Flow Measurement and Instrumentation 20 (2009) 241–251

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Flow Measurement and Instrumentation

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MULTIMAG—A MULTIpurpose MAGnetic system for physical modellingin magnetohydrodynamicsJ. Pal ∗, A. Cramer, Th. Gundrum, G. GerbethForschungszentrum Dresden-Rossendorf, Institute of Safety Research, P.O. Box 510119, 01314 Dresden, Germany

a r t i c l e i n f o

Article history:Received 5 May 2008Received in revised form20 February 2009Accepted 7 August 2009

Keywords:MagnetohydrodynamicsFlow deviceElectromagnetic stirringTailored magnetic fields

a b s t r a c t

Liquid metal model experiments (LMME) are an important tool in metallurgy and crystal growth. Theyallow investigating the flow structure and the transport properties in industrial facilities on a laboratoryscale. Further, LMME provide a profound basis for the validation of numerical simulations. Physicalmodelling as well as up-scaling is ruled by similarity criteria. These depend, besides on the physicalproperties of the fluid, on geometry and, in the case of magnetohydrodynamics, on the attainablestrengths of the magnetic fields.This paper describes the home-made MULTIpurpose MAGnetic field system, a facility composed of

compact coil systems carrying high currents. Prominent features of MULTIMAG are (i) The large boreof 400 mm in height and 365 mm in diameter, which supports, in conjunction with the high currentdensities, the attainability of similarity criteria in the industrial range. (ii) Because the use of ferromagneticmaterial was strictly avoided in the construction, the rotating, travelling, pulsating, and DC in eitherhomogeneous or cusp configurationmagnetic fieldsmay be superimposed linearly. (iii) In order to have asflexible as possible spatio-temporal distributions of the magnetic fields, the power supplies are realisedas amplifiers. Each of the seven phases, three for the rotating and the travelling field, respectively, andone for the pulsating field, comprises a pulse width modulated power amplifier controlled by its ownfreely programmable frequency synthesizer. A detailed description of the facility is followed by someflow measurement examples demonstrating the performance of MULTIMAG.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Electromagnetic processing of materials became widely spreadin industrial practice over the last decades. Optimisation ofthe according processes needs a profound knowledge about theinfluence of magnetic fields on electrically conducting melts. Stillto date, most of the investigation has been numerical simulationandmodel experiments done on water. The obvious reason is that,as a rule, melts worked on in e.g. metallurgy and semiconductorcrystal growth are opaque, hot, and chemically aggressive. First,no information can be acquired from the flow field owing toa lack of appropriate measuring techniques. Not until an ingothas cooled down are some diagnostics possible, and one is thenrestricted to properties of the final product. Second, the designof coil systems on the industrial scale would require considerableeffort. Laboratory scale experimentswith lowmelting pointmetalssuch as eutectic GaInSn, gallium, Wood’s and Rose’s metal, and Snalloys provide a resource to overcome these problems. The reduced

∗ Corresponding author. Tel.: +49 351 260 2713; fax: +49 351 260 2007.E-mail address: j.pal@fzd.de (J. Pal).

0955-5986/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.flowmeasinst.2009.08.003

temperature range up to 300 C allows much easier handling ofthe liquid alloys and flexible experimental constructional systems.Having the same or even superior electrical conductivity asindustrially relevantmelts and comparable Prandtl numbers, thesemodel fluids facilitate meaningful experiments [1–10]. Matchingof similarity criteria is accomplishable provided the coil systemscreate sufficiently strong fields of like topology.Several magnetic systems for magnetohydrodynamical experi-

ments are described in the literature, cf. [2–10] to quote a few forcomparisonwithMULTIMAGbelow.Most of themhave in commonthat theywere designed for a specific process, whereasMULTIMAGis an attempt to support the trend of a more sophisticated opti-misation: increasingly, installations of combinations of magneticfields are to be found in the industry. The lack of the influence of asingle field type on a process being far from completely understoodall the more continues to be true for such superpositions. Here iswhere the conceptual design of MULTIMAG goes. Instead of obser-vation of the action even of superimposed fields, the challenge is intailoring the spatio-temporal distribution of magnetic flux densityfor a specific metallurgical or crystal growth process. To the bestof our knowledge, MULTIMAG is the only available flow device todate thatmay act as a tool to realise the idea of such optimised flowcontrol.

