CFD Modeling of Swirl and Nonswirl Gas Injections into LiquidBaths Using Top Submerged Lances

NAZMUL HUDA, J. NASER, G. BROOKS, M.A. REUTER, and R.W. MATUSEWICZ

Fluid flow phenomena in a cylindrical bath stirred by a top submerged lance (TSL) gas injectionwas investigated by using the computational fluid dynamic (CFD) modeling technique for anisothermal air–water system. The multiphase flow simulation, based on the Euler–Eulerapproach, elucidated the effect of swirl and nonswirl flow inside the bath. The effects of the lancesubmergence level and the air flow rate also were investigated. The simulation results for thevelocity fields and the generation of turbulence in the bath were validated against existingexperimental data from the previous water model experimental study by Morsi et al.[1] Themodel was extended to measure the degree of the splash generation for different liquid densitiesat certain heights above the free surface. The simulation results showed that the two-thirds lancesubmergence level provided better mixing and high liquid velocities for the generation of tur-bulence inside the water bath. However, it is also responsible for generating more splashes in thebath compared with the one-third lance submergence level. An approach generally used byheating, ventilation, and air conditioning (HVAC) system simulations was applied to predict theconvective mixing phenomena. The simulation results for the air–water system showed thatmean convective mixing for swirl flow is more than twice than that of nonswirl in close prox-imity to the lance. A semiempirical equation was proposed from the results of the presentsimulation to measure the vertical penetration distance of the air jet injected through theannulus of the lance in the cylindrical vessel of the model, which can be expressed asLva ¼ 0:275 do � dið ÞFr0:4745m : More work still needs to be done to predict the detail processkinetics in a real furnace by considering nonisothermal high-temperature systems with chemicalreactions.

DOI: 10.1007/s11663-009-9316-1� The Minerals, Metals & Materials Society and ASM International 2009

I. INTRODUCTION

FLUID flows are an integral part of many metallur-gical processing operations. They affect the viability,effectiveness, and efficiency of many reactors regardlessof whether they are physical or chemical in nature.[2]

Gas injection methods are used frequently in modernpyrometallurgy because they allow for high-intensityand high-throughput processes in relatively small reac-tors.[3] Various methods to inject gas into molten bathsinclude top submerged lance (TSL) technology, whichuses a submerged vertical lance within an uprightcylindrical furnace. Through the lance, oxygen-enrichedair is injected into the molten bath, which creates anintense mixing of the bath and excellent contact betweenphases. Floyd[4] described the details of the TSLtechnology and its development since the 1970s.

Several experimental and numerical modeling studieshave been performed on the injection of gas into liquidbaths to understand the flow behavior inside furnaces.Mazumdar and Guthrie[5] carried out some experimen-tal work on top-submerged gas injection on a 0.3-scalecold flow water model of a 150-ton steelmaking ladlewith and without tapered side walls and surface bafflesaround the rising plume. They also developed ageneralized two-dimensional (2D) steady-state compu-tational scheme for predicting flows generated by fullysubmerged and partially submerged axisymmetric gasinjection lances. Cold flow experiments also werecarried out by Nilmani and Conochie,[6] Rankinet al.,[7] Neven et al.,[8] Iguchi et al.,[9] and Morsiet al.[1] Nilmani and Conochie[6] reported that thepresence of swirl improves the radial dispersion of gasbubbles, produces finer bubbles, and minimizes bathslopping and splashing. The authors also investigatedthe effect of gas density and the gas rise mechanismthrough the bath. In contrast, Neven et al.[8] found noeffect of swirl on bubbling frequency. Neven et al.[8]

validated the Davidson-Schuler[10] model for bubblingfrequency.Dave and Gray[11] experimentally investigated the

effect of constant and variable pitch swirled inserts intothe liquid bath for submerged vertical lances. Theirwork mainly focused on the pressure drop across the

NAZMUL HUDA, PhD Student, J. NASER, Senior Lecturer, andG. BROOKS, Professor, are with the Swinburne University ofTechnology, Hawthorn 3122, Melbourne, Vic, Australia. Contacte-mail: MHuda@swin.edu.au M.A. REUTER, Chief ExecutiveTechnologist, and R.W. MATUSEWICZ, Technical DevelopmentManager, are with the Ausmelt Limited, 12 Kitchen Rd, Dandenong3175, Melbourne, Vic, Australia.

Manuscript submitted May 20, 2009.Article published online November 17, 2009.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, FEBRUARY 2010—35

lance because of fixed and variable pitch inserts. Theyconcluded that the use of variable pitch swirlerscould improve the lance flow dynamics substantially.Solnordal and Gray[12] carried out more experimentalinvestigations on the fluid flow and heat transfercharacteristics of decaying swirl flow in a TSL-heatedannulus, and they reported that the entrance pressurelosses associated with the helical vane swirlers contrib-uted up to 80 pct of the total pressure loss. Solnordaland Gray made recommendations for optimizing theshape of the swirlers by using variable pitch swirler aswell as for optimizing the swirler position by aligningthe entrance of the swirlers with the local flow angle.Later, Solnordal et al.[13] developed a mathematicalmodel for predicting heat flow to an operating TSL.The model predicts lance wall and air temperature andthe thickness of the slag layer on the lance. Bymeasuring the distribution of wall temperature andslag thickness on an operating lance, the model wasused to determine both the heat-transfer coefficientbetween the vessel contents and the lance as well as thethermal conductivity of the slag layer. Morsi et al.[1]

experimentally investigated the effect of swirl andnonswirl gas injections into liquid baths using sub-merged vertical lances. They reported that swirl gasinjection and a two-third lance submergence levelpromoted better mixing in the bath. They also exam-ined the applicability of the isotropic turbulence con-cept inside the bath and concluded that it may holdoutside the plume region.

