Computational Fluid Dynamics Modeling of Supersonic Coherent Jets for Electric Arc Furnace Steelmaking Process MORSHED ALAM, JAMAL NASER, GEOFFREY BROOKS, and ANDREA FONTANA Supersonic coherent gas jets are now used widely in electric arc furnace steelmaking and many other industrial applications to increase the gas–liquid mixing, reaction rates, and energy efficiency of the process. However, there has been limited research on the basic physics of supersonic coherent jets. In the present study, computational fluid dynamics (CFD) simulation of the supersonic jet with and without a shrouding flame at room ambient temperature was carried out and validated against experimental data. The numerical results show that the potential core length of the supersonic oxygen and nitrogen jet with shrouding flame is more than four times and three times longer, respectively, than that without flame shrouding, which is in good agreement with the experimental data. The spreading rate of the supersonic jet decreased dramatically with the use of the shrouding flame compared with a conventional supersonic jet. The present CFD model was used to investigate the characteristics of the supersonic coherent oxygen jet at steelmaking conditions of around 1700 K (1427 C). The potential core length of the supersonic coherent oxygen jet at steelmaking conditions was 1.4 times longer than that at room ambient temperature. DOI: 10.1007/s11663-010-9436-7 The Minerals, Metals & Materials Society and ASM International 2010
I.
INTRODUCTION
IN basic oxygen furnace and electric arc furnace (EAF) steelmaking, high-speed gas jets are used widely for refining the liquid iron and stirring the liquid melt inside the furnace. Supersonic gas jets are preferred over subsonic jets because of the high dynamic pressure associated with it that results in a higher depth of penetration and better mixing. Laval nozzles are used to accelerate the gas jets to supersonic velocities of approximately 2.0 Mach number in steelmaking.[1] When a supersonic gas jet exits from a Laval nozzle, it interacts with the surrounding environment to produce a region of turbulent mixing. This process results in an increase in jet diameter and in a decrease in jet velocity with increasing distance from the nozzle exit.[1] During oxygen blowing, the higher the distance between the liquid surface and the nozzle exit, the greater the entrainment of surrounding fluid, which in turn decreases the impact velocity as well as the depth of penetration on the liquid surface. As a result, the mixing of gas and liquid inside the furnace decreases, which also reduces the reaction rates because of the small gas– liquid interfacial area. Hence, it is desirable to locate the nozzle close to the liquid-metal surface. The disadvantage of this process is the sticking of slag/metal droplets MORSHED ALAM, Ph.D. Student, JAMAL NASER, Senior Lecturer, and GEOFFREY BROOKS, Professor, are with the Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Hawthorn, Victoria 3122 Australia. Contact e-mail:
[email protected]. ANDREA FONTANA, Senior Process Engineer, is with Primary Steelmaking Manufacturing, One Steel Laverton, Laverton North, Victoria 3026, Australia. Manuscript submitted April 28, 2010. Article published online September 28, 2010. 1354—VOLUME 41B, DECEMBER 2010
on the lance tip, which results in poor tip life.[2,3] To overcome the problem, coherent jet technology was introduced in the EAF steelmaking process at the end of last century.[4,5] Coherent gas jets are produced by shrouding the conventional supersonic jet with a flame envelope. The flame envelope is created using a fuel and oxidant. Figure 1 shows a schematic of a conventional and coherent supersonic jet.[6] Because of the flame envelope, the entrainment of the surrounding gas into the supersonic jet is reduced, leading to a higher potential core length (the length up to which the axial jet velocity is equal to the exit velocity at the nozzle) of the supersonic jet. The longer potential core length of the coherent supersonic jet makes it possible to install the nozzle far from the liquid surface. In the modern EAF, the shrouding oxygen and fuel are used as burner during the melting period and thus increase the efficiency of the process.[7] It also is claimed to produce less splashing than that produced by conventional supersonic jet on the furnace wall.[8] Although the steelmaking industries have been using the coherent supersonic jets for the last 10 years, limited research work has been performed to investigate the physics of supersonic coherent jets. Anderson et al.[5] were the first to carry out an experimental study of supersonic coherent jets. Recently, Mahoney[9] investigated the effect of the shrouding fuel and oxygen flow rate on the potential core length of the supersonic coherent jet. Meidani et al.[10] also carried out an experimental study of a shrouded supersonic jet using compressed air as shrouding gas. In their study, no combustion flame surrounded the main supersonic jet. Some numerical studies[7,11,12] of supersonic jets with shrouding flame are available in the literature, but most[7,11] were not validated against experimental METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 1—Schematics of a (a) conventional and (b) coherent supersonic jet.[6]
results. The numerical simulation, performed by Jeong et al.,[12] underpredicted the potential core length of the supersonic coherent jets. In the present study, computational fluid dynamics (CFD) simulation of a supersonic jet with and without a shrouding flame at room ambient temperature was carried out. The CFD results showed good agreement with the experimental data.[5] The major characteristics of the supersonic coherent jet were investigated for the purpose a clearer understanding of how the technology works. This CFD model then was used to investigate the characteristics of the supersonic coherent jet at steelmaking conditions.
