computational fluid dynamics modeling of supersonic coherent jets for electric arc furnace...

Computational Fluid Dynamics Modeling of SupersonicCoherent 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 manyother industrial applications to increase the gas–liquid mixing, reaction rates, and energyefficiency of the process. However, there has been limited research on the basic physics ofsupersonic coherent jets. In the present study, computational fluid dynamics (CFD) simulationof the supersonic jet with and without a shrouding flame at room ambient temperature wascarried out and validated against experimental data. The numerical results show that thepotential core length of the supersonic oxygen and nitrogen jet with shrouding flame is morethan four times and three times longer, respectively, than that without flame shrouding, which isin good agreement with the experimental data. The spreading rate of the supersonic jetdecreased dramatically with the use of the shrouding flame compared with a conventionalsupersonic jet. The present CFD model was used to investigate the characteristics of thesupersonic coherent oxygen jet at steelmaking conditions of around 1700 K (1427 �C). Thepotential core length of the supersonic coherent oxygen jet at steelmaking conditions was 1.4times 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 widelyfor refining the liquid iron and stirring the liquid meltinside the furnace. Supersonic gas jets are preferred oversubsonic jets because of the high dynamic pressureassociated with it that results in a higher depth ofpenetration and better mixing. Laval nozzles are used toaccelerate the gas jets to supersonic velocities ofapproximately 2.0 Mach number in steelmaking.[1]

When a supersonic gas jet exits from a Laval nozzle, itinteracts with the surrounding environment to produce aregion of turbulent mixing. This process results in anincrease in jet diameter and in a decrease in jet velocitywith increasing distance from the nozzle exit.[1] Duringoxygen blowing, the higher the distance between theliquid surface and the nozzle exit, the greater theentrainment of surrounding fluid, which in turndecreases the impact velocity as well as the depth ofpenetration on the liquid surface. As a result, the mixingof gas and liquid inside the furnace decreases, which alsoreduces the reaction rates because of the small gas–liquid interfacial area. Hence, it is desirable to locate thenozzle close to the liquid-metal surface. The disadvan-tage of this process is the sticking of slag/metal droplets

on the lance tip, which results in poor tip life.[2,3] Toovercome the problem, coherent jet technology wasintroduced in the EAF steelmaking process at the end oflast century.[4,5] Coherent gas jets are produced byshrouding the conventional supersonic jet with a flameenvelope. The flame envelope is created using a fuel andoxidant. Figure 1 shows a schematic of a conventionaland coherent supersonic jet.[6]

Because of the flame envelope, the entrainment of thesurrounding gas into the supersonic jet is reduced,leading to a higher potential core length (the length upto which the axial jet velocity is equal to the exit velocityat the nozzle) of the supersonic jet. The longer potentialcore length of the coherent supersonic jet makes itpossible to install the nozzle far from the liquid surface.In the modern EAF, the shrouding oxygen and fuel areused as burner during the melting period and thusincrease the efficiency of the process.[7] It also is claimedto produce less splashing than that produced byconventional supersonic jet on the furnace wall.[8]

Although the steelmaking industries have been usingthe coherent supersonic jets for the last 10 years, limitedresearch work has been performed to investigate thephysics of supersonic coherent jets. Anderson et al.[5]

were the first to carry out an experimental study ofsupersonic coherent jets. Recently, Mahoney[9] investi-gated the effect of the shrouding fuel and oxygen flowrate on the potential core length of the supersoniccoherent jet. Meidani et al.[10] also carried out anexperimental study of a shrouded supersonic jet usingcompressed air as shrouding gas. In their study, nocombustion flame surrounded the main supersonic jet.Some numerical studies[7,11,12] of supersonic jets withshrouding flame are available in the literature, butmost[7,11] were not validated against experimental

MORSHED ALAM, Ph.D. Student, JAMAL NASER, SeniorLecturer, and GEOFFREY BROOKS, Professor, are with theFaculty of Engineering and Industrial Sciences, Swinburne Universityof Technology, Hawthorn, Victoria 3122 Australia. Contact e-mail:[email protected]. ANDREA FONTANA, Senior ProcessEngineer, is with Primary Steelmaking Manufacturing, One SteelLaverton, Laverton North, Victoria 3026, Australia.

Manuscript submitted April 28, 2010.Article published online September 28, 2010.

1354—VOLUME 41B, DECEMBER 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B

results. The numerical simulation, performed by Jeonget al.,[12] underpredicted the potential core length of thesupersonic coherent jets. In the present study, compu-tational fluid dynamics (CFD) simulation of a super-sonic jet with and without a shrouding flame at roomambient temperature was carried out. The CFD resultsshowed good agreement with the experimental data.[5]

The major characteristics of the supersonic coherent jetwere investigated for the purpose a clearer understand-ing of how the technology works. This CFD model thenwas used to investigate the characteristics of thesupersonic 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 thenumerical simulations. The averaged mass, momentum,and energy equations can be written in a conservativeform.