Few numerical modeling studies have been performedfor TSL gas injection. Schwarz and Koh[14] developed atwo-phase numerical model of swirl and nonswirl gasinjection through lances using finite-volume computercode PHOENICS (Wimbledon, UK). They studied thegas dispersion, recirculating flow fields, and mixing in abath sparged by top-submerged gas injection. Liovicet al.[15,16] developed a numerical model for simulatingthe transient behavior of multifluid problems. Theauthors simulated the gas injection process for a TSLas a 2D axisymmetric problem. To get a complete cross-sectional view, the results at the centerline were mir-rored. However, Liovic et al.[16] also reported that 2Daxisymmetric volume tracking could not facilitate thesimulation of fully three-dimensional (3D) interfacialphenomena. Because of the complex nature of the flowstructure involved in the gas injection system, gasinjection system hydrodynamics still need thoroughinvestigation.

The aim of this study was to investigate the physicalbehavior of the top-submerged gas injection system andto predict the effect of swirl, lance submergence level,and air injection rate into the liquid bath using the CFDmodeling technique. The present study was a numericalsimulation of the cold model experimental work ofMorsi et al.[1] Water was used as the modeling fluid, andair was used as the injected gas because it was the basisfor the previous experimental model of Morsi et al.[1]

The model developed in this study and validated againstthe cold model data will be used to develop models forindustrial systems.

A new approach to express the degree of mixing inthe liquid bath in metallurgical process simulation isproposed. In addition, a modified semiempirical equa-tion is proposed to measure the vertical penetrationdepth of the air jet injected through the annulus of thelance into the liquid bath based on the previousexperimental Iguchi et al. study.[9]

II. MODEL GEOMETRY ANDCOMPUTATIONAL METHODOLOGY

A 3D CADmodel of the one-sixteenth-scale air–watermodel of a 150-ton steelmaking ladle was developedusing the CAD tool. The CAD model is similar to theexperimental model of Morsi et al.[1] A schematicdiagram of the model is shown in Figure 1(a). Thevessel has a diameter D of 230 mm and a length Z of560 mm. The tank was filled L up to 150 mm withwater. A vertical lance with an annulus of innerdiameter di of 12.2 mm and an outer diameter do of17 mm was fitted at the center of the cylindrical vessel.Air was injected through the annulus of the lance intothe water bath. On the top of the cylindrical vessel, theoutlet was defined by Do = 60 mm.The CFDmodeling for the top-submerged gas injection

involved multiphase simulation in which gas and liquidphases interact with each other and a significant amount ofmomentum was exchanged between phases. The modelwas developed using the finite-volume method in aconventional Eulerian approach by using the commercialCFD package AVLFIRE 8.52 (AVL,Graz, Austria). Themodel that was developed included the following features:

(a) Consideration of an unsteady-state multiphasesolution for momentum.

(b) Employment of a standard k-e turbulence model forthe turbulence modeling.

(c) A cell-centered, finite-volume approach was used todiscretize the governing equations, and the resultingdiscretized equations were solved iteratively using asegregated approach.

(d) Pressure and velocity were coupled using theSIMPLE algorithm.[17]

(e) Least-squares fit approach was used to calculate thederivatives.

(f) First-order upwind differencing scheme was used formomentum and turbulence, whereas a central dif-ferencing scheme with second-order accuracy wasused for the continuity equation.

(g) Swirl flow was injected through the annulus of thelance at 57.5 deg relative to the radial direction.

(h) All boundary conditions were chosen to match theflow condition of the experimental study of Morsiet al.[1] The boundary conditions used were a massflow at the inlet and a static pressure of 100 KPa atthe outlet. Vessel walls were treated by standardwall functions with a no-slip condition.

Basic Eulerian equations that describe the multiphasesystem are given by the conservation equations for massand momentum. For the 3D fluid flow, these conservation

36—VOLUME 41B, FEBRUARY 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B

equations can be expressed as discussed in the sub-sequent sections.

A. Continuity

@akqk

@tþr:akqkvk ¼ 0 k ¼ 1; . . .. . .;N ½1�

where N is the number of phases, ak is the volumefraction of phase k, qk is the density for phase k, vk is thephase k velocity, and

PNk¼1 ak ¼ 1:

B. Momentum Conservation

@akqkvk@t

þr:akqkvkvk ¼� akrpþr:ak sk þ Ttk

� �

þ akqk fþXN

l¼1;l6¼kMkl ½2�

PNl¼1;l 6¼k Mkl represents the momentum interfacial inter-

action between phases k and l, f is the body force vector(which comprises gravity g), and p is pressure. Adetailed description of the momentum interfacial inter-action is provided. Pressure is assumed to be identicalfor all phases: p = pk k = 1, ……., N.

The phase k viscous stress integral is divided intonontransposed and transposed terms, which can beexpressed as follows:

sk ¼ lk rvk þrvTk� �

½3�

where lk is the molecular viscosity. For incompressibleflow, Reynolds stress Tt

k takes into account the turbu-lence effect. According to the Boussinesq hypothesis, itcan be expressed as follows:

Ttk ¼ �qkv

0kv0k ¼ lt

k rvk þrvTk� �

� 2

3qkkkdk ½4�

where dk is the Kronecker delta function and ltk is the

turbulent viscosity. For the continuous phase, turbu-lent viscosity was calculated by adding shear-inducedturbulent viscosity with Sato’s viscosity that wascaused by bubble-induced turbulence and is expressedas follows[18]:

ltc ¼ lt;SI

c þ lt;BIc ½5�

where shear-induced turbulent viscosity for continuousphase can be expressed as follows:

lt;SIc ¼ qcCl

k2cec

½6�

Fig. 1—(a) Schematic diagram of the model; (b): Cross-sectional view of the generated grid on the X-Z plane at the two-thirds submergencelevel.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, FEBRUARY 2010—37

