Fluid Dynamics Analysis of O₂–CaO Jet with a Shrouding Flame for EAF Steelmaking

Abstract

Compared with the traditional addition methods of lumpy lime into the electric arc furnace (EAF) for slag making, the technology of O₂–CaO jet can deliver lime powder directly into the EAF molten bath with high speed carrier gas, which demonstrates much advantages in quick melting and effective phosphorus removal. Recently, the shrouding combustion flame was proposed and applied to strengthen the CaO import capability of the O₂–CaO jet. In this study, combining the discrete particle model (DPM) and the Eddy Dissipation Concept (EDC) model with the detailed chemical kinetic mechanisms (GRI-Mech 3.0), computational fluid dynamics (CFD) models of the O₂–CaO jet with shrouding flame, with shrouding O₂ and without shrouding gas were developed. The numerical results of CFD models were firstly validated by the experimental data. The interaction between the particles and the gas jet of the O₂–CaO jet was analyzed and how the shrouding combustion flame affected the fluid flow characteristics of the O₂–CaO jet were clarified. The shrouding high-temperature combustion flame could delay the attenuation of the axial velocity of the O₂–CaO jet, heat the CaO particles effectively and make the CaO particles cluster together in a much longer distance, which is helpful to strengthen the jet impact, accelerate the meltdown of CaO particles and improve the utilization efficiency of CaO.

1. Introduction

Slag making is the key to the steelmaking process because some impurity elements, including phosphorus and sulfur, can be captured by the molten slag from the molten steel, which is important to adjust the molten steel compositions and improve the molten steel cleanliness.^1,2,3) Generally, the main raw material for slag making in an electric arc furnace (EAF) is lime (CaO) and the traditional methods of lime addition into the EAF include lime addition into the scrap bucket in advance by the conveyor system and lime addition directly into the EAF molten bath through the roof feed system of EAF.^4,5) The lime used in the above methods are in lump, which leads to slower melting rate of lumpy lime and lower dephosphorization and desulphurization efficiency.^6,7) Therefore, the technology of O₂–CaO jet was developed to deliver lime powder directly into the EAF molten bath by carrier gas of high speed, which demonstrates some advantages in quick melting and effective phosphorus removal.^8,9) However, it’s always an issue to raise the CaO supply into the molten bath of the O₂–CaO jet and therefore, the O₂–CaO jet with shrouding flame was proposed and developed.

Methods of lime powder injection into the metallurgical reaction vessels have been widely reported, including EAF and other steelmaking furnaces. Mamdouh¹⁰⁾ introduced the application of lime powder injection in electric arc furnace and reported that lime powder injection can reduce the lime and power consumption of 10%. Miyata¹¹⁾ investigated the effect of lime powder top blowing on the hot metal deposphorization with different blowing rates. Zhu¹²⁾ introduced the technology of desulphurisation by powder injection and blowing in the RH refining of molten steel and with powder injection, the rate of the desulphurization was increased noticeably. Trentini¹³⁾ reported that the lime powder injection with oxygen can easily remove the phosphors and improve the quality of the molten steel. Numata¹⁴⁾ measured the rate of nitrogen desorption from the molten steel during the lime powder injection. However, it can be found that these studies mainly aimed at analyzing the influence of lime powder injection on the metallurgical effects, including dephosphorization rate, desulphurization rate, lime powder consumption and so on. There were some researches carried out to study the fluid flow characteristics of the powder-gas jet, such as the interaction between the particles and the carrier gas jet, the energy transformation and the effect of shrouding atmosphere on the powder-gas jet. Yu^15,16) assessed the numerical model formulations in the discrete particle simulation of gas-solid flow and coupled discrete particle simulation with computational fluid dynamics to investigate the gas-solid flow within a blast furnace. Masaki¹⁷⁾ developed a computational fluid dynamics (CFD) model to investigate the powder-gas jet behavior of a single-nozzle lance and a multiple-nozzle lance. Ogawa¹⁸⁾ found that the flow rate of carrier gas and the density and diameter of particles affected the dispersion behavior of particles during the powder injection process. T. Uchiyama¹⁹⁾ analyzed the interaction between particles and carrier gas using three-dimensional Eulerian air velocities and Lagrangian particle trajectories method. Ishii²⁰⁾ developed a numerical model of gas-particle two-phase flows and estimated the transformation rates of momentum and heat from the particle phase to the gas phase. Uddin^21,22) carried out a cold model experiment on ion-exchange reaction between pearlite particles and HCl and studied the effect of particles dispersion and operating factors on solid/liquid mass transfer rate in a mechanically-vessel systematically. However, the fluid flow characteristics of the O₂–CaO jet with shrouding flame have not been reported and few findings can be referred to improve the O₂–CaO jet parameters with shrouding flame. Therefore, it is essential to analyze the influence of the shrouding combustion flame on the fundamental fluid dynamics behavior of the O₂–CaO jet, which would benefit the process optimization of EAF steelmaking with the technology of the O₂–CaO jet with shrouding flame.

