ISIJ International. Vol. 35 (1995). No. 5, pp. 472-479

Fluid Flow and Mixingthrough Multi-Tuyere

Phenomenain the Ladle Stirred by Argon

Miao-YongZHU.Takeo INOMOT0.1)Ikuo SAWADA2)and Tse-Chiang HSIAO

Ferrous Metallurgy Department, Northeastern University, Shenyang, P. R. of China. 1) Process Technology ResearchLaboratories, Nipp. on Steel Corporation, Shintomi, Futtsu, Chiba-ken, 293Japan. 2) AdvancedMaterials andTechnologyResearch Laboratories, Nippon Steel Corporation. Ida, Nakahara-ku, Kawasaki. Kanagawa-ken.21 1Japan,

(Received on October 21. l994 accepted in final form on January 27. 1995)

Water model experiments and the numerical soiution of a mathematical model with three dimensionshave been conducted to investigate the flow pattern and mixing phenomenain argon-stirred ladles with six

types of tuyere arrangement. It wasfound that the arrangement of tuyeres has a great effect on the flowpatterns and mixing in the ladle. a placement of single tuyere at off-centric position gave the shortest mixingtime whereasdouble tuyeres opposite placed at half radii wasfound to be the best arrangement consideringthe aspects of blowing, mixing. inclusion flotation and splashing. An empirical correlation for mixing timein the ladle considering the numberof tuyeres wasproposed. The predicted and measuredresults showedquantitatively good agreements.

KEYWORDS:physical modeling; mathematical modeling; fluid flow, mixing; multi-tuyere.

1. Introduction

The ladle refining by argon stirring has received con-siderable attention due to its manyadvantages suchas homogenization of temperature and chemical com-position of molten steel, acceleration of the metal/slagreaction, and removal of nonmetallic inclusion; on theother hand, its capital cost is muchlower. Due to its

wide application in iron and steelmaking industries,

extensive studies concerning important phenomenaingas-stirred ladles with single tuyere have bcen done in

the past over two decades, which can be classified asfollows:

(1) to study the structure ofthe plumesuch as the size

of bubbles, the rising velocity of liquid and bubbles, thedistribution of void fraction and bubble frequency, andthe shape of the plume, etc.1 ~ 7)

(2) to study the mean liquid fiow pattern withphysical modeling and mathematical modelling8~21)

(3) to study the mixing and masstransfer phenom-ena22~ 32)

In spite of the above studies, still manyopportunitiesexist for improving the performance of metallurgicaloperation by paying attention to these flows. Recently,for production of high quality steel, the gentle blowingtechnique in the ladle with multi-tuyere has beenput intopractice. However, the detailed information regardingthe behavior of fiuid fiow and the mixing nature whichdependon the arrangement of tuyeres and gas flowrateis still not clear, and very few studiesl9) on this aspecthas been reported till today.

The purpose of the present work was to investigate

C 1995 ISIJ 472

experimentally andnumerically the behavior of fluid flowand mixing phenomenain the argon-stirred ladle withmulti-tuyere. The effects of different arrangement oftuyeres on the flow patterns and mixing were studiedand a proper arrangement of tuyeres for the gentle andrapid mixing has been proposed.

2. Experimental

2.1. Similarity Considerations

In the gas-stirred system, the fiuid flow and mixing ofthe bath are caused by momentumtransfer betweenblown gas and liquid. The flowrate of injected gas in themodelcan be determined by the modified Froudenumberwhich is defined by

N~r=pgu2/(pl9H).........

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

where His the height of the bath.

For N tuyeres with equal inner diameter d, thesuperficial velocity u is given by

u=4Q/(1id2N)........

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

where Qis the gas flowrate.

Substitute Eq. (2) into Eq. (1), weobtain

N~r= I.62lpgQ2/(plN2d4gH) .................(3)

If we assumeboth of the full scale ladle and watermodel using the samenumberof tuyeres the followingequation can be used to determine the gas flowrate in

the model.

2 Pg2 Pll(4)=

)(lQ d 4 HQ d2 HP91 P12

ISIJ International, Vol.

where the subscripts I and 2stand for model and full

scale ladle, respectively. The main variables involved in

the present consideration are listed in Table 1.