The mass conservation equation is expressed asfollows:

@q@tþ @qUi

@Xi¼ 0 ½1�

where q is the density of the fluid and Ui is the meanvelocity component in the ith direction.

The momentum conservation equation is expressed asfollows:

@qUi

@tþ@ qUiUj

� �

@Xj¼ �@P

@Xiþ@ sij � quiuj� �

@Xj½2�

sij ¼ l@Ui

@Xjþ @Uj

@Xi� 2

3

@Uk

@Xkdij

� �

where P is the pressure of fluid, sij is viscous stress,ui and uj are the fluctuating velocity component in theith and jth directions, respectively, l is the molecu-lar viscosity, and dij is the Kronecker delta (dij = 1if i = j and dij = 0 if i „ j). �quiuj is known as

‘‘Reynold stresses’’ and is used to represent the effect ofturbulence. The Reynold stresses are modeled accordingto the following Boussinesq approximation[13]:

�quiuj ¼ lt

@Ui

@Xjþ @Uj

@Xi

� �� 2

3qkþ lt

@Uk

@Xk

� �dij ½3�

where lt is the turbulent viscosity and k is the turbulentkinetic energy. The modeling of turbulent viscosity andturbulent kinetic energy will be described later.The energy conservation equation is expressed as

follows:

@qH@tþ @ðqHUiÞ

@Xi¼ @

@Xicþ lt

Prt

� �@T

@Xi

� �þ @P@t

þ @

@XisijUj � quiujUj

� �þ SE ½4�

where H is the total enthalpy, c is the thermal conduc-tivity, Prt is the turbulent Prandtl number, and SE is theinternal source of energy (combustion and radiation).The most common values of the turbulent Prandtlnumber is 0.9, and it is satisfactory for shock-free flowswith low supersonic speeds and a low heat transferrate.[14] Wilcox[14] recommended using Prt = 0.5 for freeshear flow and high heat transfer problems. Hence,Prt = 0.5 was used in this study.To close the RANS equations, the temperature-

corrected k – e turbulence model[15] was used, which isa modification of the original k – e model proposed byLaunder and Spalding.[16] This modification was done totake into account the effect of temperature gradient onthe turbulent mixing region. In the k – e model, theturbulent kinetic energy k and the dissipation rate e areobtained from the following transport equations:

@qk@tþ @qUjk

@Xj¼ �qujui

@Ui

@Xjþ @

@Xjlþ lt

rk

@k

@Xj

� �� qe ½5�

@qe@tþ @qUje

@Xj¼ � Ce1qujui

@Ui

@Xj

ekþ @

@Xjlþ lt

re

@e@Xj

� �

� Ce2qe2

k½6�

Fig. 1—Schematics of a (a) conventional and (b) coherent supersonic jet.[6]

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, DECEMBER 2010—1355

where Ce1, Ce2, rk, and re are the constants for the k – emodel, and their values are 1.44, 1.92, 1.0, and 1.3,respectively.

The turbulent viscosity lt is defined as follows:

lt ¼ Clqk2

e½7�

The value of Cl was determined from the followingequation[15]:

Cl ¼0:09

1þ 1:2T0:6g

1þf Msð Þ

h i ½8�

where Tg is the temperature gradient normalized bylength scale and f(Ms) takes into account the compress-ibility effect. Equation [8] modifies the value of Cl

depending on the value of the temperature gradient atthe shear layer.

B. Combustion Modeling

The fuel and oxidizing agents used in the present studywere CH4 and O2. N2 and O2 were used as the centralsupersonic jet. A one-step-complete combustion reactionbetween CH4 and O2 was considered in this study. Theproducts of combustion were CO2 and H2O. In practice,however, at high temperatures, dissociation of CO2 andH2O occurs, which results in minor species like CO, H2,OH, and O2 in the products of combustion along withthe main reaction products CO2 and H2O. Dissociationreactions are endothermic; therefore, the actual flametemperature will be lower than the calculated flametemperature based on the complete combustion reac-tion.[13] But this assumption of a one-step-completecombustion reaction made the calculation simple as wellas reduced the computational time. The equation ofcombustion reaction is expressed as follows[13]:

CH416Kgþ 2O2

64Kg¼ CO2

44Kgþ 2H2O

36Kg½9�

The mass fraction of the species involved in thereaction is determined by solving a separate scalartransport equation for each species, which can bewritten conservatively as follows:

@qYi

@tþ@ qYiUj

� �

@Xj¼ � @

@XjqDi þ

lt

Sct

� �@Yi

@Xj

� �þ Si ½10�

where Yi is the mass fraction, Di is the laminar diffu-sion coefficient, and Si is the source term of speciesi. In the present study, a single diffusion coefficient ofthe gas mixture was assumed for all species (i.e.,Di = D for i = 1, 2, 3 … N, where N is the number ofspecies). The gas mixture diffusion coefficient was cal-culated assuming the laminar Schmidt numberSc = 0.7. As the flow is highly compressible, the lami-nar diffusion coefficient will have a negligible effect onthe diffusion of the species. The turbulent diffusioncoefficient affects the diffusion of different species inthe flow field. The turbulent diffusion coefficient wasdetermined by dividing the turbulent viscosity lt of the

gas mixtures by the turbulent Schmidt numberSct = 0.9. Hence, it is shown that the total diffusioncoefficient was the same for all species involved in thereaction. The source term of the species transportequation is the rate of mass production / reduction ofthat particular species. When the species transportequation for the fuel (CH4) was solved, the rate of fuelconsumption was determined by solving the followingEddy Break-Up combustion model[17]:

Sfu ¼ qekmin AYfu;A

Yox

s;B

Ypr

sþ 1

� �½11�

where Sfu is the volumetric rate of fuel consumption.A and B are the model constants, and s is thestoichiometric ratio. Yfu, Yox, and Ypr are the massfractions of the fuel, oxygen, and product of combus-tion, respectively. The Eddy Break-Up model makesgood predictions and is fairly straightforward to imple-ment in CFD calculations.[13] In the Eddy Break-Upmodel, the rate of fuel consumption is specified as afunction of local flow and thermodynamic properties.According to this model, the rate of combustion isdetermined by the rate of intermixing on a molecularscale of eddies containing reactants and those containinghot products; in other words, it is determined by the rateof dissipation of these eddies. This model calculates theindividual dissipation rates of fuel, oxygen, and prod-ucts, and the actual consumption rate is equal to theslowest of the three dissipation rates as is shown inEq. [11].[13] The first two terms inside the bracket ofEq. [11] simply determine whether fuel or oxygen ispresent in limiting quantity, and the third term ensuresthat the flame does not spread in the absence of hotproducts. In the present study, the values of A = 4 andB = 0.5 were used based on a previous study.[17] Fromthe combustion reaction, it is observed that the stoichi-ometric ratio of fuel and oxidizer is s = 4, which meansthat for complete combustion of 1 kg CH4, 4 kg O2 isrequired. Hence, the rate of O2 consumption is taken asfour times the rate of fuel consumption. The volumetricrate of fuel consumption Sfu was calculated in each cellby using Eq. [11], multiplied by the heat of combustionof that particular fuel, and then added as a source termto the energy equation to calculate the temperature.

C. Radiation Modeling

The radiative heat transfer from a system becomesimportant when the temperature exceeds 1500 K(1227 �C).[13] Here, the flame temperature of the com-bustion is around 3500 K (3227 �C), so the radiationheat transfer needs to be considered. The modeling ofthe radiation was performed using the following well-known Stefan–Boltzmann formula:

E ¼2 rA T41 � T4

2

� �½12�

where E is the radiative heat transfer per unit time, 2 isthe gas emissivity, r = 5.6703 9 10�8 W/(m2 K4) is theStefan-Boltzmann constant, A is the area of emittingbody, and T1 and T2 are the temperature of source andsink, respectively. The emissivity of a medium depends


on local fluid properties.[13] The normal atmospheric airis transparent and thus does not participate in radiativeheat exchange. Products of combustion, however, con-tain a high concentration of CO2 and H2O, which areboth strong absorbers and emitters. The weighted sumof gray gases model (WSGGM)[18] normally is used fordefining the temperature- and species-concentration-dependent emissivity of the medium. For a different gasconcentration and temperature, the emissivity of gasesvaried from 0.3 to 0.5 using the WSGGM model. In thepresent study, a constant value of the gas emissivity2 = 0.5 was used for simplicity. The radiation energyE was calculated in each cell using Eq. [12] and thensubtracted from the energy equation.