242 J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251

Fig. 1. Flow driven by a rotating magnetic field of frequency ωR . The primary swirlin the melt evoked by the Lorentz force Efem rotates at a rateΩ ωR . As is sketchedin the right panel, the weaker secondary flow consists of two toroidal vortices lyingupon each other.

Fig. 2. Sketch of the flow in an upward travelling magnetic field. The fluid followsthe travelling direction of the field at the perimeter of the container and returns inthe centre opposing the Lorentz force, which is weaker there.

2. Basics of electromagnetically driven flows

Prior to a review of existing magnetohydrodynamical flowdevices and a subsequent comparison of their performance toMULTIMAG, the principle of the action of alternating magneticfields on electrically conducting fluids is briefly recalled.Any AC magnetic field applied to a volume of liquid metal, be

that a rotating (RMF), a travelling (TMF), or a single phase pulsatingone (PMF), induces an eddy current within the electricallyconducting fluid. This induced current interacts with the field thatproduced it, and the resulting Lorentz force Efem = Ejind × EBappl maydrive a flow. For the RMF acting on a cylindrical container of heightH and radius R, in [11] the force is expressed as:

EfR = Ta rf (r, z)Eeϕ, Ta =σωRB2RR

4

2ρν2. (1)

Ta, σ , ρ, and ν are the Taylor number, electrical conductivity,density and kinematical viscosity of the melt, and ωR and BR arethe frequency and induction of the field. Note that the amplitudeto be used in Eq. (1) is the peak value of BR.Obviously, a flow driven by a mere azimuthal force (cf. Eq. (1))

should be of a swirling type. It is however shown in [12] thatthe liquid’s motion following the rotation of the magnetic fieldalso causes a secondary flow. Suchweaker recirculating convectivepatterns appear at any non-vertical boundary as a consequenceof an imbalance between centrifugal force and pressure owing toviscous friction. Fig. 1 illustrates the source of the swirl and thestructure of the secondary flow. Further experimental results areto be found in [13].The analogue to Eq. (1) for the TMF was derived in [14]:

EfT =12Fr2Eez, F =

σωTB2TkR5

4ρν2. (2)

Here, F is the forcing parameter and the wave number k is a mea-sure of the axial extension of the coil system. Eq. (2) is valid for

long wavelengths 2π/k R. It is worth noting that the expres-sions for both RMF and TMF rely on the low-frequency and thelow-induction approximations.The pure axial force produced by the interaction of the

radial field component with the azimuthal eddy current increasesradially from the centre toward the coils, thus driving a flow inthe meridional plane. A section through the torus spreading theentire height of the container is sketched in Fig. 2 for the case ofan upward travelling magnetic field. More details may be foundin [6,13].The dimensionless relative forces, Ta and F , depend, besides on

the physical properties of the melt, quadratically on the inductionB and in fourth power on the characteristic length R. Thus, inorder to reach industrially relevant parameters, a physical modelhas to have a certain combination of minimum size and fieldstrength, respectively. The relatively large bore of MULTIMAG,which is 365 mm in diameter and 400 mm in height, allows, incombination with maximum field strengths of BRMF = 17 mT andBTMF = 21.2 mT, values of Ta and F in the order of 1011 at a mainsfrequency of 50 Hz and when GaInSn is used as the working fluid.These numbers are based on the material properties σGaInSn = 3.3× 106 ( m)−1, ρGaInSn = 6361 kg m−3, and νGaInSn = 3.4 ×10−7 m2 s−1.Besides depending on Ta and F , the action of an RMF or a TMF

is also determined by the skin effect, which may be characterisedby the shielding factor S = µσωR2, where µ is the magnetic per-meability. S 1 corresponds to high field frequencies, and theshielding effect of highly conducting melts is synonymous to themagnetic field lines being expelled from the melt region.

