Canadian Metallurgical Quarterly, Vol. 28, No.1, pp. 19-27, 1989Printed in Great Britain

0008-4433/89 $3.00+ .00Canadian Institute of Mining and Metallurgy

Pergamon Press pIc

MODEL STUDIES OF MIXING PHENOMENA INSTIRRED MELTS

JURGEN MIETZ and FRANZ DETERSBerlin Technical University, Str. des 17 Juni 135, 1000Berlin 12, Federal Republic of Germany

(Received 15 October 1987; in revised form 7 July 1988)

Abstract-Mixings were performed in a water model system of a gas-stirred ladle with both an opticaldecolorization method and conductivity measurements at different positions within the vessel. The experi-mental results show that the rate by which the concentration is homogenized depends on the location ofthe measuring probe as well as on the used stirring conditions, e.g. gas flow rate and position of the gasinjection nozzle. Furthermore, a new theoretical mixing model that combines the concepts of the circulatingconcentration cloud and the two-tank model is presented. The results of numerical calculations using themodel are compared with experimental data of mixing in the water model and in a 40-tonne steel ladle.

1. INTRODUCTION Because of the stochastic nature of mixing, a large number ofmeasurements were required. The task of acquiring data wasgreatly facilitated by the development and implementation ofa computer controlled experimental device and procedure. Thetransfer of the experimental water model results to the fullscale system such as the stirred steel ladle then necessitated thedevelopment of a theoretical model. In the second part of thispaper a new mixing model that combines the concept of thecirculating concentration cloud with the typical two-tank modelis presented.

Mixing of steel in ladles has become important with the devel-opment of such processes as continuous casting and secondarymetallurgy. Steel melts are stirred with a gas which generates aflow field within the containment vessel. Mixing proceeds bythe simultaneous action of the directional circulating and therandom turbulent movement of this flow field [1]. Numerousexperimental studies, mainly with water models, have beencarried out in the last few years to study the characteristics ofthe flow fields and to assess the overall mixing process in gasstirred vessels [2-42].The intensity of mixing is normally quantified by the mixing

time which is defined as the time required for the concentrationof a given input of tracer to reach a level that is within 5% ofthe steady state concentration. In several studies relevant tometallurgical processing, mixing times were found to be related Figure 1 shows a schematic of the experimental apparatusto the flow rate of the stirring gas or to the supplied mixing used in the present study. The experiments were carried out inpower per unit of liquid mass. Furthermore, the effects of sev- a vessel of acrylic glass having an inner diameter of 630 mmeral geometrical parameters on mixing time were also inves-' and a height of 1000 mm. The vessel was filled with distilledtigated. Some of these included the location and diameter of the water to a height of 580 mm. Thus, the diameter to depth rationozzle, immersion depth of a lance, bath depth, and diameter to was 1.1, a value that is representative of a typical steel ladle.depth ratio [33-38, 40]. In some studies, mixing experiments Nozzles enabling the introduction of various stirring gases werewith various tracer input locations and positions of the meas- embedded in the bottom at a number of locations. The traceruring probe were also carried out [30, 35, 36]. used in this study was an aqueous sodium hydroxide solution.Even though numerous investigators have published results It was added into the water by an injection lance that could be

pertaining to mixing times, only a few have actually described positioned where desired. Usually, 3 ml of 0.85 M NaOH solu-the mixing process itself. Published mixing curves expressing tion were used.the transient nature of mixing, obtained for water models as The mixing of the tracer was measured by two methods.well as from full scale measurements in a steel ladle show One involved the simultaneous measurement of the electricaldamped oscillations caused by a recirculating flow in the vessel conductivity of the water at three different locations within theas well as a gradual increase in concentration during injection vessel. Each measurement thus gave the localized concentration[3, 4, 25-28, 32-36]. as a function of time. The o.ther method involved the col-In an effort to better understand the effect of the large number orization and decolorization of the indicator phenolphthalein

of parameters on mixing, it was necessary to quantify the tran- that was contained within the water. The volume of the tracersient evolution of mixing. As a contribution to this aim, mixing solution was chosen so that locally the water was colored byexperiments were performed on a water model of a gas stirred phenolphthalein, however, after complete mixing the waterladle. Moreover, it was necessary to carry out measurements was decolored. The time required for complete decolorizationwith various methods and at different positions in the vessel. was taken to indicate the end of the mixing process. This method