2.2. Experimental Set-up

Theexperimental set-up is shownin Fig. l. Thesystemconsists of a cylindrical plexiglass vessel containing tapwater at roomtemperature. Argon gas wasinjected into

the bath through nozzles which are located at the re-placeable bottom of the vessel. Different configurationsof the tuyeres used in the present study is shownin Fig.2. For each configuration, three points at the surface ofthe bath were selected as tracer adding position.

To monitor local conductivity of water after theaddition of 20 o/o NaCl, an electrical conductivity probe

was placed at 20mmabove the bottom and from thesidewall in the ladle. The output signal of electrical

conductivity meter wasrecorded by a personal computercombinedwith A/D interface on an amplifier. Mixing time

Table l. Themainvariableassociatedwithpresentstudies.

Full scale ladle Water model(350t/ch) (1 : lO)

35 (1995), No. 5

Diameter (m)Height (m)Diameter of tuyeres (mm)Argon flowrate (Nl/min)Density of liquid (kg/m3)

4.0

4.0

lO.O

35(~800

7OOO

0.400.403.0

4-8

l OOO

Fig. l. Representation of experimental set-up.

CaseA

,e

CaseB

e' e

o e

CaseC

oe e

e

CaseD CaseE case F

Fig. 2. Six types of tuyeres arrangement in the ladle.

473

is defined as the time beyond which the changes ofconductivity are less than 5o/o of the steady state. Foreach case more than 5 times measurementswere per-formed, and the meanvalue wastaken as mixing time. It

was found that individual mixing tirne fell within 10010

of the meanvalues.

In order to visualize the fiow pattern in argon-stirred

mQdelladle, alumina particles of O.2mmdiameter anddensity close to water were used.

3. Mathematical Model

3.1. Mathematical Formulation

The fluid flow, turbulent properties and tracer dis-

persion in the ladle can be described by continuityequation, Navier-Stokes equations, turbulent modelandmass conservation equation, which can be written asfollows:

Continuity equation

a(pui)

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

axi

Momentumequation

J

)J=-

,

a(puiuj) ap+ a au auJ

+F, (6)+'~ errexj exi ex ax ax

whereFi the body force is ocplgi in the case of gas blowingin the ladle.

The effective viscosity pterr showing in Eq. (6) wasdetermined by solving the k-e turbulent model33) whichcan be represented by the following:

a( ~ax

~Puik- p.rr.

ak.

)= (7)

i ak ax*

a (Pu8

~err a8

=(CleGk-C2p82)

i - . .......(8)

axi (TS exi kwhere Gk, the generation term, is given by

(t

l)8u,

~aui au.

Gk=,1 J + J.......

(9)exi axj ax.

The auxiliary relationships are:

~err=u1+'tt """"""""(lO)

where

~t=pC//k2/e.........

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

Theconstants used in present study were recommendedby Launder and Spalding.33)

For the tracer dispersion in the vessel, it wasconsidered

as the sameproperties of the bulk liquid and added at

time zero. The governing differential equation for con-servation of massis represented by

*=

I

a(pC)+

e(puiC) a aC(12)pr

at ax err axiex

where Ferr the effective massdiffusion coefficient, whichis given by

rerr~~L+ 'lt..........(13)

Sc Sct

C 1995 ISIJ

ISiJ International. Vol. 35

where S, and S.t are laminar and turbulent Schmidtnumberrespectively. In present study, S*t and S, wereconsidered to be unity and 800 respectively.

3.2. Treatment of the PlumeIn the present study, the gas voidage of the plumewas

determined by an experimental correlation proposed byCastillejos and Brimacombe,5)which has beenwell usedfor three-dimensional fluid flow simulation in the gas-stirred ladle.34)

The density of the plume can be obtained by

p=0epg+(1-oc)pl"""'

"""""(14)

3.3. BoundaryConditions

Thevelocities parallel to the walls and the turbulencequantities near to the wall nodeswerecalculated by usingwall function.33) At the free suface, the vertical velocity

and normal gradients of the other variables were set to

be zero. At the solid wall, free slip boundary condition

was set for velocity, pressure and concentration,

3.4. Numerical Solution Procedure

The differential equations have been discretized byusing a control-volume method. A hybrid differencing

scherne wasadopted to approximate the convection anddiffusion terms, whereas for the transient term in massconservation equation, an implicit differencing scheme

wasused. Eachdifference equation wassolved by usingtridiagonal matrix algorithm. The system of equations

was solved with SIMPLEalgorithm (Semi-Implicit

Method for solving Pressure-Linked Equations). Theprogramemployedwasdeveloped by present author for

simulating three-dimensional transport processes in met-allurgical reactions.34) The domain was divided into

curvilinear grids of 20 x 20 x 20 in the three directions.