3. Comparison of MULTIMAG to existing laboratory flowdevices

At first, the RMFs in [2–4] are considered. In none of thesepapers is explicitly mentioned whether the magnetic systemscomprised yokes or not. They have though in common that themagnets are referred to as 3-phase stators, in [2] it is even talkedof as a stator of a 3-phase motor, indicating that these stators mayhave included yokes. Such ferromagnetic parts in the return path ofthemagnetic field allow increasing the induction,whichwas 53mTin [2], 20 mT in [4], andmeasurements up to 10mT are reported in[3]. It can only be surmised that the comparably low value in thelatter is due to limited power of the generator, which worked inthe range of 7–200 Hz. Both other magnets were operated at thecommercial frequency of 50 Hz. If a mere RMF is the matter, yokesare not at all disadvantageous. Quite the converse, in addition toprovide an increased field strength in the experimental volumethey also improve the azimuthal homogeneity by means of phaseoverlapping. Because of the superposition, suchmeasureswere notpossible in MULTIMAG and had to be compensated by a higherelectric current and size.Bore sizes in diameter × height measured in mm were 285 ×

233 in [2], 160 × 170 in [3], and 213 × 100 in [4]. It is clearthat any vessel containing the fluid under investigation consumesspace, but for the sake of simplicity, the Taylor numbers for thecomparison here are not evaluated with the actual container sizesemployed in the experiments rather butwith the inner dimensionsof the coil systems. Mercury was used in [2] yielding Ta = 1.1 ×1012whenmaterial properties ofσHg = 1.05×106 ( m)−1,ρHg =13550 kg m−3, and νHg = 1.15×10−7m2 s−1 enter the calculationof Ta. This system was designed especially for the investigation ofdeveloped turbulence. If the authors had used GaInSn, the Taylornumber would have been 8.2 × 1011. The high field strength of53mT can be compensated in MULTIMAG by raising the frequencyfrom technical to 182 Hz, even 1 kHz is possible. At the maximumfrequency of 200Hz and for the galliumused in [3], Ta = 1.6×1010

J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251 243

was the maximum in that work. The relevant properties of thismelt are σGa = 3.82 × 106( m)−1, ρGa = 6067 kg m−3, andνGa = 3.19 × 10−7 m2 s−1. The reference value for GaInSn at50 Hz is 2.9 × 109. Operating also at power line frequency andusing GaInSn, the authors of [4] accomplished Ta = 3.6× 1010. Tosummarise, the sub-component RMF of MULTIMAG by all meanscompetes with the biggest laboratory installation brought to ourattention despite the disadvantage of having no yokes.In the following, we shall have a closer look at the TMFs

described in [5–8]. The first work was motivated by Czochralskicrystal growth and the physical model using GaInSn was intendedto reproduce the same dimensionless numbers as in actual growthfacilities for 12′′ silicon crystals from 28′′ diameter melts. A fieldstrengths of 10 mT is noted in [5], whereas the authors refer to anaccompanying numericalwork [15] for amore detailed descriptionof the experiment. There, a diameter of the coil system of 690 mmis to be found, but the height is not specified. To the best to be readoff Fig.1 in [15], it was about 435 mm. Putting it all together yieldsa forcing parameter of almost 2.5× 1012 at 50 Hz, which might bereached in MULTIMAG at a frequency of f ≈ 280 Hz. In order toachieve the necessary induction in the centre of this large setup,yokes had to be used. These do not allow linear superposition ofthe other field types that were also implemented. We shall returnto this flow device for the discussion of these below.Being intended as a model for vertical gradient freeze crystal

growth, the setup in [6] operatingwithGaInSn offers the true linearsuperposition of a TMF and a DCmagnetic field. Like in [5], a size ofthe coil systemmuch larger than the growth zone was determinedby the installation of the magnets at an existing growth facility;the magnetic system had to be build around a large oven and theinsulation. With a bore 300mm in diameter and 500mm in heightand Bmax = 5mT, F = 7.6× 109 can be reached. Whereas the TMFcreated in [5] was induced by three coils, this system uses six coilslike MULTIMAG, which produce a much more homogeneous field.A TMF employed formodelling inmetallurgy is presented in [7].

