9 © 2014 ISIJ

ISIJ International, Vol. 54 (2014), No. 1, pp. 9–18

Numerical Simulations of Inclusion Behavior and Mixing Phenomena in Gas-stirred Ladles with Different Arrangement of Tuyeres

Wentao LOU and Miaoyong ZHU*

School of Materials and Metallurgy, Northeastern University, Shenyang, 110819 People’s Republic of China.

(Received on May 10, 2013; accepted on August 22, 2013)

A CFD-PBM (Computational Fluid Dynamic-Population Balance Model) coupled model has been developedto investigate the effects of different number and position of bottom tuyeres and gas flow rate on the bubblyplume flow, inclusion removal and mixing phenomena in gas-stirred ladle. It is found that the dual blowinggives a shorter mixing time and higher inclusion removal ratio in comparison with the center blowing oreccentric blowing with one tuyere. With the increasing of separation angle of two tuyeres, the inclusionremoval ratio increases, while mixing time decreases first and then increases. With the increasing of radialposition of two tuyeres, the inclusion removal first increases and then decreases, and the mixing timedecreases until the radial position exceeds 0.7R from the bottom center, where R is the bottom radius ofladle. It is recommended to use the two tuyeres placed at radial position of 0.6R and the angle of 135 deg inladle to improve the joint efficiency both the inclusion removal and mixing. With the gas flow rate increasing,the efficiency both mixing and inclusion removal with the optimized tuyeres arrangement increases, howeverwhen the gas flow rate exceeds 300 NL/min in 150 ton ladle, the removal ratio and mixing time change little.

KEY WORDS: inclusion removal; mixing phenomena; tuyeres arrangement; CFD-PBM coupled model; ladle.

1. IntroductionDuring steelmaking process, a huge number of nonmetal-

lic inclusions are generated in metallurgical reactor and havea detrimental effect on the quality of steel especially whencoagulated large-size inclusions remain in steel products,and the inclusion removal from molten steel with moreeffectiveness is critical to improve the cleanness of moltensteel. On the other hand, in metallurgical reactor, the homo-geneity of temperature and components, and the efficiencyof many metallurgical reactions, such as degassing, deoxi-dation and desulphurization is intricately related to mixingphenomena. Therefore, improving the efficiency of both theinclusion removal and mixing in metallurgical reactor hasbecome the main objectives in steelmaking process with theincrease of demand of high quality steel. It is well knownthat gas blowing has been widely applied in metallurgicalprocesses to enhance the inclusion removal and metallurgi-cal reaction rates and to homogenize the temperature andcomposition of the melt, and the number, arrangement andgas flow rate of bottom blowing have a great impact onthese transport phenomena. Hence, the study of inclusionsremoval behavior and mixing phenomena under differentarrangement of gas blowing in gas-stirred system is necessaryand has received considerable attention1–19) over the years.

Inclusion behavior in gas-stirred system involves com-plex phenomena, such as inclusion transport due to liquidflow, inclusion growth due to inclusion-inclusion collisionand inclusion removal due to flotation and attachment tobubbles, and some models have been proposed to describethese behaviors.1–10) Miki and Thomas et al.4) predicted theinclusion removal in RH degassing vessel with PBM by tak-

ing into account inclusions growth due to turbulent shearcollision and inclusions removal due to Stokes flotation andbubble-inclusion buoyancy collision. Söder et al.5) adoptedsimilar models to study the growth and removal of inclu-sions in gas-stirring ladle, and considered inclusion flotationby spherical-cap bubbles. Furthermore, some researchers6–10)

developed CFD-based models considering not only inclu-sions growth and removal, but also their transport carried byfluid flow and spatial distribution, to simulate inclusionbehavior in a gas-stirred ladles, and the effect of bottom tuy-ere configurations on inclusion removal in the ladle were alsoinvestigated by Zhu et al.,7) Wang et al.8) and Geng et al.9)

To some extent, the existing models had succeeded in pre-dicting the inclusion removal efficiency in gas-stirred sys-tems. However, some important phenomena and mecha-nisms were still not taken into account in these models, suchas inclusion turbulent random motion, bubble wake and slageye on the liquid surface and so on, as shown in Fig. 1. Inour very recent publication,13) the model of inclusion turbu-lent random velocity was proposed to calculate the inclu-sion-inclusion and bubble-inclusion turbulent random colli-sion by introducing the correction factor. Furthermore, themodel of inclusion removal rate due to bubble wake capturewas developed, and the effect of slag eye size on the inclu-sion growth and removal were considered as well. In thisprevious work, only the center blowing was taken intoaccount. In fact, in the practical ladle metallurgy, the eccentricor dual blowing is always adopted, and the effect of differentarrangement of gas blowing on the inclusion removal is veryimportant and need to be discussed and clarified further.