D. Computational Domain

The schematic diagram of the computational domainwith boundary conditions, used in the present CFDsimulation, is shown in Figure 2. The computationaldomain is axisymmetric and wedge shaped with onlyone cell in circumferential direction. To reduce thecomputational time, flow inside the Laval nozzle wasnot included in the simulation. The flow conditions atthe nozzle exit were calculated using isentropic the-ory.[19] The exit diameter of the nozzle was 0.0147 m and

was considered as one of the inlets to the computationaldomain. The computational domain was 105 nozzle exitdiameters downstream from the nozzle exit and was 20nozzle exit diameters normal to the jet centerline. In theexperimental study, CH4 and O2 were injected throughthe holes arranged in two concentric rings surroundingthe main convergent-divergent nozzle as shown inFigure 3. The inner ring of holes was used for the CH4

gas, and the outer ring of holes was used for theshrouding oxygen supply. The diameters of the holeswere 0.00287 m and 0.00408 m for CH4 and O2,respectively. In the present study, the configuration ofthe nozzle, injecting CH4 and O2, was assumed annular,which is different from three-dimensional real nozzles.However, the injecting areas were adjusted to maintainthe same flow rates for CH4 and O2 as was used in theexperimental study.[5] This assumption made it possibleto solve the problem in two dimensions.

E. Boundary Conditions

All boundary conditions were chosen to match withthe experimental study of Anderson et al.[5] A stagna-tion pressure boundary condition was used at the mainsupersonic jet inlet of the computational domain (exit ofthe 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]


Mach number and temperature were defined at thesupersonic jet inlet. For the CH4 and shrouding O2 inlet,the mass flow rate boundary condition was used. Theoriginal mass flow rates were divided by 360 because theincluded angle of the two-dimensional computationaldomain is 1 deg. At the outlet, a static pressureboundary condition was used. For the symmetry plane,the symmetry boundary condition was used. At the solidwall, a no-slip boundary condition was imposed. Thevalues of the boundary conditions when oxygen wasused as the central supersonic jet are listed in Table I.When nitrogen was used as the central supersonicjet, only the supersonic jet inlet boundary conditionwas changed from 100 pct oxygen to 100 pct nitrogen,and the rest of the boundary conditions were keptunchanged. Although it is known that the different gaseslead to different static pressures and temperatures forsimilar stagnation conditions, we have used similarstagnation conditions for both the nitrogen and theoxygen jets to match with the experimental study.

F. Computational Procedure

The unsteady, compressible continuity, momentum,and energy equations were solved using a segregatedsolver with an implicit approach to calculate thepressure, velocity, temperature, and density. Formomentum and continuity equations, the values of thevariables at cell faces were calculated using AVLSMART scheme,[20] which is a higher order accuratetotal variable diminishing scheme. AVL SMARTscheme is a modification of the original SMART schemeproposed by Gaskell and Lau.[21] For energy andturbulence equations, the first order upwind schemewas used. The pressure–velocity correction was done byusing the SIMPLE algorithm.[22] To advance the solu-tion in time, a first order Euler scheme[20] was used. Asthe velocity of the flow was high, the time step used inthe unsteady calculation was 1 9 10�5 s. The simula-tions were assumed converged when the normalizedresiduals of the flow variables (pressure, velocity,temperature, etc.) drop down by four orders of magni-tude. The simulations were carried out using commercialCFD software AVL FIRE 2008.2, which is based on thecontrol volume approach.

G. Grid Independency Test

To study the grid sensitivity of the solution, calcula-tions for the supersonic coherent oxygen jet were doneusing 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 levelsis shown in Figure 4. The average percentage ofvariation of the axial velocity profile calculated withthe coarse and medium grid level was less than 3 pct,with a maximum deviation of 6 pct between the regionof X/De = 40 and 60. The average percentage ofvariation was calculated by averaging the differences atseveral locations in the axial direction. Between themedium and the fine grid levels, the variation isnegligible (less than 1 pct). Hence, it can be said thatthe solution is not sensitive to the grid. The computa-tional time required for the fine grid level was approx-imately twice that for the medium grid level. Hence, theresults obtained with the medium grid were used foranalysis and discussion in the present study.

III. RESULTS AND DISCUSSION

A. Velocity Distribution

Figure 5 shows the velocity distribution of the super-sonic oxygen jet with and without a shrouding flame atroom ambient temperature. For both cases, the center-line jet velocity shows repeated fluctuations just after theexit from the Laval nozzle. This occurs as a result of theincorrect expansion of the supersonic jet. The jet ismildly underexpanded because the ratio of nozzle exitpressure to the ambient pressure in the present study isaround 1.18.[23] The potential core length of the super-sonic oxygen jet with the shrouding flame is more thanfour times larger than that without the shrouding flame.The supersonic jet without the shrouding flame will beaddressed as a conventional jet from hereafter. Thevelocity of the conventional oxygen jet decreases grad-ually after 10 nozzle exit diameters from the nozzle exitplane. With the shrouding combustion flame, the oxygen