In this paper, based on the discrete particle model (DPM) and the Eddy Dissipation Concept (EDC) model with the detailed chemical kinetic mechanisms (GRI-Mech 3.0), CFD models of the O₂–CaO jet with shrouding flame, with shrouding O₂ and without shrouding gas were developed. The CFD model was firstly validated by comparing the numerical results with the experimental data. And then, the interaction between the particles and the gas jet of the O₂–CaO jet was analyzed. What’s more, how the shrouding combustion flame affected the fluid flow characteristics of the O₂–CaO jet were clarified based on the results of numerical simulations.

2. Numerical Simulation

The present study used the discrete particle model (DPM) to model CaO powder, which is following the Euler–Lagrange approach. The gas phase is defined as a continuous phase, which is modeled by considering the Eulerian approach.

2.1. Governing Equations and Their Closure Models

The following governing equations were used in the present numerical simulations.^23,24)

The mass conservation equation:   

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

The momentum conservation equation:   

$$\frac{\partial }{\partial t}(\rho \overrightarrow{v})+\nabla \cdot (\rho \overrightarrow{v}\overrightarrow{v})=-\nabla P+\nabla [\mu (\nabla \overrightarrow{v})]+\rho \overrightarrow{g}+\overrightarrow{F}$$(2)

The energy equation:   

$$\begin{array}{l}\frac{\partial }{\partial t}(\rho E)+\nabla \cdot (\overrightarrow{v}(\rho E+\rho ))\\ =\nabla \left(k_{eff}\nabla T-{\sum }_i{h}_i\overrightarrow{J_i}+(\overrightarrow{{\tau }_{eff}}\cdot \overrightarrow{v})\right)+S_h\end{array}$$(3)

In Eqs. (1), (2), (3), ρ is the fluid density, kg/m³; $\overrightarrow{v}$ is the fluid instantaneous velocity, m/s; P is the static pressure, MPa; t is the time, s; μ is the molecular viscosity, Pa·s; $\rho \overrightarrow{g}$ is the gravitational body force, N; $\overrightarrow{F}$ is the external body force, N; $\overrightarrow{J_i}$ is the diffusion flux of species i; T is the absolute temperature, K; k_eff is the effective conductivity, W/(m²·K); S_h includes the heat of chemical reaction, J; h_i is the enthalpy of species i, J/mol; and E is the total energy and is defined as:   

$$E={\int }_{298.15K}^T{C}_{P}dT+\frac{v^2}{2}$$(4)

Where, C_p is the heat capacity, J/(kg·K); v is the fluid velocity, m/s.

In the present numerical simulations, due to the high Reynolds number, the turbulent flows were modeled by a modified k–ε model, which was based on the standard k–ε model.^25,26) The transport equation for the turbulence kinetic energy k is expressed as:   

$$\begin{array}{l}{\displaystyle \frac{\partial (\rho k)}{\partial t}}+{\displaystyle \frac{\partial (\rho k{v}_{\mathrm{i}})}{\partial x_{\mathrm{i}}}}\\ ={\displaystyle \frac{\partial }{\partial x_{\mathrm{j}}}}\left[\left(\mu +{\displaystyle \frac{{\mu }_{\mathrm{t}}}{{\sigma }_{\mathrm{k}}}}\right)\cdot {\displaystyle \frac{\partial k}{\partial x_{\mathrm{i}}}}\right]+G_{\mathrm{k}}+G_{\mathrm{b}}-\rho \epsilon -Y_{\mathrm{M}}+S_{\mathrm{k}}\end{array}$$(5)

The turbulent dissipation rate ε is expressed as:   

$$\begin{array}{l}{\displaystyle \frac{\partial (\rho \epsilon )}{\partial t}}+{\displaystyle \frac{\partial (\rho \epsilon v_{\mathrm{i}})}{\partial x_{\mathrm{i}}}}={\displaystyle \frac{\partial }{\partial x_{\mathrm{j}}}}\left[\left(\mu +{\displaystyle \frac{{\mu }_{\mathrm{t}}}{{\sigma }_{\epsilon }}}\right)\cdot {\displaystyle \frac{\partial \epsilon }{\partial x_{\mathrm{i}}}}\right]\\ +C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}(G_{\mathrm{k}}+C_{3\epsilon }{G}_{\mathrm{b}})-C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}+S_{\epsilon }\end{array}$$(6)

