Fluid Flow Characteristic of EAF Molten Steel with Different Bottom-Blowing Gas Flow Rate Distributions

Abstract

As an efficient stirring method, bottom-blowing technology was applied in the present electric arc furnace (EAF) steelmaking process to improve the dynamic conditions of the molten steel. This article describes the development of a numerical model to simulate the 3D multiphase flows (gas, steel, and slag). Comparisons among uniform and non-uniform (linear and triangle distributions) bottom-blowing gas rate arrangements were performed with both metallurgic and dynamic parameters obtained from the numerical simulation process and separated liquid steel analysis. The numerical simulation results indicated that the bottom-blowing scheme with the gas rate in a linear change distribution had the best stirring effects in the molten bath. In addition, the dynamic conditions in the molten bath were worse when the bottom-blowing gas rate change was focused on the nozzle near the eccentric bottom tapping area. Furthermore, water model and industrial experiments were performed. For this purpose, 120 sets of heat industry data were collected in the 100 t EAF steelmaking process. The results showed that the non-uniform bottom-blowing scheme is more able to improve the dynamic conditions of the molten bath compared with the conventional uniform gas rate distribution, which further validated the reliability of the present numerical simulation results.

1. Introduction

As one of the two main steelmaking methods, electric arc furnace (EAF) steelmaking has many advantages, such as low investment, low cost, and environmental safety.¹⁾ In the modern EAF steelmaking process, the improvement of stirring energy is essential for obtaining better-quality steel with a short production time.^2,3,4,5) However, the special geometric structure of EAF³⁾ limits the intensity of oxygen stirring and results in molten bath stirring, which is insufficient. In order to improve the metallurgical reaction rate, promote molten bath fluid flow, and remove non-metallic inclusions, bottom-blowing technology^6,7,8) for the EAF steelmaking process has been developed.

In recent years, the bottom-blowing technology for EAF steelmaking has been widely investigated by means of water models and numerical simulation. At the same time, investigations on industrial applications of bottom-blowing technology have been reported by several researchers. Li et al.⁹⁾ studied the effects of the number and position of bottom-blowing nozzles on the dead zone area. They found that an appropriate number and distribution of nozzles can significantly improve the molten bath fluid flow. Afterwards, Ma et al.¹⁰⁾ studied the specific differences between with and without bottom-blowing technology. In their works, the velocity distribution of the fluid was obtained by computational fluid dynamics (CFD) software. The authors’ research showed the middle and bottom fluid in the molten bath with bottom-blowing could be driven by the rising gas and fluid that make the velocity and temperature distribution of the molten bath more homogeneous compared with that of without bottom-blowing. Later, Liu et al.^7,11) analyzed the effects of various positions of the nozzle on the velocity distribution and mixing time in the molten bath using the numerical simulation method. In addition, Liu et al.¹²⁾ applied the switch of nitrogen and argon as comprehensive utilization in the bottom-blowing device. They found that this method is useful for improvement of the desulphurization rate, adjustment of nitrogen content at the endpoint, and reduction of smelting time. Furthermore, Wang et al.^13,14) utilized CO₂ as a bottom-blowing gas in the EAF steelmaking process. The excess CO₂ was found to promote the slag-metal reaction rate and reduce the FeO content in slag and a good smelting environment was created. Recently, the temperature distribution of the molten bath was studied by Yigit.¹⁵⁾ In summary, the effects of the number and position of nozzles on the flow characteristic of fluid are the focus of published articles. However, few researchers have analyzed the effects of different bottom-blowing gas flow rate distributions on fluid flow in an eccentric bottom-tapping (abbreviated to “EBT”) EAF and the injection mechanism of bottom-blowing in EAF steelmaking. Although in the early study of this kind of bottom-blowing adjustment, the molten steel fluidity was promoted with the increasing gas rate at EBT area,¹⁶⁾ providing applicable probabilities, it required an additional gas input, increasing potential problems in the bottom-blowing management.

In this paper, the fluid flow of the molten bath with bottom-blowing in EAF steelmaking was investigated using numerical simulation and validation, including water model and industrial experiments. Firstly, the effects of the bottom flow rate distribution on the fluid flow for a 100 t industrial EAF were simulated and analyzed. Then, the stirring energy with various bottom flow rates was analyzed by multiple indicators, such as velocity, dynamic parameters, and dead zone. Apart from the whole bath indicators, a separation based on the bottom nozzles distribution was brought out, with corresponding flow improved steel volumes comparison. Finally, based on the simulation results, the related scheme was applied in a water model and a 100 t industrial EAF. The metallurgical indicators, endpoint slag composition, and endpoint carbon-oxygen equilibrium were obtained and compared.

2. Computational Model

2.1. Governing Equations

In this section, equations determining the basic numerical algorithm, including the transfer of mass, momentum, and energy, are introduced. Establishments of equations were under the following assumptions:

1. Gas and liquid phases were respectively considered as incompressible ideal gas and incompressible Newtonian fluid. Influences of chemical reactions and the expansion of gas during the steelmaking process were not involved;

2. The composition of each phase was considered homogenized, thus viscosity and surface tension were considered as constant;

3. Only full turbulence existed, the standard wall function was applied, as well as the nonslip wall condition.

In the present work, the volume of the fluid model (VOF)¹⁷⁾ was applied to meet the demand of multiple phases calculation. Each phase in VOF has distributed a respective volume fraction. The sum of the phase volume is represented by the following equation and equal to 1.   