The relatively high value of B = 60 mT was created in the centreof the bore, which was 100mm in diameter and 224mm in height.Whether yokes were used, which is anyhow not that crucial in astirring application, is not mentioned. The photo in Fig. 2 indicatesthat there were none. In the narrative, the authors speak abouta 3-phase stirrer, however, the photo shows six coils that easilywould allow 6-phase operation from a technical 3-phase supply asinMULTIMAG. The reference value for GaInSn is Fmax = 1.1×1010.Another larger metallurgical model with a bore diameter of

317.5 mm and height of 500 mm is described in [8]. The heightis that of the vessel so the relevant value of about 450 mm forthe coil has to be read off the sketch in Fig. 1. A field strength of35mTmeasured inside the container close to the rim is providedbythe authors. Applying the well know expression for the magneticfield produced by a single circular current loop, the field strengthson the axis can be added up with the help of a computer takinginto account the phase relations of the turns in the respectivecoil segment. The result for the centre of the coil system is B =31mT for the induction in the centre of the coil, which is in goodagreement to the measured value. It has to be considered theseare RMS values, necessitating that B = 31 mT

√2 ≈ 44 mT is

to be used for the evaluation of the forcing parameter. Therewith,the reference value for GaInSn at powerline frequency, which issignificantly higher than that of the Wood’s metal investigated bythe authors, is F = 9.6×1011. Summarising the TMF’s performanceof MULTIMAG, it can be said that it competes in the samewaywithexisting installations as for the RMF sub-component.Concerning the PMF, the problem here is that no commonly ac-

cepted dimensionless parameter equivalent to the Taylor numberfor the RMF and the forcing parameter for the TMF exists. Obvi-ously, the dependence of such a parameter on the physical prop-erties of the fluid and also the quadratic dependence on the field

strength will be the same as for Ta and F . Comparison of the lattershows that both somehow depend to the fourth power on a charac-teristic length of the system. For the RMF, this length is the radiusso as to have Ta ∝ R4. In the case of the TMF, F ∝ kR5, the wavenumber k = 2π/λ is the reciprocal of the wavelength λ. The latteris about the height of the coil stack. Since this difference is small, inMULTIMAG it is λ−H = 45 cm− 40 cm, λ is tacitly replaced by Hin the estimations above when the wavelength was not specifiedin the references. This means that F ∝ kR5 ≈ (2π/H)R5 = cR4with a geometry factor c = 2π/A, wherein A = H/R is the aspectratio of the coil system. With some allowance, an equation sim-ilar to Eqs. (1) and (2) may be also used to compare the relativestrengths between various PMFs while keeping in mind that theabsolute value might be misleading because the correct geometryfactor is missing: F = σωPB2PR

5/(ρν2H). To distinguish from theforcing parameter F of the TMF, F is used for the PMF.The PMF subsystemofMULTIMAG is now compared to the facil-

ities of two French groups having both worked with mercury. Thesingle coil of 106 mm in diameter and 80 mm in height in [9] wasfed by a current up to 400 A while the frequency of the generatorwas variable in the range from 90 to 1000 Hz. Therewith, the au-thors managed to achieve a maximum field strength of 50 mT. Thereference value of the relative strength of the flow driving force forGaInSn at 50Hz is F = 1.8×1010. Also the larger coil in [10], whichwas 284mm in diameter and 225mm in height, was operatedwitha generator allowing a variation of the frequency in the range from50 to 4700 Hz. Instead of current or induction, the authors specifythe characteristics of their flow device in terms of Alfvèn’s velocity,uA = 28 cm/s, which is defined as

uA =B√µρ

. (3)

From Eq. (3), the maximum induction is readily calculated as B =36.5mT and, in turn, the reference value is F 50HzGaInSn = 4.8×10

11. Thecoil system for the PMF in MULTIMAG is a stack of four solenoidswith a height of 346 mm. These can be loaded either with a max-imum current of 160 Aeff up to 1000 Hz or with almost 1500 Apeakup to 70 Hz, the latter yielding a field strength of 141mT. Thus, therelatively high F 50Hz = 1.6×1013 may be applied to a rather largevolume.Last to contrast is the relative strengths of the DC field

component, which is best based on the Hartmann number

Ha = BL√σ

ρν. (4)

Almost since the availability of superconducting magnets (SMs),strong DC fields in the order of several Tesla have been usedalso in magnetohydrodynamical investigations. If a DC field isthe mere objective, SMs are probably the best choice. Applyingsuch a technique for superposition with other field types ishowever difficult. The contemplation below is thus restrictedto those systems from above where a DC component was alsoimplemented [5,6]. The maximum induction in [5] is 130 mT,80 mT in [6], and 391 mT in MULTIMAG. With the radius insertedfor the typical length L in Eq. (4), this is equivalent to Hartmannnumbers of 1751 in [5], 468 in [6], and 2787 in MULTIMAG.Prior to describing the details of MULTIMAG in the next

section, Fig. 3 is referred to for a photo of the whole facility andthe Appendix for an overview on the technical parameters. TheAppendix also contains relevant data from COMMA (COMbinedMAgnetic system), which is the smaller predecessor of MULTIMAGoffering the superposition of an RMF and a TMF.