Table I. Boundary Conditions

Name of BoundaryType of Boundary

Conditions Values

Supersonicjet inlet

stagnation pressure 914,468 Pamach number 2.1total temperature 298 K (25 �C)mass fractions O2 = 100 pct

Fuel inlet mass flow rate 1.833 9 10�5 Kg/smass fractions CH4 = 100 pct

Shroudingoxygen inlet

mass flow rate 3.488 9 10�5 Kg/smass fractions O2 = 100 pct

Outlet static pressure 100,000 Pamass fractions O2 = 23 pct,

N2 = 77 pctWall no-slip 298 K (25 �C)

Fig. 4—Axial velocity distributions at the jet centerline of shroudedoxygen jet using coarse, medium and fine grid levels.


jet remains coherent up to 42 nozzle exit diametersbefore the velocity starts to decrease. The shroudingflow injection and the subsequent combustion affects thecompression and expansion wave structure within themain jet. The longer coherent length of the shrouded jetis a result of the reduction in the growth rate ofturbulent mixing layer caused by the combustion flame,which has been described in Section III–C. Papamosc-hou and Roshko[24] showed that the growth rate of theturbulent mixing layer decreases when the ratio of the

surrounding ambient density to the jet density decreases.The combustion flame creates a low-density regionsurrounding the main supersonic jet as shown inFigure 6 and thus reduces the growth rate of theturbulent mixing region. As a result, the shrouded jetspreads slowly compared with the conventional jet.The CFD results are in good agreement with the

experimental results[5] of the conventional jet. For theshrouded jet, the CFD model overpredicts the axialvelocity by 6 pct in the coherent region. This may be aresult of the assumption of using annular rings insteadof 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 ofthe jet is lower than the calculated velocity up to acertain distance after exiting from the Laval nozzle. Thecalculated jet velocity shows relatively quick diffusioncompared with the experimental velocity after thecoherent region. At X/De = 50 and 60, the differencebetween the CFD and the experimental result is about30 pct. After 70 nozzle exit diameters, the CFD resultshows good agreement with the experimental velocity.The reason for the quick diffusion after the coherentregion may be because of the use of a single totaldiffusion coefficient for all different species involved inthe combustion. Another reason may be the assumptionof a one-step combustion reaction in the combustionmodeling. In the real situation, this reaction has severalsteps. CO2 dissociates into CO and O2 at a hightemperature of approximately 1500 K (1227 �C).[13]Oxygen from the periphery of the jet reacts with theCO, which also reduces the growth rate of the turbulentmixing layer.The difference between the numerical and the

experimental studies also may have resulted fromFig. 5—Axial velocity distributions at the jet centerline of supersonicoxygen jet with and without shrouding flame.

Fig. 6—CFD plot of density for the shrouded oxygen jet.


the uncertainties involved in the numerical procedure.The possible sources of uncertainties are expressed asfollows:

(a) The turbulence model used in the simulation. Themodified k – e model used here was developed by thepresent authors[15] for simulating the supersonic gasjet behavior at steelmaking temperature with nocombustion involved. This modified k – e model mayresult in some uncertainties in the flow velocity andflame temperature predictions when simulating theturbulent combusting flow. Jones and Whitelaw[25]

reported some discrepancies in the measured andpredicted velocity and temperature contours in theircalculation of turbulent combusting flow using thestandard k – e model.

(b) Discretization of partial differential equations. Aneffort was made to overcome this error by using finegrids.

(c) The differencing schemes used for solving the RANSequations. These differencing schemes introducenumerical diffusion error in the solution. As dis-cussed earlier, higher order schemes (AVL SMART)were used in the momentum and continuity equa-tions to minimize the numerical diffusion errors.

The individual analysis of numerical error generatedby the k – e turbulence model, differencing schemes,combustion model, and discretization procedure in thesolution is beyond the scope of this study, but it can besaid that the total numerical uncertainties in the solutionare not more than the difference between the experi-mental and the numerical results, which is 6 pct in thecoherent region and 30 pct in the region betweenX/De = 50 and 60.