II.
NUMERICAL ANALYSIS
A. Governing Equations The unsteady Reynolds averaged Navier–Stokes (RANS) equations[13] were used to carry out the numerical simulations. The averaged mass, momentum, and energy equations can be written in a conservative form. The mass conservation equation is expressed as follows: @q @qUi þ ¼0 @t @Xi
½1
where q is the density of the fluid and Ui is the mean velocity component in the ith direction. The momentum conservation equation is expressed as follows: @qUi @ qUi Uj @P @ sij qui uj þ ¼ þ ½2 @Xi @Xj @Xj @t @Ui @Uj 2 @Uk þ dij sij ¼ l @Xj @Xi 3 @Xk where P is the pressure of fluid, sij is viscous stress, ui and uj are the fluctuating velocity component in the ith and jth directions, respectively, l is the molecular viscosity, and dij is the Kronecker delta (dij = 1 if i = j and dij = 0 if i „ j). qui uj is known as METALLURGICAL AND MATERIALS TRANSACTIONS B
‘‘Reynold stresses’’ and is used to represent the effect of turbulence. The Reynold stresses are modeled according to the following Boussinesq approximation[13]: @Ui @Uj 2 @Uk qk þ lt qui uj ¼ lt þ ½3 dij 3 @Xj @Xi @Xk where lt is the turbulent viscosity and k is the turbulent kinetic energy. The modeling of turbulent viscosity and turbulent kinetic energy will be described later. The energy conservation equation is expressed as follows: @qH @ðqHUi Þ @ lt @T @P þ ¼ cþ þ @t @Xi @Xi @t Prt @Xi @ þ sij Uj qui uj Uj þ SE ½4 @Xi where H is the total enthalpy, c is the thermal conductivity, Prt is the turbulent Prandtl number, and SE is the internal source of energy (combustion and radiation). The most common values of the turbulent Prandtl number is 0.9, and it is satisfactory for shock-free flows with low supersonic speeds and a low heat transfer rate.[14] Wilcox[14] recommended using Prt = 0.5 for free shear flow and high heat transfer problems. Hence, Prt = 0.5 was used in this study. To close the RANS equations, the temperaturecorrected k – e turbulence model[15] was used, which is a modification of the original k – e model proposed by Launder and Spalding.[16] This modification was done to take into account the effect of temperature gradient on the turbulent mixing region. In the k – e model, the turbulent kinetic energy k and the dissipation rate e are obtained from the following transport equations: @qk @qUj k @Ui @ l @k þ ¼ quj ui þ lþ t qe ½5 @t @Xj @Xj @Xj rk @Xj @qe @qUj e @Ui e @ lt @e þ þ ¼ Ce1 quj ui lþ @t @Xj @Xj k @Xj re @Xj Ce2 q
e2 k
½6
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where Ce1, Ce2, rk, and re are the constants for the k – e model, and their values are 1.44, 1.92, 1.0, and 1.3, respectively. The turbulent viscosity lt is defined as follows: lt ¼ C l q
k2 e
½7
The value of Cl was determined from the following equation[15]: 0:09 i Cl ¼ h 1:2T0:6 1 þ 1þfðMg s Þ
½8
where Tg is the temperature gradient normalized by length scale and f(Ms) takes into account the compressibility effect. Equation [8] modifies the value of Cl depending on the value of the temperature gradient at the shear layer. B. Combustion Modeling The fuel and oxidizing agents used in the present study were CH4 and O2. N2 and O2 were used as the central supersonic jet. A one-step-complete combustion reaction between CH4 and O2 was considered in this study. The products of combustion were CO2 and H2O. In practice, however, at high temperatures, dissociation of CO2 and H2O occurs, which results in minor species like CO, H2, OH, and O2 in the products of combustion along with the main reaction products CO2 and H2O. Dissociation reactions are endothermic; therefore, the actual flame temperature will be lower than the calculated flame temperature based on the complete combustion reaction.[13] But this assumption of a one-step-complete combustion reaction made the calculation simple as well as reduced the computational time. The equation of combustion reaction is expressed as follows[13]: CH4 þ 2O2 ¼ CO2 þ 2H2 O 16Kg
64Kg
44Kg
½9
36Kg
The mass fraction of the species involved in the reaction is determined by solving a separate scalar transport equation for each species, which can be written conservatively as follows: @qYi @ qYi Uj @ lt @Yi þ ¼ qDi þ þ Si ½10 @Xj @Xj @t Sct @Xj where Yi is the mass fraction, Di is the laminar diffusion coefficient, and Si is the source term of species i. In the present study, a single diffusion coefficient of the gas mixture was assumed for all species (i.e., Di = D for i = 1, 2, 3 … N, where N is the number of species). The gas mixture diffusion coefficient was calculated assuming the laminar Schmidt number Sc = 0.7. As the flow is highly compressible, the laminar diffusion coefficient will have a negligible effect on the diffusion of the species. The turbulent diffusion coefficient affects the diffusion of different species in the flow field. The turbulent diffusion coefficient was determined by dividing the turbulent viscosity lt of the 1356—VOLUME 41B, DECEMBER 2010
