Mixing Enhancement in Gas-Stirred Melts by Rotating Magnetic Fields

Mixing Enhancement in Gas-Stirred Melts by RotatingMagnetic Fields

TOBIAS VOGT, ARTUR ANDRUSZKIEWICZ, SVEN ECKERT, KERSTIN ECKERT,STEFAN ODENBACH, and GUNTER GERBETH

A model experiment of a submerged gas injection system in a cylindrical vessel under theinfluence of a rotating magnetic field and its effect on liquid metal mixing is presented. Argongas is injected through a nozzle into a column of the eutectic alloy GaInSn, which is liquid atroom temperature. Without a magnetic field, the bubble plume in the center region of thecylindrical vessel produces a recirculation zone with high fluid velocities near the free surface,while the fluid velocities in the bottom region are rather low. Our measurements revealed thepotential of rotating magnetic fields to control both the amplitude of the meridional flow andthe bubble distribution and to provide an effective mixing in the whole fluid volume. Variousperiodic flow patterns were observed in a certain parameter range with respect to variations ofthe magnetic field strength and the gas flow rate.

DOI: 10.1007/s11663-012-9736-1� The Minerals, Metals & Materials Society and ASM International 2012

I. INTRODUCTION

BUBBLE-DRIVEN flows are used in many indus-trial facilities. In metallurgical applications, gas bubblesare injected into furnaces, ladles, or similar melt-containing transfer vessels in order to homogenize themelt and their physical and chemical properties. Theprinciple is that a bubble plume accelerates the sur-rounding liquid upward and produces a recirculationzone. This method is used for steelmaking in bottomblown reactors, and the hydrodynamics of such gas-stirred melts were studied in depth by Sahai andGuthrie,[1,2] Johansen et al.,[3,4] and Mazumdar et al.[5]

The efficiency of gas-stirred systems can be discussed interms of mixing time, input energy rate, mixing vesselshape, or the type and location of the gas injection.

The high relevance of liquid metal stirring makes itworthwhile to search for possible improvements of such aprocess. A mixing enhancement could yield a bettermaterial quality, a reduction of the mixing time, andtherefore result in lower mixing gas consumption or lowerelectric power consumption.With respect to thewidespreadutilization of liquid metal stirrers, even a slight improve-mentwould yield tremendous energyormixing gas savings.

In bottom blown reactors, gas is injected typicallyfrom a point source at the bottom into the liquid metal.The density difference between the gas and liquid metalpushes the gas bubbles upward and results in a turbulentbubble plume. Due to their drag, the rising bubblesaccelerate the surrounding liquid metal upward. Theconservation of mass is responsible for the resultingrecirculation flow that takes the upward shifted liquidmetal down again. If the gas bubbles are injected at thesymmetry axis of a cylindrical vessel, this flow config-uration is attributed to a dead water zone in the lowerpart of the vessel which is decoupled from the recircu-lation zone in the upper part of the vessel. It is obviousthat a long mixing time is needed before a sufficient heatand mass exchange is achieved as soon as dead waterzones exist. Variations of the gas flow rate, the numberand the design of the gas injection, and the vessel designcan be used to influence the mean recirculation velocity,but the basic global flow structure and the existence ofdead water zones cannot be avoided.Another way to stir a liquid metal is the application of

AC magnetic fields. Some studies have shown that avertically traveling magnetic field can be used to drivea toroidal flow pattern.[6,7] Likewise, the application ofa rotating magnetic field (RMF) is suitable to drive aswirling flow in a liquid metal column.[8–10] But, themixing in an almost rigidly rotating fluid, which isdriven by an RMF, is rather low. This changes when theRMF is used in a pulsed mode. Here, higher mixingrates can be achieved.[11]

Only a few number of studies considered a simulta-neous usage of electromagnetic stirring and gas injection.Zhang et al.[12] studied the impact of a vertically travelingmagnetic field on the flow in a cylindrical liquid metalbubble plume. They found out that the downward orupward TMFmainly imposes a global co- or counter flowsituation compared with the original bubble-driven flow.

