the particles are studied;

5. The influence of temperature on the molten steel and particle movement is not considered.

2.2. Gas-liquid-solid Hydrodynamic Equation

2.2.1. Continuous Phase Equation

Regarding the description of the continuous phase, the Euler-Euler method has high accuracy. The state of carrier gas and molten steel is described by mass balance equation and momentum balance equation. The interaction force between the gas and liquid phases will be loaded on the source term of the momentum conservation equation.^25,26)

Mass conservation equation:   

$$\frac{\partial ({\rho }_{\mathrm{i}}{\alpha }_{\mathrm{i}})}{\partial \mathrm{t}}+\nabla \cdot ({\rho }_{\mathrm{i}}{\alpha }_{\mathrm{i}}{\overrightarrow{\mathrm{u}}}_{\mathrm{i}})=0$$(1)

where ρ_i is the density, α_i is the volume fraction, and ${\overrightarrow{\mathrm{u}}}_{\mathrm{i}}$ is the velocity vector.

Momentum conservation equation:   

$$\begin{array}{l}\frac{\partial ({\rho }_{\mathrm{i}}{\alpha }_{\mathrm{i}}{\overrightarrow{\mathrm{u}}}_{\mathrm{i}})}{\partial \mathrm{t}}+\nabla \cdot ({\rho }_{\mathrm{i}}{\alpha }_{\mathrm{i}}{\overrightarrow{\mathrm{u}}}_{\mathrm{i}}{\overrightarrow{\mathrm{u}}}_{\mathrm{i}})=\\ -{\alpha }_{\mathrm{i}}\nabla \mathrm{P}+\nabla \cdot \left[{\alpha }_{\mathrm{i}}{\mathrm{u}}_{\mathrm{e}\mathrm{f}\mathrm{f}}\cdot (\nabla {\overrightarrow{\mathrm{u}}}_{\mathrm{i}})+{(\nabla {\overrightarrow{\mathrm{u}}}_{\mathrm{i}})}^{\mathrm{T}}\right]+{\alpha }_{\mathrm{i}}{\rho }_{\mathrm{i}}\overrightarrow{\mathrm{g}}+{\overrightarrow{\mathrm{M}}}_{\mathrm{i}}\end{array}$$(2)

  

$${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}={\mathrm{u}}_{\mathrm{l}}+{\mathrm{u}}_{\mathrm{t}}$$(3)

  

$$\mu ={\alpha }_{\mathrm{s}}{\mu }_{\mathrm{s}}+(1-{\alpha }_{\mathrm{s}}){\mu }_{\mathrm{n}}$$(4)

  

$${\mu }_{\mathrm{t}}=\rho {\mathrm{C}}_{\mu }\frac{\mathrm{k}}{\epsilon }$$(5)

where μ_eff is the effective viscosity, u_l is the physical viscosity, u_t is the turbulent viscosity, P is the pressure between the gas and liquid phases, $\overrightarrow{{\mathrm{M}}_{\text{i}}}$ is the interaction force between gas and liquid.

The sum of the volume fractions of molten steel and nitrogen in the equation is equal to 1. Considering the momentum transfer from the bubble to the molten steel, it is necessary to add the gas-liquid interaction force $\overrightarrow{{\mathrm{M}}_{\text{i}}}$. It can be obtained by adding the force of the fluid acting on the bubble. In the Eq. (2), the interaction force is the momentum exchange source term. The drag force and turbulent dissipation force are used here, which have a great influence on the bubble agitating the molten steel.^25,27)   

$${\overrightarrow{\mathrm{M}}}_{\mathrm{i}}={\overrightarrow{\mathrm{M}}}_{\mathrm{l}}=-{\overrightarrow{\mathrm{M}}}_{\mathrm{g}}=({\mathrm{F}}_{\mathrm{D}}+{\mathrm{F}}_{\mathrm{T}\mathrm{D}})$$(6)

The drag force F_D usually occupies a dominant position in the force between the gas and liquid phases, and the general form of the force can be expressed as:   

$${\mathrm{F}}_{\mathrm{D}}={\mathrm{K}}_{\mathrm{g}\mathrm{l}}({\overrightarrow{\mathrm{u}}}_{\mathrm{g}}-{\overrightarrow{\mathrm{u}}}_{\mathrm{l}})$$(7)

  

$${\mathrm{K}}_{\mathrm{g}\mathrm{l}}=\frac{3{\alpha }_{\mathrm{g}}{\alpha }_{\mathrm{l}}{\rho }_{\mathrm{l}}{\mathrm{C}}_{\mathrm{D}}}{4{\mathrm{d}}_{\mathrm{g}}}\left|{\overrightarrow{\mathrm{u}}}_{\mathrm{g}}-{\overrightarrow{\mathrm{u}}}_{\mathrm{l}}\right|$$(8)

where K_gl is the momentum exchange coefficient between phases due to drag force, and d_g is the bubble diameter.