244 J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251

Fig. 3. Overview photo of the MULTIMAG facility. Three identical 3-phase powersupplies for theRMF, the TMF, and the PMF (only a single phase is used), respectivelyare to be seen at the right-hand side. The 135 kW DC supply not shown here iscontained in a 3 m × 0.7 m × 2.2 m electrical equipment cubicle further to theright. Controls and instruments for the 20 separate cooling loops are to be found inthe rear left. To prevent the user fromhazardous contact with high voltages, the coilsystems are embedded in the housing in the middle left part of the picture. Aboutthree cubic metres of capacitors for the series resonance circuits are stored at baselevel below the operating platform.

Fig. 4. Geometric arrangement of the coil systems comprising MULTIMAG.

Fig. 5. Shell-type coil system of MULTIMAG. From the outside to the inner, thesolenoid for the DC field, the six hexagonally arranged coils for the RMF, and the sixsmaller coils for the TMF and the four larger multipurpose coils at the same radialposition, respectively, the latter for either the PMF or the DC cusp field, can be seen.

Fig. 6. Photo of one of the six coils producing the RMF. Some of the relevantmetricsare included in the picture. The connectors for electric current and cooling mediaare located at the right-hand side.

4. The MULTIMAG facility

Besides the flow driving field types RMF, TMF, PMF, and theusually damping homogeneous DC field introduced in the lastsection, MULTIMAG is composed of another DC field type, whichis of cusp configuration. The arrangement of the coils is sketchedin Fig. 4 and how the assembly looks like in real life is to be seenon the photo in Fig. 5. Whereas the role of the outermost solenoid,the six hexagonally arranged coils, and the stack of the six smallercylindrical coils in the innermost layer producing the DC field, theRMF, and the TMF is obvious, the four multi purpose coils take ona special position. They can serve to increase the DC field of theoutermost solenoid, produce a PMF in the frequency range up to1 kHz or a several times stronger PMF up to 70 Hz, or the DC fieldin cusp configuration, the latter can optionally also be pulsating.All coils have in common that they are manufactured from

hollow copper profiles permitting internal circulation of coolingwater at a high flow rate, and, in turn, the high current densitiesneeded to compensate the disadvantage of the missing yokes. Allcoils except the outermost solenoidweremanufactured by OswaldElektromotoren GmbH [16] in a vacuum potting procedure toensure a non-porous insulation. This is needed to have as tightas possible winding to further increase the current density in thecoils. Also most of the power supplies were especially developedforMULTIMAG. These devices are described in detail in Section 4.5.

4.1. RMF coil system

The principle of operation of the swirling flow in an RMF isthat of an asynchronous motor, where the rotor is replaced bythe electrically conducting fluid. However, there are considerabledifferences between MULTIMAG and a motor owing to theelectrical conductivity of the rotor, which is usually aluminium ina motor (σAl ≈ 11 · σGaInSn). Hence, a much higher induction B isneeded in a flow device. Since B is related to the magnetomotiveforce aka the ampere-turn, one is, as usual, concerned with acompromise. With an increasing number of turns, the inductiveresistance increases quadratically. On the other hand, the Ohmiclosses increase along with the electric current. As a rule of thumbof electromagnetic design, the mass of the copper used and thecompactness are most crucial for efficiency. This has to be seenin conjunction with the issue of effective heat removal. Thesolution implemented in MULTIMAG are rectangular coils with80 windings, organised in five double pancakes wound from 5 ×5 mm2 copper profiles with a concentric cooling channel of 2 mmin diameter. One of the six coils is to be seen on the photo in Fig. 6.An affordable maximum current rating of Imax = 160 Aeff is notdetermined by the coils rather but by the power supply. Despitesuch a low voltage–high current solution, the inductance of a coilis 1.88 mH. This is still so much that the output voltage of 340 Vof the generator is sufficient to achieve the maximum current justup to 70 Hz. To use higher frequencies, series resonance circuitshave to be employed. About 3 m3 of capacitors are stored in the