  

$${\mu }_t=\rho C_{\mu }\frac{k^2}{\epsilon }$$(7)

In Eqs. (5), (6), (7), v_i is the fluid flow velocity in the direction i, m/s; G_k is represents the turbulent kinetic energy of average velocity gradients while G_b is the turbulent kinetic energy of buoyancy; Y_M is the turbulent dissipation rate, J; σ_k and σ_ε are, respectively, the turbulent Prandtl numbers of k and ε; S_k and S_ε are the defined source terms, J; and in this study, C_1ε = 1.6, C_2ε = 1.92, C_3ε = 0.8 C_μ = 0.09, σ_k = 1.0 and σ_ε = 1.3.

In DPM model, the continuity and momentum of particles are expressed as the following equations.^27,28,29)   

$$\frac{d{m}_p}{dt}=m$$(8)

  

$$\frac{d{u}_p}{dt}=F_D(u-u_p)+\frac{g_x({\rho }_p-\rho )}{{\rho }_p}+F_x$$(9)

Where, F_D(u − u_p) is the drag force per unit particle mass and F_D can be calculated by Eq. (10).   

$$F_D=\frac{18\mu }{{\rho }_p{d}_p{}^2}\frac{C_{D}Re}{24}$$(10)

Where, u is the gas velocity; u_p is the particle velocity; ρ is the gas density; ρ_p is the particle density; d_p is the particle diameter; Re is the Reynolds number and can be calculated by the following Eq. (11).   

$$Re\equiv \frac{\rho d_p|u_p-u|}{u}$$(11)

The temperature of shrouding flame formed by CH₄–O₂ combustion reactions can reach 3200 K and in this case, the radiation heat transfer plays an important role during the injection process of the O₂–CaO jet with shrouding flame. Therefore, the discrete ordinate (DO) radiation model was applied to solve the radiative transfer equation (RTE) for a finite number of discrete solid angles. The weighted-sum-of-gray-gases model (WSGGM) was also used in this study, which is a reasonable compromise between the oversimplified gray gas model and the complete model including particular absorption bands.

2.2. Combustion Models

In the present study, the Eddy Dissipation Concept (EDC) model was adopted to calculate the turbulence-chemistry interactions because of its better reliability in simulating the Moderate or Intense Low-oxygen Dilution combustion.^30,31,32)

The detailed chemical reaction kinetics of CH₄ combustion can be incorporated in turbulent flames through EDC combustion model. The chemical reactions and molecular mixing were assumed to be associated with turbulence dissipation occurring in the fine structure of the fluid flow. In EDC model, the species transport mode was adopted to calculate the species conservation and transportation. And the species conservation equation is as:   

$$\frac{\partial }{\partial t}(\rho Y_i)+\nabla \cdot (\rho \overrightarrow{v}{Y}_i)=-\nabla \overrightarrow{J_i}+R_i$$(12)

Where, $\overrightarrow{J_i}$ is the diffusion flux term of species i; Y_i is the local mass fraction of each species i, and R_i is the net rate of species i by chemical reactions and can be calculated by Eq. (13).   

$$R_i=\frac{\rho {\xi }^2}{t(1-{\xi }^3)}(Y_i^{*}-Y_i)$$(13)

Where, Y_i^* is the mass fraction of species i within the fine structures after reacting over the time t; ξ is the length fraction of the fine structures and t is the residence chemical time scale.   

$$\xi =C_{\xi }{\left(\frac{v\epsilon }{k^2}\right)}^2,t=C_t{\left(\frac{v}{\epsilon }\right)}^{\frac{1}{2}}$$(14)

Where, C_ξ is a volume fraction constant and its value is 2.138; C_t is a time scale constant and its value is 0.408.

Based on the previous studies,^33,34) the chemical kinetic mechanism of CH₄ combustion with oxygen plays an important role in the accuracy of the numerical results. Hence, the CH₄–O₂ combustion reaction mechanism adopted in the present study is the detailed chemical kinetic mechanisms (GRI-Mech 3.0), which consists of 325 elementary reactions with 53 components. The results of the GRI-Mech 3.0 mechanisms has also been verified by the experiments of CH₄ combustion with oxygen.³⁵⁾ In addition, it is necessary to shorten the calculation time and therefore, the in-situ adaptive tabulation (ISAT) model of Pope was used in the numerical simulations.