19

2. EXPERIMENTAL APPARATUS ANDPROCEDURE

20 J. MIETZ and F. OETERS: MIXING OF STEEL MELTS

flowmeter

air

fotoresistancearray

light--source

injectionlance

\\\\\\\

,~,e:,.,\,e:,..-=.,\ ,e:,..-=.I~~~',e:,.~1, .c=. II ~Ibl\ -= Ir=,

~It-=-PI\I

nozzle /

Fig. 1. Schematic representation of the experimental setup.

has the advantage that the mixing phenomenon becomesdirectly visible and its progress with time can be observed overan extended local range of the vessel by noting the behaviorand movement of the colored cloud. On the other hand, con-ductivity measurements give the exact development of the con-centration with time at localized points only. As a result, bothmethods were used.The transient colorization of the bath during the mixing

process was monitored with an opto-electronic system con-sisting of a matrix of single photoresistances of rectangularshape arrayed on a plate and a normal plate camera into whichthe matrix was placed. The photographic object, i.e. the sectionof the vessel where the coloring appears, was illuminated by alight source from behind the vessel as shown in Fig. 1. Theobject was focused by the camera onto the photoelectric plate.The signals from the individual photoresistances were processedby a multiprogrammer and then relayed to a computer. Uponinjection of the tracer, the opto-electronic system thus measuredlight absorption and its evolution with time as caused by thecolorization of the bath.The multiprogrammer performs a number of functions

including the handling of the gas blowing, the injection of tracerwith its accompanying handling, and the illumination. It alsohas the task of receiving the signals from the conductivity cells,the pH meter and the opto-electronic system. Moreover, itdigitizes and stores the results and in turn transfers them to thehost computer. These procedures were controlled by com-puter programs designed for this purpose. Other programswere written to evaluate and process the original measure-ments, especially the conversion of the conductivity data intodimensionless concentrations. Signals from the photoresist-ances were converted into "grey-intervals" and representedgraphically by hachures of varying intensities.Shown in Fig. 2 arc a sct of results of the optical system. In

the experiments which yielded these results, the tracer solutionwas added in the dead zone at the bottom of the vessel. Theflow rate of the stirring gas injected through the central nozzle

was 800 ncm 3/S. The quick extension' of the colored regionunder the edge of the gas bubble plume zone is clearly evident.It is to be noted that the weak grey areas at the upper left handside of the schematics are not colored but rather are caused bythe gas bubbling zone. In addition, an average value for theentire contour of the colored region was computed and itsdevelopment with time recorded. Figure 3 shows the relativeabsorption, thus determined, for three different flow rates ofstirring gas. These values were used to compute mixing timewhich was taken as the time when the relative absorption fallsbelow 5%.As stated, conductivity measurements were converted into

concentrations by a calibration formula. Calibration tests werecarried out prior to the main investigations. Dimensionlessconcentrations were computed according to equation (1) andplotted against time.

c(t)c=-

Coo(1)

where

c(t) = instantaneous concentrationCoo = concentration after complete mixing.

3. EXPERIMENTAL RESULTS

3.1. Centric gas injection

3.1.1. Tracer addition in the dead zone. In the first series ofexperiments, the tracer was injected into the dead zone at thebottom of the vessel. This position was chosen as it is importantunder practical considerations. Figure 4 shows for a gas flowrate of 1000 ncm 3/S the dimensionless concentration vs timecurves obtained from the three conductivity probes located atpositions denoted on the schematics. It is to be noted thattraces shown in Fig. 4 as well as in subsequent figures representaverages of up to 30 individual experiments.With reference to Fig. 4, it is seen that at position I, i.e.

J. MIETZ and F. OETERS: MIXING OF STEEL MELTS 21

gas flow rate'

800 [Ncm"3/s]

t = 1(s]

tit.__--measuring areaIt>I\ .----in j ect ion

t =2 [5] t = 2.5 [5]Fig. 2. Results of the decolorization measurements. Measured absorption at different times.

t = 3 [5]

100 Vg: 400 [Ncm"'3/s] 10 VG :: [Ncm"'3/s]'I 1000E 80 ,'-- B position 1

t..)

6c 60 c:~ 0u..., 40 (J) 4c.'- (J)0 ~en 20.c s ----------co I~ 10 2030..A-40 . 50 6050 time (8)W'I, 1\ I\I , "

1 !