TOBIAS VOGT, Graduate Student, SVEN ECKERT, Head ofDepartment, and GUNTER GERBETH, Head of Institute, are withthe Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Institute ofFluid Dynamics, 01314 Dresden, Germany. Contact e-mail:[email protected] ARTUR ANDRUSZKIEWICZ, Research Scientist,is with Institute of Thermal Engineering and Fluid Mechanics,Wroclaw University of Technology, and also with TechnischeUniversitat Dresden, Institute of Fluid Mechanics, 01062 DresdenGermany. KERSTIN ECKERT, Group Leader, and STEFANODENBACH, Professor, are with the Technische UniversitatDresden, Institute of Fluid Mechanics.

Manuscript submitted: May 2, 2012.Article published online October 5, 2012.

1454—VOLUME 43B, DECEMBER 2012 METALLURGICAL AND MATERIALS TRANSACTIONS B

This effect enhances the flow and supports the mixinginside the fluid volume.

The effect of an RMF on the two-phase flow in a RHvacuum degassing vessel, a facility where molten steelgets degassed, was studied by.[13] They found out that anRMF of sufficient field strength can force the bubbles tothe center of a rotating fluid. The effect of swirl motionon the mixing time in a water bath agitated by anupward directed gas injection was studied in.[14] Theauthors measured the mixing rate by means of conduc-tivity probes and concluded that the mixing can beimproved by the swirling motion. But, this study did notinclude any flow measurements.

The simultaneous usage of an RMF and a risingbubble plume is ergo a barely explored topic. For thisreason, we investigate the flow structure in a liquidmetal cylinder, while these two different driving mech-anisms are used simultaneously.

We present model experiments with the eutectic alloyGaInSn. Within this study, the gas injection wasrestricted to a position at the bottom on the symmetryaxis of the cylindrical vessel. The fluid velocities weremeasured by means of the ultrasound Doppler veloci-metry (UDV), while the path of the rising gas bubbleswas monitored by an ultrasound transit time technique(UTTT).

II. EXPERIMENTAL SETUP

Figure 1 shows a schematic drawing of the experi-mental setup. A cylinder made of Perspex with an innerdiameter of D0 = 90 mm was filled up to a height ofH0 = 180 mm with the eutectic alloy GaInSn, which isliquid at room temperature. The free surface of the liquidmetal column was covered with a thin hydrochloric acidlayer to avoid undesired oxidation effects of the GaInSnalloy. Some selected material properties of GaInSn and acomparison to molten steel are given in Table I.

Gas can be injected into the alloy through a smallnozzle. The nozzle has an outer diameter of 2 mm andwas installed near the bottom through the sidewall ofthe cylinder. The orifice of the nozzle has an innerdiameter of di = 0.9 mm and was directed upward inorder to have a constant injection position of gasbubbles at r = 0 and z = 0.15*H0. The operating gaswas Argon in order to keep the oxidation low. The gasflow rate was adjusted using a Multi Gas Controller(mks 647C) equipped with an mks Mass-Flow Control-ler for flow rates up to 8.3 cm3/s.

The measuring cylinder was placed in the middle ofthe 200-mm bore hole of the magnetic induction systemPERM at Helmholtz-Zentrum Dresden-Rossendorf.The PERM stirrer is equipped with six coils, arrangedas pole pairs in order to create the RMF with fieldstrengths up to 17 mT. The spatial homogeneity of theRMF was verified using a 3-axis Gauss meter (Lake-shore model 560, sensor type MMZ2560-UH). Thedeviation of the field strength within the measuringvolume was found to be less than 5 pct.

The fluid velocities were measured using the ultra-sound Doppler velocimetry (UDV). This method is

based on an impulse echo technique and is suitable todeliver instantaneous velocity profiles in opaque fluids.The ultrasound Doppler velocity has its origin inmedical science (Franklin et al.[18]) and was adoptedby Takeda[19–21] for experimental fluid dynamics about25 years ago. These days, the ultrasound Dopplervelocimetry has become an accepted measuring tech-nique for flow investigations in low temperature liquidmetals (see for instance Brito et al.[22]; Eckert andGerbeth[23]; Takeda and Kikura[24]; Eckert et al.[25] orAndreev et al.[26] and Franke et al.[27]). In the present

Fig. 1—Schematic drawing of the experimental setup.