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

According to the volume average method, correlative intensive property parameters in this system were accumulated by volume fraction and the parameter value of each phase. Therefore, the effective parameter was obtained. The density of the gas–slag–steel system can be expressed by Eq. (2):   

$$\rho =\sum _{l=1}^n{\alpha }_l{\rho }_l,$$(2)

Where α_l and ρ_l (l represents gas, slag, and molten steel phase) represent the volume fraction and density of the phase, respectively.

Based on the above volume distribution principle, mass transfer within this three-phase system can be expressed by Eq. (3):   

$$\frac{1}{{\rho }_i}\left[\frac{\partial }{\partial t}({\alpha }_i{\rho }_i)+\nabla \cdot ({\alpha }_i{\rho }_i{u}_i)\right]=S_{{\alpha }_i}+{\sum }_{i=1}^n(m_{ji}-m_{ij})$$(3)

where t is the time, s; u represents the velocity components in the i direction, m/s; m is the mass transfer magnitude, kg, where the first of the two subscript symbols means the source phase and the second one means the target phase; m_ji is the mass transferred from the jth phase to the ith phase; and S_αi is the user-defined source term.

The momentum transfer conservation equation can be expressed by   

$$\frac{\partial }{\partial \text{t}}(\rho \overrightarrow{u})+\nabla \cdot (\rho \overrightarrow{u}\overrightarrow{u})=-\nabla P+\nabla \cdot \left[\mu \left(\nabla \overrightarrow{u}+\nabla {\overrightarrow{u}}^T\right)\right]+\rho \text{g}+\overrightarrow{F}$$(4)

Where u is the fluid instantaneous velocity, m/s; P is the statistic pressure on the micro-body, 10⁶ Pa; μ is the dynamic viscosity, Pa∙s; g is the volume force formed by gravity, N; and F is a resultant force outside of the system, N.

The energy transfer equation is shown below:   

$$\frac{\partial (\rho E)}{\partial t}+\nabla \cdot (u(\rho E+p))=\nabla \cdot (k_{eff}\nabla T)+S_h$$(5)

where E_i is the energy of each phase (J), the magnitude of which was based on the specific heat and temperature. Effective thermal conductivity k_eff [W/(m·K)] and density ρ (kg/m³) were shared among every phase. Additionally, S_h (J) is another user-defined source term and decided by radiation heat transfer and other heat sources.

For the energy involved in the continuum, the algorithm in the VOF model was based on the mass average method and can be shown as the following equation:   

$$E=\frac{\sum _{i=1}^n{\alpha }_i{\rho }_i{E}_i}{\sum _{i=1}^n{\alpha }_i{\rho }_i}$$(6)

2.2. Turbulence Model

The standard k-ε model was finally chosen for this calculation according to the more accurate simulation of fully turbulent flow. Turbulence kinetic energy k (J) and turbulence dissipation rate ε (%) were the target parameters and are expressed by the following equations:   

$$\begin{array}{l}{\displaystyle \frac{\partial (\rho k)}{\partial t}}+{\displaystyle \frac{\partial (\rho k{v}_i)}{\partial x_i}}=\\ {\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right)\cdot {\displaystyle \frac{\partial k}{\partial x_i}}\right]+G_k+G_b-\rho \epsilon -Y_M+S_k\end{array}$$(7)

  

$$\begin{array}{l}{\displaystyle \frac{\partial (\rho \epsilon )}{\partial t}}+{\displaystyle \frac{\partial (\rho \epsilon u_i)}{\partial x_i}}=\\ {\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial k}{\partial x_i}}\right]+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}(G_k+C_{3\epsilon }{G}_b)+C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}+S_{\epsilon }\end{array}$$(8)

where ρ is the gas density, kg/m³; σ_k and σ_ε are turbulence Prandtl numbers of k and ε, which are constants with a magnitude as 1.0 and 1.3, respectively; G_k and G_b represent the turbulence kinetic energy respectively generated by the average velocity and buoyancy, J; constants C_1ε, C_2ε, and C_3ε are 1.44, 1.92, and 0.8, respectively; Y_M is the compressible turbulence pulsation of diffusion, which is dimensionless, and in the present case, Y_M equals to zero; and S_k and S_ε represent the user-defined source terms, J.

2.3. Geometry Structure of EAF

The EAF geometry structure with a capacity of 100 tons applied in this numerical simulation, together with prototype parameters, is shown in Fig. 1. Three bottom-blowing nozzles are illustrated as green circles. The diameters of the two sectors are shown in the side view, whose angles are shown in the top view.

Fig. 1.

Geometry construction of 100 t EAF. (Online version in color.)

2.4. Numerical Simulation Settings

The mesh model and numerical calculation settings are introduced in this section. The mesh was drawn with a total of around 550000 grids. Then, the coarse mesh (around 450000 grids) and the fine mesh with around 650000 grids were applied to testify the mesh independent, results are shown in Fig. 2(b). It could be concluded that the mesh with 550000 grids can satisfy the results accuracy and reduce the calculation time. Fluid parameters are shown in Table 1.¹⁸⁾ The three bottom nozzles were set as the mass flow inlet, and the upper face of the mesh was set as the outlet with the category pressure-outlet.

Fig. 2.

Mesh model (a) and the mesh independent assessment (b). (Online version in color.)

Table 1. Fluid parameters applied in the present calculation.