All the computations were performed on Sun-Sparc lO.

About 300-700 iterations were needed to reach con-verged values of velocity fields, which takes about 2~l h.

4. Results and Discussion

4. 1. The Characteristics of Fluid Flow4.1.1. Flow Patterns in the Ladle with Single Tuyere

Figures 3and5provided the predicted and visualized

flow patterns at the main vertical plane in the ladle in

CaseAand CaseB, respectively, and Figs. 4and6showthe flow pattern at the top horizontal plane for these twocases, respectively. It can be seen that two axisymmetricrecirculations are formed in the bath and the velocity in

the plume zone and near the sidewalls and free surface

are relatively large and there is almost no angular velocity

in CaseA. As contrasted with center blowing, it can befound in CaseBthat the velocity in plumezone andnearthe sidewall decreased, however the angular velocity

which will have a great effect on the mixing in the ladle

and the velocity near the bottom increased significantly

(as seen in Figs. 5and 6).

4.1.2. Flow Patterns in the Ladle with Multi-tuyereFigures 7to 10 showthe predicted and visualized flow

patterns at the main vertical plane whenargon gas wasinjected through two, three and four tuyeres respectively.

C 1995 ISIJ 474

(1995). No. 5

(a) predicted

_+~~\\~/.,tt~~.,ttt~..ttt

~ .fff~~.Iff~~_//f~ 'llP~~~_1/ff~..1//P~._1//f~\_.////~\\_'////

~.-.////P~ '-//////

///-ttfttt ' L

\~~

t~~~ J~~\ / /~~\ / l~~\~~\\

~~~\

/ l/ J/ /

~~~~ /~~~\ /

~\~\ r /

~\~~ /

~ \

\\~\\ l~~\\~\\ IJ

// / / //// ,~\\\\ \ \ /

- -? ~~_ ~.

(b) visualized

--> 0.30 m/s

Fig. 3. Predicted and visualized flow patterns as single tuyere

was placed at center in the ladle. (Case A, argonflowrate 6N//min)

~~~ 7f.~

~~{ ill

~~ fl~~~

~~:~~::~~~~~ t ///~~;~~;~

~r~~rl~/// ~ \*~~:~~~~~~

/~ ~~/~/./ \~\

/'~~ ~j

\--~ 030m/~

Fig. 4. Predicted flow pattern at free surface in the ladle. (CaseA, argon fiowrate 6N//min)

It can been seen from the figures that the configuration

of tuyeres has a great effect on flow patterns in the ladle,

which directly influences the mixing phenomena.

ISIJ International. Vol. 35 (1 995),

No. 5

(a) predicted

!

tt~

t~t~*~

~j~

.~

~~~i(;~/\

'~\f ~:/~~ ~P 'HP ~'

1~\': ~- -

~~~_~_~_'_4_4_~h~1e-~-4-*-~-4-de/4/

~:-4-~-4/4- e- e- Je/

4-4-~/k/~- de- 4/ kl

:~14/414-4- 4- ~/ 'el

,~,:~,:4,4,~, 4, 4,~1~- ~r

:~L-~-~- ~-:~~~-~- ~~

~-~- ~-

//

/

////

~>

*$IJfJIJlllll,/ '

~

-~> 0.30 m/s

(a) predicted

1~ ~~~ J>

J~tl_l

'1~~~~/~f ~~' t~:s: t~,*,t

,, ~tj~~-

tt ~ L ',f t

tf ~t I tf tt ~~ t ' ft ~\ t 'l

~~ t ll~~ t ,l

~~ \t,//~\~t//j~\tt//

Tft~~t~~~

11~\~tf// ttff

tt~~ ~\\t/// tfftt~\~t ~\ \ t ! ll tlfft

~~ ~ / ;?

---> 0.30m/s

(b) visualized

Frg. 5. Predicted and visualized fiow patterns as single tuyere

wasplace at half radius in the ladle. (Case B, argonfiowrate 6Nl/min)

~~

~~~~~~~

:~~~ t~++ *

~'' "/// ~IJ~~J ~~

~~

p//

\\~

~~//~// /////__

/~ //~/////////j~~_~-~~

/7 ;////////'~.-'~_'~~'~"~

/ ///~~~~~~_.~'_.