Figure 5 also shows the axial velocity distribution ofthe supersonic coherent oxygen jet at steelmakingconditions. In this study, we have considered only airat 1700 K (1427 �C) as the steelmaking condition. Inreality, the furnace environment consists of CO, CO2,O2, H2, N2, and some other minor species. The potentialcore length of the coherent oxygen jet is approximately58 nozzle exit diameters at steelmaking condition, whichis approximately 1.4 times larger than that of thecoherent oxygen jet at room ambient temperature. Thisincrease occurs because after the combustion flame thedensity of the gases surrounding the supersonic jetapproaches the ambient density, which is much lower insteelmaking conditions. Hence, the jet spreads moreslowly at steelmaking conditions because of the low-density ratio. No experimental data are available in theliterature for the coherent jet at steelmaking tempera-tures because it is difficult to perform experimentalstudies at such high temperatures. Figure 7 shows thevelocity distribution of the supersonic nitrogen jet withand without a shrouding flame at room ambienttemperature. The potential core length of the shroudednitrogen jet is more than three times longer than theconventional nitrogen jet. The shrouded nitrogen jetremains coherent up to 32 nozzle exit diameters com-pared with 10 nozzle exit diameters for the conventionaljet. The CFD results for the shrouded nitrogen jet are ingood agreement with the experimental data with an

average of 6 pct deviation only. From Figures 5 and 7, itis evident that the increase in potential core length bythe use of a shrouding flame is higher for supersonicoxygen jet compared with the supersonic nitrogen jet.The explanation behind this observation is described inthe next section.Figure 8 shows the dimensionless half-jet width of the

supersonic oxygen and nitrogen jet with and withoutshrouding combustion flame. ‘‘Half-jet width’’ refers tothe radial distance from the jet centerline where thevelocity of the jet becomes half of the axial velocity. Thefigure shows that the half width of the jet is similar forthe conventional nitrogen and oxygen jet. The jet widthincreases slowly up to X/De = 10, which is the coherentregion, and then starts to increase at a higher rate. Forthe shrouded oxygen jet, the jet width increases just afterthe exit from the nozzle up to X/De = 1 and thenincreases slowly up to 42 nozzle exit diameters, and afterthat, it starts to increase at a higher rate. The reason forthe rapid increase in jet width just after the exit from thenozzle is the additional combustion at the periphery of

Fig. 7—Axial velocity distributions at the jet centerline of supersonicnitrogen jet with and without shrouding flame.

Fig. 8—Half-jet width of the supersonic oxygen and nitrogen jetswith and without shrouding flame.


the central O2 jet. Because of the combustion, thedensity of the gases is low at this region, which in turnaccelerates the gas mixtures at the jet periphery equal to

the supersonic jet velocity and results in the increase ofjet width just after the exit from the Laval nozzle. Forthe supersonic shrouded nitrogen jet, the jet widthincreases slowly up to X/De = 32 and then increases at ahigher rate.This rate of increase of jet width also can be defined

as the jet spreading rate of the jet, which is expressedas follows[26]:

Sp ¼r1=2

X� X0½13�

where Sp is the jet spreading rate, r1=2 is the width of thehalf value of jet axial velocity, and X0 is the potentialcore length of the jet. Figure 8 shows that the spreadingof the jet is restrained by the use of a shroudingcombustion flame. In other words, the shroudingcombustion flame dramatically reduces the entrainmentof the ambient fluid into the central supersonic jet. Thefigure also shows that all four different jets spread at aconstant rate after the potential core length of the jet.The spreading rate is 0.107 for all four cases, which is inexcellent agreement with the theoretical spreading rate

Fig. 9—Axial static temperature distributions at the jet centerline ofshrouded oxygen and nitrogen jet.

Fig. 10—(a) Shape of the combustion flame for shrouded oxygen jet. (b) Shape of the combustion flame for shrouded nitrogen jet.


of 0.1 for a free turbulent jet.[26] This is because after thepotential core region the flow becomes fully turbulentand acts as a free turbulent jet for all cases.

B. Temperature Distribution

Figure 9 shows the static axial temperature distribu-tion for both the supersonic oxygen and nitrogen jetwith the shrouding combustion flame. The temperatureof the supersonic jets shows some fluctuation afterexiting from the Laval nozzle, increases rapidly from theflame end position to a maximum value, and thendecreases slowly to ambient temperature. The reason forthe difference in static temperature of the O2 and N2 jetsafter exiting from the Laval nozzle is the use of similar

stagnation temperature for both jets. The different gaseslead to different static temperatures for the samestagnation temperature. Sumi et al.[27] also observedthe similar axial static temperature distribution in theirexperimental study. This distribution is most likelybecause at the end of the coherent length the central jetmixes with the surrounding hot atmosphere created bythe combustion flame, and the temperature of the jetincreases. After this increase, heat transfer occurs fromthe jet to the ambient fluid, and the temperature of thejet slowly approaches the ambient condition. Thenumerical results of Jeong et al.[12] did not predict thistype of behavior.Figures 10(a) and (b) show the shape of combus-

tion 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.