On the other hand, there were also many physical andmathematical investigations been carried out to study theeffect of different arrangement of bottom tuyeres on themixing phenomena,14–19) but the bubble turbulent dispersionforce and bubble-induced turbulence, which have important

* Corresponding author: E-mail:myzhu@mail.neu.edu.cnDOI: http://dx.doi.org/10.2355/isijinternational.54.9

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ISIJ International, Vol. 54 (2014), No. 1

effect on the transport phenomena in gas-stirred systems,13)

were not well considered in these mathematical mod-el.14,16,18) Furthermore it is worth noting that there is still nosuch work published to study the optimization of bottomtuyeres from the viewpoints of improving both inclusionremoval and mixing efficiency. In gas-stirred systems, theinclusion removal occurring mainly in bubbly plume regionand liquid surface, is directly related to the degree of turbu-lence and bubble dispersion in these regions, while the mix-ing phenomena is mainly directly related to the uniformityof liquid velocity and turbulence, and distribution of deadzone in the whole metallurgical reactor. Therefore theeffects of number, arrangement of gas blowing on the inclu-sion removal and mixing phenomena are important andgreatly different, and it is necessary to optimize the arrange-ments of bottom tuyeres to ensure the higher efficiency ofboth inclusion removal and mixing in metallurgical reactors.

The objectives of present work were to present a CFD-PBM coupled model to investigate the effects of number,arrangement and gas flow rate of bottom blowing on theinclusion behavior and mixing phenomena in gas-stirredladle for steelmaking. A proper arrangement of tuyeres hadbeen proposed for improving the efficiency both inclusionremoval and mixing.

In present model, the bubble-induced turbulence and bub-ble turbulent dispersion force were considered to predictbubbly plume flow, which has an important effect on theinclusion removal and mixing phenomena in the turbulentgas-stirred system. For the inclusion behavior, the multiplemechanisms both that promote inclusion growth due toinclusion-inclusion collision caused by turbulent randommotion, shear rate in turbulent eddy and difference inclusionStokes velocities, and that promote inclusion removal due tobubble-inclusion turbulence random collision, bubble-inclu-sion turbulent shear collision, bubble-inclusion buoyancycollision, inclusion own floating including Stokes floatingand turbulent random floating near slag-metal interface,bubble wake capture were considered, as schematicallyshown in Fig. 1. For the mixing phenomena, tracer transportequation was adopted to describe the mixing time whichwas defined as that time when all the local concentrationsof tracer reached within 5 pct deviation of the homogeneousvalue in ladle, and in order to eliminate deviation of mixingtime in ladle, the multi tracer addition and monitoring loca-tions were adopted in present work.

2. Governing Equations for CFD-PBM Coupled Model

2.1. AssumptionsThe mathematical model for fluid flow and inclusion

behavior in gas-stirred systems is based on the followingassumptions:

(1) The molten steel in the ladle is incompressible New-tonian fluid, and the turbulent flow is isotropic.

(2) Both the bubbles and inclusions are assumed to bespherical, and the diameter of bubbles is regarded as a con-stant during bubbles rising in ladle.

(3) The effect of top slag on fluid flow is neglected, anda flat free surface was assumed at the top surface of ladle.

(4) The generation of inclusions in gas-stirred ladle dueto erosion of refractory, entrapment of top slag or chemicalreactions is ignored.

(5) Inclusion collision occurring between two sphericalparticles form a bigger spherical inclusion. Cluster forma-tion due to collision between several inclusions is not con-sidered, and the effect of the Brownian collisions on theinclusion growth is not considered as well.

(6) Inclusions reaching the top surface excluding slageye, is considered ideal absorption by the slag layer and notto revert back into the ladle at a later time.

(7) The shape of slag eye is circular and does not varietywith time. When the bubbles rise to the top surface in ladle,the inclusions attaching to bubbles would return to the mol-ten steel with the rupture of the bubbles in slag eye zone.

(8) Inclusions in ladle larger than the Kolmogoroffmicroscale, would appear turbulent random motion and takethe turbulent velocity of an equal-sized eddy.

2.2. Model StructureThe basic ideas of the present model are schematically

structured in Fig. 2. The entire model consists of two mainblocks; i.e., a CFD block and inclusion population balancemodel (PBM) block. The local flow field, gas volume frac-tion and liquid turbulent energy dissipation rate are calcu-lated by CFD, which are then used to solve the PBM. Themean diameter and total mass source term of inclusions cal-culated from the PBM is used to update the momentum andmass conservation equations of inclusions phase for the nexttime step. In this work, Sp is the total mass source term dueto inclusion removal and used to update the mass conserva-tion equations of inclusions particle phase. d32 is inclusionSauter mean diameter, which is calculated from inclusion

Fig. 1. Inclusion removal behavior in a gas-stirred ladle.

Fig. 2. Overall solution schematic of the CFD-PBM coupledmodel.

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size distribution predicted by PBM (Eq. (1)) and then usedto update interfacial momentum exchange term betweeninclusion and liquid. On the basis of steady flow regime pre-dicted by CFD model, the tracer transport equation is solvedto determine the mixing time in ladle.

.............................. (1)

where ni is the number density of inclusion with diameter di.