Sato’s viscosity caused by bubble-induced turbulencecan expressed as follows[18]:

lt;BIc ¼ CsatoqcDb vrj jad ½7�

where Cl = 0.09 and Csato = 0.6, and they both aredimensionless constants, k is the turbulent kineticenergy, and e is its dissipation rate, which can beobtained by solving equations for the standard k-eturbulence model that was put forward by Launder andSpalding.[19]

The turbulent kinetic energy (k) equation is expressedas follows:

@akqkkk@t

þrakqkvkkk

¼ rak lk þltk

rk

� �

rkk þ akqk � akqkek þXN

l¼1;l6¼kKkl

k ¼ 1; . . .. . .. . .;N ½8�PN

l¼1;l 6¼k Kkl is the interfacial turbulence exchangebetween phases and Pk is the production term causedby shear.

The turbulence dissipation (e) equation is expressed asfollows:

@akqkek@t

þrakqkvkek

¼ rak lk þltk

re

� �

rek þXN

l¼1;l6¼kDkl þ akC1Pk

ekkk

� akC2qk

e2kkk

½9�

Closure coefficients used in the model are rk = 1.0,re = 1.3, C1 = 1.44, C2 = 1.92, and Cl = 0.09.PN

l¼1;l 6¼k Dkl represents interfacial dissipationexchange between phases. In the present simulation,the dispersed phase turbulence level was assumed toequal the continuous-phase turbulence level. The inter-facial interaction between the two phases, thereby, isneglected.

The momentum interfacial exchange between gas andliquid was modeled by implementing the interfacialmomentum source at the interface, which includes dragand turbulent dispersion forces, as follows[20]:

Mc ¼ CD1

8qcA

000i vrj jvr þ CTDqckcrad ¼ �Md ½10�

where c denotes the continuous phase and d denotes thedispersed phase. The first term in Eq. [10] representsmean contributions because of drag force, and thesecond term takes the turbulence effect into account.The turbulence effect is represented by a global disper-sion effect, which is proportional to the void fractiongradient.[21]

The drag coefficient CD is a function of the bubbleReynolds number Reb. The following correlation for CD

was used[20]:

CD ¼24

Reb1þ 0:15Re0:687b

� �Reb � 1000 ½11�

The bubble Reynolds number Reb can be defined asfollows:

Reb ¼vrDb

tc½12�

where tc is the kinematic viscosity for the continuousphase.Relative velocity is defined as follows:

vr ¼ vd � vc

The interfacial area density for bubble flow can be ex-pressed as follows[20]:

A000i ¼6adDb

½13�

where Db = 0.01 mm and is the bubble diameter and adis the dispersed-phase volume fraction. Bubbles induceturbulent fluctuations that enhance the global liquidturbulence level. Bubble diameter also plays a significantrole in the momentum exchange term. A smaller bubblediameter increases the interfacial area density, whichcreates greater momentum transfer between the phases.The bubble dispersion coefficient used in Eq. [10] isCTD = 0.1.Figure 2 shows the velocity vectors at the lance inlet

for the swirl air injection. The increase in tangentialvelocity because of the swirling effect creates a finedispersion of gas bubbles in the bath, and the bubbleplume extends radially outward.In all simulations, the flow began from rest with small

initial values assigned to k and e, which made the initialturbulent viscosity roughly equal to the kinematic viscos-ity for water. The fluid properties for air and water weretaken as the properties at normal temperature andpressure (NTP) (T = 293.15 K, P = 1 atm). Typicalturbulence quantities at the inlet of the domain werecalculated from inlet velocities by considering the turbu-lence intensity I = 0.05, where I ¼ u0=Uinlet ffi 0:16Re�

18:

Fig. 2—Velocity vectors (m/s) for swirl air injection at the lance tip(Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 57.5�).

38—VOLUME 41B, FEBRUARY 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B

An overview of the simulation and experimentalconditions is provided in Table I. The calculation fordifferent simulation conditions as mentioned in Table Iwas solved as an unsteady-state problem with time stepsof Dt = 0.01 second. The total time for each run was180 seconds, which was adequate to obtain time-averaged, steady-state results and ensured numericalstability. Four grid resolutions were tested for a gridindependency test, which mostly increased the numberof cells in the water bath. The purpose of the gridindependency test was to determine the minimum gridresolution required to generate a solution independentof the grid used. Starting with a coarse grid, the numberof cells was increased in the region of interest until thesolution from each grid was unchanged for successivegrid refinements. All cells in the calculation domain werepolyhedral with several hexahedral cells. Because thecomputational domain consisted of hybrid unstructuredmeshes in a curvilinear nonorthogonal coordinate sys-tem with Cartesian base vectors and refined regions insome locations, mentioning the number of cells in eachdirection was complicated. The computational grid(213,344 cells) used in the present study was too densefor visual presentation. A cross-sectional view of thecoarse computational grid in the X-Z plane is shown inFigure 1(b), which consists of 89,492 cells in a 360�domain. The meshing procedure was performed by thefame advanced hybrid meshing technique.[20] Table IIrepresents an overview of the grid information studiedin the grid independency test.