Table I. Material Properties of GaInSn[15]

and StainlessSteel[16,17]

PropertyGaInSn

[298 K(25�C)]Steel

[1873 K(1600�C)]

Viscosity (m) (m2/s) 3.4 9 10�7 9.13 9 10�7

Density (q) (kg/m3) 6.36 9 103 7.01 9 103

Electrical conductivity(r) (S/m)

3.2 9 106 0.79 9 106 (*)

Surface tension(c) (N/m)

0.53 1.6

*measured at 1596 K (1323�C).

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 43B, DECEMBER 2012—1455

study, we have utilized the DOP2000 velocimeter (model2125, Signal Processing SA, Lausanne) equipped with8 MHz transducers (TR0805LS, acoustic active diame-ter 5 mm). Five ultrasonic transducers were attached atthe Perspex bottom of the fluid container. The verticalalignment of the transducers allows for recording axialprofiles of the vertical velocity between the bottom andthe free surface of the fluid cylinder at different radialpositions r/R0 and different azimuthal positions. Therespective sensor positions are shown in Figure 1.Sensor 1 is located at the radial position r/R0 = 0.3.Sensor 2 is placed at r/R0 = 0.6, and the three outersensors (3, 4, and 5) are located at r/R0 = 0.9 with anangle of 45 deg between neighboring sensors. Velocitydata were obtained with an accuracy better than0.15 mm/s. The spatial resolution of the ultrasoundtransducers is about 1.4 mm in an axial direction and5 mm in a lateral direction. The latter increases slightlyin measuring direction due to a divergence of theultrasound beam of about 3 deg. The sampling fre-quency for the velocity profiles was about 5 Hz.

The detection of the gas bubbles in the liquid metalwas realized with an ultrasound transit time tech-nique.[28] Two ultrasonic heads, each consisting of 10ultrasonic transducers, were placed horizontally atdifferent heights at the sidewall of the cylinder. Anultrasound defectoscope (USIP 40), together with thesoftware UltraPROOF (both from GE Inspection Tech-nologies), was used to calculate the bubble position fromthe transit time of the ultrasound signal from thetransducer to the bubble and return. The time resolutionof the measuring system is about 2.5 ns. Twenty

ultrasound transducers were allocated along the vesselheight to monitor the full vessel height, while only 10transducers could be multiplexed. For a particularmeasurement, the respective 10 transducers were se-lected according to the best compromise with respect toa suitable detection of the bubble path variations.

III. RESULTS

To support the understanding of the considerableflow changes provoked by the simultaneous action ofthe two driving mechanisms, we first present the basis ofpure bubble-driven (Section III-A) and RMF-inducedflows (Section III-B).

A. Pure Bubble-Driven Flow

The analysis of the pure bubble-driven flow showedthe well-known existence of two different regimes.[29]

The first regime occurs at low gas flow rates (QG) and isrelated to a constant bubble size. The frequency of thebubble formation increases at higher gas flow rates.When QG exceeds a certain value, the second flowregime is entered where the bubble formation frequencyremains constant. Consequently, the bubbles becomelarger and larger when the gas flow rate is furtherincreased.In the measurements presented in this article, the

bubble formation frequency varies between 8.3 and11.6 Hz. Figure 2 shows a measurement of a purebubble-driven flow atQG = 1.67 cm3/s. In these contour

Fig. 2—UDV measurement of a bubble-driven flow without a magnetic field, recorded at r/R0 = 0.3 (top), r/R0 = 0.6 (middle), and r/R0 = 0.9(below); QG = 1.67 cm3/s.


plots, the flow structure of one measurement, recorded atthree different radial positions, is plotted. The particularvelocity profiles have been drawn along the verticalz-coordinate, whereas the abscissa is the running time.The amplitude of the vertical velocity uz is represented bythe color map.

Figure 3 shows the corresponding histogram of thespatial distribution of the bubbles for ten transducersplaced at an increasing distance from the orifice. Thevalue on the left hand side in the histogram is the totalnumber of bubbles detected of each transducer withinthe measuring interval of DT = 360 seconds. This valuedecreases in z-direction due to the increase of the radialspreading of the gas bubbles during their rise. The lowbubble number at z = 82 mm was caused by a pooracoustic coupling of the respective transducer. However,the key information of these bubble histograms is thespatially varying bubble distribution over the crosssection of the vessel. One can see that the rising bubblesare located in a quite narrow area at the center region ofthe vessel. Due to their drag, these rising bubblesaccelerate the surrounding fluid upward. This effect isindicated by the red color region in the upper half of theupper contour plot in Figure 2, which was recordedclose to the vessel axis at r/R0 = 0.3. The consequenceof the rising bubbles is the formation of a recirculation

zone located in the upper half of the fluid container(Figure 2 middle and below). One can easily see that thefluid velocities, and therefore the mixing, in the lowerhalf of the fluid container are rather low. This is a cleardisadvantage when this flow configuration is applied formixing (Figure 4).