J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251 245

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Fig. 7. Iso-contours in sections of Br (upper left), Bϕ (upper right), and Bz through the RMF. The coordinate z = 0 represents the vertical centre of the coil system. Unitsare mm for lengths and mT for B. The data acquisition was performed with a 3D Gaussmeter manufactured by Lakeshore, the sensor of which was moved by a computercontrolled 3-axes cross bar, at ωR = 2π50 Hz and Icoil = 30 Aeff in the case of Br and Bϕ , and Icoil = 18 Aeff in the case of Bz .

space below theworking platform. This amount includes also thosefor the TMF. The relatively large volume is not only determined bythe number of independent circuits—owing to the quality factor ofa resonance circuit, the frequency range over that the maximumcurrent is achievable is limited. Several gradations of capacitancevalues have to be provided, which are controllable by a switchingunit, to ensure the maximum current for the entire frequencyrange: seven for the RMF, and three for the TMF. The secondrequirement leading to this large volume is the ability of a high∂U/∂t of the capacitors, which can only be acccomplished witha large construction. Special cabling has to be used for the wiringdue to the combination of high voltages and high currents. At themaximum frequency of 1 kHz, the voltage drop across the seriesconnection of two opposing coils in the loopUL+UGenerator+UC = 0is UL = 3 kV. Relatively thick insulation has to be used in order toprevent the operator from hazardous voltages. In turn, the cross-section of the cables has to be increased because the accruing heatmust diffuse through the thick insulation. The conductors in thecables have cross-sections of 70mm2, and the diameter is 19.5mm.As the characteristic field strength entering Eq. (1), the value

of B =√2Beff in the centre of the coil system has to be taken.

Measurements with a 3-axis Gaussmeter yielded a result of Beff =12 mT at Imaxeff = 160 A. Bz vanishes in the idealisation of an in-finitely extended coil, and Br and Bϕ are of samemagnitude. Such a

homogeneousmagnetic field is the basic assumption in almost anynumerical work done on RMFs. Whether a flow device meets thecriteria of comparability to numerics should thus be always a mat-ter of measurement of the entire field distribution. Fig. 7 showsthat the z-component is indeed small compared to both horizontalcomponents (Bz < 0.1 · Br ≈ 0.1 · Bϕ) with the inhomogene-ity being restricted to the annular ends of the measuring volume.From the upper two panels, it can be further read off that Bminr =

Bminϕ and Bmaxr = Bmaxϕ within themeasuring accuracywith 2(Bmax−Bmin)/(Bmax + Bmin) · 100 < 3.7%. It is in the first place this ho-mogeneity that allowed the striking agreement of experiment andnumerical simulation in [17].

4.2. TMF coil system

Six solenoids of 365 mm in inner diameter, 468 mm in outerdiameter, and 27 mm in height comprise the magnetic systemthat produces the TMF. Since these are the innermost of the shell-like structure of MULTIMAG, they determine the size of the boreavailable as the experimental volume. The arrangement of the coilswas chosen such that the overall height from the lower face ofthe lowest coil to the upper face of the uppermost coil is identicalto the height of the RMF coils, leaving 47.6 mm spacing between

246 J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251

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Fig. 8. The analogue of Fig. 7 for the TMF. All measurements were performed at Icoil = 30 Aeff and ωT = 2π50 Hz. Unlike as in Fig. 7, the measuring volume covers theentire upper part of the bore. Since Br has to vanish on the axis, which is to be seen in the upper left panel, a travelling magnetic field is not homogeneous, above all not inthe central part whatever the size of the volume considered. An idealised TMF does not have a ϕ-component. The lower panel reveals that the actual deviations from zeroare typically in the order of 2.5% of Bmaxr and 5% of Bmaxz , respectively. This non-vanishing azimuthal component owes most probably to the connectors for electric current,which pose an asymmetry of the coils. Because of the compact design and the bus bar construction required therefore, these connectors are all located on one side.

