Effect of shrouding CH4 flow rate on flow field and stirring ability of coherent jet in steelmaking process

Characteristics of flow field and stirring ability of coherent jet with various shrouding CH4 flow rates on the molten bath were studied by combustion experiment and numerical simulation. The axial velocity and total temperature distributions of coherent jet under hot (1700 K) and cold (298 K) ambient condition were analyzed. The Eddy Dissipation Concept model was used in simulation with detail chemical kinetic mechanisms, and the numerical simulation results were agreed well with the combustion experiment in this research. Based on the simulation and experiment results, when the CH4 rate was 230, 207 and 184 Nm3/h, their disparity rate of average velocity and total temperature was small than 5 and 6 %, respectively, at high ambient temperature. Hence, the same stirring effect might be achieved by those three kinds of CH4 flow rates in EAF steelmaking process. According to the industrial application research, the best CH4 flow rate is 184 Nm3/h, which could stir molten bath well and reduce energy consumption in steelmaking process.

length of potential core and increase the kinetic energy of the main oxygen jet. The key of this technology is suppressing the ambient gas to interact with main oxygen jet by a shrouding flame. Therefore, the oxygen jet could keep original diameter and velocity over long distance, and remain the stirring ability. Moreover, with the greater penetration capacity, the supersonic oxygen jet could deliver greater amounts of oxygen into the molten bath and decrease the splash of liquid slag, comparing with the traditional supersonic oxygen lance (Nordquist et al. (2006); Mahoney (2008)).
The coherent jet technology was proposed by , and then Mathur (1999b) showed the fundamental results in industrial production. Sarma et al. (1998) analyzed the characteristics of supersonic jet and coherent jet at different ambient temperatures by combustion experiment. Alam et al. (2010) reported the behaviors of the supersonic jet with and without shrouding flame by the numerical simulation and validated their results against previously experimental data. To date, although substantial works have been performed for researching the differences between conventional oxygen jet and coherent jet Mathur 1999b;Sarma et al. 1998;Alam et al. 2010a;Mahoney 2010;Meidani et al. 2004;Liu et al. 2016;Jeong et al. 2004), little research has been paid to how the flow field is influenced by flow rate of shrouding flow.
The present study is to make some contributions to address this deficit by combustion experiment and numerical simulation. During the combustion process, the process products are formed such as CH 5 , CH 2 and OH, which could not be tracked by conventional one-step complete combustion. Therefore, the numerical simulation is performed with detail chemical kinetic mechanisms to analyze the effect of process products on coherent jet flow field, and EDC model is used to analyze how the shrouding flow rate affects the potential core length and stirring ability of coherent jet under two kinds of ambient temperatures. Based on results, the metallurgical effects of various CH 4 flow rates are analyzed in a 75 t electric arc furnace.

Combustion experiment
The present research used a combustion system to produce a hot ambient temperature for the coherent jet. The details of the system were described in Ref. , and only a brief description was given here. In this paper, the coherent jet lance had a water-cooled system, and the design flow rate of main oxygen was 2300 Nm 3 /h. Moreover, the throat and exit diameter of Laval nozzle was 25.3 and 32.9 mm, respectively. There were three concentric rings supplying the shrouding CH 4 and O 2 , as presented in Fig. 1a. The inner hydraulic, intermediate and outer hydraulic diameter is 3.2, 4.5 and 4.8 mm, respectively. For combustion experiment and numerical simulation, the same parameters of supersonic jet nozzle were applied in this paper.
The point tube with water-cooling was adopted to measure the static pressure and total pressure of coherent jet in the combustion experiment, as shown in the Fig. 1b. The Mach number of coherent jet should be calculated by following formation (Anderson 2013): (1) where P 0 is the pressure at the A location, P is the pressure at the B location and γ is the ratio of heat capacity.