gas mixtures by the turbulent Schmidt number Sct = 0.9. Hence, it is shown that the total diffusion coefficient was the same for all species involved in the reaction. The source term of the species transport equation is the rate of mass production / reduction of that particular species. When the species transport equation for the fuel (CH4) was solved, the rate of fuel consumption was determined by solving the following Eddy Break-Up combustion model[17]: e Yox Ypr ;B Sfu ¼ q min AYfu ; A ½11 k s sþ1 where Sfu is the volumetric rate of fuel consumption. A and B are the model constants, and s is the stoichiometric ratio. Yfu, Yox, and Ypr are the mass fractions of the fuel, oxygen, and product of combustion, respectively. The Eddy Break-Up model makes good predictions and is fairly straightforward to implement in CFD calculations.[13] In the Eddy Break-Up model, the rate of fuel consumption is specified as a function of local flow and thermodynamic properties. According to this model, the rate of combustion is determined by the rate of intermixing on a molecular scale of eddies containing reactants and those containing hot products; in other words, it is determined by the rate of dissipation of these eddies. This model calculates the individual dissipation rates of fuel, oxygen, and products, and the actual consumption rate is equal to the slowest of the three dissipation rates as is shown in Eq. [11].[13] The first two terms inside the bracket of Eq. [11] simply determine whether fuel or oxygen is present in limiting quantity, and the third term ensures that the flame does not spread in the absence of hot products. In the present study, the values of A = 4 and B = 0.5 were used based on a previous study.[17] From the combustion reaction, it is observed that the stoichiometric ratio of fuel and oxidizer is s = 4, which means that for complete combustion of 1 kg CH4, 4 kg O2 is required. Hence, the rate of O2 consumption is taken as four times the rate of fuel consumption. The volumetric rate of fuel consumption Sfu was calculated in each cell by using Eq. [11], multiplied by the heat of combustion of that particular fuel, and then added as a source term to the energy equation to calculate the temperature. C. Radiation Modeling The radiative heat transfer from a system becomes important when the temperature exceeds 1500 K (1227 C).[13] Here, the flame temperature of the combustion is around 3500 K (3227 C), so the radiation heat transfer needs to be considered. The modeling of the radiation was performed using the following wellknown Stefan–Boltzmann formula: ½12 E ¼ 2 rA T41 T42 where E is the radiative heat transfer per unit time, 2 is the gas emissivity, r = 5.6703 9 108 W/(m2 K4) is the Stefan-Boltzmann constant, A is the area of emitting body, and T1 and T2 are the temperature of source and sink, respectively. The emissivity of a medium depends METALLURGICAL AND MATERIALS TRANSACTIONS B
on local fluid properties.[13] The normal atmospheric air is transparent and thus does not participate in radiative heat exchange. Products of combustion, however, contain a high concentration of CO2 and H2O, which are both strong absorbers and emitters. The weighted sum of gray gases model (WSGGM)[18] normally is used for defining the temperature- and species-concentrationdependent emissivity of the medium. For a different gas concentration and temperature, the emissivity of gases varied from 0.3 to 0.5 using the WSGGM model. In the present study, a constant value of the gas emissivity 2 = 0.5 was used for simplicity. The radiation energy E was calculated in each cell using Eq. [12] and then subtracted from the energy equation. D. Computational Domain The schematic diagram of the computational domain with boundary conditions, used in the present CFD simulation, is shown in Figure 2. The computational domain is axisymmetric and wedge shaped with only one cell in circumferential direction. To reduce the computational time, flow inside the Laval nozzle was not included in the simulation. The flow conditions at the nozzle exit were calculated using isentropic theory.[19] The exit diameter of the nozzle was 0.0147 m and
was considered as one of the inlets to the computational domain. The computational domain was 105 nozzle exit diameters downstream from the nozzle exit and was 20 nozzle exit diameters normal to the jet centerline. In the experimental study, CH4 and O2 were injected through the holes arranged in two concentric rings surrounding the main convergent-divergent nozzle as shown in Figure 3. The inner ring of holes was used for the CH4 gas, and the outer ring of holes was used for the shrouding oxygen supply. The diameters of the holes were 0.00287 m and 0.00408 m for CH4 and O2, respectively. In the present study, the configuration of the nozzle, injecting CH4 and O2, was assumed annular, which is different from three-dimensional real nozzles. However, the injecting areas were adjusted to maintain the same flow rates for CH4 and O2 as was used in the experimental study.[5] This assumption made it possible to solve the problem in two dimensions. E. Boundary Conditions All boundary conditions were chosen to match with the experimental study of Anderson et al.[5] A stagnation pressure boundary condition was used at the main supersonic jet inlet of the computational domain (exit of the convergent-divergent nozzle). The values of the
Fig. 2—Computational domain with boundary conditions.