Vs = 1000 (Ncm"3/s1 I-~f100 Vg: 800

[NcmA3/s]I

E 80 ~c 60 c: _6t 2-illj0.~ U \ 1.4 position 2 \ I..., 40 til \1C. til'- ~ ,0 .2 I(I) 20.c .~co 00"C 10 20 30 40 50 -'6050 time [s]

Fig. 3. Measured total absorption vs time at different gas flow rates(centric nozzle position, tracer addition in the dead zone).

Fig. 4. Dimensionless concentration vs time at different positions in thevessel (centric nozzle position, tracer addition in the dead zone). 1=position of tracer injection. 1, 2, 3 resp. = positions of concentration

measurement. Vg = volume flow rate of stirring gas.

100 Vg: 1200 [NcmA3/s] IE 80

.8~ ~Ezjc 60 c .6 VG = 1000 [NcmA3/s] \ 10 \ 1.~ u position 3 \1..., 40 (J) .4 \c.. enCo. ~ I0 .2(J) 20.c ~rc 00"C 10 20 30 40 50 6050 time [5]

adjacent to the tracer input point, the concentration increasesvery rapidly and subsequently falls back gradually to the finalconcentration level. At positions 2 and 3, i.e. near the wallimmediately below the water surface and somewhat lower andmore distant from the wall respectively, the concentration

increases gradually and only after a delay time. The time lag ofseveral seconds for these two positions represents the flowingtime between the tracer input position and the measuringpoints.

J. MIETZ and F. OETERS: MIXING OF STEEL MELTS22

50

40

~ 30OJE.r-!~0)

.S 20X.r-!

E

10

00

5 VG = 500I [Ncm"3!s]4 I~ position 1 I._---. c: 30

.0\ ~"--- -.- -.- - - ~ u~ C/) 2 I' \ /\ C/)

\/

\\ ~ v\, tmix .~\ \ 00\ \ "C 10 20 30 40 50 60, " time [5]\ 0,

\ "+"~

+', ,5' -+- VG = 500I [Nc:m"3!s]4 I- -- ~ position 2 I

2, position 1 + c: 3 \J,'0\/ 03' + position 2 u \ /0 position 3 C/) 2 \/

l' \IC/) v

~ I.~ / 2500 1000 1500 "C 00 10 20 30 40 50 60

gas f lovl rate [Ncm"3/s] time [5]

Fig. 5. Mixing time vs gas flow rate at different measuring positions inthe vessel (centric nozzle position, tracer addition in the dead zone).

Figure 5 shows mixing times for the three probes as deter-mined with the 5% criterion. As may be expected, mixing timeis reduced as gas flow rate is increased. At the position of thetracer addition, mixing time is longest which is a result of thelow flow velocities at this location. The curves drawn in Fig. 5were obtained by a regression analysis of the measured valuesaccording to the following function:

tmix = aV~where

a,b = constants obtained from regression analysis andVg = volume flow rate of stirring gas.

The exponent, b, for position 2 was found to be -0.54 whilethat for position 3 was - 0.38. These values agree with .pub-lished data [25, 27, 30-33, '38, 39]. The exponent for position 1was determined to be only - 0.06. This indicates that mixingin the dead zone is much less influenced by flow conditions thanit is in the upper part of the vessel.3.1.2. Tracer addition in the plume zone. In the second series

of experiments, the tracer was added in the gas plume zoneabout 25 cm below the surface. Figure 6 presents the dimen-sionless concentration traces for three locations as noted on theaccompanying schematics. Also shown is the position of thetracer injection lance. In these experiments the probes werepositioned at nearly the same locations as in the first exper-imental series with the exception that the two probes near thetop surface were placed on opposite sides, whereas in the firstseries they were located on the same side. The gas flow rate forthe results shown in Fig. 6 was 500 ncm3js.