B. RMF-Induced Swirling Flow

An RMF induces an azimuthal body force in a liquidmetal column. This force, called the Lorentz force,generates a swirling flow in the liquid metal that consistsof an inviscid, almost rigidly rotating core, separated bypronounced boundary layers from the solid walls(Grants and Gerbeth[30]). These boundary layers areresponsible for the development of a double vortex in themeridional plane of the cylinder.[31] The magnetic Taylornumber is a dimensionless parameter that is used todescribe the amplitude of the RMF-induced body force:

Ta ¼ rxB20R

40

2qt2½1�

where the value x = 2*p*50 Hz stands for the fre-quency of the RMF. The resulting angular velocity ofthe swirling flow is given by[32] the following:

Xce ¼ g4=31

4 � cB

� �2=3

XfXfH

20

m

� �1=3" #

½2�

with

Xf ¼ B

ffiffiffiffiffiffiffirxq

r½3�

The index ‘‘ce’’ stands for ‘‘core effective.’’ The termcB � 1.35 is the Bodewadt coefficient and g = 0.8 is theefficiency factor of the Lorentz force.

Fig. 3—Bubble-driven flow: histogram of the bubble distributionbetween �1 £ r/R0 £ 1 showing the path of the rising bubbles inthe liquid metal column. QG = 1.67 cm3/s.

Fig. 4—Schematic drawing of the flow structure in a pure bubble-driven flow (left) and the double vortex in an RMF-induced swirlingflow (right).


The application of an RMF to liquid metal industriescan be found, for instance, in crystal growth facilities orin order to control the microstructure of a melt duringtheir solidification. But, if a large amount of liquid metalshould be mixed homogeneously in an effective manner,the continuous usage of RMF alone is inappropriate.[10]

The reason is simply the low mixing rate in an almostrigidly rotating fluid. Only a small amount of mixing canbe expected by the formation of the Tayler–Gortlervortices near the sidewall of the vessel[10,33] and due tothe double vortex in the meridional plane of the vessel,which is produced by the Ekman-pumping at thebottom of the vessel. The double vortex, also calledthe secondary flow, is about one magnitude lower thanthe primary swirling flow.[34] An exemplary measure-ment of an RMF-induced swirling flow is shown inFigure 5.

C. Superposition of RMF and Rising Bubble Plume

As previously mentioned, a rising bubble plume at thecenter of a cylindrical vessel results in a recirculatingflow, while a pure RMF induces a swirling motion(primary flow) and a double vortex in the meridionalplane (secondary flow) of a cylindrical vessel. If bothdriving mechanisms are used in combination at compa-rable intensity, we can distinguish between three differ-ent dynamic regimes. Their occurrence with respect tothe two governing parameters, the Taylor number (Ta)and flow rate (QG), is shown in Figure 10. Beforedescribing their features, we first qualitatively addressthe limiting scenarios. The first one occurs when thebubble-driven flow is superposed with an RMF of verylow magnetic induction. Here, the bubble-driven recir-culation flow is dominant and almost no impact can beseen from the RMF. In the following, such a flow

Fig. 5—Double vortex in an RMF-induced swirling flow, recorded at r/R0 = 0.9; B = 1.02 mT (Ta = 28.6 9 105).