Figure 3 shows the mean tangential velocity distribu-tion (V) on the X-Z plane. The radius of the cylinder(R = 115 mm) normalized the radial distance r, and thelength of the cylinder (Z = 560 mm)normalized the

axial distance z. Both Grid 3 and Grid 4 gave accuratepredictions compared with the experimental results. Thedifference in predictions between Grid 3 and Grid 4 wassmall enough (around 5 pct) to suggest that any moregrid refinement would not yield a substantially differentprofile in that plane. Therefore, it was decided that thefine grid resolution (Grid 3) of 213, 344 cells wassufficient to obtain grid-independent results.For the entire simulation, time periodic results were

taken at the end of every 2 seconds for a total time of180 seconds. Then, different values for velocities andturbulence properties were taken as the average valuesfor all time steps. To get a converged solution, thenormalized sum of absolute residuals was reduced to1.0 9 10�4 for each time step. The entire simulation wascarried out using Swinburne’s Supercomputer(Melbourne, Australia) in one cluster of 8 Intel QuadCore CPU (Intel Corporation, Santa Clara, CA), eachwith 2.3-GHz speed.

III. RESULTS AND DISCUSSION

The results discussed are presented in terms of thefollowing three major hydrodynamic parameters: swirlintensity, gas injection rate, and lance submergencelevel. The simulation condition and correspondingfigures described in this article are summarized inTable III, which refers to an air–water system unlessotherwise stated.

A. Effect of Swirl Intensity

The effect of swirl intensity on axial velocity is shownin Figure 4, which shows that the instantaneous axialvelocity (w) contours for swirl and nonswirl flow werebetween �0.3 and 0.4 m/s. Time instances are men-tioned in the corresponding figures at which contourplots are taken. The color bar represents the velocitymagnitudes (m/s), and the sign in the color bar indicatesthe velocity direction (either downward or upward).

Table I. Overview of the Simulation and Experimental

Conditions

ParametersExperimentalCondition[1]

PresentSimulation

Air injection rate 1.50 9 10�3 1.00 9 10�3

Q (Nm3/s) 2.67 9 10�3 1.50 9 10�3

2.00 9 10�3

2.67 9 10�3

3.50 9 10�3

4.00 9 10�3

Fraction of lancesubmergence H/L

1/3, 2/3 1/6, 1/3, 2/3

Swirl Intensity F (�) 0�, 57.5� 0�, 57.5�

Table II. Overview of Computational Grids

Name Grid DensityNumber

of Computational Cells

Grid 1 coarse 89,492Grid 2 medium 154,072Grid 3 fine 213,344Grid 4 very fine 361,024

Fig. 3—Mean tangential velocity (m/s) distribution for different gridconfigurations (Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 0�) for watermodel simulation.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, FEBRUARY 2010—39

The axial velocity near the lance showed an upwardtrend because of the buoyant force of the rising airbubbles. No significant change in axial velocity wasobserved because of swirl. In Figure 4, swirl injectionseemed to have a larger penetration envelope in the caseof two-thirds lance depth, whereas the reverse was truefor one-third lance depth. This observation can beattributed to the transient nature, sloshing, and splash-ing phenomena in the water bath. By comparingFigure 4(a) with (b), it is clear that only a little increaseoccurs in the axial velocity at the bottom of the tank andnear the top surface of the bath. This trend is also clearin Figures 4(c) and (d). Change in the axial velocity isevident because of the change in flow rate whencomparing Figures 4(c) and (e) with (d) and (f). Thesevelocity contours reasonably agree with the experimen-tal results of Morsi et al.[1] presented in Figure 5. Acomparison of Figures 4(b) and 5(b) shows that approx-imately 5 pct discrepancy is present between the exper-imental and simulation results near the lance tip.Nevertheless, the simulation results predicted a highervalue in the remaining portion of the liquid bath becausethe movements of the fluid particles were not uniformand turbulence was generated inside the bath. Thetransient effect of the flow fields might be one factor thatcaused the discrepancies in the contour plots betweenthe simulation and experimental results. The contourplots presented here from the simulation are instanta-neous, but in Figure 5, the contour plots derived fromthe experimental results of Morsi et al.[1] are timeaveraged and are shown for qualitative validationpurposes only. This validation exercise represents thequalitative accuracy of the present study against existingexperimental data.

Figure 6 shows the instantaneous tangential velocity(v) contours on the X-Z plane. The effect of swirl isnoticeable in the figures. A significant increase intangential velocities only will occur because of the swirlcomponent presence, which is revealed by comparingFigures 6(a) and (b) with (c) and (d). The change intangential velocity component because of the swirl wasmuch higher than the change in the axial velocitycomponent. The tangential velocity distribution inFigure 6(d) revealed the so-called dead water region inthe bath and showed that the bottom half of the liquidbath was almost unaffected by the gas injection processfor the one-third lance submergence and the nonswirlcases. The simulation results for tangential velocity

contours agreed with the experimental results of Morsiet al.,[1] as shown in Figure 7.Figure 8 shows a comparison of mean tangential

velocities between swirl and nonswirl injection. Theexperimental data also are presented in Figure 8 forvalidation. The radius of the cylinder (R = 115 mm)normalized the radial distance (r), and the length of thecylinder (Z = 560 mm) normalized the axial distance z.As expected, the magnitudes of the tangential velocitieswere low under the nonswirl conditions. Tangentialvelocity near the lance showed a significant rise in swirlcondition but drops off to around zero after r/R ‡ 0.20.The mean tangential velocities were calculated atz/Z = 0.92, which is just below the exit of the lancez/Z = 0.91 for H/L = 2/3. The mean tangential veloc-ity distribution for the nonswirl flow agreed with theexisting experimental values of Morsi et al.[1] Thediscrepancy between the two results lies within a rangeof 0 to 10 pct. But for swirl flow, the present simulationshowed the peak value of mean tangential velocity to be1.1 at a radial distance of r/R = 0.11, whereas theexperimental results of Morsi et al.[1] showed thatthe peak was 0.7 at a radial distance of r/R = 0.128.The discrepancies between the experimental and thesimulation results may be attributed to the following:

(a) The differencing scheme used for momentum andturbulence is upwind, which provides false diffusionin complex flow phenomena. However, this trend isreduced by use of fine grids in the liquid bath.