Items	Molten Steel	Liquid Slag	Nitrogen	Air
Viscosity (kg/m/s)	0.0065	0.35	1.663 × 10−5	1.789 × 10−5
Density (kg/m3)	7200	3000	1.138	1.25
Thermal conductivity (W/m/K)	15	1.2	0.0242	0.0242
Specific heat (J/kg/K)	670	1200	1040.67	1006.43
Surface tension (N/m)	1.6	0.4	＼	＼
Temperature (K)	1873	1873	300	300

The pressure-velocity coupling calculation was carried out using the PISO algorithm. Each calculation interval was regarded as convergent when the residuals of energy were less than 10⁻⁶, and the other dependent variants were all less than 10⁻³. A 30-s transient calculation was arranged to ensure that the bath was fully stirred within a certain mixing time. The global Courant number was kept at 2. According to Eq. (9), the time of each calculation interval was more or less than 10⁻⁴ s.   

$$\mathrm{\Delta }{t}_{global}={\displaystyle \frac{CF{L}_{global}}{max\left(\sum {\displaystyle \frac{outgoing\mathrm{\hspace{0.17em} }fluxes}{volume}}\right)}},$$(9)

Where CFL_global represents the courant number value and the ratio $\sum {\displaystyle \frac{outgoing\mathrm{\hspace{0.17em} }fluxes}{volume}}$ is calculated for each cell, which is dimensionless.

The gas rate distribution schemes applied in the present study are shown in Table 2. Abbreviations of each scheme are listed in the brackets on account of the bottom-blowing gas distribution features. In this study, the results of all bottom-blowing schemes were the average of several identical calculations.

Table 2. Simulation experiment schemes.

Schemes (L/min)	Nozzle. 1	Nozzle. 2 (EBT)	Nozzle. 3
Uniform bottom-blowing (UB)	133	133	133
Linear distribution 1 (L1)	186	133	80
Linear distribution 2 (L2)	80	133	186
Triangle distribution 1 (T1)	106	186	106
Triangle distribution 2 (T2)	160	80	160

3. Results and Discussions

3.1. Numerical Experiments

3.1.1. Bath Overall Improvements Analysis

(1) Velocity Distribution

Velocity distributions at 0.2, 0.4, and 0.6 meters from the slag–steel interface cross-section were shown in Fig. 3, with a velocity range from 0 m/s to 0.3 m/s. The average velocity comparison of each cross section is presented in Table 3. Generally, molten steel movements near the surface were better than those near the bottom, suggested by the fewer number of areas of a blue color, because the bottom gas was continuously driven by the buoyancy, and the speed reached the highest value when it was near the surface of the molten steel. The molten steel near the furnace wall flowed slower than that in the bath center, caused by the friction with the wall. With the increase of gas flow rates from bottom nozzle 1, the flow of molten steel was improved.

Fig. 3.

Velocity courant of the cross-section at different distances from the slag–steel interface. (Online version in color.)

Table 3. Average velocity comparison of each cross-section (10⁻² m/s).

Distance (m)	UB	L1	L2	T1	T2
0.2	1.985	2.154	2.170	1.981	2.064
0.4	1.845	2.023	2.007	1.836	1.915
0.6	1.871	2.032	2.012	1.823	1.885
0.8	1.913	2.073	2.117	1.832	1.908
Average	1.9035	2.0705	2.0765	1.868	1.943

As shown in Fig. 3 and Table 3, the velocity distributions in scheme T1 suggested that the single concentrated kinetic energy was severely dissipated by the surroundings. Merely increasing the gas rate of the eccentric nozzle was not efficient and should be abandoned. It should be noted that schemes L1 and L2 illustrated a better velocity distribution compared with the other schemes. This is because nozzle 1 is isolated on the right half of the bath of the EAF, and the collision in the radial direction was weakened. Simultaneously, the radial kinetic collision is strengthened in the bottom-blowing scheme UB, T1, and T2, resulting in a slightly worse flow distribution than L1 and L2. In summary, under some equal bottom-nozzle gas flow rate arrangements, the stirring effects of bottom-bowing that were dragged by the kinetic energy dissipation resulted from the opposite radial flow direction of the bath continuum. The application of a non-uniform bottom gas rate could weaken this defect and improve the bath dynamic condition.

Also, the slow flow regions, in which the velocity of molten steel was nearly motionless, of scheme UB, T1, and T2, appeared in the EBT area. This is because the molten steel in the EBT area is remote from the bottom nozzles, and kinetic transfer is severely attenuated. The continuum circulation covers the largest distance. Moreover, the kinetic energy dissipation results in an unsatisfied velocity distribution of molten steel in the cross-section paralleled to the bath surface. It is worth mentioning that the slow speed region in scheme UB shows the worst velocity distribution, while the gas flow rate of bottom nozzle 2 in scheme T2 is set lower than the one in scheme UB.

For further comparison of the influence of each bottom-blowing scheme on the low-speed region (named after the ‘dead zone’), the volume of the dead zone, of which the velocity is lower than 0.0008 m/s, was obtained from each scheme, to assess the bottom-blowing effects. Meanwhile, the average fluid flow of the molten bath and maximum slag height were applied to suggest the overall agitation effects on the molten bath. The comparison of those parameters mentioned above among different bottom-blowing schemes is presented in Fig. 4.

Fig. 4.

Changes of maximum slag height, average flow fluid of the molten bath, and volume of the dead zone in the molten bath. (Online version in color.)

In general, it can be concluded that the molten bath average fluid flow velocity increases and the dead zone volume decrease with an increasing bottom-blowing gas flow rate. Some properties have been concluded in Table 4. According to the comprehensive comparison of various kinetic indicators, the schemes L1 and L2 can obtain better mixing effects in the molten bath than UB, T1, and T2.

Table 4. Properties of the molten bath parameters.