The turbulent pulsation of molten steel will have a greater influence on the bubble diffusion distribution, and the turbulent diffusion force can be expressed as:^25,28)   

$${\mathrm{F}}_{\mathrm{T}\mathrm{D}}=-{\mathrm{K}}_{\mathrm{g}\mathrm{l}}{\mathrm{u}}_{\mathrm{d}\mathrm{r}\mathrm{i}\mathrm{f}\mathrm{t}}$$(9)

where u_drift is the slip velocity, which represents the influence of liquid turbulent pulsation on the spatial distribution of bubbles.

2.2.2. Discrete Phase Equation

The movement behavior of particles in molten steel is described by Lagrangian method. Newton’s second law can be used to analyze the speed and displacement changes of particles under unbalanced forces, which makes each particle can be calculated in space and time.²¹⁾ During the movement of the particles in the molten steel, the most force they receive is the resistance brought by the molten steel, as well as their own gravity and buoyancy. In addition, the pressure gradient force and virtual mass force generated by the change of the liquid steel pressure and the secondary flow will also affect its trajectory.^22,29)

The force experienced by a single particle can be described as:   

$$\frac{\mathrm{d}{\mathrm{x}}_{\mathrm{p}}}{\mathrm{d}\mathrm{t}}={\mathrm{u}}_{\mathrm{p}}$$(10)

  

$$\frac{\mathrm{d}{\overrightarrow{\mathrm{u}}}_{\mathrm{p}}}{\mathrm{d}\mathrm{t}}=\frac{\overrightarrow{\mathrm{u}}-{\overrightarrow{\mathrm{u}}}_{\mathrm{p}}}{{\tau }_{\mathrm{r}}}+\frac{\overrightarrow{\mathrm{g}}({\rho }_{\mathrm{p}}-\rho )}{{\rho }_{\mathrm{p}}}+{\overrightarrow{\mathrm{F}}}_{\mathrm{p}}+{\overrightarrow{\mathrm{F}}}_{\mathrm{m}}$$(11)

where $\overrightarrow{\mathrm{u}}$ is the continuous phase velocity vector, ${\overrightarrow{\mathrm{u}}}_{\mathrm{p}}$ is the discrete particle velocity vector, ρ is the continuous phase density, ρ_p is the discrete particle velocity vector, $\frac{\overrightarrow{\mathrm{u}}-{\overrightarrow{\mathrm{u}}}_{\mathrm{p}}}{{\tau }_{\mathrm{r}}}$ is the resistance experienced by the particle, $\frac{\overrightarrow{\mathrm{g}}({\rho }_{\mathrm{p}}-\rho )}{{\rho }_{\mathrm{p}}}$ is the gravity and buoyancy experienced by the particle, ${\overrightarrow{\mathrm{F}}}_{\mathrm{p}}$ is the pressure gradient force experienced by the particle, ${\overrightarrow{\mathrm{F}}}_{\mathrm{m}}$ is virtual mass force.   

$${\tau }_{\mathrm{r}}=\frac{{\rho }_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}^2}{18\mu }\frac{24}{{\mathrm{C}}_{\mathrm{D}}{\mathrm{R}}_{\mathrm{e}}}$$(12)

  

$${\mathrm{R}}_{\mathrm{e}}=\frac{\rho {\mathrm{d}}_{\mathrm{p}}\left|\overrightarrow{\mathrm{u}}-{\overrightarrow{\mathrm{u}}}_{\mathrm{p}}\right|}{\mu }$$(13)

The drag coefficient can be expressed as:   

$${\mathrm{C}}_{\mathrm{D}}={\alpha }_1+\frac{{\alpha }_2}{{\mathrm{R}}_{\mathrm{e}}}+\frac{{\alpha }_3}{{\mathrm{R}}_{\mathrm{e}}}$$(14)

where α₁, α₂ and α₃ are constants.