Fig. 3—Cross-sectional and front view of a supersonic coherent jet nozzle.[5] METALLURGICAL AND MATERIALS TRANSACTIONS B
VOLUME 41B, DECEMBER 2010—1357
Table I. Name of Boundary Supersonic jet inlet Fuel inlet Shrouding oxygen inlet Outlet Wall
Boundary Conditions
Type of Boundary Conditions stagnation pressure mach number total temperature mass fractions mass flow rate mass fractions mass flow rate mass fractions static pressure mass fractions no-slip
Values 914,468 Pa 2.1 298 K (25 C) O2 = 100 pct 1.833 9 105 Kg/s CH4 = 100 pct 3.488 9 105 Kg/s O2 = 100 pct 100,000 Pa O2 = 23 pct, N2 = 77 pct 298 K (25 C)
Mach number and temperature were defined at the supersonic jet inlet. For the CH4 and shrouding O2 inlet, the mass flow rate boundary condition was used. The original mass flow rates were divided by 360 because the included angle of the two-dimensional computational domain is 1 deg. At the outlet, a static pressure boundary condition was used. For the symmetry plane, the symmetry boundary condition was used. At the solid wall, a no-slip boundary condition was imposed. The values of the boundary conditions when oxygen was used as the central supersonic jet are listed in Table I. When nitrogen was used as the central supersonic jet, only the supersonic jet inlet boundary condition was changed from 100 pct oxygen to 100 pct nitrogen, and the rest of the boundary conditions were kept unchanged. Although it is known that the different gases lead to different static pressures and temperatures for similar stagnation conditions, we have used similar stagnation conditions for both the nitrogen and the oxygen jets to match with the experimental study. F. Computational Procedure The unsteady, compressible continuity, momentum, and energy equations were solved using a segregated solver with an implicit approach to calculate the pressure, velocity, temperature, and density. For momentum and continuity equations, the values of the variables at cell faces were calculated using AVL SMART scheme,[20] which is a higher order accurate total variable diminishing scheme. AVL SMART scheme is a modification of the original SMART scheme proposed by Gaskell and Lau.[21] For energy and turbulence equations, the first order upwind scheme was used. The pressure–velocity correction was done by using the SIMPLE algorithm.[22] To advance the solution in time, a first order Euler scheme[20] was used. As the velocity of the flow was high, the time step used in the unsteady calculation was 1 9 105 s. The simulations were assumed converged when the normalized residuals of the flow variables (pressure, velocity, temperature, etc.) drop down by four orders of magnitude. The simulations were carried out using commercial CFD software AVL FIRE 2008.2, which is based on the control volume approach. 1358—VOLUME 41B, DECEMBER 2010
Fig. 4—Axial velocity distributions at the jet centerline of shrouded oxygen jet using coarse, medium and fine grid levels.
G. Grid Independency Test To study the grid sensitivity of the solution, calculations for the supersonic coherent oxygen jet were done using the following different grid levels: coarse grid (20,100 cells), medium grid (28,000 cells), and fine grid (39,000 cells). The axial velocity profile for all grid levels is shown in Figure 4. The average percentage of variation of the axial velocity profile calculated with the coarse and medium grid level was less than 3 pct, with a maximum deviation of 6 pct between the region of X/De = 40 and 60. The average percentage of variation was calculated by averaging the differences at several locations in the axial direction. Between the medium and the fine grid levels, the variation is negligible (less than 1 pct). Hence, it can be said that the solution is not sensitive to the grid. The computational time required for the fine grid level was approximately twice that for the medium grid level. Hence, the results obtained with the medium grid were used for analysis and discussion in the present study.
III.