(b) The standard k-e turbulence model[19] may result inpoor performance in several important cases, suchas flows with large extra strains (e.g., curvedboundary layers or swirling flows) and rotatingflows.[22] Still, it is a well-established model, themost widely validated turbulence model, and pro-vides an excellent performance for many industriallyrelevant flows.

(c) An inaccuracy of ±6 pct associated with the exper-imental technique such as optical component align-ment, seeding, filtering, signal processing, andcalibration.[1]

B. Effect of Submergence Level

Different lance submergence levels also play a signif-icant role on the fluid flow characteristic in the TSLgas injection systems. The greater volume of splash

Table III. Simulation Conditions and Corresponding Figures

Air Injection Rate Fraction of LanceSubmergence H/L

Swirl IntensityFigure NumberQ (Nm3/s) F (�)

2.67 9 10�3 1/3 0 4(d), 5(d), 6(d), 7(d)2.67 9 10�3 2/3 0 3, 4(b), 5(b), 6(b), 7(b), 8, 11(a), 12(a)2.67 9 10�3 1/3 57.5 4(c), 5(c), 6(c), 7(c), 16(a), 16(b)2.67 9 10�3 2/3 57.5 2, 4(a), 5(a), 6(a), 7(a), 8, 11(b), 12(b), 13(a), 13(b)1.50 9 10�3 1/3 0 4(f)1.50 9 10�3 1/3 57.5 4(e)

40—VOLUME 41B, FEBRUARY 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B

generation theory that was put forward by Koh andTaylor[23] was revealed in the present simulation data. Inaddition to the one-third and two-thirds lance submer-gence levels, the simulation was extended for theone-sixth submergence level. Figure 9 shows the time-averaged volume fraction of water that was generated bysplashing at 30 mm above the bath (z/Z = 0.68). Nosurface tracking method such as volume of fluid (VOF)was used in the present simulation to represent quan-titatively the formation of each small droplet that wasgenerated from splashing. The tracking of each smalldroplet would require massive computer resources andtime, which was avoided in the present study because the

qualitative flow pattern in the liquid bath was the maininterest. In the present simulation, because the approachused was conventional Eulerian, the time-averagedvolume fraction was measured at certain heights abovethe liquid bath to get a qualitative idea of splash. Usingsurface tracking methods, such as VOF, can give a morequantitative analysis of the splash formation. From thefigure, it is evident that increasing the submergence levelgenerates a greater splash volume. It is because of anincrease in the air jet penetration depth in a deeper bath,which releases more buoyancy energy and producesmore splashes. This result is also consistent with theexperimental study of Igwe et al.[24] In the Igwe et al.[25]

Fig. 4—Axial velocity (w) distribution (m/s) for the water model simulation: (a) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 57.5�, t = 60 s;(b) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 0�, t = 60 s; (c) Q = 2.67 9 10�3 m3/s, H/L = 1/3, F = 57.5�, t = 60 s; (d) Q = 2.67 9 10�3 m3/s,H/L = 1/3, F = 0�, t = 60 s; (e) Q = 1.5 9 10�3 m3/s, H/L = 1/3, F = 57.5�, t = 60 s; (f) Q = 1.5 9 10�3 m3/s, H/L = 1/3, F = 0�, t = 60 s.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, FEBRUARY 2010—41

water model experimental study, the degree ofsplashing increased with the increase in the depth ofsubmergence.

C. Effect of Air Flow Rate

The air jet penetration depth increased with anincreasing air flow rate, which is shown by comparingFigures 4(c) and (e) with (d) and (f). Figures 4(e) and (f)show the so-called dead water region near the bottom ofthe cylindrical vessel that was used for water modeling.

The increase in air jet penetration depth created moreagitation in the bath and, therefore, better mixing. Thepenetration of the air jet is a function of the term ‘‘Fr¢’’,which is a modification of the jet Froude number putforward by Igwe et al.[24]

Fr0 ¼qgv

2

g q1 � qg

� �d

½14�

where q1 is the liquid phase density, qg is the den-sity of gas, g is the gravitational constant, v isthe gas flow velocity, and d is the orifice diameter.

Fig. 5—Axial velocity (w) distribution (m/s) from experimental results of Morsi et al.[1]: (a) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 57.5�;(b) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 0�; (c) Q = 2.67 9 10�3 m3/s, H/L = 1/3, F = 57.5�; (d) Q = 2.67 9 10�3 m3/s, H/L = 1/3, F = 0�.

42—VOLUME 41B, FEBRUARY 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B

The higher the number, Fr¢, the greater the jet pene-trates the liquid bath. Iguchi et al.[9] developed asemiempirical equation from an air–water experimen-tal study to calculate the air jet vertical penetrationdistance for TSL gas injection, which also dependedon the air flow rate. According to Iguchi et al.,[9]

the semiempirical equation for injected air vertical

penetration distance into the liquid bath can beexpressed as follows:

Lv ¼ 4:1dnFr1=3m ; 2<Frm<6� 103 ½15�

where Lv is the vertical penetration distance of theinjected air, dn is the nozzle inner diameter at the exit,

Fig. 6—Tangential velocity (v) distribution (m/s) for the water model simulation: (a) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 57.5�, t = 60 s;(b) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 0�, t = 60 s; (c) Q = 2.67 9 10�3 m3/s, H/L = 1/3, F = 57.5�, t = 60 s; (d) Q = 2.67 9 10�3 m3/s,H/L = 1/3, F = 0�, t = 60 s.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, FEBRUARY 2010—43

and Frm is the modified Froude number, which can beexpressed as follows:

Frm ¼qgQ

2g

qLgd5n

½16�

where qg is the density of gas, qL is the density of liquid,Qg is the gas flow rate, and g is the acceleration causedby gravity. Equation [15], however, is not valid for theannulus air inlet of swirled lances. For air jet injectionthrough the annulus of the TSL, a semiempirical

equation was proposed from the present simulationdata based on the relationship proposed by Iguchiet al.,[9] which can be expressed as follows:

Lva ¼ 0:275 do � dið ÞFr0:4745m ½17�

where Lva is the air jet vertical penetration distanceinjected through annulus, do and di are the outer and innerdiameters of the lance, respectively, neglecting the thick-ness of the lance wall, and Frm is the modified Froudenumber, which can be obtained through Eq. [16].