Categories	Items	Value	Schemes	Maximum slag height (mm)
Linear distribution	Maximum velocity	2.5 × 10−2 m/s	L1	111.7
	Minimum dead zone volume	0.14 m3	L2	148.6
Triangle distribution	Minimum velocity	1.6 × 10−2 m/s	T1	98.7
	Maximum dead zone volume	0.57 m3	T2	201.3

(2) Dynamic Parameter Analyses

To clarify and quantify the kinetic effect of each scheme, several dynamic parameters were applied during the entire calculation. The velocity and dynamic pressure of the slag–steel interface, the radial velocity of molten steel, and the dynamic pressure of the whole bath were obtained per calculation interval and were used to record the trends and calculate the average magnitude. Figure 5 shows the slag–steel interface velocity distribution of uniform bottom-blowing, where the straight red line represents the mean average velocity. For each scheme, the number of calculations was over 250000. In the early calculation process, the velocity increased abnormally, caused by the unstable change relative to the initial state of the system when the first bottom gas bubble reached the interface. Additionally, a sharp velocity increase was applied to avoid a calculation crash.

Fig. 5.

Process data of one dynamic parameter. (Online version in color.)

The mean velocity (red line) was used to conduct a lateral comparison among blowing schemes and shown in the figure. Apparently, the mean velocity could not represent the velocity of slag–steel under uniform bottom-blowing because the early high-speed data improved the mean value non-ideally in terms of the means of the weighted average algorithm. As the weight of each interval was difficult to define, the effective mean velocity (blue line) that calculated the average value after the 50000th interval was proposed to represent the interface velocity more accurately. Thus, several dynamic parameters of the molten bath are shown in Fig. 6.

Fig. 6.

Dynamic data comparison of all bottom-blowing schemes. (Online version in color.)

For scheme L2, all four dynamic parameters are slightly lower than those in schemes UB and T2. However, scheme L2 can achieve a better average fluid flow and a smaller dead zone in the molten bath, which are key indicators in the smelting process, than those of schemes UB, T1, and T2. In consideration of all technical indicators, especially the minimum dead zone volume, the bottom gas flow rate distributions in scheme L2 can achieve better efficient bath agitation than those in schemes UB, T1, and T2. Also, better active interaction between slag and molten steel was found in scheme L1 than that in scheme L2, which agrees well with the maximum slag height comparison. This suggests that some of the kinetic energy of the bottom gas from nozzle 1 was not participating in the velocity improvement of molten steel, despite the average velocity of the molten bath. It could be possible that the slight decrease in the gas flow rate in nozzle 1 did not affect the velocity distributions of molten steel significantly.

The average velocity of the slag–steel interface is presented with four significant digits. Furthermore, parameters of scheme T1 suggest an interaction between gas and molten steel, even slag, which is the worst one, resulting from severe kinetic energy collision in the radial direction. This means that in order to improve the molten steel circulation in the EBT area, a sole increase in gas flow rates near this region is not effective.

For the bottom-blowing scheme T2, dynamic parameters, except for the average axial velocity of molten steel, are better than those of scheme UB owing to the good agitation in the main part of the bath. However, the poor gas flow rates in bottom nozzle 2 caused a bad molten steel fluid flow in the EBT area, which led to the maximum dead zone volume of approximate 0.55 m³, while the average fluid flow of the molten bath was close to the one of UB scheme. Thus, it is crucial to calculate the bath mixing time considering both the average velocity of the molten bath and the dead zone volume. Besides, from the maximum slag height, it could be seen in scheme T2 that an insufficient gas-steel kinetic energy transfer existed during the bottom-blowing process. To save the agitation energy, the difference between nozzle 2 and the other two nozzles in the main region should be controlled to a certain degree.

3.1.2. Separated Liquid Steel Analysis

Aside from the whole influences on the molten bath, the non-uniform bottom-blowing is considered to have individual impacts on the different regions near the three bottom nozzles. The separation of molten steel was brought out as an indicator to investigate how the non-uniform gas rates help in improving bath fluidity. The separation methodology is by drawing the angular bisector of each angle that was formed from the lines of different nozzles to furnace central point. The separated regions were named correspondingly with the nozzle number, as shown in Fig. 7(a). Right to it are the cross-sections at 0.2 meter below the liquid steel surface, inserted with streamlines and Parts boundary lines. The streamlines represent the path of the continuums at the edge of the furnace, and the arrows on the streamlines represent the direction of every continuum. It could be concluded that the surrounding continuum moves toward the center area and is slightly rotated. Some move to the high-speed center and ends up moving, while some are influenced by the resultant force of the three bottom gases and gather at the middle area of every second high-speed area.

Fig. 7.

Region separation (a) and separation with streamlines in schemes (b). (Online version in color.)

Combining the low-speed flow areas (marked with red circles) obtained from streamlines with velocity distribution courants, it can be concluded that the slow flow areas varied obviously under different schemes, reflecting the relative velocity difference of molten steel at different parts.

Based on the above discussion, the comparison with specific volume change was carried out by calculating the steel volume with improved flow speed, where the velocity is larger than 0.05 m/s (set in this work). The volume of each part can be calculated via the following integration equation:   

$${\text{V}}_{\text{P}}=\iint {}_{D}f(x,y,v,f)d\sigma$$(10)

where f(x, y, v, f) is the iso-surface function¹⁹⁾ containing two other parameters apart from Cartesian Coordinator; v is the velocity of the molten steel, m/s; and f is the volume of the molten steel, dimensionless. In this case, v and f were set at the same magnitude of 0.05. Therefore,   

$$f(x,y,v,f)={f(x,y)|}_{\begin{array}{l}v=0.05\\ f=0.05\end{array}}$$(11)

The integral regions D of different part according to the Cartesian coordinates in Fig. 8 are listed in Table 5, as well as the volumes of each part to the whole molten steel volume, obtained via excluding v and f. The results of liquid steel volume change in these three parts under different schemes are shown in Fig. 8. The volume change is shown in the form of a ratio of flow improved steel volume to the steel volume of the corresponding part. Bars titled with “Total” represent the ratio of the whole flow improved steel to the whole molten steel.