2.3. Simulation Details

Figure 1 shows the nozzle of O₂–CaO jet used in this study. The CaO particles were injected though the central nozzle by the carrier oxygen and the diameter of the central nozzle is 15 mm (De). In addition, there are two rings of nozzles for injecting the shrouding gas medium. Shrouding CH₄ was injected by the inner rings of nozzles and shrouding O₂ was injected by the outer rings of nozzles. Figure 2 depicts the boundary conditions of the computational domain in the numerical simulation. To increase the accuracy of the numerical results, a three-dimensional (3D) geometrical model was built to study the fluid flow field characteristics of O₂–CaO jet . The computational zone was, respectively, 2000 mm in the axial direction and 500 mm in the radial direction. Figure 3 shows the detailed mesh configuration of the 3D geometrical model. The grids close to the nozzle exit was refined to obtain more satisfactory numerical results.

Fig. 1.

Cross-sectional view of the O₂–CaO jet nozzle with shrouding flame.

Fig. 2.

Computational domain for the numerical simulation.

Fig. 3.

Detailed mesh configuration of the numerical model. (Online version in color.)

In the present study, a non-slip condition was applied to the walls and the standard wall function was applied. Mass-flow inlet boundary conditions were applied at the inlet of the main O₂–CaO jet, the shrouding CH₄ nozzle and the shrouding O₂ nozzle. A pressure boundary condition was applied at the outlet position of the combustion zone. Table 1 lists the detailed information of boundary conditions. And there are three cases used to investigate the fluid flow characteristics of O₂–CaO jet with a shrouding flame. Case 1: the O₂–CaO jet with shrouding CH₄ and O₂, Case 2: the O₂–CaO jet with shrouding O₂ only and Case 3: the O₂–CaO jet without shrouding gas.

Table 1. Boundary conditions in the numerical simulations.

Name of Boundary	Type of Boundary Conditions	Values
Main O2–CaO inlet	Gas species	O2
	Temperature	298 K
	Gas flow rate (Nm3/h)	400
	Powder species	CaO
	Temperature	298 K
	Diameter of powder (mm)	0.05
	Powder injection rate (kg/min)	20
	Gas species	CH4
Shrouding CH4 inlet	Temperature	298 K
	Gas flow rate (Nm3/h)	150
	Gas species	O2
Shrouding O2 inlet	Temperature	298 K
	Gas flow rate (Nm3/h)	300
	volume fraction	O2 = 21 pct, N2 = 79 pct
Outlet	ambient temperature	1573 K
Wall	no-slip	298 K

The numerical simulations in the present work were performed by using the commercial software package ANSYS Fluent 16.0. The Navier-Stokes equation was calculated by a pressure-based solver by a steady-state solution model to simulate the fluid flow of the O₂–CaO jet, with the pressure-velocity scheme being coupled with the SIMPLE algorithm. Second order upwind scheme was applied to calculate the momentum and mass equations. In this study, the solution convergence conditions for the numerical simulation were that the residual of energy is less than 10⁻⁶ and the residuals for other variables were less than 10⁻⁴.

2.4. Model Validation

The cold test experiment was carried out to validate the results of the numerical simulations. Figure 4 shows the experimental platform for gas-solid injection. During the test experiment, the gas flow rate was controlled the gas valve group and the powder injection rates was monitored by the on-line weighing sensor. Besides, a diaphragm type pressure transmitter PT10-11AFKMS (0–1.6 MPa) was adopted to monitor the nozzle inlet pressure with different powder injection rates. Figure 5 shows the comparison of the calculated value of the nozzle inlet pressure with the measured value in different powder injection rates. The calculated value is the calculated nozzle inlet pressure obtained by numerical simulation and the measured value is the nozzle inlet pressure obtained by the pressure transmitter. It can be found that the calculated nozzle inlet pressure is very close to the measured values and the error is no more than 4.27 pct, which demonstrates that the results of numerical model concur reasonably closely with the experiments. Note that the deviation between the calculated value and the measured value increases with the increase of powder injection rate. The mean reason is that with a certain flow rate of the carrier gas, the larger the powder injection rate, the larger the resistance of ducting. In this study, the distance of between the monitor point in numerical model and the monitor point in test experiment is about 1000 mm and therefore, the tendency of deviation change occurs. As can be seen, the results show the change tendency that the nozzle inlet pressure increases with powder injection rate increasing, which also means that the numerical simulations are reasonable on a macro basis as previous study¹¹⁾ reported.

Fig. 4.