each two coils. Thus, the nominal distance between the coils is1z = 74.6 mm, from which the precise value of the wavelengthof the TMF is calculated as 61z = 447.6mm. The pre-requisite forthe validity of Eq. (2), which is a long wavelength TMFwith λ R,is fairly fulfilled.Copper profiles identical to those used for the RMF (cf. previous

section) constitute also the 32 windings in the circular TMF coils.The latter are organised in two double pancakes with each ofthe single pancakes having eight turns. Although the inductanceof 0.24 mH of a single TMF coil is much smaller than thecorresponding value of 1.88 mH of an RMF coil, resonance circuitsare still needed for the higher frequency ranges. This is, in part, dueto an electromagnetic coupling of the coil pairs. In the RMF systemas well as in the TMF system, two coils for each phase are wiredin series. In the case of the RMF, the distance between the twocoils comprising a pair is larger than the size of the coils, whereasthis ratio is opposite in the TMF configuration. Thus, the inductionof an RMF pair is about the sum of the single inductances. Thevalue for the TMF pair is significantly larger than twice the singleinductance because of the significant contribution of the quadraticdependence on the number of turns. It is also a consequence ofthe serial wiring that TMF systems may operate with six phasesgenerated out of the three phases of a technical installation. If, ina sequence of coils n = 1, . . . , 6, coil n is wired to coil n + 3 forn = 1, . . . , 3 in an opposing sense of winding, the sequence of

phases is R/ − T/S/ − R/T/ − S in the usual technical notationwith a phase shift of 60 , respectively.Limited, as said above also in the case of the RMF, to 160 Aeff

of the power supplies, the maximum attainable induction inthe centre of the TMF is 15 mTeff. Measurements of the threecomponents Br , Bz , and Bϕ within the entire upper half of theexperimental volume are presented in Fig. 8. A more detaileddescription of the field distribution is to be found in the relevantcapture.

4.3. DC solenoid

MULTIMAG is composed of two different systems to generatestatic magnetic fields. The special features of a cusp configurationas well as the upper range of static homogeneous induction arerealised by the multipurpose coil system described below. Here,it is restricted to the outermost single coil producing the basichomogeneous field of B = 244 mT. Seeing the big solenoid onthe photo in Fig. 5 having an inner diameter of 75 cm, it becomesimmediately clear that a quite high value of the ampere-turn isneeded for the field strength aimed at. The decision favouredwater-cooled hollow copper profiles also for the DC component,since otherwise the mass of copper and the outer diameter wouldhave increased tremendously. 120 turns wound from 12×20mm2profile comprising an elliptic cooling channel led to an outer

J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251 247

Fig. 9. Sketch of a DC magnetic field in cusp configuration. The upper and lowercoils carry currents of same intensity, but of opposing direction, respectively.

diameter of 93 cm and a height of 40 cm. Unlike all other coils,the insulation between adjacent windings was established bysurrounding the conductor with a plastic tube. To realise n · I =180 000 ampere-turns, an electric power of 135 kW is required.In Section 3, the DC performance of MULTIMAG was compared

to that of other flow devices based on the Hartmann number forthemaximum total static field strength produced by the outermostsolenoid and the multipurpose coils. It is, however, instructive toconsider the damping effect produced by the big solenoid alone.The relevant Hartmann number is Ha = 1739, and a significantdamping of a flow is said to occur for Ha2 Re, where Re isthe Reynolds number. If, with some allowance, the being largecompared to is interpreted as one order of magnitude, the flowwillbe damped if its Reynolds number is kept below Re ≈ 3×105. Thecorresponding velocity for GaInSn in a cavity of radius identical toMULTIMAGs bore is about 0.5 m/s.

4.4. Multipurpose coil system

This coil system consists of four solenoids having the sameinner radius of 182.5 mm as the TMF coils, and which is locatedwithin the gaps of the latter (cf. Fig. 4). It differs significantlyfrom the RMF and TMF coils with respect to the copper profileused for the conductors—a cross-section of 9 × 9 mm2 with a6 mm cooling channel may carry a current of 1100 A at permanentload or 1500 A for several minutes. The choice for that profilewas motivated by the availability of relevant power supplies (cf.Section 4.5) in conjunction with a difference in the mechanismdriving flow specific to a PMF. That is, a forcewill not drive any flowif it is conservative. In an infinitely extended PMF, E∇ × EFL = 0: theLorentz force produced in such a PMF is a pressure directed radiallyinwards. It is solely the axial variation caused by end effects, whichare finite extensions of both liquid metal column and magneticfield, that actually impelsmotion. A PMF significantly stronger thana TMF or an RMF is required to enter flow regimes of comparablevigour. Further reading on the details of the flow structure in a PMFis provided in [18], and some corresponding experiments may befound in [19].Having an outer diameter of 445 mm, each coil is made of 16