Fig. 8.

Comparison of flow improved steel volumes. (Online version in color.)

Table 5. Integral regions of different parts.

Integral region	Region scope	Steel volume	Volume ratio
D1	y > tan(11°)x, y > tan(60°)x, (x,y) < = F(x,y)	8.55 m3	34.3%
D2	y < -tan(64°)x, y < tan(11°) x, (x,y) < = F(x,y)	8.20 m3	32.9%
D3	-tan(64°) x < y < tan(60°) x, (x,y) < = F(x,y)	8.19 m3	32.8%

The F(x,y) is the outline function of the furnace wall, varies at different cross section.

In the UB scheme, the steel in Part 3 was most effectively stirred with bottom-blowing, suggesting the efficient gas-steel momentum exchange resulted from the appropriate distance from the bottom nozzle to the furnace wall. However, under the UB scheme, the molten steel flow was the most unbalanced, with the smallest flow improved steel in Part 1 and 2, mainly caused by the colliding of steel flow with similar velocity.

The flow improved steel of L1 and L2 presented not only a balance volume distribution, but also high percentages among other schemes. This means it is feasible to adjust the gas flow rates far from EBT zones to avoid the colliding effects. Moreover, the largest steel volumes in Part 3 and whole were obtained under the L2 scheme, with a slight decrease of volumes in Part 1 and 2. Combined with the results of other indicators, keeping the highest bottom-blowing gas rates in nozzle 3 could help the bath flow pattern achieved the best dynamic conditions.

As for the triangle bottom-blowing schemes, the T1 bottom-blowing scheme showed the worst result at every aspect, this suggested again that it is not a cost-effective way to simply increase the gas flow rates in the nozzle near EBT zone to achieve a better bath flow pattern. Although the flow improved steel volumes of T2 in Part 1 and 2 are higher than those under the UB scheme, combined with other indicators, the gas-steel momentum exchange under T2 still did not perform ideally. It could be concluded that when the equal bottom-blowing gas rates were applied, in no matter two or three nozzles, the stirring effects would not perform perfectly as the equal gas rates due to similar velocity causing collisions with one another.

3.2. Validations

3.2.1. Water Model Experiments Validation

The water model experiments are widely used in the validation of bath fluid flow.^20,21,22) Conventionally, the water was applied to present the molten bath, and the air was applied to present the bottom gas. Figure 9 presents the water model experiment equipment. Two conductometers were applied and three bottom-blowing gas rates were controlled by three flowmeters. The mixing time was considered the most relevant indicator to show how well the bottom-blowing scheme improved the bath fluidity. During the experiment process, KCl solution was added simultaneously with bottom-blowing, and the mixing time was recorded when the conductivity difference between the two conductivity electrodes installed in the model bottom below 5%.

Fig. 9.

Water model equipment.

In this case, the effects of uniform bottom-blowing and L2 blowing schemes were compared, and each scheme was tested twice. The bottom gas flow rates in water model were calculated based on the Froude number similarity criterion, presented in the following equation:⁶⁾   

$$Q_{\text{W}}=Q\sqrt{\frac{d_{\text{W}}^2\times D_{\text{W}}^2\times H_W\times {\rho }_{l\text{W}}\times {\rho }_{g\text{W}}}{d^2\times D^2\times H\times {\rho }_l\times {\rho }_g}}$$(12)

Here, parameters with subscript W are those of water model; parameters without W represent those of the furnace prototype; Q is the gas flow rate, L/min; d is the nozzle diameter, m; D is the hydraulic diameter, calculated via π dividing into perimeter of wall, m; H is the depth of bath, m; and ρ is the density, where subscripts l and g represent liquid and gas, respectively, kg/m³. The calculated bottom gas rates of these two schemes and results are listed in Table 6. Apparently, the L2 scheme saw a significant improvement in terms of bath fluidity. Moreover, the mixing time under the L2 scheme presented a nearly 30% decrease in the mixing time. Compared with the average molten bath velocity obtained from numerical simulation, the water model experiment matched the numerical result roughly.

Table 6. Water model experiment results.

Bottom-blowing scheme	Bottom gas rates (L/min)	Mixing Time (s)
		T1	T2	T
Uniform blowing	2.5-2.5-2.5	97.5	95.8	96.65
Liner arrangement 2	2.25-3.75-5.25	68.1	69.4	68.75

3.2.2. Industrial Experiments Validation

The same bottom-blowing arrangements were applied in a commercial 100 t EAF, in order to study the metallurgical effects of bottom-blowing in the EAF steelmaking process and further validate the numerical results. In total, 80 heats with bottom-blowing have been collected in the industrial melting process, including 40 heats with the same bottom-blowing schemes and 40 heats with non-uniform bottom-blowing. Non-uniform bottom-blowing schemes are 10-15-20 L/min. The same bottom-blowing schemes are all 15-15-15 L/min, respectively, and 40 heats without bottom-blowing have been collected in the industrial melting process.