' ~~~=~~~~~~\~ ~~~:~:~~::~~~~;~~r~-~-~- ~~~~ ~~~~~~~~:~~:i~:'~~il~~~~~:1~~

~ ~~~\~~

-=~> 0,30 m/s

Frg. 6. Predicted fiow pattern at free surface in the ladle.(Case

B, argon flowrate 6Nl/min)

Figure 7 shows the fluid movementis in upwardsdirection and recirculates in the region of top surface

and there wasno dead zone whentwo opposed tuyeres

were placed at half radii (Case C). Figure 8shows the

flow pattern when two tuyeres were vertically placed

at half radii (Case D). Contrary to Case C, the fluid

(b) visuaiizecL

Fig. 7. Predicted and visualized flow patterns as two tuyeres

were opposite place at half radii in the ladle. (Case C,

argon flowrate 6Nl/min)

movementis in downwardsdirection near the sidewalls

of the ladle. The total average velocity seemedto besmaller and there wasa deadzone at the corner betweenthe side andbottom wall. In addition, Fig. 11 showsthat

the velocity at the free surface in CaseCseemsto be

more homogenousthan that of CaseD, which will bein favor of preventing splashing, spitting and non-metallic inclusion from entrapping into molten steel, aswell as produces good mixing in the ladle (as discussedlater)

.

Figures 9(a) and9(b) showthe predicted andvisualized

flow patterns respectively whenargon gas was injected

through three tuyeres. The flow pattern of Case E is

similar to that of CaseC. In this case the flow near the

sidewall is stronger than that of CaseC, but the averagevelocity is less.

Figures 10(a) and 10(b) show the predicted and vi-

sualized flow patterns respectively at the main vertical

plane whenargon gas was injected through four tuyereslocated at half radii in the ladle (Case F). Figure IOshowstwo big and strong cloud of recirculations near the

regions of sidewalls were formed which are very similar

to the case of center blowing (as seen in Fig. 3). Dueto

475 C 1995 Is[J

ISIJ International, Vol. 35 (1995), No. 5

(a) predicted

~~~~

~~/ \stst~f\ /

\ /

~\/~+/

~f~ * / f~ * f~ ~ /1 /If

ll

/ ~\-~~~~'~~rl~-~~-~"~~-~ \ \ ~' ,, ~~~~-'t ~~\\~~t ' , ,,~ ~ ' t SJ\ \ I L t~ ' ' I IJ\\\\\~ ~~//j\\\\\ ~-//~\~\\~ I~

~\'\~~-~~1/jJ~~\~~'h-~~1//J~\\\~__-rl//c,\'\~___-////~,R\\~'___'r!1//J

~ 'r////J'~~l~\~___~ 'r//// ~\\~~~~\~\'\'h___-!/// t-f'/// J

- /~r 7\\~1~ / i*• ;~

a pre lcte

~F - - 1~

~~\~//

~ ~t,f~_f~ f~*/~~l

-?~~ ._~:~

\ 4 / ~T.

~~~

~ tttt ~ Jttt ~ Jttt \ /ttf \ /ttt /

\ _l \ttt /~\~/~ \~/

~\

ttt /\ ~'tTf IJ

\ _ -' / ,~~~1~

ttff !. lllft ! , / ttttf ~"\\\ .

\ \ \ 1tftlf ttttt ~~ttttft ,l tt,tt \\ ttt! , , / / ~ t , t t ~ / ~ \ ~ t t

*, *~- ~~

(a) predicted

--> 0.30m/s

--> 0.30 m/s

(b) visualized(b) visualized

Fig. 8. Predicted and visualized flow patterns as two tuyeres

were vertically placed at half radii in the ladle. (Case

D, argon flowrate 6Nl/min)

the symmetric arrangement of tuyeres, there wasalmost

no angular velocity in the ladle (as seen in Fig. 12).