RESULTS AND DISCUSSION
A. Velocity Distribution Figure 5 shows the velocity distribution of the supersonic oxygen jet with and without a shrouding flame at room ambient temperature. For both cases, the centerline jet velocity shows repeated fluctuations just after the exit from the Laval nozzle. This occurs as a result of the incorrect expansion of the supersonic jet. The jet is mildly underexpanded because the ratio of nozzle exit pressure to the ambient pressure in the present study is around 1.18.[23] The potential core length of the supersonic oxygen jet with the shrouding flame is more than four times larger than that without the shrouding flame. The supersonic jet without the shrouding flame will be addressed as a conventional jet from hereafter. The velocity of the conventional oxygen jet decreases gradually after 10 nozzle exit diameters from the nozzle exit plane. With the shrouding combustion flame, the oxygen METALLURGICAL AND MATERIALS TRANSACTIONS B
jet remains coherent up to 42 nozzle exit diameters before the velocity starts to decrease. The shrouding flow injection and the subsequent combustion affects the compression and expansion wave structure within the main jet. The longer coherent length of the shrouded jet is a result of the reduction in the growth rate of turbulent mixing layer caused by the combustion flame, which has been described in Section III–C. Papamoschou and Roshko[24] showed that the growth rate of the turbulent mixing layer decreases when the ratio of the
Fig. 5—Axial velocity distributions at the jet centerline of supersonic oxygen jet with and without shrouding flame.
surrounding ambient density to the jet density decreases. The combustion flame creates a low-density region surrounding the main supersonic jet as shown in Figure 6 and thus reduces the growth rate of the turbulent mixing region. As a result, the shrouded jet spreads slowly compared with the conventional jet. The CFD results are in good agreement with the experimental results[5] of the conventional jet. For the shrouded jet, the CFD model overpredicts the axial velocity by 6 pct in the coherent region. This may be a result of the assumption of using annular rings instead of discrete holes for the CH4 and shrouding O2 inlets. Injection from the discrete holes increases the mixing, and as a result of that, the experimental axial velocity of the jet is lower than the calculated velocity up to a certain distance after exiting from the Laval nozzle. The calculated jet velocity shows relatively quick diffusion compared with the experimental velocity after the coherent region. At X/De = 50 and 60, the difference between the CFD and the experimental result is about 30 pct. After 70 nozzle exit diameters, the CFD result shows good agreement with the experimental velocity. The reason for the quick diffusion after the coherent region may be because of the use of a single total diffusion coefficient for all different species involved in the combustion. Another reason may be the assumption of a one-step combustion reaction in the combustion modeling. In the real situation, this reaction has several steps. CO2 dissociates into CO and O2 at a high temperature of approximately 1500 K (1227 C).[13] Oxygen from the periphery of the jet reacts with the CO, which also reduces the growth rate of the turbulent mixing layer. The difference between the numerical and the experimental studies also may have resulted from
Fig. 6—CFD plot of density for the shrouded oxygen jet. METALLURGICAL AND MATERIALS TRANSACTIONS B
VOLUME 41B, DECEMBER 2010—1359
the uncertainties involved in the numerical procedure. The possible sources of uncertainties are expressed as follows: (a) The turbulence model used in the simulation. The modified k – e model used here was developed by the present authors[15] for simulating the supersonic gas jet behavior at steelmaking temperature with no combustion involved. This modified k – e model may result in some uncertainties in the flow velocity and flame temperature predictions when simulating the turbulent combusting flow. Jones and Whitelaw[25] reported some discrepancies in the measured and predicted velocity and temperature contours in their calculation of turbulent combusting flow using the standard k – e model. (b) Discretization of partial differential equations. An effort was made to overcome this error by using fine grids. (c) The differencing schemes used for solving the RANS equations. These differencing schemes introduce numerical diffusion error in the solution. As discussed earlier, higher order schemes (AVL SMART) were used in the momentum and continuity equations to minimize the numerical diffusion errors. The individual analysis of numerical error generated by the k – e turbulence model, differencing schemes, combustion model, and discretization procedure in the solution is beyond the scope of this study, but it can be said that the total numerical uncertainties in the solution are not more than the difference between the experimental and the numerical results, which is 6 pct in the coherent region and 30 pct in the region between X/De = 50 and 60. Figure 5 also shows the axial velocity distribution of the supersonic coherent oxygen jet at steelmaking conditions. In this study, we have considered only air at 1700 K (1427 C) as the steelmaking condition. In reality, the furnace environment consists of CO, CO2, O2, H2, N2, and some other minor species. The potential core length of the coherent oxygen jet is approximately 58 nozzle exit diameters at steelmaking condition, which is approximately 1.4 times larger than that of the coherent oxygen jet at room ambient temperature. This increase occurs because after the combustion flame the density of the gases surrounding the supersonic jet approaches the ambient density, which is much lower in steelmaking conditions. Hence, the jet spreads more slowly at steelmaking conditions because of the lowdensity ratio. No experimental data are available in the literature for the coherent jet at steelmaking temperatures because it is difficult to perform experimental studies at such high temperatures. Figure 7 shows the velocity distribution of the supersonic nitrogen jet with and without a shrouding flame at room ambient temperature. The potential core length of the shrouded nitrogen jet is more than three times longer than the conventional nitrogen jet. The shrouded nitrogen jet remains coherent up to 32 nozzle exit diameters compared with 10 nozzle exit diameters for the conventional jet. The CFD results for the shrouded nitrogen jet are in good agreement with the experimental data with an 1360—VOLUME 41B, DECEMBER 2010
Fig. 7—Axial velocity distributions at the jet centerline of supersonic nitrogen jet with and without shrouding flame.