Experimental platform for gas-solid injection. (Online version in color.)

Fig. 5.

Comparison of calculated pressure values at nozzle inlet with measured ones.

3. Results and Discussion

3.1. Velocity Distribution

Figure 6 shows the axial velocity distributions of the gas and particles of the O₂–CaO jet at the jet centerline with different conditions. In Figs. 6, 6(a-1), 6(b-1) and 6(c-1) depict the axial velocity distribution of gas and particles of the O₂–CaO jet with shrouding flame, with shrouding O₂ and without shrouding gas, respectively. And (a-2), (b-2) and (c-2) are corresponding to the partial enlarged detail in the case that the distance from the nozzle exit is in the range from 0 to 200 mm. The change tendency of axial velocity of the gas and particle are similar for the three cases. The gas velocity is about 260 m/s to 270 m/s at the nozzle exit, but it subsequently increased to 380 m/s within a short distance and meanwhile, there is also a sharp increase for the velocity of the particles. For this phenomena, the rapid expansion is the main reason when the O₂–CaO jet of high pressure is injected out from the nozzle to the free space and the pressure potential energy is transformed into the kinetic energy of the O₂–CaO jet rapidly. Then, a sharp drop occurs in the gas velocity and accordingly, the velocity of particles increases slowly and next, the velocity of the gas is in accord with the velocity of particles. During this process, a part of the gas momentum is transferred to the particles and the particle velocity is thus increased following the decrease in gas velocity. Results show that the attenuation rate of the gas velocity is much larger than the ascending velocity of the particle velocity because the density of CaO powder is larger than that of O₂ in the case the powder injection rate was 20 kg/min in this study. After that, the axial velocity of the O₂–CaO jet reaches steady state and the potential core forms. Finally, the velocity of the O₂–CaO jet decreases and due to the inertial force of the particles, the decrease of the particle velocity is delayed with regard to the decrease of the gas velocity, which is in consistent with the previous report.¹¹⁾ Just as the velocity behavior around the point of 500 mm in Figs. 6(b-1) and 6(c-1), the decrease of the gas velocity is ahead of that of the particle velocity.

Fig. 6.

Axial velocity distributions of gas and particles of the O₂–CaO jet at the jet centerline. (Online version in color.)

As depicted in Fig. 6, the potential core length of the O₂–CaO jet with shrouding flame, with shrouding O₂ and without shrouding gas is about 1000 mm, 410 mm and 300 mm, respectively. Compared with the O₂–CaO jet without shrouding gas, the potential core length of the O₂–CaO jet was increased 3.33 and 1.24 times by the shrouding flame and the shrouding O₂, respectively. The shrouding flame formed by the combustion of the shrouding CH₄ and O₂ affects the compression and expansion wave structure within the central O₂–CaO jet. The longer potential core length of the O₂–CaO jet is a result of the attenuation in the increase speed of the turbulent mixing layer because the shrouding high-temperature flame can create a region of lower density surrounding the central O₂–CaO jet, which has been described in Section 3.4.

Figure 7 shows the gas velocity contours of the O₂–CaO jet with shrouding flame, with shrouding O₂ and without shrouding gas on cross section. Figure 8 depicts the radial distributions of gas velocity of the O₂–CaO jet at different axial locations. It can be seen that the results in Fig. 8 are in accorded with those shown in Fig. 7. Noticeably, the central gas velocity of the O₂–CaO jet with shrouding flame is larger than that of the other two cases and when the distance from the nozzle exit is in the range from 250 to 750 mm, the central gas velocity is in a steady state without attenuation. In addition, as can been seen in Fig. 8, for the O₂–CaO jet with shrouding flame, the gas velocity around the distance of 25 mm is larger than the central gas velocity. As reported, the particles are clustered near the central axis and the maximum gas velocity is shifted from the central axis to the periphery.¹⁵⁾ Meanwhile, the shrouding high-temperature flame can also accelerate the surrounding gas velocity.

Fig. 7.

Gas velocity contours of the O₂–CaO jet on cross section. (a) With shrouding flame. (b) With shrouding O₂. (c) Without shrouding gas. (Online version in color.)

Fig. 8.

Radial distributions of gas velocity of the O₂–CaO jet at different axial locations. (Online version in color.)