The similarity of fiow pattern between predicted andvisualized shows that the present mathematical modelis capable of describing the fluid flow in argon-stirred

ladle with multi-tuyere. However, there are somesmalldistinctions because the flow in the argon-stirred ladle is

turbulent and cannot keep stable all the time while it hasbeentaken into account stable state in the calculations.

4.2. The Effect of Tracer Adding Position on Mixing

A complete and consistent description for mixingphenomenain argon-stirred ladle with multi-tuyere hasnot been reported at present. The present study maybethe first study on the mixing phenomenain argon-stirred

ladles with multi-tuyere by numerical analysis. Figure13(a) showsthe predicted andmeasuredvalues of mixingtime in the ladle with various arrangement of tuyeres

whenthe tracer wasaddedat the center of the surface,

whereasFig. 13(b) shows the predicted and meanmea-sured mixing time for three tracer adding positions.

It can be seen that the position of tracer addition has

C 1995 ISIJ 476

Fig. 9. Predicted and visualized flow patterns as three tuyeres

were place at half radii in the ladle. (Case E, argonflowrate 6Nl/min)

a great effect on mixing in the ladle, especially in CaseA and Case F which are muchmore sensitive due to

almost no angular mixing in the ladle. In CaseBandCase D, mixing time becomesinsensitive to the tracer

adding position due to the larger angular velocity. Thepredicted mixing time is on good agreement with the

measuredvalues.

4.3. The Effect of Configuration of Tuyeres on MixingFor the sake of comparison, the meanvalue of pre-

dicted and measuredmixing time were obtained fromthree different tracer adding positions for different ar-

rangementof tuyeres as shownin Fig. 14. Figure clearly

indicates that the shortest mixing time is obtained in the

case of single tuyere placed off center (Case B). Duetothis reason, most of steelmaking shops still work withthis type of arrangement. However, our main aim is to

achieve the gentle but rapid mixing to promotemetal/slag

interaction, and to avoid splashing, spitting and en-trapping of non-metallic incluSion into bulk phase. Tosatisfy all these purposes, multi-bubbling is needed. Onthe basis of measuredand predicted values as it can be

ISIJ International, Vol.

seen in Fig. 14, Case Cwas found to be the best ar-

rangement, namely, two tuyeres are opposite placed at

half radii in the ladle, CaseFand CaseDare reasonable

and CaseEwasfound to be the worst. Theseresults canbe explained by their characteristics of fluid fiow andmixing mechanismin the ladle. In CaseD, a dead zonewasfound andmeanvelocity is smaller than that of Case

C(as seen in Figs. 7and 8). In CaseD, since the two

(aj predi*ted

I~ ~/c~~~~\IJ/~/-~\

~~J'tiii:i

~ ~~~\~~/~\'_~/

L 4 J a

~ .