The first trace shown in Fig. 6 was obtained for position Iwhich corresponds to the center of the toroidal loop in theupper part of the vessel. Initially, the concentration exceeds thefinal value by a considerable margin. From the maximum theconcentration then gradually falls to its final value. Such a curveindicates that during the first circulation of the tracer enriched

5 VG = 500I .~ [Ncm"3!s]4~ position 3c: 30u(J) 2(f] \j-~.~"C 00 10 20 30 40 50 60

time [5]

(2) Fig. 6. Dimensionless concentration vs time at different positions inthe vessel (centric nozzle position, tracer addition in the plume). 1=position of tracer injection. 1, 2, 3 resp. = positions of concentration

measurements. Vg = volume flow rate of stirring gas.

liquid, a large part of this volume comes into the region wherethe probe is positioned. As this region has only a low flowvelocity, it behaves like a storage device from which the traceris gradually transferred into the surrounding liquid by randommovement. Thus, the decrease in concentrat.ion is slow. Themiddle figure shows the concentration trace for the dead zone.Contrary to the upper figure, the tracer is not itnitially enriched,however, after a certain latent time, gradually rises to the finalvalue. The bottom figure shows the concentration trace for theposition of strong flow. It reveals a damped oscillation of theconcentration. This oscillation typifies the circulating characterof the flow. The enriched region moves likl~ a cloud in thedirection of the flow and simultaneously extends by randomturbulent diffusion, thus gradually decreasing in concentration.After each loop the enriched region passes the probe and pro-duces a peak on the trace. Thus, the time between two maximarepresents the circulation time. At least three circulations areafforded before the concentration is equalized. This number isa measure of the interaction between directional and randomturbulent flows. This means that for the upper figure directionalflow is relatively unimportant compared to mixing by randomdiffusion as only one peak in the concentration trace isobserved.

23J. MIETZ and F. OETERS: MIXING OF STEEL MELTS

50 + - type a) l= 10 l'pas.'it ~~31- .0\/ * pas. - type b) t= ' I position 3\!

40 8* * * *

,* * .~

\.\

~ * -..,.

30 Q) 6\. I

ID.~ \. /

E4J /

.~, ./

-I-J C,

"-./

CJ 'w.....__ - ./OJ \

.~c 20 \ 4J 4 .~ rt:X

, t r-t.~ t '- .... ::J= U... ... L.....t_ ri

- -+- t u10 --- --- 2t

0 0a 500 1000 1500 0 500 1000 1500

gas flow rate [Ncm"'3/s] gas flow rate [Ncm"'3/s]

Fig. 7. Mixing time vs gas flow rate for different types of concentrationvs time curves (centric nozzle position, tracer addition in the plume).

The results presented thus far were averaged from a largenumber of single experiments. When each experiment wasviewed as a separate entity, it was remarkable to note the largedifferences which were more than just statistical in nature. Infact, especially at position 1 (Fig. 6), completely different con-centration traces were generated by what should have beenide~tical experiments. In explaining this, the decolorizationmethod described above was found to be more useful. Testsshowed that the colored cloud generated by the addition ofthe tracer was not always equally distributed in each radialdirection-sometimes it moved in a preferred direction. If theposition of the conductivity probe did not lie in this direction,the first circulation transferred little enriched volume to theprobe. Hence, a latent period followed by a gradual increase inthe concentration was observed. If however the probe waslocated in the preferential direction of the cloud, enriched vol-ume was transferred to the probe by the first circulation. As aresult, a maximum was noted with a subsequent decrease to thefinal concentration. Thus, the decolorization method confirmedthe observations made with the conductivity probes. The reasonfor this phenomenon lies in the eventual positioning of thegas bubbling column. In many cases the distribution of tracerenriched liquid was not axisymmetric because of slight incli-nations of the bubbling column. This was judged to be themajor cause of the differences in the individual concentrationtraces.Associated with the various concentration traces are remark-

able differences in the mixing times. Figure 7 presents mixingtimes for two types of concentration curves plotted as a functionof gas blowing rate. For the range of flow rates investigated,the mixing times for curves of type (b) where the probe waslocated in the preferential direction of the cloud are more thantwice as long as those for type (a). Moreover, the mixing timesfor type (a) become shorter with increasing gas blowing ratewhereas those for type (b) remain nearly constant. Type (a)

Fig. 8. Circulation time vs gas flow rate (centric nozzle position, traceraddition in the plume).

mixing times can be expressed by a power function similar tothat given by equation (2). The exponent (b) was found to be-0.37, a value which is in good agreement with publishedresults. Mixing times for type (b) curves showed no such depen-dence.Figure 8 shows the circulation times for different gas flow

rates obtained from concentration traces at position 3 (see Fig.6). The shape of the curve is somewhat surprising, however itcan be rationalized by considering the flow patterns at differentgas flow rates. As gas flow rate is increased, the flow velocityof the liquid increases and hence the recirculating volume flowrate increases. On the other hand, with increasing volume flowthe enriched concentration cloud reaches deeper regions of thevessel and thus the circulation loop is enlarged. This impliesthat there are two effects responsible for the characteristic shapeof the curve plotted in Fig. 8. One is the increase of volumeflow of liquid with higher gas flow rates while the other is theenlargement of the circulating loop implying a greater distanceof travel for one circulation. Since neither effect is mutuallyexclusive, the result is a curve of the type shown in Fig. 8.