Fig. 7—Tangential velocity (v) distribution (m/s) from experimental results of Morsi et al.[1]: (a) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 57.5�;(b) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 0�; (c) Q = 2.67 9 10�3 m3/s, H/L = 1/3, F = 57.5� (d) Q = 2.67 9 10�3 m3/s, H/L = 1/3, F = 0�.

44—VOLUME 41B, FEBRUARY 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B

Figure 10 shows the relationship between the annulusair jet vertical penetration distance (Lva) and themodified Froude number (Frm). The coefficients inEq. [17] are from the fitted curve shown in Figure 10with the correlation factor, R2 = 0.98. Six different flowrates were used, as mentioned in Table I for the one-third submergence level and the nonswirl flow. Air jetvertical penetration distance was measured as the meanvalue for different time steps.

IV. MIXING IN THE LIQUID BATH

Mixing phenomena process kinetics in the real TSLsmelting furnaces are complex. Mixing in the bath in areal furnace scenario is vigorous, and several factorsaffect the mixing process, some of which are as follows:

(a) High-temperature chemical reactions in the slag aredominant factors that affect the mixing phenomena.

(b) Expansion of gases in the molten bath because ofhigh temperature and air injected through the lanceaccelerate the mixing.

(c) Sidewise and vertical movement of the lance in themolten bath affects the total mixing process.

(d) Splashing phenomena at the free surface alsoincreases the mixing process in the bath.

However, in the present simulation, only the isother-mal cold model air–water system was considered.Therefore, many factors that affect the mixing phenom-ena are absent. In the present simulation, the mixingphenomena studied were turbulence mixing through theturbulent diffusion as well as macro mixing throughconvection.

A. Turbulence Mixing

Figures 11(a) and (b) show the effect of swirl onturbulent kinetic energy (k) distribution for the sameflow rate and submergence level. The color bar showsthe magnitude range of the turbulence kinetic energy inthe figure from 0 to 0.2 m2/s2. Figures 12(a) and (b)show the turbulent kinetic energy distribution from theMorsi et al.[1] experimental results. The values obtainedfrom the present study were consistent with the valuesobserved in the experimental study. The generation ofturbulence near the lance was increased for the two-thirds lance submergence level and swirl flow. Themaximum value of turbulent kinetic energy existed nearthe lance, as expected, which also was revealed from theexisting experimental data. However, this turbulencewas reduced significantly with an increase in distancefrom the lance tip, and it did not exist near the vesselwall. Although no noticeable change in turbulent kineticenergy was observed for swirl and nonswirl injection asshown in Figure 12(a) and 12(b), our present simulationresults showed a noticeable change in the generation ofturbulent kinetic energy near the lance. The rising gasplume was extended radially from the lance toward thewall as a result of swirl air injection.

Fig. 8—Mean tangential velocity comparison between swirl and non-swirl flow from the simulation results and comparison with watermodel experiment of Morsi et al.[1] (z/Z = 0.92, H/L = 2/3,Q = 2.67 9 10�3 m3/s).

Fig. 9—Average volume fraction of water at z=Z ¼ 0:68 for differentsubmergence levels for the water model simulation (Q = 2.67 910�3 m3/s, F = 57.5�).

Fig. 10—Relation between vertical penetration distance for annulusair injection (Lva) and modified Froude number (Frm) as derivedfrom the water modeling simulation results (H/L = 1/3, F = 0�).

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, FEBRUARY 2010—45

Because the relative density of air is low comparedwith water, the velocity of air in this study did not givesufficient momentum to penetrate the liquid water andcreate turbulence in the entire bath. The formation ofbubbles and high velocity gradients, which resultedfrom a momentum transfer between the gas and liquidphases, created more turbulence near the lance. In theregion above the lance exit, the rising bubbles lost mostof their initial momentum. Only the buoyancy forces

exerted by the rising bubbles assisted in the generationof turbulence near the lance wall.Figure 13(a) shows the volume fraction for two-thirds

lance submergence in water after 180 seconds of a highinjection rate. The figure shows a significant asymmetrybecause of the sloshing and splashing in the water bath,which represents the transient nature of the simulation.This observation is the essence of the 3D transientmultiphase flow simulation, which can give more

Fig. 11—Turbulent kinetic energy (k) distribution (m2/s2): (a) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 0�, t = 60 s; (b) Q = 2.67 9 10�3 m3/s,H/L = 2/3, F = 57.5�, t = 60 s.

Fig. 12—Turbulent kinetic energy (k) distribution (m2/s2) from experimental results of Morsi et al.[1]: (a) Q = 2.67 9 10�3 m3/s, H/L = 2/3,F = 0�; (b) Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 57.5�.

46—VOLUME 41B, FEBRUARY 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B

insights into metallurgical flows of interest. The volumefraction plot for the nonswirl case (not presented in thisarticle) showed no significant difference with the swirlcase. Velocity vectors for the same condition are shownin Figure 13(b), which shows the formation of a weakrecirculating vortex near the top level of the liquid.Formation of this weak recirculation region was randomand transient in nature as observed from the simulationresults. The rising bubbles in the liquid induced theseshort-lived vortices. Formation of the recirculatingvortex inside the bath was favorable for the generationof uniform mixing inside the bath. However, nosignificant vortex was observed inside the bath in thepresent study. The magnitude of the velocity vectorsnear the wall of the vessel were negligible compared withthe values near the lance. Liquid near the bottom cornerof the vessel was almost unaffected by the air injectionprocess because it was observed from the present air–water simulation.