The maximum flame temperature is different for the twocases. As expected, the flame maximum temperature ishigher for the oxygen jet because of the availability ofextra oxygen. For the shrouded oxygen jet, Figure 10(a)shows two combustion flames just after the exit from thenozzle because oxygen is supplied from both the centralLaval nozzle and the outer ring of holes as shown inFigure 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 flamedownstream of their initial reaction zone. The flametemperature becomes maximum at around X/De = 10.The axial velocity distribution in the previous sectionshows that the coherent length of the shrouded oxygenjet is higher than the shrouded nitrogen jet because ofthe secondary flame, which is generated at the peripheryof the shrouded oxygen jet along with the primarycombustion flame. The combustion that occurs in theshear-mixing layer acts as a suppressant that delays themixing of the central oxygen jet with the surroundingambient. However, for the shrouded nitrogen jet, thissecondary flame structure cannot form. The flametemperature for the shrouded nitrogen jet reaches itsmaximum just after the exit from the nozzle as shown inFigure 10(b). Then because of the high suction effect ofthe supersonic jet, the flame moves toward the centralsupersonic jet and propagates along with it.

The predicted maximum combustion flame tempera-ture fluctuated by 4 pct throughout the simulation. Itvaried with time from around 3450 K (3177 �C) to3600 K (3327 �C) for the supersonic oxygen jet, whichrepresents the actual turbulent combustion sce-nario.[28,29] For the supersonic nitrogen jet, it variedfrom 2400 K (2127 �C) to 2500 K (2227 �C). The

predicted flame temperature distributions that areshown in Figure 10 are instantaneous values.

C. Vorticity and Turbulent Shear Stress Distribution

The vorticity is a measure of the rotation of a fluidelement as it moves in the flow field. Vorticity is also ameasure of mixing among the fluids. The higher thevorticity, the greater the mixing. In Cartesian coordi-nates, the vorticity vector is expressed as follows:

f!¼ r!� U

! ½14�

When the supersonic jet passes through the relativelystill air, rotational flow is developed at the periphery ofthe jet because of a large velocity gradient at that region.Figure 11 shows the vorticity contour of the supersonicoxygen jet with and without a shrouding flame. For thesupersonic jet without a shrouding flame, the vorticityregion merges to the jet centerline more quickly com-pared with the supersonic jet with a shrouding flamebecause the shrouding flame delays the mixing of thecentral supersonic jet with the surroundings. Figure 12shows the vorticity magnitude in radial direction atX/De = 1, 3, 8, and 12. The figure shows that theshrouding flame has shifted the vorticity region far fromthe jet periphery (radial distance/De = 0.5). With theincreasing distance from the nozzle exit plane, thevorticty region gradually is approaching the jet center-line, and the shrouding flame is delaying the merging ofthe vorticity region with the jet centerline. For example,at X/De = 12, the vorticty region extends to the jetcenterline for the conventional oxygen jet, whereas thevorticity 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.


shrouded oxygen jet. For the shrouded jet, additionalvorticity regions are created by the shrouding gases justafter the exit from the nozzle as shown in Figure 12 (X/De = 1). However, the magnitude of the vorticitybecomes negligible with the increasing distance fromthe nozzle exit plane.

Figure 13 shows the turbulent shear stress distribu-tion of the supersonic oxygen jet for both the shroudingand the nonshrouding cases. For the shrouded oxygenjet, the maximum shear stress value in the shear layer isapproximately half that of the conventional jet. Theshrouding combustion flame reduces the density of thegases surrounding the main supersonic jet, which in turnreduces the viscosity and turbulent shear stress in theshear layer. The reduced turbulent shear stress thendelays the mixing of supersonic oxygen jet with thesurroundings, which in turn increases the potential corelength of the jet. With the shrouding flame, the shear-mixing layer merges with the jet centerline at approx-imately 40 nozzle exit diameters, which is approximatelyequal to the potential core length of the coherent

supersonic jet. For the conventional jet, the shear-mixing layer merges with the jet centerline at around 10nozzle exit diameters showing the end of the potentialcore region of the jet.

D. Species Mass Fractions

Figure 14 shows the mass fraction of the oxygenalong the central axis of the supersonic oxygen jet forboth the shrouding and nonshrouding cases. After thepotential core region, the mass fraction of oxygen inthe central jet starts to decrease and becomes equal tothe ambient oxygen mass fraction. In steelmaking,oxygen is used to refine the liquid iron into steel, andknowledge of the oxygen mass fraction distribution atthe liquid–metal interface is important for calculatingthe iron oxidation and decarburization rates. Also thehigher the oxygen content at the impact area, the greaterthe temperature developed at the impact zone.[30]

Figure 15 shows the radial profile of the CO2 massfraction 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.