Pressure gradient force:   

$${\overrightarrow{\mathrm{F}}}_{\mathrm{p}}=\frac{\pi {\mathrm{d}}_{\mathrm{p}}^3}{6}\nabla \mathrm{p}$$(15)

Virtual mass force:   

$${\overrightarrow{\mathrm{F}}}_{\mathrm{m}}={\mathrm{C}}_{\mathrm{v}}\frac{\pi {\mathrm{d}}_{\mathrm{p}}^3{\mathrm{p}}_{\mathrm{p}}}{6}\frac{\mathrm{d}({\overrightarrow{\mathrm{u}}}_{\mathrm{p}}-\overrightarrow{\mathrm{u}})}{\mathrm{d}\mathrm{t}}$$(16)

where C_v is the virtual mass force coefficient.

Through the Lagrangian method, the initial trajectory of a discrete particle can be obtained, and the kinetic energy and heat that the particle gains or losses from the continuous phase along the trajectory can also be calculated. In this work, only the momentum exchange between the two is considered. When the particle passes through each continuous phase control body, the momentum value transferred from the continuous phase to the discrete phase is solved by calculating the momentum change of the particle. The particle momentum change value is:   

$$\mathrm{F}=\sum \left(\frac{18\beta \mu {\mathrm{C}}_{\mathrm{D}}{\mathrm{R}}_{\mathrm{e}}}{24{\rho }_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}^2}({\mathrm{u}}_{\mathrm{p}}-\mathrm{u})+{\overrightarrow{\mathrm{F}}}_{\mathrm{p}}+{\overrightarrow{\mathrm{F}}}_{\mathrm{m}}\right){\mathrm{m}}_{\mathrm{p}}\mathrm{\Delta }\mathrm{t}$$(17)

where m_p is the mass flow rate and Δt is the time step.

2.2.3. Turbulence Model

For the turbulent motion of gas-liquid-solid coexistence in the converter, this work uses the standard k-ε model to describe, in which the turbulent kinetic energy k and the turbulent dissipation rate ε equation are expressed as:^30,32)   

$$\begin{array}{l}\frac{\partial (\rho \mathrm{k})}{\partial \mathrm{t}}+\frac{\partial (\rho \mathrm{k}{\mathrm{u}}_{\mathrm{i}})}{\partial {\mathrm{x}}_{\mathrm{i}}}=\\ \frac{\partial }{\partial {\mathrm{x}}_{\mathrm{i}}}\left[\left(\mu +\frac{{\mathrm{u}}_{\mathrm{t}}}{{\sigma }_{\mathrm{k}}}\right)\frac{\partial \mathrm{k}}{\partial {\mathrm{x}}_{\mathrm{j}}}\right]+{\mathrm{G}}_{\mathrm{k}}+{\mathrm{G}}_{\mathrm{b}}-\rho \epsilon -{\mathrm{Y}}_{\mathrm{M}}+{\mathrm{S}}_{\mathrm{k}}\end{array}$$(18)

  

$$\begin{array}{l}\frac{\partial (\rho \mathrm{k})}{\partial \mathrm{t}}+\frac{\partial (\rho \mathrm{k}{\mathrm{u}}_{\mathrm{i}})}{\partial {\mathrm{x}}_{\mathrm{i}}}=\\ \frac{\partial }{\partial {\mathrm{x}}_{\mathrm{i}}}\left[\left(\mu +\frac{{\mathrm{u}}_{\mathrm{t}}}{{\sigma }_{\epsilon }}\right)\frac{\partial \epsilon }{\partial {\mathrm{x}}_{\mathrm{j}}}\right]+{\mathrm{C}}_{1\epsilon }\frac{\epsilon }{\mathrm{k}}\left({\mathrm{G}}_{\mathrm{k}}+{\mathrm{C}}_{3\epsilon }{\mathrm{G}}_{\mathrm{b}}\right)-{\mathrm{C}}_{2\epsilon }\rho \frac{{\epsilon }^2}{\mathrm{k}}+{\mathrm{S}}_{\epsilon }\end{array}$$(19)

where G_k is the production term of k caused by the average velocity gradient, G_b is the production term of k caused by buoyancy, Y_M represents the influence of pulsation expansion, C_1ε, C_2ε, C_3ε, σ_k and σ_ε are constants.