Governing equations
The numerical simulations were conducted by integrating the Navier-Stokes equations with Reynolds averaging method, and following equations was used to simulated combustion process (Malalasekera and Versteeg 2007).
Mass conservation equation

Momentum conservation equation
Energy equation In (2-4), − → v was the velocity vector; k eff was the effective conductivity and − → J j was the diffusion flux of species j; S h included the heat of chemical reaction, and any other volumetric heat sources.
The discrete ordinate (DO) radiation model (Christo and Dally 2005;Chui and Raith 1993) with weighted sum of gray gas model (WSGGM) was used to model the radiation of the combustion process. In the present study, the modified k-ε model with the standard wall function was implemented for modeling the turbulent flows. The standard k-ε model (Launder and Spalding 1972) was a semi-empirical model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε).
Turbulence kinetic energy equation for EDC model (k equation): (2) ∂ρ ∂τ In the equations, the G k and G b presented was the generation of turbulence kinetic energy due to the mean velocity gradient and the buoyancy, respectively. Y M represented the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. S k and Sε were user-defined source terms. In combustion process, the temperature gradient was an important factor to obtain the flow field Magnussen and Hjertager 1977). Hence, the turbulent viscosity (μ t ) is addressed as the following equation (Alam et al. 2010b): The EDC model with overall and detailed chemical kinetic mechanisms (GRI-Mech 3.0) were presently used for the modeling of reactions (Frassoldati et al. 2010;Mardani and Tabejama 2010;Galletti et al. 2009). The GRI-Mech 3.0 was the full chemical mechanism, which consisted of 53 species and 325 reversible reactions. In EDC model, the species conservation equation for chemical species taken the following general form: where Y i was the local mass fraction of each species (i), − → J i was the diffusion flux of species, and R i was the net rate of production of species by chemical reaction. The length fraction of the fine scales (ξ) and the residence chemical time scale (τ) of fluid in the fine structures was expressed by: where C ξ and C s were time scale constants equal to 2.138 and 0.408, respectively.

Simulation details
Because the vortices in flow field could not be correctly reflected by the symmetry of the system, a 3D geometrical model of computation was constructed in Fig. 2. The computational domain started at the entrance of the coherent jet nozzle, and extended 70D e downstream in the axial direction and 23D e in the radial direction.
The main oxygen used pressure inlet condition, surrounding CH 4 and O 2 adopted mass-flow inlet condition for and outlet position of combustion zone adopted pressureoutlet. The Table 1 listed the detail values of boundary conditions.
In present study, The SIMPLE algorithm method (Chui and Raith 1993;Launder and Spalding 1972) was utilized to solve pressure velocity coupling. The second-order upwind scheme was employed for discretizing the equations in order to improve the accuracy of the simulations. Solution convergence was determined by two criteria. The first one was to ensure that the numerical residuals were <10 −6 for the energy and <10 −5 for all the other variables. The second criterion was to ensure that the variations between consecutive iterations of temperature and velocity were kept within 10 K and 2 m/s, respectively, at the downstream outlet of the computational domain.
There were large quantities of previous studies Magnussen and Hjertager 1977;Frassoldati et al. 2010;Mardani and Tabejama 2010;Galletti et al. 2009) had used GRI-Mech 3.0 to model the combustion process. Thus, the EDC model with the detailed chemical kinetic mechanism of GRI-Mech 3.0 was used for the modeling of reactions. To reduce the calculation time, the in situ adaptive tabulation (ISAT) model of Pope (1997) was adopted. Figure 3 shows the axial velocity profiles for the simulation results in three grid levels, coarse grid (275,000 cells), medium grid (417,000 cells), and fine grid (564,000 cells), respectively. It seems that the simulation results agree well with the each other, for the  medium and the fine grid, and the variation of axial velocity is within 0.7 pct. This result suggests that the solution is not sensitive to the grid. However, the variation calculated with the coarse and medium grid level was about 2.4 pct. Therefore, the mesh of 417,000 cells was used in combustion simulation in consideration of reducing the computational time.