2.3. CFD ModelIn the present study, based on Euler-Euler approach, the

mass and momentum balance equations are solved for eachphase separately. For instance, the mass balance equation ofeach phase which can be expressed as

................ (2)

where ρk, αk, and Sk are the density, volume fraction,averaged velocity vector and mass source term of liquidphase (k = l), gas phase (k = g) and inclusion particle phase(k = p) respectively. Both Sl and Sg are zero, and Sp is cal-culated by PBM of inclusions and discussed later. Since thewhole space domain is shared by the three phase, the con-straint condition α l + αg + αp = 1 needs to be satisfied toenclose the model.

In the momentum equations, the drag and turbulent dis-persion force among three phases, which have importanteffect on the transport phenomena in gas-stirred systems, areconsidered as momentum exchange source terms, and thebubble-induced turbulence produced during bubble floatingwas considered in k – ε turbulence model. The detailedexpression for the gas-liquid-inclusion three phase hydrody-namic equations together with the k – ε turbulence model(CFD model) had been described in our very recentpublication13) and would not be reproduced here.

2.4. Inclusion Population Balance Model (PBM)For the description of the PBM, a number density of

inclusion n(Vi) can be postulated, and the transport equationfor the number density n(Vi) is given by

......... (3)

where β(Vi, Vj) represents the inclusion coalescence rate,and Vi is the inclusion volume of size i. The three terms onthe right-hand side of Eq. (3) are the birth rate due to thecoalescence of smaller inclusions, the death rate due to thecoalescence with other inclusions, and inclusion removalrate respectively.

The population balance equation can be solved by the dis-crete method, which is based on representing the continuousparticle size distribution (PSD) in terms of a set of discretesize classes or bins. The advantages of this method are itsrobust numeric and that it gives the PSD directly. Therefore,the Eq. (3) can be written in terms of volume fraction ofeach particle size i.

... (4)

............ (5)

where ρp and up are the density and velocity of the inclusionphase respectively, δ k j is assigned to 0 (k ≠ j) or 1 (k = j),Vag is the volume resulting from the aggregation of twoinclusion, and α i is the volume fraction of inclusion size iand defined as follow

................ (6)Furthermore, in order to ensure the mass conservation of

inclusion, the Eqs. (7) and (8) need to be satisfied:

................................ (7)

............................. (8)

where αp and Sp are the volume fraction and source term ofinclusion phase respectively, which are included in Eq. (2).

.......................... (9)

...... (10)where , and represent inclusion coalescence ratedue to turbulent random collision, shear collision in turbu-lent eddies and Stokes buoyancy collision respectively, and

, , , and represent the masssource terms of inclusion removal due to wall adhesion,inclusions own floating near slag-metal interface, bubble-inclusion buoyancy collision, bubble-inclusion turbulencerandom collision, bubble-inclusion turbulent shear collisionand bubble wake capture respectively. Furthermore, theeffect of slag eye size on the inclusion removal is taken intoaccount as well in the present study. The is ignored inpresent work because of its little influence on inclusionremoval in ladle.13) The detailed expressions for inclusioncoalescence and removal rate due to these mechanisms havebeen studied and described in our latest publication13) andwill not be reproduced here.

2.5. Tracer Transport EquationThe mixing process in chemical and metallurgical pro-

cessing vessels could be described by mixing time which isdefined as that time when all the local concentrations oftracer reached within 5 pct deviation of the homogeneousvalue. In order to determine the mixing time in the vessel,the tracer dispersion equation need to be solved and can beexpressed as follows

..........(11)

where C is the local mass fraction of tracer, Sct is the turbu-lent Schmidt number and the default Sct is 0.7.

2.6. Boundary Conditions and Numerical SchemeIn present work, the CFD-PBM coupled model was

solved using the commercial computational fluid dynamicssoftware Fluent 12.0 combined with User-Defined Function(UDF), to describe the inclusion behavior and mixing phe-nomena in 150 ton gas-stirred ladle. The dimensions of ladleand other parameters are shown in Table 1. Due to the sym-metry of the flow, only half of the geometric model wasbuilt as computational domain with a total about 143 000meshes. The bottom and side walls were set as no-slip solid

dn d

n di i

i i32

3

2= ∑

∑

∂∂

( ) + ∇ ⋅( ) =t

u u Sk k k k k k kα ρ α ρ

uk

∂ ( )∂

+ ∇ ⋅ ( )( )= −( ) −( ) ( )−

∫

n V

tu n V

V V V n V V n V dV

V

ip i

i j j

V

i j j ji1

2 0β

β

,

ii j

V

i j j iV n V n V dV S,max ( ) ( ) ( ) +∫0

∂( )∂

+∇⋅( )= −⎛

⎝⎜⎞⎠⎟==

∑

ρ αρ α

ρ δ β ξ

p i

p p i

p i kj kj k j kjj

N

k

Nt

u

V n n11

211∑∑ ∑−

⎛

⎝⎜⎜

⎞

⎠⎟⎟ +

=β ρij i

j i

N

j p i in n V S

ξkj

ag i

i ii ag i

i ag

i ii ag

V V

V Vfor V V V

V V

V Vfor V V=

−−

< <

−−

< <

−

−−

+

+

1

11

1

1

VV

otherwise

i+

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

1

0

αi i i iV n V i N= ( ) = ⋅⋅ ⋅ −0 1 1, , ,

α αp ii

N

==

−

∑0

1

S V Sp p i ii

N

==

−

∑ ρ0

1

β β β βij ijR

ijS

ijB= + +

S S S S S S Si iWall

iIF

iBIB

iBIR

iBIS

iWake= + + + + +

βijR βij

S βijB

SiWall SiIF SiBIB SiBIR SiBIS SiWake

SiWall

∂∂ ( ) + ∇ ⋅( ) = ∇ ⋅ ∇( )⎛

⎝⎜

⎞⎠⎟t

C u CSc

Clt

t

ρ ρμ

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ISIJ International, Vol. 54 (2014), No. 1