Fig. 6—Combination between RMF and rising bubble plume—mode 2; recorded at r/R0 = 0.3 (top), r/R0 = 0.6 (middle), and r/R0 = 0.9 (be-low); QG = 1.67 cm3/s; B = 1.02 mT (Ta = 28.6 9 105).


pattern will be called ‘‘mode 1.’’ The other limiting caseis given when the bubble-driven flow is superposed witha very strong RMF, featuring a high Ta number. Theresult is a strong swirling motion of the liquid metal anda strong radial pressure gradient due to the centrifugalforce. As a consequence, the gas bubbles are pushedtoward the rotational axis of the liquid metal. Theresulting flow does not differ significantly from the flowpattern of a pure RMF-induced swirling flow (in thefollowing, denoted with ‘‘mode 5’’). The intermediateregime in between both limiting scenarios is associatedwith a complete reorganization of the flow in the liquidmetal column. Within this parameter regime, weobserved three remarkable flow patterns, mode 2, 3,and 4 as shown in Figure 10.‘‘Mode 2’’ denotes the flow pattern that was observed

in our experiments most frequently and over the widestparameter range. A respective flow measurement isshown in Figure 6. In this measurement, one can see aregular and periodical flow pattern with a period ofT = 8.6 seconds. The measured azimuthal velocity ofthe primary swirling flow is v/ = 53.8 mm/s. This value

Fig. 7—Bubble histogram corresponding to the measurement shownin Fig. 6. QG = 1.67 cm3/s; B = 1.02 mT (Ta = 28.6 9 105);DT = 360 s.

Fig. 8—Snapshots of the free surface showing the movement of thebubble plume along a circular path. DT = T/4 = 2.15 s;QG = 1.67 cm3/s; B = 1.02 mT (Ta = 28.6 9 105).

Fig. 9—Schematic drawing of the flow structure produced by thesuperposition from RMF and rising bubbles—mode 2.

Fig. 10—Map of the specific flow patterns at different parametercombinations.


was measured at the half height of the vessel at a radialdistance of r = 20 mm from the vessel axis with avertically aligned ultrasound transducer. Accordingly,the primary swirling flow needs Tswirl = 2.3 seconds forone complete revolution. This value is about 3.7 timeslower than the period of T = 8.6 seconds deduced fromFigure 6. The axial wave number of the observed flowpattern is n = 1; hence, there is no reversal of the sign ofuz along the axis. The flow structure recorded from theUDV sensors at r/R0 = 0.3 (Figure 6, top), r/R0 = 0.6(Figure 6, middle) reveals an almost identical flowpattern. The flow pattern close to the sidewall(r/R0 = 0.9 (Figure 6, below)) differs from the othertwo mainly by the downward directed fluid velocities,especially in the upper part of the vessel. The maximumfluid velocities of about uz,max � 80 mm/s do not differsignificantly at the different radial positions and alongthe vessel height. The bubble histogram correspondingto this flow pattern is shown in Figure 7. One can seethat the highest probability for the rising bubbles tooccur is r � 0.3*R0. This is in contrast to the purebubble-driven flow where the maximum is at r = 0.This shifted bubble path rotates around the vessel axiswith the same period (T = 8.6 seconds) as the flowpattern oscillates in Figure 6. This is confirmed byFigure 8 which shows four snapshots taken from amovie of the free surface. The snapshots demonstratethat the point of impact of the bubble plume at the freesurface moves indeed along a circular path.Taking the information from Figures 6, 7, and 8 into

account, one can interpret the spatio-temporal flow struc-ture as follows.A largenon-axisymmetric recirculation roll,

Fig. 11—Correlation between rotary frequency of the flow pattern(mode 2) and magnetic forcing (Ta).

Fig. 12—Dependence of the spatio-temporally averaged axial veloc-ity of mode 2 on the Ta number for different flow rates.

Fig. 13—Combination between RMF and rising bubble column—mode 3; recorded at r/R0 = 0.3 (top), r/R0 = 0.6 (middle), and r/R0 = 0.9(below); QG = 1.67 cm3/s; B = 1.02 mT (Ta = 28.6 9 105).


that occupies almost the entire fluid volume, is produced byan off-axis rising bubble plume. This flow structure rotates,driven by the RMF, around the vessel axis, whereby theprimary swirling flow rotates about 3.7 times faster than thebubble plume. Figure 9 presents a schematic drawing ofthis configuration.

As shown in Figure 10, this flow pattern (mode 2) wasobserved at different parameter combinations. Thecorrelation of this flow pattern to the different param-eters is as follows: An increase of the magnetic induc-tion, hence of Ta, yields lower periods (Figure 11). Thevariation of the flow intensity at the different parametercombinations is shown in Figure 12. The velocity valuesplotted in this figure are the spatio-temporally averagedaxial velocities which were calculated as follows:

uz ¼1

n

Xni¼1

1

t

Xtj¼1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

m

Xmk¼1

u2kðj; iÞ !vuut

24

35

8<:

9=; ½4�

where n represents the number of ultrasound transduc-ers, t is the number of measured time steps, and m standsfor the number of measuring gates in the axial direction.From the uz values plotted in Figure 12, it can bededuced that an increase of both, the gas flow rate andthe magnetic forcing, results in higher fluid velocitiesand, therefore, in higher mixing rates.