In this study, half-jet width was corresponded to reflect the behavior of the O₂–CaO jet, which was usually used to depict the spreading rate of supersonic jet. Half-jet width refers to the radial distance from the jet centerline where the velocity of the jet becomes half of the axial velocity. Figure 9 shows that the half width of the O₂–CaO jet without shrouding gas is similar to the jet with shrouding O₂. In Fig. 9, R_1/2 is the half-jet width and De is the nozzle exit diameter. The half-jet width increases slowly up to about 400 mm and then starts to increase at a larger rate. For the O₂–CaO jet with shrouding flame, the half-jet width increases just after the nozzle exit and then increases slowly up to about 1000 mm, and finally, it increases at a larger rate. After the nozzle exit, the shrouding CH₄ and O₂ jets at the periphery of the O₂–CaO jet account for the rapid increase of the half-jet width. And in the range from 250 to 1000 mm, the shrouding high-temperature flame can reduce the gas mixtures at the jet periphery and this has also been described in Section 3.4. Figure 9 also shows that the O₂–CaO jets of these three cases spread at a constant rate after the jet potential core region because the O₂–CaO jets after the potential core region of these three cases become fully turbulent jets.³⁶⁾

Fig. 9.

Half-jet width distributions of the O₂–CaO jet. (Online version in color.)

3.2. Temperature Distribution

Figure 10 shows the distributions of axial static temperature of gas and particles of the O₂–CaO jet at the centerline. Because of the rapid expansion of the gas and particles, there is a fluctuation for the static temperature of the O₂–CaO jet at the nozzle exit for all cases, which has been illustrated in Section 3.1. During the potential core, the thermal energy and the kinetic energy was not lost and the value of the static temperature is constant. As shown in Fig. 10(a), at the end of the potential core, the central gas and particles mix with the shrouding hot atmosphere created by the high-temperature combustion flame and then, the temperature of gas and particles was increased. After that, heat and mass are transferred from the central O₂–CaO jet to the surroundings and finally, the static temperature of gas and particles gradually approach the ambient temperature. As Figs. 10(b) and 10(c) show, for the O₂–CaO jet with shrouding O₂ and without shrouding gas, the axial static temperature of gas and particles also slowly approach the ambient temperature after the potential core under the heating effect of the ambient atmosphere of high temperature.

Fig. 10.

Axial static temperature distributions of gas and particles of the O₂–CaO jet at the jet centerline. (Online version in color.)

Figure 11 depicts the gas static temperature distributions of the O₂–CaO jet on longitudinal section and Fig. 12 shows the gas static temperature contours of the O₂–CaO jet on cross section. In Figs. 11(a) and 12(a), the red part is the high temperature zone created by the shrouding high-temperature combustion flame. The gas density in the surrounding high temperature zone can be reduced and the central O₂–CaO jet can be protected against the mixing of the surrounding ambient atmosphere. As Figs. 11 and 12 show, there is no obvious difference between the distributions of gas static temperature of the O₂–CaO jet with shrouding O₂ and without shrouding gas. Meanwhile, with shrouding CH₄ injection, the maximum combustion flame temperature can be up to 3200 K and a great temperature gradient is generated between the shrouding flame and the powder-gas flow, which can accelerate the heat transfer from the shrouding combustion flame to the gas and particles. And the CaO particles can be heated effectively. Figure 13 presents the particle static temperature distributions of the O₂–CaO jet on longitudinal section with shrouding flame, with shrouding O₂ and without shrouding gas. Compared with the O₂–CaO jet with shrouding O₂ and without shrouding gas as shown in Figs. 13(b) and 13(c), the temperature of CaO particles are noticeably higher with the shrouding combustion flame as shown in Fig. 13(a). As presented in Fig. 10(a), the axial static temperature of the central particles can be up to 2200 K. In EAF steelmaking, the CaO powder which was injected into the molten bath should be melted down before its slag making to remove phosphorous and form foaming slag. A large amount of heat in the molten bath would be consumed and the smelting rhythm would be slowed down by the process. Therefore, not only the shrouding combustion flame can maintain the impact force of the O₂–CaO jet but also the heating effect of the shrouding flame to CaO powder would benefit the slag-making process in EAF steelmaking.

Fig. 11.

Gas static temperature distributions of the O₂–CaO jet on longitudinal section. (a) With shrouding flame. (b) With shrouding O₂. (c) Without shrouding gas. (Online version in color.)

Fig. 12.

Gas static temperature contours of the O₂–CaO jet on cross section. (a) With shrouding flame. (b) With shrouding O₂. (c) Without shrouding gas. (Online version in color.)

Fig. 13.

Particle static temperature distributions of the O₂–CaO jet on longitudinal section. (a) With shrouding flame. (b) With shrouding O₂. (c) Without shrouding gas. (Online version in color.)