\

t t f

~

~~~~l~~/~~~_\ ~/~~~tl~~;;

~/J~/d~_

~_ ll~\_ ll~~\~ ll

fftt ~\T- -lJttttt / /

/// 'F\\~t / /// t,,~ttt ~\\ \ t

/ ;~ ~- '~

(b) visualized

--> 0.30 m/s

Fig. 10. Predicted and visualized flow patterns as four tuyeres

were placed at half radii in the ladle. (Case F, argonflowrate 6Nl/min)

35 (1995), No. 5

bubble streams are closer than in CaseC, the interaction

between them is high, therefore it is not favorable for

the whole flow development (as seen in Fig. I l). For the

purpose of gentle blowing, Case D also loses its ad-

vantage comparedwith Case C. So, thc arrangementof CaseCis better than CaseD.

As Fig. 10 indicated, in Case F, the bulk motion is

very strong, although the angular velocity is very small.

Increase in diffusive components is the resultant ofincrease the interaction and shearing action amongthe

bubbles streams. As it is well known that the mixing

process in ladles is controlled by both bulk convection

and eddy diffusion. In CaseF, the tuyere configuration

can be considered better becauseof short time of mixing.

Of course, in this case the materials consumption of

tuyeres will be more.Goodagreementbetweencalculated mixing time and

measured data shows that the mixing behavior in

argon-stirred ladles with single or multi=tuyere can beproperly described by using the present mathematicalmodel.

4.4. The Effect of GasFlowrate on Mixing

Thetendency for predicted mixing time to changewiththe injected gas flowrate with different configuration of

tuyere is shownin Fig. 15. In general, it can be concludedthat the mixing time decreases with increasing gasflowrate but the effect is not impressive.

4.5. ACorrelation for Mixing TimeIn the stirring system, mixing greatly dependson the

intensity of agitation, so the specific stirring power has

been used to express the relationship with mixing time.

Nakanishi et al,22) has proposed the first correlation

T~ 800e~o.40 according to measurementsin the argon-stirred ladle for RHand ASEA-SKFand T~=800e~0.40

N1/3 for combinedblowing converters.35) In the present'

study, a relationship wasfound to be similar to the latter

type which wasdetermined to describe the mixing timein the argon-stirred ladle with single or multi-tuyere.

Figure 16 shows the relationship between the predicted

mixing time with respect to CaseB. CaseCand CaseEand 8~o.33N0'33 or 8~0.40 N0.33. Since the mixing timein gas-stirred ladle is proportional to Q~0.33 and the

buoyancy power is the main part contributing to the

mixing,1 ~2,14,25,26,3s) the order of 8~ should be close to

Fig. Il.

~~~~ ~/~~tttfjtfj;}{tt

tttftff/

~~~~ f~/_/_./_.~/'_.~f~~_'_>~;_~\~~ fl"

.

~~~~~~tt ji;li~~~ ftffll

~~-- - - -~~~ ///t\~~ t/ ~~~~_~~~~~ t /1lt\~~ t f ///

~~_F~~~~\t

~- ' s \~'~ '~~___- \ "--'+-\ \ / '~~ __~+ '

' s L\~*~~~~~~-_ _

~ ~ \ ~~~~~~~~~~~~- / ~ '-~'--' / + +~~ ~~-/ L \~~~*\~~~~\~~~ ~*~~/// I ~~\'/// J ~~~,~~~~~: /// / ~~~~,~~\~~~~~\~ ~~~~// / J ~~~~// / ~~~ / I ~\~~~~~~/j ~ ~~~~//j ~ ~ l/jJ ~~~~\~\~ll!J~l.

~~~~{t!i! ~~ ~~~~ jIJJJ~ ~~~~~~~\\\\

~~~~JJJ

(*) c*se c ~~>o30 */~(b) cas* D

predicted flow patterns at free surface in the ladle for CaseCand CaseD' (argon fiowrate 6Nl/min)