walls, and the standard wall function was used to model theturbulence characteristic in the near-wall region. The veloc-ity-inlet was used for gas blowing at the bottom tuyeres, anda flat free surface was assumed at the top surface, where thestirring gas is completely discharged and thus the remainingliquid completes the circulation flow.

In gas-stirred ladle, different bubble diameters could beobtained by changing the type and size of bottom tuyere, suchas porous brick or different diameter of nozzle. In the practicalladle metallurgy, the porous bricks are widely to produce avery small bubbles due to their fine pores with radii usuallynot more than 75 μm. In present work, the bubble diameterswere proportional to according to the study of Sano andMori,20) and set to 4 mm under 50 NL/min of Qg.

The inclusion sizes of 4 to 200 μ m were considered,which were divided into 18 groups having characteristicparticle volume from V0 to V17. The particle volume of eachgroup was determined based on Vi+l = 2Vi, i.e., the characteristicdiameter of each group was determined by di+l = 21/3di(i =0,1,2,…,16). The smallest characteristic size d0 was 4 μ m.The size distribution and removal rate of inclusions werecalculated by solving the PBM equations for each group ateach time step (Δt = 0.25 s). It was assumed that there weremainly small inclusions in ladle at initial time (t = 0), and thenumber density of different size of inclusions complied withthe exponential function which can be expressed as follow

.................. (12)The mixing process was evaluated by introducing a small

amount of tracer into the ladle at steady-state flow regime(t = t0) and then monitoring its dispersion at sampling posi-tions with time (t – t0). In present model, the flow regimewith blowing time t0 of 600 s was used to calculate the mix-ing process in gas-stirred ladle.

For the case of eccentric position and multi-tuyeres, theslag eye position would change with tuyeres arrangement. Inpresent model, the circle center of slag eye was determinedon the position of maximum gas volume fraction of eachbubbly plume in the liquid surface, and the circle radius reof slag eye could be calculated by the following expression.21)

....... (13)

3. Resulte and DiscussionIt is well known that the liquid turbulent flow and gas vol-

ume fraction distribution have an important impact on theinclusion behavior and mixing phenomena in gas-stirredsystem, and the accurate prediction of hydrodynamics is thebasis for describing these behaviors. In our latest publica-

tion,13) the predicted bubbly plume flow have been validatedagainst experimental data, and the importance of differentmechanisms of inclusion removal in ladle with center blow-ing has also been discussed and clarified. In present work, theeffects of different arrangement of bottom tuyeres on the fluidflow, inclusion removal and mixing efficient were studied anda proper arrangement of tuyeres was proposed from the view-points of both inclusion removal and mixing efficiency.

3.1. Comparison of Center Blowing, Eccentric Blowingand Dual Blowing

In the practical steelmaking process, the center blowing,eccentric blowing and dual blowing have been widelyadopted in gas stirred ladles. Figure 3 gives the typicalarrangement of one tuyere placed centrally, eccentrically at0.5R (R is bottom radius of ladle) and two tuyeres placedsymmetrically at 0.5R.

3.1.1. Bubbly Plume FlowFigures 4 and 5 show the predicted liquid velocity and

turbulent kinetic energy in 150 ton ladle with center blow-ing, eccentric blowing and dual blowing respectively. It isnoted that only half of the geometric model is built as com-putational domain in present model, but the predicted resultsare shown symmetrically in figures to better clarify thearrangement of tuyeres. From these figure, it is clear thatwhen only one tuyere is placed at the bottom center, theupwelling steel flow forming in bubbly plume zone turnshorizontally toward the sidewall in the vicinity of the freesurface, and descends further along the wall. Two main cir-culations form between bubbly plume and size wall, asshown in Fig. 4(a). As one tuyere is moved away from thecenter toward the position of half radius, the bubbly plumewould bends toward the side wall because of influence ofliquid flow, and only a larger circulation forms in the wholeladle as shown in Fig. 4(b). Furthermore, the liquid velocityand turbulent kinetic energy become more uniform in thewhole ladle and weaker in bubbly plume. As the number oftuyere increase from one to two, this trend would becomemore obvious, as shown in Figs. 4(c) and 5(c).

3.1.2. Inclusion RemovalIn present model, five types of mechanisms for inclusions

removal, including inclusion own floating near slag-metalinterface, bubble-inclusion buoyancy collision, bubble-inclusion turbulence random collision, bubble-inclusion tur-bulent shear collision and bubble wake capture, and theeffect of slag eye size on inclusion removal are considered.