3.3. Particles Distribution

Figure 14 shows the particle trajectories of the O₂–CaO jet with shrouding flame, with shrouding O₂ and without shrouding gas. For the O₂–CaO jet with shrouding flame, the particles get together noticeably in a long distance after the nozzle exit and the divergence degree of the particles is much weaker with the shrouding high-temperature combustion flame, as shown in Fig. 14(a). Meanwhile, as presented in Figs. 14(b) and 14(c), the particles diverge seriously along their ejection process. Therefore, it can be concluded that in EAF steelmaking, the shrouding flame can make the O₂–CaO jet deliver more CaO into the molten bath and the utilization efficiency of CaO can be improved effectively, while a part of CaO powder would escape into the free space of EAF without being captured by the molten bath for the O₂–CaO jet with shrouding O₂ or without shrouding gas.

Fig. 14.

Particle Trajectories of the O₂–CaO jet. (a) With shrouding flame. (b) With shrouding O₂. (c) Without shrouding gas. (Online version in color.)

Figure 15 shows the distributions of particle density of the O₂–CaO jet at different axial locations with shrouding flame, with shrouding O₂ and without shrouding gas. The powder particles are concentrated close to the central axis of the nozzle. On one hand, with the distance from the nozzle exit increasing, the concentrated distribution area of particles expands and the concentration of particles decreases gradually. On the other hand, at each vertical plane, the concentrated distribution area of particles of the O₂–CaO jet with shrouding flame is smaller noticeably than that with shrouding O₂ and that without shrouding gas. Just as Fig. 15 shows, the concentration of particles of the O₂–CaO jet with shrouding flame is larger noticeably than that with shrouding O₂ and that without shrouding gas. The contrast among these three cases is more obvious with the increase of the distance from the nozzle exit and therefore, it further demonstrates that the shrouding combustion flame plays a key role in making the particles cluster.

Fig. 15.

Distributions of particle density of the O₂–CaO jet at different axial locations. (a) With shrouding flame. (b) With shrouding O₂. (c) Without shrouding gas. (Online version in color.)

3.4. Vorticity and Turbulent Kinetic Energy Distribution

When a fluid element moves in the flow field, the vorticity is always used to measure the rotation of the fluid element. Meanwhile, the vorticity is also adopted to reflect the mixing degree among the fluid flows.^37,38) The smaller the vorticity is, the weaker the mixing degree of the fluids is. The following equation is the calculation formula of the vorticity vector.   

$$\overrightarrow{\zeta }=\overrightarrow{\nabla }\times \overrightarrow{U}$$(15)

Where, $\overrightarrow{\zeta }$ is the vorticity vector and $\overrightarrow{U}$ is the velocity. When the supersonic jet passes through the relatively still air, rotational flow is developed at the periphery of jet because of a large velocity gradient at that region.³⁸⁾ Figure 16 shows the radial distributions of vorticity magnitude of the O₂–CaO jet at different axial locations in the case of shrouding flame, with shrouding O₂ and without shrouding gas. It can be found that the vorticity of the O₂–CaO jet are different after the nozzle exit for the three cases. The vorticity region draws nearer to the centerline of the O₂–CaO jet with the distance from the nozzle exit increasing. On the whole, the vorticity first increases and then decreases with the radial distance increasing for all the cases. Compared with the O₂–CaO jet without shrouding gas, the shrouding O₂ can delay the merging of vorticity region with the jet centerline and with the axial distance from the nozzle exit increasing, the difference between these two cases gradually decreases. With X = 300 mm, it can be seen that the vorticity curve of the O₂–CaO jet with shrouding O₂ is consistent with that without shrouding gas basically. As for the O₂–CaO jet with shrouding flame, the vorticity region merges to the jet centerline more slowly compared with the O₂–CaO jet with shrouding O₂ or without shrouding gas. The main reason is that the shrouding combustion flame can delay the mixing of the central O₂–CaO jet with the surrounding ambient atmosphere. In addition, it can be found that when the radial distance being within 25 mm, there are some fluctuations for the vorticity of O₂–CaO jet with shrouding flame. The main reason is that the interactions among the particles, the carrier gas, the shrouding CH₄ and shrouding O₂ are disorder due to the powder blowing according to the study on the fluid dynamics analysis of single gas jet with particles carried out by Masaki.¹¹⁾

Fig. 16.

Radial distributions of vorticity magnitude of the O₂–CaO jet at different axial locations. (Online version in color.)