2.3. Boundary Conditions and Solution Method

This work takes a 60 t converter in a steel plant as the research object, and uses ANSYS FLUENT 2020 r2 to solve the Euler-DPM coupling model to describe the phenomenon that high-speed nitrogen drives solid particles into the molten pool through the four symmetrical powder spray guns at the bottom of the converter. The geometrical dimensions and materials used for the calculation are shown in Table 1. As shown in Fig. 1, the inlet of the model adopts the velocity inlet and the nitrogen volume fraction at the inlet is set to 1. Refine the mesh at the entrance, and the velocity direction is the normal direction of the nozzle. The outlet of the model is set using UDF to allow gas to go out, and molten steel and discrete particles are not allowed to go out. At the model wall, the velocity perpendicular to the model wall is 0, and the component parallel to the wall adopts the non-slip boundary condition, and the standard wall function is used to deal with the flow near the wall. In order to reduce the computational cost, taking into account the symmetry of the computational domain, one-quarter of the model is taken as the computational domain. The normal gradient of all variables of the symmetry plane is 0, and the normal velocity is 0. The total number of grids in the computational domain is approximately 700000.

Table 1. Converter geometric parameters and material physical properties.

Parameter	Value
The diameter of the converter (m)	3.24
Depth of molten pool (m)	1.38
The diameter of spray gun (m)	0.018
The position of the spray gun	Symmetrical 4-hole arrangement
Density of molten steel (kg/m3)	7100
Surface tension coefficient of molten steel (N/m)	1.6
Viscosity of molten steel (kg/(m·s))	0.0055
Density of carrier gas (kg/m3)	1.25
Density of particle (kg/m3)	3500

Fig. 1.

Mesh and boundary conditions of the model. (Online version in color.)

The equations that need to be solved are the mass and kinetic energy conservation equations of the continuous phase, the standard k-ε equation describing the movement of molten steel, and the discrete phase equations of particles. Before calculating the coupling equation, the flow field of molten steel should be calculated for 20 seconds to obtain an initial continuous phase flow field. Then create a jet source to calculate the particle trajectory, thereby introducing a discrete phase in the computational domain. In the calculation of each jet source, the particle trajectory is calculated by the discrete phase equation according to the force of the particle in the flow field and the momentum and mass exchange source terms in each fluid calculation unit are updated. Next, use the obtained exchange source terms to recalculate the continuous phase equation. Then calculate the particle trajectory of the continuous phase after correction. The coupled calculation will not stop until the calculation result of the continuous phase does not change with the increase in the number of iteration steps. At this time, the trajectory of the discrete phase will not change.

Based on the hexahedral structure grid, the Phase Coupled SIMPLE algorithm is used to solve the coupling of pressure and velocity. Select the staggered pressure discrete format (PRESTO!) to obtain higher stability. A second-order upwind scheme was applied to calculate the momentum and mass equations. The convergence condition of the simulated solution is that the residual of energy was <10⁻⁶, and the residual of other variables were <10⁻⁴.

3. Results and Discussion

3.1. Model Validation

Figure 2 shows the schematic diagram of physical simulation experimental set. The following is the detailed information of the physical simulation process. Air supplied from air compressor is introduced to the converter, When the molten pool is stable, the powder spraying starts by switch on the valve of the powder spray tank. The carrier gas is adjusted by the flow meter, while the powder feeding speed is controlled by the pressure difference of the powder spray tank. Once the powder is entering the molten pool, high-solution pictures have been taken each half second by the camera. Thus, the powder spraying process of the converter at a flow rate of 353 m³/h, the solid-gas ratio of 50 kg/m³, and the particle size of about 0.15 mm can be simulated and recorded.

Fig. 2.

Schematic diagram of the process and equipment of the physical simulation. (Online version in color.)

Concentration distribution cloud diagrams of powders at different times can be obtained through numerical simulation. In order to verify the accuracy of the simulation model, compare its results with the results of previous physical simulations. Figure 3 shows the results of physical simulation and numerical simulation under the same conditions. It can be seen that at the initial state of 0.5 s, the powders under the two simulation methods have reached the liquid surface and spread to the edge of the liquid surface. Then in 1–1.5 s, the particles have spread downward following the molten steel. Afterwards in 2–2.5 s, the powder in the two ways has reached the bottom of the molten pool. The powder has already followed the molten steel and began to circulate in 3–3.5 s. The powder movement trajectory under the two simulation methods shows approximately the same results.

Fig. 3.

Comparison of the results of physical simulation and numerical simulation. (Online version in color.)