Figure 6 illustrates the contour map of total source termSp of inclusion mass equations (Eq. (9)) due to all theremoval mechanisms in 30 minutes after the start of gasblowing through different arrangement of bottom tuyeres.From this figure, it can be found that the source term Sp inbubbly plume zone is negative, which indicates that theinclusions are removed from the liquid steel to the bubblesurface due to the bubble-inclusion collision, and the maxi-mum removal rate of inclusions mainly attributed to thebubble-inclusion turbulent random collision, appears nearbottom tuyeres where the gas volume fraction gather andturbulence is very strong. With the increase of height awayfrom the bath bottom, the bubbly plume occur dispersion

Table 1. Dimensions of ladle and other parameters in model.

Diameter of ladle (top) 3 115 mmDiameter of ladle (bottom) 2 578 mm

Depth of the liquid steel 3 200 mmArgon gas flow rate 50–400 NL/minDensity of molten steel 7 100 kg/m3

Surface tension between molten steel and Argon gas 1.4 N/mDensity of gas 0.865 kg/m3

Density of inclusions 3 900 kg/m3

Molecular viscosity of molten steel 0.0055 Pa sThickness of the slag layer 96 mm

Qg0 289.

n d ei tdi( ) .

=− ×= ×0

14 1 0 102 106

r HQ

g He

g= −⎛

⎝⎜

⎞

⎠⎟0 56 0 76

0 5 2 5

0 4

. .. .

.⎛

⎝⎜⎜

Q

gs

l

g+ −⎛⎝⎜

⎞⎠⎟

−

7 15 10 5

0.

.

.

ρρ 55 2 5

0 73 0 50 5

HhH.

. ..

⎛

⎝⎜

⎞

⎠⎟ ⎛

⎝⎜⎞⎠⎟

⎞

⎠⎟⎟

−

Fig. 3. Arrangement of bottom tuyeres in the ladle.

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and the inclusion removal rate decreases. Furthermore, it isalso noticed that the source terms Sp in liquid surface centerare positive, which means that the inclusions attaching tobubbles would return to the liquid steel with the rupture ofthe bubbles in slag eye zone, where the molten steel isdirectly exposed to the ambient environment.

Figure 7 shows the predicted typical inclusion removalrate due to various mechanisms with time under differentarrangement of tuyeres. From this figure, it can be seen thatat the early stages of blowing, the inclusion removal ismainly attributed to the joint effort of both the bubble-inclu-sion collisions and bubble-wake capture which is the pre-vailing mechanism for inclusion removal. At the middle andlater stages, with the coalescence of inclusions, the inertiaeffects of lager inclusions would become remarkable, andthe bubble-inclusion turbulent random collisions graduallystrengthen and dominate the inclusion removal with timeincrease. Furthermore, it is worth noting that compared withresults reported in our very recent publication,13) the inclu-sion removal rate contributed by their own floating nearslag-metal interface significantly decreases in present work,while that contributed by bubble-inclusion collision andbubble wake capture increases greatly. This is mainly

because that the slag eye size proportional to the non-dimen-sional slag height (h/H)–0.5 according to the study ofKrishnapisharody and Irons,21) is different, and h/H is 0.03in present work and 0.01 in previous work.13) With theincreasing of slag eye size, more inclusions attaching tobubbles would return to the liquid surface in slag eye zone,which improves the inclusions concentration near the sur-face and facilitates the inclusion removal due to its ownfloating. It shows that the thickness of slag layer has anobvious effect on the inclusion removal, and more deep studyis necessary to understand the mechanism. We are carryingout such study now and will present the results in future.

In present work, θ is the integration removal rate of inclu-sions in molten steel, and computed by integrating the localvolume fraction Sp and cell volume Vcell throughout the ladle:

............................ (14)then the removal ratio ϕ of inclusions is given as

................... (15)

where αp,0 is the local volume fraction of inclusion at the

θt p cellS dV= ∫

ϕθ

ρ α= ×∫

∫t

t

p p cell

dt

dV0

0

100,

%

Fig. 4. Predicted liquid velocity in the melt bath of 150 ton gas-stirred ladle with different arrangement of gas blowing. (a)center blowing, (b) eccentric blowing, (c) dual blowing. The gas flow rate Qg is 200 NL/min.

Fig. 5. Predicted liquid turbulent kinetic energy in the melt bath of 150 ton gas-stirred ladle with different arrangement ofgas blowing. (a) center blowing, (b) eccentric blowing, (c) dual blowing. The gas flow rate Qg is 200 NL/min.

Fig. 6. Predicted the contour map of total source terms of inclusion mass equations (Eq. (9)) in the melt bath of 150 tongas-stirred ladle with different arrangement of gas blowing. (a) center blowing, (b) eccentric blowing, (c) dualblowing. The gas flow rate Qg is 200 NL/min.