A second periodic flow pattern, mode 3, appearedsomehow randomly in a couple of measurements for highTa and moderate QG, cf. Figure 10. This flow pattern ischaracterized by an axial wave number of n = 2 and istherefore associated with a change of sign of the axialvelocity along the vessel height. A corresponding UDVmeasurement of this flowpattern is shown inFigure 13. Incontrast to the previously described flow pattern, which isvery stable and reproducible, the generation of this one israther tricky.Thismode 3 emergedonly in a small amountof measurements (�15 pct), and it was not possible todetermine a clear procedure to generate this mode 3.However, once generated, it also exhibits a long-termstability. Compared to Figure 6, which was recorded atan identical parameter combination, this mode 3 flowpattern has a period twice as high (T = 18.4 secondscompared to T = 8.7 seconds in mode 2). The spatio-temporally averaged axial velocity is about half as high asinmode 2 (uz = 13.4 mm/s compared to uz = 21.3 mm/sin mode 2).

Figure 14 shows the corresponding bubble histogramin the lower part of the vessel. For this measurement, weused the 10 ultrasound transducers from the lowersensor array for the bubble detection in order to obtaina higher axial resolution in the lower part of the vessel.This histogram shows that the bubble path is S-shapedin this mode 3 flow pattern. A schematic drawing of thisflow mode is shown in Figure 15.

Finally, a third periodic flow pattern was observed(Figure 16). It occurred at only one parameter combina-tion with a strong magnetic field and a low gas flow rate(Figure 10, mode 4). In this flow mode, which does notdiffer significantly from mode 5, the RMF-induced swirl-ing flow is dominant, but superposed with a slight bubble-induced oscillation. The period of T � 5.1 seconds is the

lowest of all three periodic flow patterns. The time-averaged axial velocity profiles of this flow mode aresimilar to that derived from a pure RMF-driven flow(mode 5). The spatio-temporally averaged axial velocity is

Fig. 14—Bubble histogram for mode 3 corresponding to the mea-surement shown in Fig. 13. QG = 1.67 cm3/s; B = 1.02 mT(Ta = 28.6 9 105); DT = 360 s.

Fig. 15—Schematic drawing of the flow structure produced by thesuperposition from RMF and rising bubbles—mode 3.


uz = 8.3 mm/s. The bubble path is congruent with thevessel axis (Figure 17).

IV. DISCUSSION

The mixing of a liquid metal, forced by a rising bubbleplume, is a widespread technique and can be found inmany metallurgical applications. The mixing in such agas-stirred liquid metal depends mainly on the gas flowrate, the bubble size, the bubble inlet position, and theladle geometry.

However, significant mixing rates are bounded to theregion of the vessel where the bubble plume is located.Relatively large dead water areas can be found usuallyin the lower region of the ladle, which is unfavorablewhen a complete mixing is desired in a reasonable time.When such a bubble-driven liquid metal flow is super-posed with an RMF, some striking new flow patternscan be observed. These new flow patterns have a highpotential to amplify the mixing in the whole fluiddomain. The undesired dead water areas can be effec-tively avoided. Simultaneously, the fluid velocities,especially in the regions outside the rising bubble plume,can be enhanced significantly. The new flow patterns areattributed to a reorganisation of the flow, when thesetwo driving mechanisms (RMF and rising bubbleplume) are used simultaneously within an appropriateparameter range. The resulting new flow structure isalways of a periodic flow pattern. Depending on theparameter combination, these periodic flow patterns