Image processing is performed on the results of the two simulation methods, and the longitudinal cross-sectional area of the powder distributed in the molten pool per 0.5 s can be obtained. Finally, the ratio of the longitudinal cross-sectional area of the powder distribution area to the longitudinal cross-sectional area of the entire molten pool can be calculated, and the powder distribution ratio is used to measure the degree of powder diffusion in the molten pool.^32,33) As can be seen in Fig. 4, as the powder spraying time increases, the powder distribution ratio under the two simulation methods gradually increases, and the powder fills the entire molten pool at about 3 seconds. The main reason for some differences is that in the case of physical simulation, some errors will be brought about due to the camera position and the light. Therefore, the results of the numerical simulation can be considered reasonable.

Fig. 4.

Comparison of powder distribution ratio between physical simulation and numerical simulation. (Online version in color.)

3.2. Movement Behavior and Residence Time of Particles in the Molten Pool

The particle concentration distribution and movement trajectory have a very important effect on increasing the steel-slag interface area and improving the reaction kinetics. This work mainly studied the distribution characteristics of particles steel under different injection speeds, solid-gas ratios, particle sizes and injection positions. Since the particles are driven by the carrier gas from the powder spraying tank into the molten pool, the spray velocity of the particles can be analyzed by the carrier gas flow rate at the bottom of the converter. The solid-gas ratio can be measured by the weight of the ore powder carried by the carrier gas. In this work, the influence of the three different solid-gas ratios of 10 kg/m³, 30 kg/m³ and 50 kg/m³ on the distribution of the ore powder has been studied. The reduction of the particle size is beneficial to increase the steel-slag reaction interface area and facilitate the progress of the reaction in the molten pool. In this work, t the three different sizes of particles (dimeter 0.05 mm, 0.15 mm and 0.5 mm) are investigated. And the influence of the blowing position on the particle trajectory, three arrangements of 0.3 R, 0.5 R and 0.7 R are selected. The parameters in each simulation are listed in Table 2.

Table 2. Single factor simulation scheme.

	Carrier gas flow (m3·h−1)	Solid-gas ratio (kg·m−3)	Particle size (mm)	Spraying position
M1	235	30	0.15	0.5 R
M2	353	30	0.15	0.5 R
M3	470	30	0.15	0.5 R
M4	353	10	0.15	0.5 R
M5	353	50	0.15	0.5 R
M6	353	30	0.05	0.5 R
M7	353	30	0.5	0.5 R
M8	353	30	0.15	0.3 R
M9	353	30	0.15	0.7 R

3.2.1. Effect of Powder Spraying Speed on Particle Trajectory

Figure 5 shows the morphological characteristics of particles moving in the molten pool at 5 s under M2 conditions. It can be seen that the speed of the particles is very large when they follow the carrier gas to the liquid surface. However, the velocity of the particles will decrease sharply after reaching the liquid surface. This can be attributed to the particles with an upward initial velocity at initial. When the particles reach the liquid surface, the carrier gas will leave the liquid surface, but the particles will still stay in the molten pool, so the particles can only diffuse around the liquid surface under the action of molten steel. At this time, the particles can no longer bring energy to the molten steel. Instead, the particles need to obtain the energy of the molten steel to move. After the particles near the surface of the molten steel accumulate to a certain concentration, the particles will follow the molten steel to move downward. A part of the powder will stay on the surface of the molten pool and react with the slag into the slag, and most of the remaining particles will be carried by the molten steel to the bottom of the molten pool and react with harmful elements.

Fig. 5.

The velocity (a) and motion trajectory (b) diagram of particles in the molten pool. (Online version in color.)

Figure 6 is a front view of the particle trajectory in the molten pool at different times. It can be observed that the particles have reached the position of the furnace wall at 1.5 s, and there has been a tendency to diffuse downward. However, the spraying direction of the spray gun is the normal direction of the bottom of the converter, so the particle-carrier gas flow is biased toward the center of the molten pool to impact the molten steel. This makes the average velocity of the flow field in the middle of the molten pool larger, and the particles reach the bottom of the molten pool faster. After 2 s, the particles near the furnace wall have begun to move downwards. At 5 s, the particles had reached the bottom of the converter, and the molten pool was already full of powder. It can be found from Fig. 7 that the concentration of particles is the largest when they follow the bubble column to the liquid surface. After reaching the liquid surface, the particles begin to spread around, which causes the local concentration decrease rapidly. And the concentration of particles on the surface of the molten pool is greater than that on the bottom, which indicates that particles are more likely to aggregate around the liquid surface.