Results and discussions
Axial velocity distribution research Figure 4 shows the axial velocity distribution of the supersonic oxygen jet with different shrouding CH 4 flow rates and ambient temperatures. Moreover, the simulation results would be addressed as line or line segment, and the experiment data would be presented as quadrangle, roundness or triangle in Figs. 4 and 6. The mass flow rates of CH 4 in different unit are shown in the Table 2. In this paper, the percent of main oxygen design flow rate will be used to replace CH 4 mass flow rate, hereafter. For instance, 10 %-CH 4 represents the shrouding CH 4 mass flow rate being 0.0456 kg/s. 471 ± 10 m/s at the jet centerline. As the results show, more shrouding CH 4 rate does not increase the maximum velocity of main oxygen jet, and it just makes the maximum velocity remain a longer distance at the jet centerline. Therefore, CH 4 flow rate could only protect the stirring ability of main oxygen jet, but not improve the stirring ability at a certain extent. 1 nozzle exit diameter will be addressed as 1D e hereafter. The potential core of coherent jet is supposed to be end, when the axial velocity of supersonic oxygen jet continues to decline more than 5D e at the jet centerline, and the first point of this kind of downtrend is addressed as the end point of potential core. The length between the end point of potential core and the tip of Laval nozzel is defined as the potential core length of coherent jet.
Based on the results, the average potential core length of the coherent jet is 3.5 times larger than that of the conventional jet. That means the CH 4 flow rate could effectively improve the potential core length of the main oxygen jet, which protect the stirring ability of the supersonic oxygen jet.
There are four cross sections have been selected at the jet centerline which radius is 100 mm, and the location is 10D e , 20D e , 30D e and 40D e , respectively. The Fig. 5 shows the average axial velocities of different sections, which are calculated by numerical simulation. Although the coherent jet have a potential core at centerline, the average velocity shows a reduce trend, because periphery of main oxygen would mix with the combustion flame, which suppresses the average velocity of oxygen jet. The average velocity of the coherent jet at high temperature condition with 10 %-CH 4 , 9 %-CH 4 , 8 %-CH 4 , 7 %-CH 4 , 6 %-CH 4 and 5 %-CH 4 is 1.07, 1.09, 1.11, 1.16, 1.21 and 1.25 times higher than that of the coherent jet at room ambient temperature, respectively. Therefore, if the ambient temperature rises, the increasing trend of average velocity is suppressed with CH 4 flow rate improving, which is the same as increasing trend of potential core.
In this research, the distance between the coherent jet tip and molten bath surface is approximately 20D e . When the location of cross section is 20D e at centerline, the average velocity of the coherent jet at high temperature condition with 9 %-CH 4 , 8 %-CH 4 , 7 %-CH 4 , 6 %-CH 4 and 5 %-CH 4 is 98.3, 95.4, 92.0, 87.7 and 83.2 % of the 10 %-CH 4 coherent jet, respectively. It seems that when the CH 4 flow rate is 9 %-CH 4 and 8 %-CH 4 , the disparity rate of average velocity is all small than 5 %.
Based on the preview research (Anderson 2013;Alam et al. 2012;Hale 2013), the velocity contour of main oxygen jet would be compressed due to the obstruction of molten bath surface. Therefore, the difference of main oxygen velocity with 10 %-CH 4 , 9 %-CH 4 and 8 %-CH 4 may be suppressed at 20D e , which makes the coherent jet may achieve the same stirring effect with three kinds of CH 4 flow rate in EAF steelmaking process. The Fig. 4 presents numerical simulation results are agreed well with the combustion experiment in this research, and the average error of axial velocity is about 1.7 %. The oxygen is addressed as an ideal-gas in simulation process. However, the oxygen has a deviation from the ideal gas, when the ambient temperature is improving, referring to the previous study (Irvin and Richard 2008). Therefore, the error would be formed under the influence of shrouding flame temperature.