axial locations X/De = 1, 3, 8, and 12. This figure showstwo peaks of CO2 mass fraction at X/De = 1 and 3 andonly shows one peak at X/De = 8 and 12 because of theformation of two combustion flames just after the exit ofthe nozzle as discussed earlier. When the two flamesmerge, radial distribution of the CO2 mass fractionshows only one peak. Figure 16 shows the radial profileof the mass fraction of CO2 at the same axial locationsfor the supersonic coherent nitrogen jet. As expected,only one peak of CO2 mass fraction is notedbecause combustion occurs only on one side of the fuelstream.Figure 17 shows the calculated CO2 mass fraction

distribution for the supersonic coherent O2 jet. Thefigure shows that the CO2 mass fraction is higher inthe vicinity of the combustion flame because CO2 is theproduct of combustion. The mass fraction of H2Oshows a similar trend to that of CO2 and therefore wasnot presented here.

Fig. 14—Axial mass fraction distributions at the jet centerline ofconventional and shrouded oxygen jet.

Fig. 15—Radial distributions of the CO2 mass fractions at differentaxial locations for shrouded oxygen jet.

Fig. 16—Radial distributions of the CO2 mass fractions at differentaxial locations for shrouded nitrogen jet.

Fig. 17—CFD plot of the CO2 mass fractions for shrouded oxygen jet.


IV. CONCLUSIONS

CFD simulation of the supersonic oxygen and nitro-gen jet with and without shrouding flame were per-formed. The present study showed that the shroudingcombustion flame reduces the entrainment of the sur-rounding gas to the central supersonic jet, which resultsin a low spreading rate for the coherent supersonic jet.It also reduces the magnitude of turbulent shear stress inthe shear layer, which in turn delays the mixing of thesupersonic jet with the surroundings. As a result, thepotential core length of the supersonic coherent jet isincreased compared with the conventional jet. Thepotential core length of the shrouded oxygen jet is morethan four times greater than the conventional oxygenjet. At steelmaking temperatures, the potential corelength of the coherent supersonic oxygen jet is 1.4 timesgreater than that at room ambient temperature. For theshrouded nitrogen jet, the potential core length is morethan times greater than the conventional nitrogen jet.The CFD results showed a good agreement with theexperimental data.

The present study only considered the one-stepcomplete 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, andOH also are produced.[13] For the coherent supersonicoxygen jet, the CO produced by incomplete combustionof CH4 gas reacts with the O2, which also creates a flamesurrounding the jet and affects the potential core lengthof the jet. Additional work is required to incorporate themultistep combustion reaction.

The CFD model only was validated against experi-mental velocity distribution data. No experimental dataare available in the literature for the flame temperatureor mass fraction of different species to compare theCFD results against the experimental data. Hence, moreexperimental study is required to establish a morerigorous CFD model of the coherent supersonic jet.

The present study can provide some useful insightsinto coherent jet technology. The shape and tempera-ture of the combustion flame is important for coherentjets, and this study shows that the combustion flametemperature varies significantly when different gases areused as a central supersonic jet. The model developedalso predicts the location of the hot spots of thecombustion flame as well as the impact velocitydistribution for different blowing conditions. Theimpact velocity of the gas jet on a liquid surface willbe higher if the potential core length is increased,which also should increase the droplet generationrate;[31] although, it is claimed that coherent jetsproduce less splashing.[4,6] This model also can providethe distribution of mass fractions of different species,which is important to the process. The mass fraction ofdifferent species inside the furnace affects the partialpressure of the gases inside the furnace, which in turninfluences the kinetics of the reactions inside thefurnace. The model developed in the present studyshould be helpful in determining the optimum flow rateof the shrouding gas and in designing a more efficientcoherent jet nozzle.

ACKNOWLEDGMENT

The authors would like to thank the members of theOne Steel, Melbourne for their financial support anduseful discussions in this project.

NOMENCLATURE

Di diffusion coefficient of species iE radiative heat transfer (J/s)H total enthalpy (J/kg)k turbulent kinetic energy (m2/s2)P pressure (N/m2)Prt turbulent Prandtl numberSct turbulent Schmidt numberSfu volumetric rate of fuel consumption (kg/m3 s)Sp spreading rateT temperature (K)t time (s)U velocity (m/s)u fluctuating velocity (m/s)X distance (m)Yi mass fraction of species iq density (kg/m3)l molecular viscosity (Ns/m2)lt turbulent viscosity (Ns/m2)c thermal conductivity (W/mK)e turbulent dissipation rate (m2/s3)2 emissivityf vorticity (1/s)De nozzle exit diameter (m)

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computational fluid dynamics modeling of supersonic coherent jets for electric arc furnace...

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