3.2. Eccentric gas injection

To study the effect of the radial position of the gas injectionnozzle on the mixing process, additional experiments werecarried out with an eccentric location of the nozzle at rlR = 2/3(where r = radial displacement and R = radius of the vessel).Figure 9 presents dimensionless concentration traces for thethree positions noted on the schematics. The flow rate was setat 1000 ncm3js. The three conductivity probes were positionedon the vertical plane which crosses both the nozzle and thecenter of the vessel. All three locations showed damped oscil-lation behavior. As a consequence, these locations wereassumed to be within the main circulating flow of liquid. How-ever, the results for a centric nozzle were not comparable. Forexample, position 2 in Fig. 6, i.e. with centric gas injection,

24

10I 8~ 6t::0U

en 4en~ 2.~ 00"C

10I 8r..i

6t::0uen 4tr.I

~ 2.~'C

J. MIETZ and F. OETERS: MIXING OF STEEL MELTS

VG = 500 [Nc:m"'3/s]position 1

7,'1 ,I' 0

'"" I10 20 30 40 50 60

time [5]

VG = 500 [Nc:m"3/s]position 2 I,

I

'11, I

"II""2

20 30 40 50 60time Is]

vG = 500 [Ncm"3/s]position 3 :t ,3: ,,

III'II

""

10 20 30 40 50 60time [5]

10I 8r..i

6t::0U

tr.I 4ttl

~ 2.~'C

Fig. 9. Dimensionless concentration vs time at different positions inthe vessel (eccentric nozzle position, tracer addition in the plume).I = position of tracer injection. 1, 2, 3 resp. = positions of con-

centration measurement. Vg = volume flow rate of stirring gas.

behaved like a dead zone with its characteristic long incubationperiod and the gradual concentration increase up to the finalvalue. However, at the same position with eccentric gas stirring(as shown in the second curve of Fig. 9), a recirculating flowwas apparent. This different mixing behavior for various nozzlepositions was caused by the formation of different flow patterns.Flow measurements during stirring indicated that the dead zoneat the bottom of a vessel can be largely eliminated by using aneccentric nozzle position instead of a centric one [13,41].

Figure 10 presents circulation times obtained at various pos-itions plotted as a function of gas flow rate. Circulation timeswere obtained from concentration traces as described in anearlier section. These results show that the circulation timesteadily decreases with increasing gas flow rate. This was notthe case for centric gas injection as shown in Fig. 8. The factthat the measured circulation times for a constant gas flow rateare independent of position over a wide range of locationsindicates that the eccentric gas injection conditions used in thisstudy eliminated dead zones. Only a main recirculating flowexisted. The curve in Fig. 10 can be regressed by the followingpower function

tc = aV~

where tc is the circulation time.

++ pos i Ulon 1* positilon 2'# position 3 posit:lon 4o posit:lon 5 pos i t:LOn 6o pos i t:lon 7 posit:lon B(:, posit:lon 9

20

~

-5'6I... ..

10, -2,3s-- (l'i''''

, I

7 B 1.4

15

\~\

~\\\

tiQ>+ #1?' .... ....ef.-. ~ A

4f -:r- -J->- _ ~r-----~----,

10BV-0.36g

[l)

E ..-1~c:: 10o.~~1'0.....:::::JU

.~u 5

o ...L.J....-Jo 500 1000 1500

gas f lOH rate [Ncm" 3/s)

Fig. 10. Effect of gas flow rate and probe position on circulation time.

For eccentric gas injection, the length of the circulation loopdoes not depend on the gas flow rate, so that, the volumecontacted by the circulating liquid is essentially constant. There-fore, the main parameter determining the circulation timeshould be the circulation volume flow rate of liquid. From thetheory of the gas bubbling column, the voluITle flow rate in theplume zone VI,p can be calculated from the following [6, 10, 16,31,42]

v = KTi'(1/3)I,p g (4)

where K = constant (dependent on geometrical and physicalfactors).