In the study of jet flow, the turbulence kinetic energy is also a key parameter to reflect the mixing degree among the fluid flows, which demonstrates the mean kinetic energy per unit mass associated with eddies in turbulent flow. The smaller the turbulence kinetic energy is, the weaker the mixing degree of the fluid is. Figure 17 shows the turbulent kinetic energy distributions of the O₂–CaO jet on longitudinal section with shrouding flame, with shrouding O₂ and without shrouding gas. For the O₂–CaO jet with shrouding flame, with shrouding O₂ and without shrouding gas, the turbulent kinetic energy region merges the jet centerline at around 1000 mm, 400 mm and 300 mm, which is consistent with the change tendency of the axial velocity and static temperature of the O₂–CaO jet shown in Figs. 6 and 10. In addition, it also can be found that the maximum value of the turbulent kinetic energy is largest without shrouding gas and that is smallest with shrouding flame. Because a high temperature zone can be created and the surrounding ambient gas density around the central O₂–CaO jet can be reduced by the shrouding flame. Hence, the turbulent kinetic energy in the shear layer is reduced and as a result, the potential core length of O₂–CaO jet can be increased by delaying the mixing of the central O₂–CaO jet with the surroundings.

Fig. 17.

Turbulent kinetic energy distributions of the O₂–CaO jet on longitudinal section. (a) With shrouding flame. (b) With shrouding O₂. (c) Without shrouding gas. (Online version in color.)

3.5. Species Mass Fractions

The expression of reaction formula were omitted in this section because they have already been reported by the plenty of previous studies. Figure 18 shows the radial distributions of the CO₂ and H₂O mass fractions of the O₂–CaO jet with shrouding flame at different axial locations X = 150 mm, 225 mm and 300 mm. As presented in Figs. 18(a) and 18(b), there are two peaks of the CO₂ mass fraction and the H₂O mass fraction at X = 150 mm, 225 mm and 300 mm and there is only one peak at X = 450 mm. Because oxygen is supplied from the central nozzle and the outer shrouding O₂ nozzles as shown in Fig. 1 and CH₄ is supplied from the middle shrouding CH₄ nozzles. Thus, after the nozzle exit, combustion reaction between CH₄ and O₂ occurs from both sides of the CH₄ flow and two flames forms in this range. With the axial distance from the nozzle exit increasing, the two flame would merge to form a single flame and as a result, radial distributions of the CO₂ and H₂O mass fraction show only one peak.

Fig. 18.

Radial distributions of the CO₂ and H₂O mass fractions of the O₂–CaO jet with shrouding flame at different axial locations. (Online version in color.)

Figure 19 show the distributions of the CO₂ and H₂O mass fractions of the O₂–CaO jet with shrouding flame on longitudinal section. In Fig. 19, both the CO₂ mass fraction and the H₂O mass fraction are higher in the combustion flame area just because CO₂ and the H₂O are the products of the combustion reaction of CH₄ with O₂. In addition, in Fig. 19, it also can be found that there are two flames when the distance from the nozzle exit is in the range from 0 to 300 mm, which is corresponded to the results shown in Fig. 18 as discussed earlier.

Fig. 19.

Distributions of the CO₂ and H₂O mass fractions of the O₂–CaO jet with shrouding flame on longitudinal section. (Online version in color.)

4. Conclusions

In this study, CFD models of the O₂–CaO jet with shrouding flame, with shrouding O₂ and without shrouding gas were developed by combining the DPM model and the EDC model with GRI-Mech 3.0. And the effects of the shrouding combustion flame on the fluid flow characteristics of the O₂–CaO jet were analyzed according to the results of numerical simulations. The conclusion are as follws:

(1) The applicability of the CFD model was validated by the reasonably good agreement between the measured data and the calculated values of the numerical simulation.

(2) Compared with the O₂–CaO jet with shrouding O₂ or without shrouding gas, the shrouding combustion flame of CH₄ could delay the attenuation of the axial velocity of the O₂–CaO jet and increase the potential core length by creating a region of lower density surrounding the central O₂–CaO jet. The potential core length of the O₂–CaO jet with shrouding flame was estimated by 3.33 times longer than that without shrouding gas.

(3) According to the simulation, the CaO particles will diverge seriously along the ejection process for the O₂–CaO jet with shrouding O₂ or without shrouding gas and with the shrouding high-temperature combustion flame. And as a result, the CaO particles can be clustered together in a long distance, which makes the O₂–CaO jet deliver more CaO into the molten bath. And the utilization efficiency of CaO can be improved noticeably.

Acknowledgements

The authors would like to express their thanks for the support by the National Nature Science Foundation of China (NO. 51804345 & NO. 51734003).

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