Fig. 6.

The residence time and trajectory of particles at different moments of M2. (Online version in color.)

Fig. 7.

The concentration distribution of particles at different moments of M2. (Online version in color.)

Particles entering the converter at a certain initial velocity will cause a strong impact on the molten pool. And circulating molten steel will in turn have different effects on particle trajectories. As shown in the Fig. 8, the particle concentration cloud diagram obtained on the cross-section between the updrafts (YZ plane) can more intuitively analyze the movement of particles to the bottom of the molten pool under different powder injection parameters. And because the particle density is smaller, there is a tendency to stay near the surface of the molten steel. By quantitatively comparing the particle concentration on the line A near the liquid surface (Y = 1.35 m), the tendency of particles to stay on the liquid surface and enter the molten steel under different injection parameters can be analyzed.

Fig. 8.

The position of YZ plane, line A and line B in the molten pool. (Online version in color.)

Figure 9 shows the particle trajectory and concentration distribution in the molten pool at different spraying speeds at the 5th second. It can be found from Fig. 9(a) that as the powder spraying speed increases, the particle-carrier gas flow will stir the molten pool more strongly, which will make the particles spread over the entire molten pool faster. Figure 9(b) intuitively shows that the concentration of particles near the inner wall becomes smaller under the condition of M3.

Fig. 9.

Particle trajectory (a) in the molten pool and particle concentration (b) in the YZ section at different powder injection speeds. (Online version in color.)

It can be known from Fig. 10(a) that the particle concentration on the line A decreases as it moves away from the center of the molten pool. When the carrier gas flow rate is 470 m³/h, the particle concentration at the edge of the molten pool is 1.18 kg/m³, which is lower than the 2.3 kg/m³ and 1.39 kg/m³ at 235 m³/h and 353 m³/h respectively. This shows that increasing the spraying speed can effectively reduce the accumulation of particles on the liquid surface, which is conducive to more particles circulating and reacting in the molten steel. The particle concentration cloud image on the YZ section every 0.5 s can be simulated during the 5 s spraying process. The distribution area of the powder in the cross-section and the ratio of the powder area to the longitudinal cross-sectional area of the molten pool can be calculated by image processing respectively. This area ratio can be called the powder distribution ratio. It is possible to compare the efficiency of particles filling the whole molten pool under different processes through the powder distribution ratio. In Fig. 10(b), it can be found that the powder distribution ratio of M3 has reached 98.1% at 3 s, almost filling the entire molten pool, while M1 and M2 only reached 61.3% and 81.7% at this time. Therefore, increasing the blowing speed can make the particles in the molten pool more uniformly distributed, which is conducive to the rapid removal of harmful elements in the molten steel, and can also reduce the “concentration dead zone” in the molten pool.

Fig. 10.

The particle concentration (a) on the Z axis and the powder distribution area ratio (b) at different powder injection speeds. (Online version in color.)

3.2.2. Effect of Different Solid-gas Ratios on the Residence Time of Particles

The solid-gas ratio can control the powder feeding speed. When the spraying speed, particle size and spraying position are the same, this work has studied the distribution characteristics of the particles in the molten pool when the solid-gas ratio is 10 kg/m³, 30 kg/m³, and 50 kg/m³, respectively. As shown in Fig. 11(a), the movement trajectory of the particles in the molten pool under the conditions of M4, M2 and M5 does not change much, which shows that increasing the solid-gas ratio from 10 kg/m³ to 50 kg/m³ has little effect on the diffusion rate of the particles. However, increasing the solid-gas ratio has a great effect on the concentration distribution of particles. Figure 12(a) shows that the larger the solid-gas ratio, the greater the concentration of particles near the liquid surface. When the solid-gas ratio is 50 kg/m³, the highest concentration reaches 8.36 kg/m³, which is much higher than the concentration at 10 kg/m³ and 30 kg/m³. On the one hand, due to the increase in the mass of particles entering the molten pool within the same time, on the other hand, the diffusion rate of the particles has not increased. This causes the particle concentration gradient of the molten steel to be too high, and more particles stay near the surface of the molten steel. Therefore, it can be seen from Fig. 11(b) that when the solid-gas ratio reaches 50 kg/m³, the area where the particle concentration in the middle of the molten pool exceeds 6 kg/m³ is much larger than that at 10 kg/m³ and 30 kg/m³. This will not only cause the local concentration of the molten pool to be too high, which will affect the reaction effect, but also cause the local molten steel temperature to drop too much, making the smelting effect worse. However, it can be seen from Fig. 12(b) that within 4.5 s, the powder distribution ratios of M4, M2 and M5 reached 70.9%, 93.1% and 97.4%, respectively, which increasing the solid-gas ratio can effectively promote the increase of the particle concentration in the molten pool. However, when the solid-gas ratio is increased from 30 kg/m³ to 50 kg/m³, the powder distribution ratio only increases by 4.3%, so this effect becomes insignificant when the solid-gas ratio is large. Therefore, the solid-gas ratio should be selected reasonably according to the actual process. When the amount of powder spraying is relatively small, the solid-gas ratio should be appropriately reduced, which is conducive to the uniform distribution of particle concentration and reduces local aggregation of particles. However, if the amount of powder sprayed is large, increasing the solid-gas ratio can complete the powder spraying in a short time, which is beneficial to shorten the smelting cycle.