477 C 1995 ISIJ

ISIJ International. Vol. 35 (1995), No. 5

~~ ~t f ///\~\\ \ t / ///

~~~\~\ \\\\\ I ///// /llF~~\~\\\ \ ~ - - ' / / ////~r~+1""~\ \ \ ' ' ' ' / / ///-?'~-~-1~ \ \ * / / "_?=~

~-~/// / ' ' * ~ \ ~L~L~~~~fl/// / ' - - + \ \\~L~~L~s///r ' / \ '

'!/////// / I \ \\\\\~L~~~~~~

/// / $ \ \\~a~~t

l//j ~~\~ \///// //1 i }~~~~

1oo

o(Dco

(D

E 50

o)c

.~~

E

O

e measuredo calculated

--> 030m/s

Fig. 12. Predicted flow pattern at free surface in the ladle for

CaseF. (argon flowrate 6Nl/min)

1OO(a)

Fig. 14.

A B C D E FRelationship between tuyere configuration95 o/, bulk mixing time. (gas fiowrate 6Nl/min)

and

70

oa)u)

Q)

E 50c')c:

.2~

E

O

~\ ~cal'

~8 ~

.

~8.

ge

I

1~a) ,an~~ uva)

E:~ 50c')

c:~E 40

30

EADFC

B

Fig. 15.

4 6 8Gasflow rate (Nl/min)

Effect of gas fiowrate on mixing time.

A FCB D

1OO(b)

80

o(Du)

CD

E 50

o)c.~

E

O

' 1 IF measured

~H:n~ predicted

a

b

C

I

_~

hc~!\ue

A C D E FBFig. 13. Predicted and measuredmixing time for each tracer

adding position. (gas fiowrate 6N//min)

-0.33 which can also be seen in Fig. 16. Therefore, thecorrelation for mixing time can be written as follows:

lr~ 8528~0.33No33' (N=1-3). .......

...(15)

where

e~-8 +n8 and n=0.1......

..........(16)

eb the buoyancypower is given by36):

60

l~C,)

~~,~~ 40

20

033 0338.528- N\

[] O[] O

[] O

O\6. O58-0.40 N0,3 3

8b := -1484QTb HPlILD2H

2ln(1+0097H)l0'3+H

.(17)

ek the kinetic energy of injected gas can be given as:

32pgQ38k

lr3d4D2Hpl """'"""""'(18)

Theunit of 8~ is standard, namelywatt/kg. If it is used

C 1995 ISIJ 478

O 105-0.33 0.33

8 N or 8~m0.40N0.33m

Fig. 16. Mixing time as a function of stirring power andnumberof tuyere.

the sameas Nakanishi's, namely watt/t, the coefficients

of present correlation will increase ten times. However,there is still a big difference comparedwith Nakanishi'swhich maybe attributed to that of vessel size and theconsideration of contribution of kinetic energy of injected

gas to the mixing.

5. Conclusions

Thefluid flow andmixing phenomenain argon-stirredladles with multi-tuyere were studied with the help ofphysical modeling and mathematical modeling. Con-sidering the effects of tracer adding position, tuyere

ISIJ International, Vol. 35 (1 995), No. 5

arrangement and injected gas flowrate on mixing, aproper configuration of tuyeres for gentle blowing butrapid mixing has been proposed. Onthe basis of aboveresults and discussions, the following conclusion can bedrawn.

(1) Theconfiguration oftuyeres has a great influence

on the fluid flow andmixing in the ladles. Theasymmetricarrangements are in favor of increasing the angular

momentumwhereas in the case of symmetric arrange-ment, there is almost no angular motion in the ladle.

(2) Mixing time is greatly influenced by tracer addingposition, especially in the case of exactly symmetric ar-

rangementof tuyeres.(3) It is possible to obtain gentle blowing but rapid

mixing in the ladle by using multiple bubbling. Twotuyeres opposite placed at half radii in the ladle showsthe best arrangement to realize the various purposes ofsecondary refining.

(4) Generally, mixing time decreases with increasing

gas flowrate, but the effect is not great.(5) Theempirical relationship for mixing time in the

ladle can be given by T~=8.528~0.33N0.33(N=1-3).

(6) Thepredicted results by using present mathemati-cal model are on very good agreement with measuredresults.

Acknowledgments

The principal author wishes to express his sincere

appreciation to Professor T. Fuwa for his valuable

guidance, constant encouragementand valuable supportthroughout this work. The author is grateful to Dr. K.Umezawa.Dr. T. Matsumiya and Dr. M. Yano of