In this experiment, the carbon-oxygen equilibrium was chosen to investigate the effects of these three stirring schemes. Carbon-oxygen equilibrium is the product of oxygen and carbon content due to the chemical balance in the carbon-oxygen reaction (Eq. (13)) during the process. A better dynamic condition can reduce the endpoint carbon-oxygen equilibrium.   

$$[C]+[O]=CO$$(13)

The equilibrium constant of this reaction was obtained by Eq. (14). The f_C and f_O are close to 1 in the steelmaking process, according to Henry’s Law. Because the gaseous reaction product CO was the dominant gas in the reaction interface, the p_co was regarded as 1. Therefore, Eq. (14) can be converted into Eq. (15).   

$$K_C=p_{co}/f_C[\%C]f_O[\%O]$$(14)

  

$$K_C=1/[\%C][\%O],$$(15)

Theoretically, the carbon-oxygen equilibrium is constant owing to the stable temperature in the EAF steelmaking process. However, affected by different smelting conditions of metallurgy dynamics conditions in the actual production process, the C–O equilibrium differs from the theoretical value. Research has concluded that the smaller value of C–O equilibrium indicates better molten bath fluidity.

The average endpoint carbon-oxygen equilibrium without bottom-blowing is 0.00408, with a standard deviation of 26%, while the average C–O equilibriums were 0.00340 under bottom-blowing and 0.00301 under non-uniform bottom-blowing. The average carbon-oxygen equilibrium of the endpoint molten steel is improved by 17% with bottom-blowing and is significantly improved by 27% with non-uniform bottom-blowing. The results suggested that the slag and molten steel are thoroughly incorporated with non-uniform bottom-blowing, which reduces the molten steel over-oxidization at the end of the EAF steelmaking process. Besides, compared with that obtained with uniform bottom-blowing, the average carbon-oxygen equilibrium of the endpoint molten steel with non-uniform bottom-blowing is improved by 11%. The statistical results showed that these two schemes had nearly the same standard deviation of 15%.

Meanwhile, several indicators obtained suggested some metallurgical improvements. As shown in Figs. 10 and 11, the tap-to-tap time and two main materials consumptions were reduced, indicating the cost decrease with non-uniform bottom blowing. Due to the bottom blowing agitation, the average lime added to increase the slag fluidity and help accelerate dephosphorization and desulfurization was decreased by 7% with uniform blowing and nearly 10% with non-uniform blowing. Nevertheless, in Fig. 12, the CaO composition in the endpoint slag remained stable, resulting from the more sufficient metallurgical reactions among elements resolved in the liquid steel. It should be noted that compared with uniform bottom blowing, the non-uniform scheme presented a less lime consumption and higher CaO content, this might be caused by the more active reaction in the EBT area.

Fig. 10.

Tap-to-tap time reduction.

Fig. 11.

Materials consumptions reduction. (Online version in color.)

Fig. 12.

Chemical composition of the endpoint slag. (Online version in color.)

From Fig. 12, the improvements in the slag composition showed a potential possibility in optimizing the endpoint product quality. In the steelmaking process, the dephosphorization effect could be improved with less amount of SiO₂ in the steel, and the average SiO₂ content in the endpoint slag was increased by some 50% with non-uniform blowing. The higher content of MgO in the slag can help reduce the refractory loss and prolong the furnace lining longevity. Surprisingly, the MgO content in the slag was significantly increased by 91% with uniform bottom blowing and by 161% with non-uniform bottom blowing. Al₂O₃ presented the contradictory bath fluidity change effects with CaO; thus, with less Al₂O₃, the slag taping process could require less time. From Fig. 12, it could be said that Al₂O₃ in the endpoint slag could be reduced by nearly 60% when applying non-uniform bottom blowing into the regular schemes.

Apart from the physical characteristics the slag changed, the Fe and FeO acted as decarburization reaction intermediates through the following equations:   

$$2[Fe]+O_2=2(FeO)$$(16)

  

$$(FeO)+[C]=[Fe]+CO(g)$$(17)

The limiting factor of these reactions is the C content in the steel, specifically, in the interface of slag and steel. With a higher steel fluid flow, the diffusion of C was accelerated, which caused less intermediate content in the slag. According to the FeO differences among these three schemes, by applying bottom blowing, the FeO content was decreased by 6.35% and by 8.08% with the non-uniform scheme. This suggests that the better bath fluid flow, the lower carbon-oxygen equilibrium.

3.2.3. Experiments Results Comparison

In order to compare the results of both numerical and validation experiments, the comparison between with indicators obtained from uniform bottom-blowing and non-uniform bottom-blowing schemes was presented in Fig. 13, as the scheme without bottom-blowing was not calculated via numerical simulation. The indicator differences were obtained from the following equation:   

$$D_{\text{i}}=I_{non}/I_u\times 100\%-100\%$$(18)

where D_i is the difference of different indicator, %, when D_i < 0, the indicator value decreased in the non-uniform scheme and vice versa. I_non is the indicator value of non-uniform bottom-blowing.; similarly, I_u is the indicator value of uniform bottom-blowing, units changed with different indicator. Based on the indicator differences, the relevant degrees among all indicators to the major indicator of numerical simulation, the average molten bath velocities (abbreviated as “Velocities” in Fig. 13), were obtained from the Eq. (19):   

$$R_{\text{i}}=D_{\text{i}}/D_{\text{V}}$$(19)

where D_V is the indicator difference of molten bath velocities, %; R_i is the relevant degree of different indicator, dimensionless. If the mean value of R_i > 1, it suggested that the corresponding indicator has a certain relevance with bath velocity. If the mean value of R_i > 2, then the indicator may be adjusted via non-uniform bottom-blowing technology.

Fig. 13.

Indicators comparison between simulation and validation experiments. (Online version in color.)