Total temperature distribution research
As depicted in Fig. 6, the simulations using the EDC model with full detailed chemistry are performed to predict the flame characteristics with various CH 4 flow rates. In this study, the total temperature distributions at the jet centerline are measured only at cold ambient temperature, and the simulation results agree well with the combustion experiment data.
When oxygen jet passes though the Laval nozzle, the pressure potential energy is transformed into the kinetic energy. During this process, although the energy form of oxygen jet is changing, the total energy of oxygen remains unchanged, and then the central jet mixes with combustion flame at the end of the potential core. With a great temperature gradient, the flame transmits thermal energy into oxygen jet, which makes centre of oxygen jet rise rapidly. At last, both kinetic energy and thermal energy of oxygen jet keeps reducing due to the energy gradient between the jet and the ambient flow. As a result, total temperature of the jet gradually approaches the ambient temperature. As described above, the total temperature at jet centerline just one of flow field characteristics, which could not represent the total stirring ability of coherent jet. The average total temperatures of different sections are studied, as shown in Fig. 7.
Under room ambient temperature, when the CH 4 flow rate is small than 6 %-CH 4 , the average total temperature show a reduce trend with X/D e increasing. However, when the CH 4 flow rate is bigger than 7 %-CH 4 , the average total temperature increases first, and then approaches to the ambient temperature at centerline direction, as presented in Fig. 7a. It seems that the high-temperature zone (the total temperature >2600 K) is formed near the exit of coherent, when CH 4 flow rate is small, as depicted in Fig. 8. With the combustion flame flowing to the downstream, the thermal energy of coherent jet transmits into the ambient gas due to the temperature gradient, which makes its average total temperature keep reducing. When CH 4 flow rate is bigger, the high-temperature zone is enlarged making the average total temperature of combustion flame higher at 20X/D e . At the same time, the average total temperature of main oxygen increase, because the peripheral of oxygen jet absorbs heat from flame. As a result, the average total temperature at 20X/D e is higher than that at 10X/D e . And then, the total temperature reduce rate of flame is bigger than total temperature rise rate of oxygen jet, which makes the average total temperature of coherent jet decreases with X/De increasing.
When the ambient temperature is high, the average total temperature shows an increasing trend with different CH 4 flow rates, as presented in Fig. 7b. Although the CH 4 has been exhausted, the combustion flame could keep its total temperature being 1700 K, because of the high ambient temperature. In the meantime, the main oxygen jet could keep absorbing heat until its total temperature being 1700 K. Therefore, on the cross sections, the average total temperature of coherent jet increases, because of the limited reduction rate of flame total temperature and increasing trend of oxygen jet total temperature.
The average total temperature of the coherent jet at high temperature condition with 10 %-CH 4 , 9 %-CH 4 , 8 %-CH 4 , 7 %-CH 4 , 6 %-CH 4 and 5 %-CH 4 is 1.28, 1.33, 1.43, 1.58, 1.76 and 1.92 times higher than that of the coherent jet at room ambient temperature, respectively. Therefore, if the ambient temperature rises, the increasing trend of average total temperature is suppressed with CH 4 flow rate improving, which is the same as increasing trend of average velocity.
It seems that when the CH 4 flow rate is 9 %-CH 4 and 8 %-CH 4 , the disparity rate of average velocity is all small than 6 %. Therefore, the 9 %-CH 4 and 8 %-CH 4 may achieve the same stirring effect in EAF steelmaking process.