Fig. 8—Half-jet width of the supersonic oxygen and nitrogen jets with and without shrouding flame.
average of 6 pct deviation only. From Figures 5 and 7, it is evident that the increase in potential core length by the use of a shrouding flame is higher for supersonic oxygen jet compared with the supersonic nitrogen jet. The explanation behind this observation is described in the next section. Figure 8 shows the dimensionless half-jet width of the supersonic oxygen and nitrogen jet with and without shrouding combustion flame. ‘‘Half-jet width’’ refers to the radial distance from the jet centerline where the velocity of the jet becomes half of the axial velocity. The figure shows that the half width of the jet is similar for the conventional nitrogen and oxygen jet. The jet width increases slowly up to X/De = 10, which is the coherent region, and then starts to increase at a higher rate. For the shrouded oxygen jet, the jet width increases just after the exit from the nozzle up to X/De = 1 and then increases slowly up to 42 nozzle exit diameters, and after that, it starts to increase at a higher rate. The reason for the rapid increase in jet width just after the exit from the nozzle is the additional combustion at the periphery of METALLURGICAL AND MATERIALS TRANSACTIONS B
the central O2 jet. Because of the combustion, the density of the gases is low at this region, which in turn accelerates the gas mixtures at the jet periphery equal to
the supersonic jet velocity and results in the increase of jet width just after the exit from the Laval nozzle. For the supersonic shrouded nitrogen jet, the jet width increases slowly up to X/De = 32 and then increases at a higher rate. This rate of increase of jet width also can be defined as the jet spreading rate of the jet, which is expressed as follows[26]: Sp ¼
Fig. 9—Axial static temperature distributions at the jet centerline of shrouded oxygen and nitrogen jet.
r1=2 X X0
½13
where Sp is the jet spreading rate, r1=2 is the width of the half value of jet axial velocity, and X0 is the potential core length of the jet. Figure 8 shows that the spreading of the jet is restrained by the use of a shrouding combustion flame. In other words, the shrouding combustion flame dramatically reduces the entrainment of the ambient fluid into the central supersonic jet. The figure also shows that all four different jets spread at a constant rate after the potential core length of the jet. The spreading rate is 0.107 for all four cases, which is in excellent agreement with the theoretical spreading rate
Fig. 10—(a) Shape of the combustion flame for shrouded oxygen jet. (b) Shape of the combustion flame for shrouded nitrogen jet. METALLURGICAL AND MATERIALS TRANSACTIONS B
VOLUME 41B, DECEMBER 2010—1361
of 0.1 for a free turbulent jet.[26] This is because after the potential core region the flow becomes fully turbulent and acts as a free turbulent jet for all cases. B. Temperature Distribution Figure 9 shows the static axial temperature distribution for both the supersonic oxygen and nitrogen jet with the shrouding combustion flame. The temperature of the supersonic jets shows some fluctuation after exiting from the Laval nozzle, increases rapidly from the flame end position to a maximum value, and then decreases slowly to ambient temperature. The reason for the difference in static temperature of the O2 and N2 jets after exiting from the Laval nozzle is the use of similar
stagnation temperature for both jets. The different gases lead to different static temperatures for the same stagnation temperature. Sumi et al.[27] also observed the similar axial static temperature distribution in their experimental study. This distribution is most likely because at the end of the coherent length the central jet mixes with the surrounding hot atmosphere created by the combustion flame, and the temperature of the jet increases. After this increase, heat transfer occurs from the jet to the ambient fluid, and the temperature of the jet slowly approaches the ambient condition. The numerical results of Jeong et al.[12] did not predict this type of behavior. Figures 10(a) and (b) show the shape of combustion flame for both the oxygen and the nitrogen jet.