Nippon Steel Corporation for support of this work andfruitful discussions.

Nomenclature

C: Tracer concentration

C1'C2,Cu: Empirical turbulent constants

D: Vessel diameterGk: Generation term of turbulent kinetic

energy

g: Gravitational acceleration

H: Bath height

k: Kinetic energy of turbulence

p: Pressure

Q: Gasflowrate at NTPS. : Laminar Schmidt number

S,t : Turbulent Schmidt numbert: Time

Tb : Bath temperatureui : Velocity componentin i direction; i=1-3xi : Coordinate; i=1-3

Greek symbols

oc : Volumefraction ofgasin the plumezone8: Dissipation rate ofturbulentkineticenergy

e~ : Specific mixing powerT~ : Mixing time

F.ff : Effective massdiffusion coefficient

/ll : Molecular viscosity

l)

2)

3)

4)

5)

6)

7)

8)

9)

lO)

1l)

12)

l3)

14)

15)

l6)

17)

l 8)

l9)

20)

21)

22)

23)

24)

25)

26)

27)

28)

29)

30)

31)

32)

33)

34)

35)

36)

pt : Turbulent viscosity

~err : Effective viscosity

p: Density of fiuid

pg : Density of gaspl : Density of liquid

n: Efficiencies (O. l)

REFERENCESM. Sanoand K. Mori: Trans. Iron Steel Inst. Jpn., 20 (1980),

668.

T. C. Hsiao. T. Lehner and B. Kjellberg: Scand. J. Metall., 9(1980), 105.

Y. Sahai and R. I. L. Guthrie: Metal/. Trans., 13B (1982), 193.

K.-H. Tache, H.-G. Schubert, D. J. WeberandK. Schwerdtfeger:

Metall. Trans., 16B (1985), 263.

A. H. Castillejos and J. K. Brimacombe: Metal/. Trans., 18B(1987), 659.

G. G. Krishna Murthy, A. Ghoshand S. P. Mehrotra: Metall.

Trans., 19B (1988), 885.

Y. Y. Shengand G. A. Irons: Metall. Trans., 23B(1992), 779.

J. Szekely, H. J. WangandK. M. Kiser: Metall. Trans., 7B(1976),

287.

T. DebRoy,A. H. MajumdarandD. B. Spalding; J. Met., (1981),

l l, 42.

J. H. Grevet, J. Szekely and N. EI-Kaddah: Int. J. Heat MassTransfer, 25 (1982), 487.

Y. Sahai and R. I. L. Guthrie: Metall. Trans., 13B (1982), 203.

F. Oeters. H.-C. Dromer and J. Kepura: SCANlNJECT111,

Lulea, Sweden,(1983), paper 7.

S. T. Johansenand T. A. Engh: Scand. J. Metall., 16B (1985),

83.

D. Mazumdarand R. I. L. Guthrie: Metall. Trans., 16B (1985),

83.

I. Sawadaand T. Ohashi: Tetsu-to-Haganb, 73 (1987), 669.

S. T. Johansenand F. Boyan: Metall. Trans., 19B (1988), 775.

J. Mietz and F. Oeters: Steel Res., 60 (1989), 387.

A. H. Castillejos, M. E. Salcudeanand J. K. Brimacombe:Metall.

Trans., 20B (1988), 603.

S. Joo, R. I. L. Guthrie and K. Kamal: Steelmaking Proc.,

ISS-AIME, 72 (1989), 517.

H. Turkoglu and B. Farouk: ISIJ Int., 31 (1991), 1371.S.-1. Chung, Y. H. Shin ~nd J.-K. Yoon: ISIJ Int., 32 (1992),

1287.

K. Nakanishi, T. Fujiii and J. Szekely: Ironmaking Steelmaking,

2(1975), 193.

O. Haida, T. Emi, S. Yamadaand F. Sudo: SCANlNJECTII,

Lulea, Sweden,(1980), paper 20.

N. EI-Kaddahand J. Szekely: Ironmaking Steelmaking, 8(1981),

269.S. Asai, T. Okamoto,J.-C Heand I. Muchi: Trans. Iron Steel

Inst. Jpn., 23 (1983), 43.

M. Sano and K. Mori: Trans. Iron Steel Inst. Jpn., 23 (1983),

169.

Y. Ohga,S, Taniguchi andJ. Kikuchi:. Tetsu-to-Hagan~, 71 (1985),

S897.

U. P. Sinha andM. J. McNallan: Metall. Trans., 16B(1985), 850.

D. Mazumdarand R. I. L. Guthrie: Metall. Trans., 17B(1986),

725.

S.-H Kimand R. J. Fruehan: Metall. Trans., 18B (1987), 381.

J, Mietz and F. Oeters: Steel Res., 59 (1988), 52.

G. G. Krishna Murthy, S. P. Mehrotra and A. Ghosh: Metal/.

Trans., 19B (1988), 839.

B. E. Launder and D. B. Spalding: Comput. Meth. Appl, Mech.Eng., (1974), No. 3, 269.

M. Y. Zhu, I. SawadaandT. C. Hsiao: to be published in ISIJlnt.

K. Nakanishi, K. Saito and T. Nozaki: Steelmaking Conf.,

ISS-AIME, PA., 65 (1982), 101.

M. P. Schwarz: ISIJ Int., 31 (1991), 947.

479 C 1995 ISIJ