It should be noted that the mixing time obtained from water model experiments has the nearest oppose relevance with bath velocity. Additionally, the endpoint slag composition of industrial experiments showed that different element could be influenced by the bath velocity diversely. As for the FeO composition and C–O equilibrium, the enhancement of molten bath fluidity might only cause slightly change, despite that the improvement of these two indicators was significant after the application of bottom-blowing. This quantization comparison preliminarily revealed the relationship between some metallurgical indicators which can be easily measured from the field with the molten bath velocities which currently can only be calculated through CFD. To accurately conclude the relevant degree, further simulation including more factors and industrial experiments are on the schedule.

In conclusion, both the numerical simulation and validation experiments suggested the effects of non-uniform bottom blowing arrangement on enhancement of bath fluidity via better gas-liquid momentum transportation. This led to the content and temperature homogenization. Additionally, the improvements of some major metallurgical indicators with further bath velocity optimization suggested the potential of producing high quality steel with less time and less materials cost.

4. Conclusions

In this paper, fluid flow characteristics under five various bottom-blowing gas distribution schemes of the electric arc furnace, which was capable of a 100 tons capacity and applied with three bottom-blowing nozzles, were studied by means of numerical simulation and validation experiments. Additionally, results of water model and industrial experiments were applied against the numerical ones. Conclusions drawn based on numerical and experimental data are as follows:

(1) According to the numerical simulation results, a comparatively better velocity, averaging 2.0765 × 10⁻² m/s existed in the bottom-blowing scheme of a linear change among five schemes, of which the gas flow rate in the nozzle furthest from the EBT area was set as the lowest. A further comparison of the average velocity of the molten steel and area of the dead zone of each scheme was then conducted. Additionally, several molten bath parameters were obtained, as well as those calculated at each transient calculation interval. The purpose of reducing the dead zone area was only achieved in the linear schemes according to these parameters, roughly by 0.15 m³. The effectiveness of adjusting the gas rate of the nozzle near the EBT area while keeping the gas rate of other nozzles equal proved to be hardly ideal;

(2) The separated molten bath analysis was carried out in order to understand how different bath fluidity could be improved via different gas flow rates and bottom nozzles. The results showed, when applied the lineal schemes, a better movement of fluid with some 50% molten steel flow exceeding 0.05 m/s was caused by the attenuation of kinetic collisions under the circumstance of an uneven gas flow rate distribution. The collision effect would exist whenever some equal gas rates were used.

(3) In order to verify the numerical results, the water model experiment and industrial experiment were carried out. According to the industrial experimental results, the carbon-oxygen equilibrium in non-uniform bottom-blowing significantly was decreased by 27% from that without bottom-blowing and by 11% from that with uniform bottom-blowing. Comparisons among several other metallurgical indicators also suggested the advantages of bottom-blowing. Both the numerical simulation and validation experiments suggested the effects of non-uniform bottom blowing arrangement could improve bath fluidity via better gas-liquid momentum transportation.

Acknowledgement

Financial support from the National Natural Science Foundation of China (No. 51804345) and Natural Science Foundation of Hunan province in China (No. 2017JJ3386) is gratefully acknowledged.

Appendix

Appendix A. The carbon-oxygen equilibrium of bottom-blowing industrial validation experiment.

Without bottom-blowing			With uniform bottom-blowing			With nonuniform bottom-blowing
C (wt%)	O (wt%)	C–O equilibrium	C (wt%)	O (wt%)	C–O equilibrium	C (wt%)	O (wt%)	C–O equilibrium
0.136	0.0312	0.0042432	0.066	0.057	0.003762	0.116	0.022	0.002552
0.085	0.0674	0.005729	0.096	0.041	0.003936	0.224	0.013	0.002912
0.174	0.0229	0.0039846	0.129	0.023	0.002967	0.175	0.015	0.002625
0.216	0.0195	0.004212	0.166	0.016	0.002656	0.148	0.017	0.002516
0.099	0.0564	0.0055836	0.135	0.02	0.0027	0.271	0.011	0.002981
0.06	0.0893	0.005358	0.05	0.063	0.00315	0.236	0.01	0.00236
0.099	0.0409	0.0040491	0.147	0.019	0.002793	0.259	0.01	0.00259
0.122	0.032	0.003904	0.086	0.036	0.003096	0.24	0.011	0.00264
0.215	0.0173	0.0037195	0.07	0.043	0.00301	0.174	0.016	0.002784
0.175	0.0229	0.0040075	0.106	0.023	0.002438	0.216	0.011	0.002376
0.084	0.0401	0.0033684	0.089	0.035	0.003115	0.099	0.027	0.002673
0.066	0.0563	0.0037158	0.085	0.038	0.00323	0.06	0.062	0.00372
0.066	0.0604	0.0039864	0.065	0.058	0.00377	0.099	0.025	0.002475
0.129	0.0262	0.0033798	0.056	0.074	0.004144	0.122	0.022	0.002684
0.166	0.0197	0.0032702	0.065	0.048	0.00312	0.215	0.013	0.002795
0.135	0.0433	0.0058455	0.076	0.052	0.003952	0.076	0.039	0.002964
0.05	0.0869	0.004345	0.158	0.0218	0.003444	0.084	0.034	0.002856
0.147	0.0173	0.0025431	0.135	0.032	0.00432	0.089	0.035	0.003115
0.086	0.0751	0.0064586	0.259	0.0125	0.003238	0.259	0.01	0.00259
0.07	0.0438	0.003066	0.235	0.0178	0.004183	0.178	0.018	0.003204
0.106	0.0642	0.0068052	0.224	0.0182	0.004077	0.076	0.0316	0.002402
0.089	0.0388	0.0034532	0.24	0.013	0.00312	0.065	0.0511	0.003322
0.053	0.0639	0.0033867	0.065	0.057	0.003705	0.056	0.0662	0.003707
0.21	0.0205	0.004305	0.056	0.063	0.003528	0.065	0.0543	0.00353
0.04	0.086	0.00344	0.065	0.049	0.003185	0.09	0.0369	0.003321
0.05	0.0899	0.004495	0.07	0.05	0.0035	0.04	0.0934	0.003736
0.26	0.0125	0.00325	0.04	0.096	0.00384	0.06	0.0637	0.003822
0.178	0.0234	0.0041652	0.05	0.074	0.0037	0.26	0.0121	0.003146
0.116	0.0286	0.0033176	0.26	0.014	0.00364	0.178	0.0189	0.003364
0.224	0.0166	0.0037184	0.178	0.019	0.003382	0.054	0.0639	0.003451
0.175	0.0202	0.003535	0.116	0.024	0.002784	0.053	0.0639	0.003387
0.148	0.0174	0.0025752	0.224	0.012	0.002688	0.07	0.0527	0.003689
0.271	0.0138	0.0037398	0.175	0.018	0.00315	0.07	0.05	0.0035
0.236	0.0135	0.003186	0.148	0.019	0.002812	0.053	0.069	0.003657
0.259	0.0122	0.0031598	0.076	0.048	0.003648	0.21	0.013	0.00273
0.24	0.014	0.00336	0.054	0.063	0.003402	0.271	0.01	0.00271
0.065	0.0536	0.003484	0.045	0.083	0.003735	0.236	0.012	0.002832
0.056	0.0783	0.0043848	0.076	0.054	0.004104	0.259	0.01	0.00259
0.065	0.0617	0.0040105	0.158	0.024	0.003792	0.116	0.03	0.00348
0.076	0.0895	0.006802	0.135	0.022	0.00297	0.145	0.019	0.002755