B. Mean Convective Mixing

To measure the convective mixing efficiency inside thephysical models, traditional tracer studies generally areused. In the present study, the mean convective mixingwas evaluated using the ‘‘volume exchange effective-ness’’ concept. This approach generally is used inheating, ventilation, and air-conditioning (HVAC) pro-cess simulations.[25] The term ‘‘volume exchange effec-tiveness,’’ which is actually a measure of the meanconvective mixing, may be defined as the net exchanged

fluid volume in each computational cell divided by thevolume of that cell and can be expressed as follows:

Veef ¼Volume flow rate through a computational cell

Volume of the cell

½18�

where Veef expresses the volume exchange rate through acell, which in turn represents the convective mixing. Ithas a unit of (time)�1.

Fig. 13—Volume fraction and velocity vectors for water after 180 seconds (Q = 2.67 9 10�3 m3/s, H/L = 2/3, F = 57.5�): (a) volume fraction;(b) velocity vectors for liquid phase (m/s).

Fig. 14—Volume exchange effectiveness along radial direction frompresent water model simulation (Q = 2.67 9 10�3 m3/s, H/L = 1/3).

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, FEBRUARY 2010—47

Figure 14 shows the time-averaged volume exchangeeffectiveness (Veef) of the air–water system for swirl andnonswirl injection at z/Z = 0.84 (which is 10 mm belowthe lance exit in the water bath) along the radialdirection. This depth was chosen because the presentauthors were interested in the bath interactions belowthe lance exit in the water bath. As shown, swirl flowprovided greater convection mixing for up to r/R = 0.1.The swirl flow set up a centrifugal force field, which hada favorable convection effect. Swirl flow dominated overthe nonswirl in the region ranging from r/R = 0 to 0.1.However, at a distance of r/R ‡ 0.1, no significantchange occurred in the convective mixing processbecause of the swirling effect. This mixing phenomenonis only valid for the air–water system not in the realfurnace scenario. Figure 15 shows the contour plots ofthe Veef for the swirl and nonswirl flows. The plots alsoconfirm that the swirl flow only can increase mixingclose to the lance for the air–water system, specifically.

V. EFFECT OF DENSITY

To investigate the effect of density change on thesplashing formation, the liquid density was increased to3 times of density of water. The new fluid was denotedas D3 qD3 ¼ 3000 kg/m3

� �: The viscosity of the liquid

was kept constant as water. However, because of a lackof experimental data, these results could not be vali-dated and must be considered as exploratory. Therefore,these results are presented for discussion only.

The effect of density on splashing generation is shownin Figures 16(a) and(b). Figure 16(a) shows the averagevolume fraction at 40 mm (z/Z = 0.66) above the liquidbath as well as the generated splash pattern along theradial direction. As expected, the degree of splashgeneration for the higher density liquid is reduced

significantly. At 60 mm (z/Z = 0.625) above the liquidbath (Figure 16(b)), the curves show a similar trend. Thebubbles from the injected air jet through the annulus ofthe lance move radially outward and approach the freesurface. This trend leads to the creation of broad spoutsin the free surface. The highest expulsion of the risingplume was in the vicinity of the lance. When the bubblescollapsed at the free surface, splashing occurred.In the experimental study by Nilmani and Cono-

chie,[6] the effect of different gas densities was investi-gated by injecting helium instead of air. They reportedthat with a less dense gas, a greater volume flow isrequired to maintain the same injection characteristics.However, no experimental study was found in the openliterature on splashing formation for higher liquiddensity for TSL gas injection.

VI. EFFECT OF VISCOSITY

Nilmani and Conochie[6] investigated the effect ofviscosity on splashing and slopping in which threedifferent liquids of different viscosity (water, glycerol/water of viscosity 56 centipoise, and glycerol/water ofviscosity 200 centipoise) were used. They reported thatsplashing and slopping were not as pronounced as in theair–water system. They also reported that gas penetra-tion of the viscous liquid on the lance axis was alsosmall and that increasing liquid viscosity reduces gasdispersion.Liovic et al.[16] also investigated the effect of viscosity

change on the formation of splashing by numericaltechnique. In their numerical simulation, Liovic et al.[16]

used 95 pct glycerol solution to observe the effect ofviscosity on splashing generation. They reported thathigh viscosity suppressed splashing and free surfacedistortions. They also reported that a high liquid

Fig. 15—Contours for volume exchange effectiveness from present water model simulation: (a) Q = 2.67 9 10�3 m3/s, H/L = 1/3, F = 0�,t = 30 s; (b) Q = 2.67 9 10�3 m3/s, H/L = 1/3, F = 57.5�, t = 30 s.

48—VOLUME 41B, FEBRUARY 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B

viscosity of the glycerol solution also damped out bulkbath motion and significantly reduced liquid backpenetration up the lance.

VII. CONCLUSIONS

Gas injection characteristics in a water bath wereinvestigated using the CFD modeling technique, andswirled gas injection played a role in improving themixing process near the lance tip. The simulation resultsfor velocity fields and the turbulence generation inside thebath agreed with the previous water model experimentalstudy by Morsi et al.[1] A semiempirical equation wasproposed for the vertical penetration distance of theannulus air jet into the water bath from the presentsimulation. The concept of mean convective mixing byvolume exchange concept revealed that the mixing wasnonuniform and concentrated near the lance for thespecific air–water system studied. A study of the mixingprocess by turbulence mixing through turbulent diffusion

also revealed the similar phenomena. The formation of arecirculation zone in the water bath is favorable foruniform mixing; however, the recirculation zonesobserved in this study were weak for water. This modelnow forms the basis to assess the typically complexturbulent flows encountered in the actual smeltingprocess. Some exploratory work applying this model toa higher density liquid is the first step on this path.