differ in their axial wave number, their velocity magni-tude, and their period. The strongest mixing enhance-ment can be achieved with the flow mode 2 (Figures 6and 7). This mode 2 is a flow pattern where the risingbubble plume is shifted outward, yielding a strongglobal recirculation zone associated with the highestfluid velocities observed in our experiments. Fortu-nately, this desirable flow pattern is also the mostfrequently observed one (of the three periodic flowpatterns). A further advantage is that this flow mode isvery stable and reproducible without any special trig-gering effort. The spatio-temporally averaged axialvelocities are approximately 30 pct higher compared tothat of a purely bubble-driven flow (mode 1). Comparedto a purely RMF-driven flow, the intensification is evenhigher (Factor 3.8). As soon as the flow mode 2 isgenerated, a further amplification of the driving forces isonly conditionally useful. For example, a doubling ofthe gas flow rate results in only 12 pct higher fluidvelocities. An increase of the Taylor number far beyondTa = 3 9 106 leads to a strong swirling motion of theliquid metal and to a strong radial pressure gradient.Owing to this pressure gradient, the gas bubbles areforced to the rotational axis of the liquid metal, yieldinga loss of the periodic flow pattern. However, even moreimportant than the intensification of the global fluidvelocities in flow mode 2 is the almost completeelimination of dead water areas.The other two periodic flow patterns observed in our

experiments are of minor importance for mixing appli-cations. The reason is the decrease of fluid velocities,

Fig. 16—Combination between RMF and rising bubble column—mode 4; recorded at r/R0 = 0.3 (top), r/R0 = 0.6 (middle), and r/R0 = 0.9(below); QG = 0.83 cm3/s; B = 1.02 mT (Ta = 28.6 9 105).


and therefore the mixing rate, both in mode 3 and mode4. In addition, the parameter range, where these flowmodes can be observed, becomes narrower (Figure 10).

The transitional flow occurring between the initiationof any flow agitation and the achievement of quasi-stationary flow patterns was not presented in this article.The transitional flow in mode 2 was found to beindependent of the starting conditions. Regardless ofwhether the initial flow, before the second drivingmechanism is applied, is a pure RMF flow or a purelybubble-driven recirculation flow, the presented periodicflow structure in mode 2 developed in typically 30 to40 seconds (QG = 1.67 cm3/s; Ta = 28.6 9 105).

In contrast, flow mode 3 was found to depend verysensitively on the initial conditions and appears difficultto trigger. In this study, we applied different nozzles(di = 0.4 mm made of ceramics, di = 0.7 mm made ofsteel, and di = 0.9 mm made of ceramics) at otherwiseidentical parameter combinations, but no impact wasfound. Furthermore, we made attempts where the initialflow was a pure RMF flow or a purely bubble-drivenrecirculation flow and attempts where the liquid metalwas initially at rest and the RMF and the gas bubbleswere initiated simultaneously. However, we were notable to determine a clear procedure for how mode 3could be triggered reliably. Further work is needed if

one is interested in these transient flows and thedependency of the initial conditions.

V. CONCLUSIONS

In this article, a model experiment is presented wherea gas-stirred liquid metal column is superposed by anRMF. The experiments were carried out with theeutectic alloy GaInSn, which is liquid at room temper-ature. The resulting flow field and the path of the risinggas bubbles were measured by means of the ultrasoundDoppler velocimetry and ultrasound transit time tech-nique, respectively.The recirculation flow, which results from a rising

bubble plume, is a common mixing tool and can befound in many industrial applications such as steelmak-ing. Our experiments have shown that the mixing rate ina gas-stirred liquid metal column can be tremendouslyincreased when it is superposed with an RMF. Theresulting periodic flow patterns are associated with highand alternating fluid velocities, even close to the sidewallof the vessel, where the fluid velocities are usually ratherlow. The undesired dead water zones in the bottomregion of a gas-stirred liquid metal column can becompletely eliminated. Therefore, the mixing times canbe reduced significantly. The presented superposition ofa rising bubble plume with an RMF provides a powerfultool for mixing in liquid metals.A continuation of the present study with respect to a

quantification of the mixing rate and variations of thegas injection position appears to be attractive. Mixingtime measurements are being planned. Moreover, thecurrent study provides a valuable experimental databasefor the validation of CFD calculations which mayfacilitate a more detailed analysis of the new flowpatterns. Further research will also be concerned withthe gas injection in case of a non-axisymmetric nozzleposition.

ACKNOWLEDGMENTS

The research is supported by the DeutscheForschungsgemeinschaft (DFG) in form of the SFB609 ‘‘Electromagnetic Flow Control in Metallurgy,Crystal Growth and Electrochemistry.’’ This support isgratefully acknowledged by the authors.

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