Industrial application research
Based on the combustion experiment and numerical simulation study, the 10 %-CH 4 , 9 %-CH 4 and 8 %-CH 4 may achieve the same stirring effect in a 75t electrical arc furnace. In order to study metallurgical effects and technical indicators of the various CH 4 flow rate in steelmaking process, 10 %-CH 4 , 8 %-CH 4 and 6 %-CH 4 are adopted in a 75 t electrical arc furnace. There are 180 heats collected in the industrial smelting process, and each CH 4 flow rate has same heats. Molten steel component, steelmaking time and dephosphorization rate are analyzed in this research.
The conditions of liquid iron (prior to steelmaking process), and molten steel (after steelmaking process) are shown in Table 3 along with the average components, temperature, and smelting time. When smelting with different CH 4 flow rates, the conditions of liquid iron are fundamentally the same, which mean the initial conditions have no influence to the industrial application research.
Based on the carbon content and temperature of molten steel are same, both 10 %-CH 4 and 8 %-CH 4 make no difference on [C]·[O] and steelmaking time. When the CH 4 flow rate is 6 %-CH 4 , the average [C]·[O] is improved by 16.2 % and the steelmaking time is increased by 7.4 %. This fact can prove that the stirring ability of coherent jet with 10 %-CH 4 and 8 %-CH 4 is fundamentally same. Therefore, the dynamic condition of molten bath remains unchanged, when the CH 4 flow rate is reduced at appropriate situation as observed by the combustion experiment and numerical simulation. Figure 9 shows the distribution of phosphorus in molten steel with different CH 4 flow rates. As shown in Fig. 9, the content of phosphorus in molten steel with 10 %-CH 4 , 8 %-CH 4 and 6 %-CH 4 distributes from 0.006 to 0.008, 0.006 to 0.008 and 0.009 to 0.011 mass%, respectively. Based on the results, the average content of phosphorus in molten steel is basically same when the CH 4 flow rate is 10 %-CH 4 and 8 %-CH 4 . However, the average content of phosphorus is increased by 0.003 mass % with 6 %-CH 4 , and the dephosphorization rate is reduced by 2.3 %.
CaO, SiO 2 , FeO and P contents in end-point slag are shown in Fig. 10. While the basicities of slag are same being 2.1, compared with 6 %-CH 4 , average P is increased by 0.07 mass% and FeO is dropped by 2.2 mass% in slag with 10 %-CH 4 and 8 %-CH 4 . The reduction of FeO loss will be beneficial to improve the metal yield rate.
Based on steelmaking temperature, components of slag layer and molten steel, the equilibrium phosphorus content with various CH 4 flow rate has been obtained by the Eq. 10 reported by Healy (1970  The content of equilibrium phosphorus in molten steel is 4.2 × 10 −5 , 4.3 × 10 −5 and 3.0 × 10 −5 mass% with 10 %-CH 4 , 8 %-CH 4 and 6 %-CH 4 , respectively. It is obvious that all equilibrium phosphorus contents are most importantly negligibly small. According to the results of combustion experiment, numerical simulation and industrial application research, it can prove that the reaction rate and stirring effect with 10 %-CH 4 and 8 %-CH 4 is same, and both are better than that with 6 %-CH 4 .
Above all, it shows that the stirring ability of coherent jet with 10 %-CH 4 and 8 %-CH 4 is fundamental same, and both metallurgical effect is better than with 6 %-CH 4 in steelmaking process for the 75 t EAF, which agrees well with the results of the combustion experiment and the numerical simulation.

Conclusions
1. The bigger CH 4 -rate and higher ambient temperature can prolong the potential core of coherent jet, and the numerical simulation results show a good agreement with the combustion experimental data. Moreover, when the ambient temperature rises, the increasing trend of potential core is suppressed with CH 4 flow rate improving, which is the same as increasing trend of average velocity and total temperature. 2. Based on the results, at high temperature condition, the disparity rate of average velocity and total temperature of the coherent jet, which is between 10 %-CH 4 , 9 %-CH 4 and 8 %-CH 4 , is all small than 5 and 6 %, respectively. Therefore, the coherent jet may achieve the same stirring effect with three kinds of CH 4 flow rates in EAF steelmaking process. 3. Compared with 10 %-CH 4 and 6 %-CH 4 flow rates at industrial application research, the best CH 4 flow rate is 8 %-CH 4 , which could stir molten bath well and reduce energy consumption in steelmaking process, with the condition of liquid iron being fundamentally the same.