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ISIJ International, Vol. 54 (2014), No. 1

initial time (t = 0) in gas-stirred ladle.Figure 8 shows the predicted inclusion removal ratio due

to various mechanisms in 30 minutes after the start of gasblowing through different arrangement of bottom tuyeres.ϕ tot is the total ratio due to the joint action of the differentmechanisms, and ϕ BIB, ϕ BIR, ϕ BIS, ϕ Wake, ϕ IF are sub-ratioattributed by bubble-inclusion buoyancy collision, bubble-inclusion turbulent random collision, bubble-inclusion tur-bulent shear collision, bubble wake capture, inclusion ownfloating near slag-metal interface respectively. It should bestated that with one tuyere moving away from the centertowards the half radius, the bubbly plume bending towardthe side wall as shown in Figs. 4 and 5, increase residencetime of bubbles in ladle, thus the inclusion removal sub-ratioϕ Wake and ϕ BIR due to bubble wake capture and buoyancycollision increases respectively. However the inclusionremoval sub-ratio ϕ BIR due to bubble-inclusion turbulentcollision decreases significantly because of decreases of theturbulent kinetic energy in bubbly plume region, as shownin Fig. 5. Furthermore, as the number of tuyere increasesfrom one to two, the inclusion removal sub-ratio ϕ Wake andϕ BIR due to bubble-wake capture and bubble-inclusion buoy-ancy collision increased significantly because of well dis-persion of bubbly plume in ladle. Overall, the total inclusionremoval ratio with dual blowing is the highest, while theeccentric blowing is the lowest.

3.1.3. Mixing PhenomenonThe mixing degree determining the efficiency of metal-

lurgical reactions in ladles can be evaluated from a degree95 pct bulk mixing time, which is defined as the maximumtime when all the local concentrations of tracer reach within5 pct deviation of the homogeneous value. Severalinvestigations14,15) have concluded that mixing time is

affected by the tracer addition location and monitoring pointwhich should be placed exactly in the dead zone. From Fig.4, it is observed that the lowest flow velocity zone is alwaysat the bottom closer to the walls. In present work, as shownin Fig. 9, multiple tracer addition locations (A1 to A5) andtracer monitoring points (M1 to M6) are adopted to elimi-nate deviation of mixing time as far as possible.

Figure 10 shows the typical variation of tracer mass con-centration of the six monitoring point (M1 to M6) with timeafter the trace added to point A1 and A2 respectively. In thisfigure, the C/Cave represents the ratio of the local tracer con-centration and the homogeneous value. It is observed thatthe location of tracer addition has a great impact on the mix-ing times even under the same blowing conditions, and thetimes that the concentration of each monitoring point reach-es within 5 pct deviation of the homogeneous value, are dif-ferent. For example, when the tracer is added to point A1,the monitoring point M4 is the last one reaching within 5 pctdeviation of the homogeneous value, and the mixing time tA1is 71 s. But when the trace is added to point A2, the moni-toring point M2 is the last one, and the mixing time tA2 is109 s. Correspondingly, the local distribution of trace massconcentration in the whole ladle is given in Fig. 11. Fromthis figure, it can be observed that all the local concentra-tions of tracer in whole ladle have reached within 5 pct devi-ation of the homogeneous value at the predicted mixing timetA1 of 71 s and tA2 of 109 s respectively, and the mixing timepredicted by six monitoring point (M1 to M6) in ladle canreflect the mixing phenomenon of the whole ladle.

Figure 12 shows the effect of different arrangement oftuyeres on the mixing times in 150 ton ladle. In presentwork, the time tave, which is the average of the five mixingtime (tA1 to tA5) predicted by adding the trace on five differ-ent point in ladle (A1 to A5), is proposed to represent themixing efficiency of the ladle. From this figure, it can be

Fig. 7. Predicted typical change of inclusion removal rate due to various mechanisms with time. (a) center blowing (b)dual blowing. The gas flow rate Qg is 200 NL/min.

Fig. 8. Predicted inclusion removal ratio due to various mecha-nisms in 30 min after the start of gas blowing with differenttuyeres arrangement. The gas flow rate Qg is 200 NL/min.

Fig. 9. Arrangement of tracer addition points (A1 to A5) and tracermonitoring points (M1 to M6) in ladle.

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found that when the center blowing is adopted, the mixingtime is the maximum, since the uniformity of liquid velocityand turbulent kinetic energy in whole ladle is the worst, andit is also difficult for tracer transport between the two separatecirculation flows formed by center blowing, as shown in Fig.4(a). When the dual blowing is adopted, the average mixingtime is shortest due to well dispersion of bubbly plume flow.

Overall, the dual blowing could give a shorter mixingtime and higher inclusion removal ratio in 150 ton ladle incomparision with center blowing or eccentric blowing withone tuyere. However, in order to obtain higher process effi-ciency of the ladle with two tuyeres gas blowing, the effectsof different separation angle θ and radial position on theinclusion removal and mixing phenomena have been inves-tigated, which will be discussed in the following section.

3.2. Effect of the Different Separation Angle of TwoTuyeres

Figure 13 shows the arrangement of the different separa-tion angle θ of two tuyeres in 150 ton ladle. In these schemes,the two tuyeres are placed at the half radius position, and theangle θ is set to 45 deg, 90 deg and 135 deg respectively.