Fig. 11.

Particle trajectory (a) in the molten pool and particle concentration (b) in the YZ section at different solid-gas ratios. (Online version in color.)

Fig. 12.

The particle concentration (a) on the Z axis and the powder distribution area ratio (b) at different solid-gas ratios. (Online version in color.)

3.2.3. Effect of Different Particle Sizes on the Residence Time of Particles

The particle size has great influence on the movement characteristics of the particles in the spray gun.²¹⁾ In this work, the influence of particle size on its trajectory and distribution characteristics after entering the molten pool was studied. In Fig. 13 the particles are more distributed at the bottom of the converter under the condition of M6 than those in M7, which shows that smaller particles are beneficial to the diffusion in the molten pool. In Fig. 14(a), it can also be observed that as the particle size increases, the particles are more likely to accumulate on the liquid surface near the furnace wall, and the particle concentration below the molten pool is smaller. And under the conditions of M7, the particle concentration near the furnace wall reached the highest 2.13 kg/m³, which was higher than the 1.68 kg/m³ and 1.80 kg/m³ under the conditions of M6 and M2. This shows that the increase in particle size will make it more difficult for the particles to follow the movement of the molten steel, which is not conducive to the chemical reaction of the particles. The possible reason is that the larger the size, the greater the buoyancy of the particles, or the increase in the mass of a single particle will increase the kinetic energy transferred from the molten pool to the particles, which will make the particles easier to aggregate near the liquid surface. From the distribution characteristics of the particles at different times in Fig. 14(b), it can be found that during the particle-carrier gas rising stage, the size has almost no effect on the particle distribution. At the 5th second, the powder distribution ratios from small to large particles were 96.8%, 96.6%, and 93.3%, respectively. The diffusion rate of particles under the condition of M7 is relatively slow, but the difference is only 3.5% compared with the distribution ratio of M6.

Fig. 13.

Particle trajectory (a) in the molten pool and particle concentration (b) in the YZ section of different particle sizes. (Online version in color.)

Fig. 14.

The particle concentration (a) on the Z axis and the powder distribution area ratio (b) of different particle sizes. (Online version in color.)

3.2.4. The Effect of Spray Position on Particle Distribution

The injection position determines the initial distribution position of the particles in the molten steel, which can greatly optimize the distribution of particles. In this work, the symmetrical arrangement of four holes located at 0.3 R, 0.5 R and 0.7 R was studied respectively. Figure 15(a) shows that the four bubble columns are far apart at M9, which greatly reduces the energy offset between the airflows, and makes the particles reach the bottom of the molten pool faster. And it can be seen that the powder spraying at 0.7 R can make the powder more uniformly distributed in the molten pool from Fig. 15(b). From Fig. 16(a), it can be seen that the particle concentration near the liquid surface under the condition of M8 reaches 6.32 kg/m³, which is much higher than 4.74 kg/m³ at M2 and 4.51 kg/m³ at M9. It can also be found from Fig. 16(b) that at the 5th second, the powder distribution ratio of M9 is 97.7%, which is higher than 85.6% of M8. The distribution ratio of powder spraying at 0.5 R is only 1.1% different from that at 0.7 R. However, the powder movement rate of M9 is always faster than that of M2 during the whole process. Therefore, because the arc-shaped bottom surface of the converter makes the airflow inclined to rise, the powder spraying away from the center of the bottom of the converter is more conducive to the uniform distribution of powder in the molten pool.