ACKNOWLEDGMENT

The authors would like to express their gratitude tothe Faculty of Engineering and Industrial Science,Swinburne University of Technology, and AusmeltLimited for their financial and technical support.

NOMENCLATURE

CD Drag coefficientD Cylinder diameterDo Outlet diameter of the cylinderDb Bubble diameterdo Outer diameter of the lancedi Inner diameter of the lanceFrm Modified Froude numberf Body force vectorg Gravitational body forceH Lance submergence LevelK Turbulent kinetic energyL Liquid level in the cylinderLva Vertical penetration distance for air jet injected

through annulusN Number of phasesQ Air flow rate through lanceReb Bubble Reynolds numberR Radius of the cylindrical vesselr Radial distance from the centre pointTt

k Phase k reynolds stressv Velocity vectorX Radial coordinateY Tangential coordinateZ Axial coordinatelk Molecular viscositylt

k Turbulent viscosity for phase klt;SI

c Shear induced turbulent viscosity for continuousphase

lt;BIc Bubble induced turbulent viscosity for

continuous phaseak Volume fraction of phase kqk Density for phase ksk Phase k shear stressdk Kronecker delta functionek Dissipation rate

REFERENCES1. Y.S. Morsi, W. Yang, B.R. Clayton, and N.B. Gray: Can. Metall.

Q., 2000, vol. 39 (1), pp. 87–98.2. R.I.L. Guthrie: Metall. Mater. Trans. B, 2004, vol. 35B, pp. 417–

37.

Fig. 16—(a) Average volume fraction at 40 mm height (z/Z = 0.66)above the liquid bath (Q = 2.67 9 10�3 m3/s, H/L = 1/3, F =57.5�); (b) average volume fraction at 60 mm height (z/Z = 0.625)above the liquid bath (Q = 2.67 9 10�3 m3/s, H/L = 1/3, F =57.5�).

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, FEBRUARY 2010—49

3. J. Floyd: Howard Worner Int. Symp. Inj. Pyro., TMS, Melbourne,Australia, 1996, pp. 417–28.

4. J. Floyd: Metall. Mater. Trans. B, 2005, vol. 36B, pp. 557–75.5. D. Mazumdar and R.I.L. Guthrie:Metall. Trans. B, 1985, vol. 16B

(1), pp. 83–90.6. M. Nilmani and D.S. Conochie: 4th Int. Conf. Inj. Met.: Scaninject

IV, MEFOS, Lulea, Sweden, 1986, pp. 7.1–7.19.7. W.J. Rankin, F.R.A. Jorgensen, T.V. Nguyen, P.T.L. Koh, and

R.N. Taylor: Extractive Metallurgy, 1989, pp. 577–99.8. S. Neven, B. Blanpain, and P. Wollants: EPD Cong. 2002, TMS,

2002, pp. 449–59.9. M. Iguchi, T. Uemura, H. Yamaguchi, T. Kuranaga, and Z.-i.

Morita: ISIJ Int., 1994, vol. 34 (12), pp. 973–79.10. J.F. Davidson and B.O.G. Schuler: Trans. Inst. Chem. Eng., 1960,

vol. 38, pp. 335–42.11. N.Dave andN.B.Gray:Metall. Trans. B, 1991, vol. 22B, pp. 13–20.12. C.B. Solnordal and N.B. Gray: Metall. Mater. Trans. B, 1996,

vol. 27 (2), pp. 221–30.13. C.B. Solnordal, F.R.A. Jorgensen, and R.N. Taylor: Metall.

Mater. Trans. B, 1998, vol. 29 (2), pp. 485–92.14. M.P. Schwarz and P.T.L. Koh: 4th Int. Conf. Inj. Met.: Scaninject

IV, MEFOS, Lulea, Sweden, 1986, pp. 6.1–6.17.

15. P. Liovic, J.-L. Liow, and M. Rudman: ISIJ Int., 2001, vol. 41 (3),pp. 225–33.

16. P. Liovic, M. Rudman, and J.-L. Liow: App. Math. Mod., 2002,vol. 26, pp. 113–40.

17. S.V. Patankar and D.B. Spalding: Int. J. Heat. Mass. Trans., 1972,vol. 15, pp. 1787–1806.

18. Y. Sato and K. Sekoguchi: Int. J. Multiphase Flow, 1975, vol. 2 (1),pp. 79–95.

19. B.E. Launder and D.B. Spalding: Com. Meth. App. Mech. Eng.,1974, vol. 3 (2), pp. 269–89.

20. AVL FIRE CFD Multiphase Manual v 8.5, AVL, Graz, Austria,2006.

21. J. Chahed, V. Roig, and L. Masbernat: Int. J. Multiphase Flow,2003, vol. 29, pp. 23–49.

22. J.A. Naser and A.D. Gosman: J. Auto. Eng., 1995, vol. 209 (4),pp. 289–95.

23. P.T.L. Koh and R.N. Taylor: CHEMECA’90. Auckland,New Zealand, 1990, pp. 183–89.

24. B.U.N. Igwe, S. Ramachandran, and J.C. Fulton: Metall. Trans.B, 1973, vol. 4, pp. 1887–94.

25. R. Daghigh, N.M. Adam, and B. Saharib: Eu. J. Sci. Resear.,2009, vol. 25 (2), pp. 174–91.

50—VOLUME 41B, FEBRUARY 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B