3.2.1. Bubbly Plume FlowIn Figs. 14 and 15, the effects of the different separation

angle θ of two tuyeres on the liquid velocity and turbulentkinetic energy in 150 ton ladle are illustrated. From thesefigures, it is observed that when 45 deg is adopted for theangle θ , the bubbly plume overlap partly and bends intense-ly toward the side wall, and a large recirculation forms inthe ladle. With the increase of angle θ, the bending of bub-bly plume and the uniformity of the liquid velocity and tur-bulent kinetic energy in whole ladle become weak gradually,however, the liquid velocity and turbulent kinetic energy

become more intense in bubbly plume region.

3.2.2. Inclusion RemovalFigure 16 shows the effect of different angle θ between

the two tuyeres on the inclusion removal ratio in l50 tonladle. From this figure, it is can be seen that the total inclu-sion removal ratio ϕ tot increases with the increasing of angleθ, and remains essentially unchanged with the angle θexceeding 135 deg. When the tuyeres angle θ of 45 deg isadopted in ladle, the inclusion removal ratio is the lowest.This is because the turbulence in bubbly plume is weakerthan that with the other angle arrangement, and on the otherhand, the two bubbly plumes attract each other and overlappartly as shown in Fig. 14(a), which also causes the decreaseof bubble-inclusion collision. When a larger angle θ isadopted, such as 135 deg or 180 deg, the two bubbly plumecompletely separated from each other, and turbulent kinetic

Fig. 10. Variation of tracer mass concentration of the six monitoring points (M1 to M6) with time after the tracer added to(a) point A1 and (b) point A2 respectively. The gas flow rate Qg is 200 NL/min.

Fig. 11. Contour map of tracer mass concentration in 150 ton ladle at the predicted mixing time (a) tA1 of 71 s and (b) tA2

of 109 s. The gas flow rate Qg is 200 NL/min.

Fig. 12. Predicted mixing time in 150 ton ladle with different tuy-eres arrangement. The gas flow rate Qg is 200 NL/min.

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energy in the bubbly plume is more intense, as shown in Fig.14(c), thus, the inclusion removal ratio changes little.

3.2.3. Mixing TimeFigure 17 illustrates the predicted mixing time under dif-

ferent angle θ between the two tuyeres. As shown in Fig. 17,with the increase of angle θ from 45 deg to 180 deg, theaverage mixing time decreased first and then increased.When the tuyeres angle θ of 45 deg is adopted, the two bub-bly plume overlap partly, and the utilization of gas-stirredenergy is relatively low. With the increase of angle θ, thetwo bubbly plumes separated from each other, and the mix-ing time decreases. On the other hand, the uniformity of theliquid velocity and turbulent kinetic energy in whole ladlewould become weak gradually as shown in Figs. 14 and 15.Overall, the mixing time with angle θ of 90 deg is the short-est, and that with angle θ of 180 deg is the longest.

Through the above comparison of inclusion removal ratioand mixing efficiency under different separation angle, itcan be found that when a smaller angle is adopted in ladle,the inclusion removal ratio becomes worse, but when a larg-er angle is adopted, the mixing efficient becomes lower.Therefore the separation angle θ of 135 deg is recommendedto improve the joint efficient both the inclusion removal andmixing phenomena.

3.3. Effect of the Different Radial Postion of Two TuyereFigure 18 shows the arrangement of the different radial

position of two tuyere placed in ladle bottom. In these

schemes, the separation angle θ of two tuyeres is 135 deg,and the multiple radial potions from 0.3R to 0.8R are con-sidered in present work.

3.3.1. Bubbly Plume FlowFigures 19 and 20 show the predicted liquid velocity and

turbulent kinetic energy in 150 ton ladle with two tuyeresplaced at different radial position. From these figures, it isclear that when the tuyeres radial position of 0.3R is adoptedin ladle, the two bubbly plumes attract each other and bendtoward center, and the two main circulations form betweenthe bubbly plume and side wall. With the increasing of radi-al position of two tuyeres, the two bubbly plumes graduallyseparate from each other and move to the side wall, and theuniformity of the liquid velocity and turbulent kinetic ener-gy in whole ladle become well. But the bubbly plume wouldcontact with the wall with the radial position of two tuyeresexceeeding 0.7R from the bottom center.

3.3.2. Inclusion RemovalFigure 21 shows the effect of different radial positions of

Fig. 13. Different separation angle θ of two tuyeres in the ladle.

Fig. 14. Predicted liquid velocity in the melt bath of 150 ton gas-stirred ladle with different angle θ between two tuyeres.(a) θ = 45 deg, (b) θ = 90 deg, (c) θ = 135 deg. The gas flow rate Qg is 200 NL/min.

Fig. 15. Predicted liquid kinetic energy in the melt bath of 150 ton gas-stirred ladle with different angle θ between twotuyeres. (a) θ = 45 deg, (b) θ = 90 deg, (c) θ = 135 deg. The gas flow rate Qg is 200 NL/min.

Fig. 16. Predicted inclusion removal ratio due to various mecha-nisms in 30 min after the start of gas blowing with differ-ent angle θ between two tuyeres. The gas flow rate Qg is200 NL/min.