Moreover, it can be assumed that the recirculating flow rate,Vc, is mainly controlled by the volume flow rate of liquid in thebubble plume zone. Thus,

(5)

The circulation time, te, is defined by the ratio of the liquidvolume, V, to the circulating volume flow rate, T/c'

(6)

The exponent b in equation (3), as determined by regressionanalysis, yielded a value of -0.36 which is in good agreementwith the result produced by the theoretical approach embodiedby equations 4-6.

4. MIXING THEORY

(3)

4.1. Fundamentals

In order to describe the mixing process, two types of modelswere developed. These are referred to as turbulent and tankmodels. Turbulent models enable one to simulate mixing fromfirst principles, however they require much computation. Onthe other hand, tank models use empirical parameters and as

J. MIETZ and F. OETERS: MIXING OF STEELMELTS 25

v--- VN

Fig. 11. Combinedrecirculationand two-tankmodel.

such are much more simple. Moreover, they are flexible in theirapplication to various vessel shapes.Results published in the literature [3, 4, 15, 18,24-28, 31-36,

38] as well as the results of the present work suggest that thefollowing parameters are important in the modelling of themixing process. These are: the recirculating flow, the turbulentdiffusion of the enriched cloud, and the exchange between thedead zone and bulk volume. A model that includes these par-ameters was developed. The model draws upon the conceptsof the recirculating cloud and the two-tank model. Figure 11presents a schematic of the model. The simultaneous effect ofdirectional and random flow was modelled by a number oftanks in series through which a flow is circulating [43]. thismodel is characterized by three parameters:

-the total volume, VtOb-the recirculation volume flow rate through the tanks, V,

and-the number of tanks, N.

The tank-in-series model was then combined with the two-tankmodel. The two-tank model has two characteristic parameters:

-the exchange volume flow rate, Vd and-the ratio of the dead volume Vd to the remaining volume,

Vtot- Vd

In the combined model the remaining volume is identical to thevolume of the tanks in series. Thus, the combined model has,in total, the following five parameters:

-the recirculating volume flow rate, V;-the total volume, Vtot;-the ratio of the exchange volume flow rate to the recir-

culation volume flow rate, VdlV;-the ratio of the dead volume to the total volume, Vdl Vtot ;-the number of tanks in series, N.

The combined model thus contains five characteristic par-ameters and as such should be able to describe the mixingprocess in sufficient detail to enable it to answer practical ques-tions. A mathematical description of the model is publishedelsewhere [22].

4.2. Application of the combined model to experimental results

Figure 12 illustrates the degree of agreement between com-puted and measured concentration traces for a typical experi-ment. Experimental curves are presented on the left hand sidein Fig. 12awhile Fig. 12b shows the corresponding results fromthe mathematical model. The size of the dead volume, Vd, wasmeasured from visual observations of decolorization experi-ments. The basis for determining the recirculating volume flowrate, V, was the volume flow at the upper part of the gasbubbling column as computed from theory [6, 10, 16, 31, 42].Comparison of Figs 12a and b shows good agreement between

calculated and measured results. Thus, the model is able todescribe the mixing behavior of a gas-stirred water model sys-tem of the type used here.Confirmation of its validity for the stirring of steel ladles

must be established. Measurements of the concentration of atracer, added to a steel ladle, as a function of time were carriedout in Sweden by T. Lehner et at. [3,4, 28].Experiments were carried out in a 6-tonne ladle using copper

as the tracer and in 40- and 50-tonne melts using radioactivegold as the tracer. Since the Froude number and the height-to-diameter ratio for both the water model and steel ladle experi-ments were equal, geometrical and physical similarity criteriawere fulfilled. Thus, it should be possible to calculate the mixingbehavior in the steel melt by using the same dimensionlessparameters as for the water model. Only the ratio of the deadvolume to the total volume was increased from 0.17 for thewater model to 0.25 for the steel ladle. The use of a higherfraction for the dead zone was viewed as reasonable becausefor the ladle the gas was blown into the melt through a lance,whereas in the water model experiments a nozzle in the bottomwas used. A comparison of the computed and measured resultsfor the 40-tonne steel ladle is shown in Fig. 13. It is apparentthat mixing in the steel ladle can be described by the proposedmodel.