Fig. 15.

Particle trajectory (a) in the molten pool and particle concentration (b) in the YZ section under different spraying positions. (Online version in color.)

Fig. 16.

The particle concentration (a) on the Z axis and the powder distribution area ratio (b) of under different spraying positions. (Online version in color.)

3.3. The Influence of Powder Spraying on the Flow Field of the Molten Pool

After the particles are carried into the molten pool by the carrier gas, the molten steel will have a great influence on the movement trajectory and distribution of the particles. However, due to the coupling effect of discrete particles and continuous phase, the particles will also have a certain effect on the molten steel. In this work, the effect of different spraying parameters on the molten pool was studied. In Fig. 8, the molten steel velocity on the B line is used to compare the impact effect of different powder spraying methods on the continuous phase. Figure 17 shows that the velocity of molten steel above the blowing position is the largest under any condition, and the velocity begins to decay when it is far from the particle-carrier gas flow.

Fig. 17.

The influence of powder injection parameters on the velocity field of the molten pool. (Online version in color.)

Figure 17(a) shows that under M3 conditions, the maximum velocity of molten steel on the surface of the molten pool reached 3.15 m/s, which was much higher than 1.73 m/s at M1 and 2.50 m/s at M2. This is because the kinetic energy carried by the high-velocity particle flow is greater, and the particle-carrier gas flow has a larger impact surface on the molten pool than pure gas. These reasons can effectively strengthen the stirring of the molten pool and promote the reaction at the steel-slag interface. From Fig. 17(b), it can be found that increasing the solid-gas ratio from 10 kg/m³ to 50 kg/m³ can strengthen the stirring of the molten steel, but the effect of improvement is not significant, only an increase of 0.06 m/s. In addition, Li’s research has found that the mixing time is basically no longer shortened after the solid-gas ratio reaches 9.¹⁸⁾ Therefore, when there are fewer particles to be sprayed, a relatively low solid-gas ratio can shorten the mixing time and prolong the impact of the particle-carrier gas on the molten steel. Reducing the particle size is beneficial to increase the area of the reaction interface, however, it can be found from Fig. 17(c) that the particle size has a negligible effect on the molten steel. Changing the position of the particles impacting the molten pool not only has a great impact on the distribution of the particles, but also has a non-negligible effect on the molten pool. It can be seen from Fig. 17(d) that the closer the injection position is to the furnace wall, the faster the molten steel moves. Even though the velocity at the center of the molten pool is slightly reduced, the velocity above the bubble column reaches 3.0 m/s, which is much greater than the 1.89 m/s at M8. This shows that when the blowing position is located at 0.7 R, the kinetic energy loss between the four airflows is much lower than that of spraying at 0.3 R, and most of the kinetic energy is transferred to the molten steel.

4. Conclusion

(1) Through the physical experiment of powder spraying at the bottom of the single hole of the converter, it is found that the movement trajectory and distribution characteristics of the particles in the molten pool are consistent with the model results, which verifies the rationality of the numerical simulation.

(2) The effect of the spraying parameters on the powder distribution in the molten steel is studied. It is found that increasing the spraying speed can effectively increase the movement speed of particles in the molten pool, and can also reduce the particle concentration near the liquid level from 2.3 kg/m³ to 1.18 kg/m³. Increasing the solid-gas ratio from 10 kg/m³ to 30 kg/m³ can effectively increase the powder distribution ratio, but the change from 30 kg/m³ to 50 kg/m³ is not significant. The larger the size of the particles, the easier it is to stay near the liquid surface, and the concentration can reach 2.13 kg/m³. Finally, it was also found that spraying powder at the position of 0.7 R at the bottom can make the powder distribution more uniform.

(3) By studying the flow field of the molten pool, it is found that increasing the injection speed and the bottom spraying position far from the center of the molten pool will greatly improve the flow field of the molten pool, which can be increased to 3.15 m/s and 3.0 m/s, respectively. After the solid-gas ratio is increased to a certain level, the stirring effect on the flow field will not be greatly improved. After increasing from 30 kg/m³ to 50 kg/m³, it only increases by 0.06 m/s. The particle size has a negligible effect on the speed of the molten pool.

Acknowledgment

The authors are grateful for the financial support of this work from the National Natural Science Foundation of China (No. 51922003, FRF-TP-19-004C1).

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