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two tuyeres on the inclusion removal ratio. It can be observethat the inclusion removal ratio first increases, and thendecreases with the movement of the two tuyeres along theradial direction from 0.3R to 0.8R. This is because thatwhen the two tuyeres placed at 0.3R, the turbulence in bub-bly plume is the weakest, and the bubbly plume overlappartly as shown in Figs. 19 and 20. With the increase of thetuyeres radial positions, the turbulence in bubbly plumebecome more intense, and the bubbly plume also becomesmore dispersed. Thus, the inclusion removal ratios due tobubble-inclusion collision and bubble wake captureincrease. However, when the tuyeres radial distance exceed0.7R, the dispersion of bubbly plume is blocked by the wall,the effective collision frequency between bubble and inclu-sion will decrease. Overall, the tuyeres radial position of0.6R provides the best inclusion removal.

3.3.3. Mixing TimeFigure 22 shows the effect of different radial positions of

two tuyeres on the mixng time, it is clear that when the 0.3Ris adopted in ladle, the mixing time is very much longer than

that with the other radial positions, this is because that theuniformity of the liquid velocity and turbulent kinetic energyin whole ladle is the worst, and on the other hand, it is alsodifficult for tracer transport between these two separate circu-lations as shown in Fig. 19(a). With the increasing of radialpositions of two tuyeres, the average mixing time decreases,but when the tuyeres are placed at 0.8R, the average mixingtime increases because of the influence of side wall.

Overall, the effects of different arrangement of tuyere inladle on the inclusion removal and mixing time are veryimportant, and the two tuyeres radial position of 0.6R andthe angle of 135 deg are recommended to improve the jointefficient both the inclusion removal and mixing.

3.4. The Effect of Gas Flow RateFigures 23 and 24 show the effect of gas flow rate on the

inclusion removal ratio and mixing time in 150 ton ladle. Inthese figures, the angle θ and the radial distance of two tuy-eres are 135 deg and 0.6R respectively. It can be found thatwith the gas flow rate increasing, the mixing time decrease,and the inclusion removal increases. However when the gasflow rate exceeds 300 NL/min, the total removal ratio andmixing time change weakly.

Fig. 17. Predicted mixing time in 150 ton ladle with different angleθ between two tuyeres. The gas flow rate Qg is 200 NL/min.

Fig. 19. Predicted liquid velocity in the melt bath of 150 ton gas-stirred ladle with different radial position of gas blowing.(a) 0.3R, (b) 0.5R, (c) 0.7R. The gas flow rate Qg is 200 NL/min.

Fig. 20. Predicted liquid turbulent kinetic energy in the melt bath of 150 ton gas-stirred ladle with different radial positionof gas blowing. (a) 0.3R, (b) 0.5R, (c) 0.7R. The gas flow rate Qg is 200 NL/min.

Fig. 18. Different radial position of two tuyeres in the ladle.

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4. ConclusionA CFD-PBM coupled model has been proposed to

describe the behavior of inclusion and mixing phenomena ingas-stirred turbulent systems for steelmaking. The effects ofdifferent arrangement of bottom tuyeres on the inclusionmechanisms and mixing efficient were studied and a properarrangement of tuyeres had been proposed from the view-points of both of inclusion removal and mixing efficiency.

(1) The dual blowing could give a shorter mixing timeand higher inclusion removal ratio in 150 ton ladle in com-parision with center blowing or eccentric blowing with onetuyere. The mixing time with center blowing is the longest,and the inclusion removal ratio with eccentric blowing is thelowest.

(2) For the two tuyeres placed in ladles, total inclusionremoval ratio ϕ tot increases with separate angle θ increasing,but remain essentially unchanged with the angle θ exceed-ing 135 deg. The average mixing time decreased first andthen increased, with the increase of angle θ from 45 deg to180 deg. The separation angle θ of 135 deg is recommendedto improve the joint efficient both the inclusion removal andmixing in ladle.

(3) With the movement of the two tuyeres along theradial direction from 0.3R to 0.8R, the inclusion removalratio first increases, and then decreases, and the mixing timedecreases first and then increases. It is recommended to usethe radial position of 0.6R and the angle of 135 deg.

(4) With the gas flow rate increasing, the mixing timedecrease, and the inclusion removal increases. However whenthe gas flow rate exceeds 300 NL/min in the 150 ton ladle,the total removal ratio and mixing time change weakly.

AcknowledgementsThe authors wish to express thanks to the National

Outstanding Young Scientist Foundation of China (GrantNo.50925415), and National Natural Science Foundation ofChina (Grant No.51134009) for supporting this work.

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Fig. 21. Predicted inclusion removal ratio due to various mecha-nisms in 30 min after the start of gas blowing with differ-ent radial position of two tuyeres. The gas flow rate Qg is200 NL/min.

Fig. 22. Predicted mixing time in 150 ton ladle with differentradial position between two tuyeres.

Fig. 23. Predicted inclusion removal ratio due to various mecha-nisms in 30 min after the start of gas blowing.

Fig. 24. Predicted mixing time in 150 ton ladle under different gasflow rate.