Fig. 11—(a) CFD plot of vorticity contour for conventional oxygen jet. (b) CFD plot of vorticity contour for shrouded oxygen jet. 1362—VOLUME 41B, DECEMBER 2010
METALLURGICAL AND MATERIALS TRANSACTIONS B
The maximum flame temperature is different for the two cases. As expected, the flame maximum temperature is higher for the oxygen jet because of the availability of extra oxygen. For the shrouded oxygen jet, Figure 10(a) shows two combustion flames just after the exit from the nozzle because oxygen is supplied from both the central Laval nozzle and the outer ring of holes as shown in Figure 3 and fuel is injected from the inner ring of holes. Combustion occurs from both sides of the fuel stream, and the two flames merge to form a single flame downstream of their initial reaction zone. The flame temperature becomes maximum at around X/De = 10. The axial velocity distribution in the previous section shows that the coherent length of the shrouded oxygen jet is higher than the shrouded nitrogen jet because of the secondary flame, which is generated at the periphery of the shrouded oxygen jet along with the primary combustion flame. The combustion that occurs in the shear-mixing layer acts as a suppressant that delays the mixing of the central oxygen jet with the surrounding ambient. However, for the shrouded nitrogen jet, this secondary flame structure cannot form. The flame temperature for the shrouded nitrogen jet reaches its maximum just after the exit from the nozzle as shown in Figure 10(b). Then because of the high suction effect of the supersonic jet, the flame moves toward the central supersonic jet and propagates along with it. The predicted maximum combustion flame temperature fluctuated by 4 pct throughout the simulation. It varied with time from around 3450 K (3177 C) to 3600 K (3327 C) for the supersonic oxygen jet, which represents the actual turbulent combustion scenario.[28,29] For the supersonic nitrogen jet, it varied from 2400 K (2127 C) to 2500 K (2227 C). The
predicted flame temperature distributions that are shown in Figure 10 are instantaneous values. C. Vorticity and Turbulent Shear Stress Distribution The vorticity is a measure of the rotation of a fluid element as it moves in the flow field. Vorticity is also a measure of mixing among the fluids. The higher the vorticity, the greater the mixing. In Cartesian coordinates, the vorticity vector is expressed as follows: ! ! ! f ¼rU ½14 When the supersonic jet passes through the relatively still air, rotational flow is developed at the periphery of the jet because of a large velocity gradient at that region. Figure 11 shows the vorticity contour of the supersonic oxygen jet with and without a shrouding flame. For the supersonic jet without a shrouding flame, the vorticity region merges to the jet centerline more quickly compared with the supersonic jet with a shrouding flame because the shrouding flame delays the mixing of the central supersonic jet with the surroundings. Figure 12 shows the vorticity magnitude in radial direction at X/De = 1, 3, 8, and 12. The figure shows that the shrouding flame has shifted the vorticity region far from the jet periphery (radial distance/De = 0.5). With the increasing distance from the nozzle exit plane, the vorticty region gradually is approaching the jet centerline, and the shrouding flame is delaying the merging of the vorticity region with the jet centerline. For example, at X/De = 12, the vorticty region extends to the jet centerline for the conventional oxygen jet, whereas the vorticity region is still at the jet periphery of the
Fig. 12—Radial distribution of vorticity magnitude at different axial locations for both conventional and shrouded oxygen jet. METALLURGICAL AND MATERIALS TRANSACTIONS B
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shrouded oxygen jet. For the shrouded jet, additional vorticity regions are created by the shrouding gases just after the exit from the nozzle as shown in Figure 12 (X/ De = 1). However, the magnitude of the vorticity becomes negligible with the increasing distance from the nozzle exit plane. Figure 13 shows the turbulent shear stress distribution of the supersonic oxygen jet for both the shrouding and the nonshrouding cases. For the shrouded oxygen jet, the maximum shear stress value in the shear layer is approximately half that of the conventional jet. The shrouding combustion flame reduces the density of the gases surrounding the main supersonic jet, which in turn reduces the viscosity and turbulent shear stress in the shear layer. The reduced turbulent shear stress then delays the mixing of supersonic oxygen jet with the surroundings, which in turn increases the potential core length of the jet. With the shrouding flame, the shearmixing layer merges with the jet centerline at approximately 40 nozzle exit diameters, which is approximately equal to the potential core length of the coherent
supersonic jet. For the conventional jet, the shearmixing layer merges with the jet centerline at around 10 nozzle exit diameters showing the end of the potential core region of the jet. D. Species Mass Fractions Figure 14 shows the mass fraction of the oxygen along the central axis of the supersonic oxygen jet for both the shrouding and nonshrouding cases. After the potential core region, the mass fraction of oxygen in the central jet starts to decrease and becomes equal to the ambient oxygen mass fraction. In steelmaking, oxygen is used to refine the liquid iron into steel, and knowledge of the oxygen mass fraction distribution at the liquid–metal interface is important for calculating the iron oxidation and decarburization rates. Also the higher the oxygen content at the impact area, the greater the temperature developed at the impact zone.[30] Figure 15 shows the radial profile of the CO2 mass fraction for the supersonic shrouded O2 jet at different
Fig. 13—(a) CFD plot of turbulent shear stress for conventional oxygen jet. (b) CFD plot of turbulent shear stress for shrouded oxygen jet. 1364—VOLUME 41B, DECEMBER 2010
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Fig. 14—Axial mass fraction distributions at the jet centerline of conventional and shrouded oxygen jet.