5. CONCLUSIONS

The results of the mixing experiments show that the shapesof the concentration traces strongly depend on the location ofthe tracer input as well as on the position of the measuringprobes and the location of the gas injection nozzle. Variabilityin mixing times can be significant especially when the stirringgas is injected by a centrally positioned nozzle. In such cases,regions of very low flow velocities, i.e. dead zones, are foundto occur at the bottom of the vessel. Mixing times were longestin these areas.The adoption of an eccentric gas nozzle location can be used

to avoid dead zones. Practical applications for stirring shouldmake use of this fact. It was also observed that circulation timesfor bulk recirculating flow are independent of probe location.This indicates that only one main circulating loop exists underthis condition.By combining the concepts of the tank-in-series model and

the two-tank model, a new recirculation model was developed.The measured and calculated values produced by this modelfor a 40-tonne steel ladle and for a water model of this ladlewere found to be in good agreement. This leads to the con-clusion that, provided the dimensionless parameters are thesame for the ladle and water model, water model results canbe applied to full-scale plant situations. This is of practicalimportance because it implies that the mixing behavior of ves-selswith different shapes and flow conditions can be determinedwith water models coupled with our mathematical model.

Acknowledgements-This researchwork was supported financiallybythe German Federal Ministry of Researchand Technologywhich isgratefullyacknowledged.The authors would also like to thank ProfessorFrank Mucciardi

Department of Mining and MetallurgicalEngineering,McGill Uni~versity,for hishelpin preparingthe Englishversionof our manuscriptfor publication.

26 J. MIETZ and F. OETERS: MIXING OF STEEL MELTS

5VG = 500

5I [Ncm'"3!s] I CiO (t)4 I 4t.i position 1

I ~c: 3 I C 30\ ~ 1

0U u2 I, .0 \ 1 2CJ) \ 1 CJ)CJ) \1 CJ)

o~~ u ~.~

00 .~"'C 10 20 30 40 50 60 "C 0 10 20 30 40 50 60time [5] time [5]

15

VG = 5005

I [Ncm"3!s] I I c d (t)4 4~ position 2 I ~c: 3 \J,' c 30 0u u2 \ 1 2CJ) \1 CJ)CJ) U tn~ 1 ~.~ 2 .~ ~"C 00 10 20 30 40 50 60 "C 00 10 20 30 40 50 60time [s] time [5]

5 5I A vG = 500 [Ncm'"3!s] I c 3 (t)4 I 4 ~U position 3 I UIc: 3 -3 c 30 \ 1/0 0U \ 1 U

CJ) 2 \ I tn 2en \I- \' tn~ U ~.~ .~"'C 00 10 20 30 40 50 60 "C 00 10 20 30 40 50 60time [s] time [5]

(a) measu red data (b) calculated data

Fig. 12. Dimensionless concentration vs time at different positions in the vessel (measured and calculateddata). I = position of tracer injection. 1,2,3 resp. = positions of concentration measurements. Vg = volume

flow rate of stirring gas.

4

I 3c.~./.J10t.../.J

2cQ.IUC0U

tntn

~.~'C

00

3. T. Lehner, Scaninject I, Lulea, Sweden, paper 11 (1977).4. J. Szekely, T. Lehner and C. W. Chang, Ironmaking Steelmaking

6,285 (1979).5. J. Szekely N. H. EI-Kaddah and J. H. Grevet, Seaninject II, Lulea,

Sweden, paper 5 (1980).6. T. C. Hsiao, T. Lehner and B. Kjellberg, Scand. J. Metallurgy 9,

105 (1980).7. N. EI-Kaddah and J. Szekely, Ironmaking Steelmaking 6, 269

(1979).8. T. Deb Roy and A. K. Majumdar, J. Metals 33" 42 (1981).9. J. H. Grevet, J. Szekely and N. EI-Kaddah, Int. J. Heat Afass

Transfer 25(4),487 (1982).10. Y. Sahai and R. 1. L. Guthrie, Metall. Trans. I3B, 193 (1982).11. Q. He, Y. Pen, T. C. Hsiao, W. Zhao, L. Hu and P. Liu, Proc.

Shenyang Symp. on Injection Metallurgy & Secondary Refining ofSteel, Shenyang, September 1984, pp. 98-113.

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-- model calculations

measured datafrom 40 t ladle

II

50 100time [s]

150 200

Fig. 13. Transient response of dimensionless concentration fora 40-tonne steel melt.

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