References

• 1)   P.  Wang,  Z. Y.  Jiang,  X. X.  Zhang,  X. Y.  Geng and  S. Y.  Hao: J. Univ. Sci. Technol. Beijing, 36 (2014), 1683 (in Chinese).
• 2)   R.  Zhu,  G.  Wei and  R.  Liu: Ind. Heat., 44 (2015), 1 (in Chinese).
• 3)   S.  Timoshenko: Наукові праці Донецького національного технічного університету. Сер.: Металургія (Sci. Works DonNTU. Metall.), 5 (2012), 36.
• 4)   R. Y.  Yin: China Metall., 15 (2005), 1 (in Chinese).
• 5)   J.  Fu,  Z.  Wang,  X.  Wang and  X.  Mao: J. Iron Steel Res. Int., 11 (2004), 1.
• 6)   G.  Wei,  R.  Zhu,  K. A. I.  Dong,  G.  Ma and  T.  Cheng: Metall. Mater. Trans. B, 47 (2016), 3066.
• 7)   F.  Liu,  R.  Zhu,  K.  Dong,  X.  Bao and  S.  Fan: ISIJ Int., 55 (2015), 2365.
• 8)   K.  Dong,  R.  Zhu and  W. J.  Liu: Adv. Mater. Res., 361–363 (2012), 639.
• 9)   B.  Li: Computational Fluid Dynamics in Steelmaking, Metallurgical Industy Press, Beijing, (1998), 187.
• 10)   G.  Ma,  R.  Zhu,  K.  Dong,  Z.  Li,  R.  Liu,  L.  Yang and  G.  Wei: Ironmaking Steelmaking, 43 (2016), 594.
• 11)   F.  Liu,  R.  Zhu,  K.  Dong and  R.  Bai: Ironmaking Steelmaking, 44 (2017), 159.
• 12)   Y.  Liu,  S.  Chen,  J.  Wang and  K.  Dong: Ind. Heat., 40 (2011), 63 (in Chinese).
• 13)   H.  Wang,  R.  Zhu,  R.  Liu,  D.  Shou,  G.  Xie,  S.  Fan and  Y.  Gu.: Ind. Heat., 43 (2014), 12 (in Chinese).
• 14)   H.  Wang,  R.  Zhu,  X.  Wang and  Z.  Li: Miner. Process. Extr. Metall., 126 (2017), 47.
• 15)   C.  Yigit,  G.  Coskun,  E.  Buyukkaya,  U.  Durmaz and  H. R.  Güven: Appl. Therm. Eng., 90 (2015), 831.
• 16)   Z.-s.  Yang,  L.-z.  Yang,  Y.-f.  Guo,  G.-s.  Wei and  T.  Cheng: 9th Int. Symp. on High-Temperature Metallurgical Processing, Springer, Berlin, (2018), 69.
• 17)   C. W.  Hirt and  B. D.  Nichols: J. Comput. Phys., 39 (1981), 201.
• 18)   X.  Huang: Principles of Ferrous Metallurgy, Metallurgical Industry Press, Beijing, (2002), 121 (in Chinese).
• 19)  ANSYS FLUENT 18.2 User’s Guide, ANSYS, Inc., Canonsburg, PA, (2018).
• 20)   L. X.  Qin,  D. Q.  Cang,  D.  Xu and  J. F.  Duan: Adv. Mater. Res., 402 (2011), 425.
• 21)   M.  Alam,  G. A.  Irons,  G.  Brooks,  A.  Fontana and  J.  Naser: ISIJ Int., 51 (2011), 1439.
• 22)   A.  Nordquist,  N.  Kumbhat,  L.  Jonsson and  P.  Jonsson: Steel Res. Int., 77 (2006), 82.