axial locations X/De = 1, 3, 8, and 12. This figure shows two peaks of CO2 mass fraction at X/De = 1 and 3 and only shows one peak at X/De = 8 and 12 because of the formation of two combustion flames just after the exit of the nozzle as discussed earlier. When the two flames merge, radial distribution of the CO2 mass fraction shows only one peak. Figure 16 shows the radial profile of the mass fraction of CO2 at the same axial locations for the supersonic coherent nitrogen jet. As expected, only one peak of CO2 mass fraction is noted because combustion occurs only on one side of the fuel stream. Figure 17 shows the calculated CO2 mass fraction distribution for the supersonic coherent O2 jet. The figure shows that the CO2 mass fraction is higher in the vicinity of the combustion flame because CO2 is the product of combustion. The mass fraction of H2O shows a similar trend to that of CO2 and therefore was not presented here.
Fig. 15—Radial distributions of the CO2 mass fractions at different axial locations for shrouded oxygen jet.
Fig. 16—Radial distributions of the CO2 mass fractions at different axial locations for shrouded nitrogen jet.
Fig. 17—CFD plot of the CO2 mass fractions for shrouded oxygen jet. METALLURGICAL AND MATERIALS TRANSACTIONS B
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IV.
CONCLUSIONS
CFD simulation of the supersonic oxygen and nitrogen jet with and without shrouding flame were performed. The present study showed that the shrouding combustion flame reduces the entrainment of the surrounding gas to the central supersonic jet, which results in a low spreading rate for the coherent supersonic jet. It also reduces the magnitude of turbulent shear stress in the shear layer, which in turn delays the mixing of the supersonic jet with the surroundings. As a result, the potential core length of the supersonic coherent jet is increased compared with the conventional jet. The potential core length of the shrouded oxygen jet is more than four times greater than the conventional oxygen jet. At steelmaking temperatures, the potential core length of the coherent supersonic oxygen jet is 1.4 times greater than that at room ambient temperature. For the shrouded nitrogen jet, the potential core length is more than times greater than the conventional nitrogen jet. The CFD results showed a good agreement with the experimental data. The present study only considered the one-step complete combustion between CH4 and O2. In reality, this combustion occurs in several steps. Apart from CO2 and H2O, some other minor species like CO, H2, and OH also are produced.[13] For the coherent supersonic oxygen jet, the CO produced by incomplete combustion of CH4 gas reacts with the O2, which also creates a flame surrounding the jet and affects the potential core length of the jet. Additional work is required to incorporate the multistep combustion reaction. The CFD model only was validated against experimental velocity distribution data. No experimental data are available in the literature for the flame temperature or mass fraction of different species to compare the CFD results against the experimental data. Hence, more experimental study is required to establish a more rigorous CFD model of the coherent supersonic jet. The present study can provide some useful insights into coherent jet technology. The shape and temperature of the combustion flame is important for coherent jets, and this study shows that the combustion flame temperature varies significantly when different gases are used as a central supersonic jet. The model developed also predicts the location of the hot spots of the combustion flame as well as the impact velocity distribution for different blowing conditions. The impact velocity of the gas jet on a liquid surface will be higher if the potential core length is increased, which also should increase the droplet generation rate;[31] although, it is claimed that coherent jets produce less splashing.[4,6] This model also can provide the distribution of mass fractions of different species, which is important to the process. The mass fraction of different species inside the furnace affects the partial pressure of the gases inside the furnace, which in turn influences the kinetics of the reactions inside the furnace. The model developed in the present study should be helpful in determining the optimum flow rate of the shrouding gas and in designing a more efficient coherent jet nozzle. 1366—VOLUME 41B, DECEMBER 2010
ACKNOWLEDGMENT The authors would like to thank the members of the One Steel, Melbourne for their financial support and useful discussions in this project.
NOMENCLATURE Di E H k P Prt Sct Sfu Sp T t U u X Yi q l lt c e 2 f De
diffusion coefficient of species i radiative heat transfer (J/s) total enthalpy (J/kg) turbulent kinetic energy (m2/s2) pressure (N/m2) turbulent Prandtl number turbulent Schmidt number volumetric rate of fuel consumption (kg/m3 s) spreading rate temperature (K) time (s) velocity (m/s) fluctuating velocity (m/s) distance (m) mass fraction of species i density (kg/m3) molecular viscosity (Ns/m2) turbulent viscosity (Ns/m2) thermal conductivity (W/mK) turbulent dissipation rate (m2/s3) emissivity vorticity (1/s) nozzle exit diameter (m)
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