windings organised in two double pancakes. Because of the smallnumber of windings, the inductance is significantly lower thanthose of the RMF and TMF coils. L = 0.136 mH allows operatingthe multipurpose coils up to the maximum frequency of 1 kHz ofthe AC source without the need of a resonance circuit.Depending on the wiring schema and which of the power sup-

plies is used, quite a lot of configurations might be realised, how-ever, most of themwould not be verymeaningful. Themajormodeof operation is that of a PFM to model the magnetohydrodynam-ics frequently present in melt pools produced by induction heat-ing. Any combination of one up to all of the coils may be used toaccount for various geometries, i.e. modelling an aspect ratio ofabout unity or a flat inductor that covers only a small fraction of

Fig. 10. Measurement of the cusp field produced in MULTIMAG at a coil current of500 A. The plot depicts iso-levels of the absolute values of the magnetic induction.

the height of the liquid metal column. Two regimes of PMF oper-ation are to be distinguished, depending on which power supplyis going to be employed. If one phase of a 160 A-source is used,BPMF = 21.3mTeff is realisable in the frequency range up to 1 kHzwith a series connection of all four coils. 52 or 141 mTeff are possi-blewith one or four coils, respectively,when the system is suppliedby the 1500 A-source in the frequency range up to 70 Hz. Sincethis power supply normally operates the outermost solenoid,MUL-TIMAG does not seem to offer the superposition of such a strongPMF with a DC field. It is nonetheless possible, the details are de-scribed in Section 4.5.Besides a homogeneous DC field, static magnetic fields in the

cusp configuration became an important tool for flow stabilisationin crystal growth over the past years. A cusp field may be realisedin MULTIMAG with a series wiring of all four multipurpose coilswith, e.g., the upper two coils in one common sense of winding andthe lower both in opposing sense of winding. A unique measureof the strength of a cusp field does not exist to the best of ourknowledge since the induction in the geometric centre of the coilsystem is zero. The field distribution within the bore depends onthe details of the geometric arrangement of the segments, which ismost prominently the aspect ratio. Fig. 9 sketches the principle ofa cusp field while Fig. 10 illustrates the field distributionmeasuredin MULTIMAG.It is well known that the strengths of a DC field required to

damp a flowhaving a certain characteristic velocity u0 significantlyhas to be much higher than that of an AC magnetic field to drivea flow of same u0. Although this is fulfilled in MULTIMAG withthe outermost solenoid offering values of the induction about oneorder of magnitude higher than those achievable with either ACfield type, at times it is desired to have an even stronger DCmagnetic field. For that purpose, the series connection of all fourmultipurpose coils allows boosting the DC field by another 147mTin permanent load at 1100 A coil current.

4.5. Power supplies

MULTIMAG is operated with several power supplies, themajority of which were specifically developed to the demands ofsuperposition to achieve the flexible flow control mentioned in thebeginning in Section 1 and matching to the coil systems requiredtherefore. Regarding the AC sources, a development was anywayrequired since nothing is available in the performance categoryneeded by the coil systems ofMULTIMAG commercially to the best

248 J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251

Fig. 11. Photo of one of the three 3-phase power supplies for the AC magneticfields. At the maximum power rating of 70 kW of the device, each phase is capableof delivering 160 Aeff at permanent load. The three independently programmablefrequency synthesisers allow freewaveforms of the output current in the frequencyrange from DC to 1 kHz.

of our knowledge. As the 1500 A-source was intended to operatein a dual mode, which is either supplying the outermost solenoidwith DC current or the multipurpose coils with AC current, adevelopment was also mandatory here. Only two almost identicalDC supplies offering 1100 A at 30 and 35 V, respectively, could bebought off the shelf.For the RMF, the TMF, and the PMF, three identical AC supplies,

each offering three phases of 160 Aeff at 340 V in the frequencyrange up to 1 kHz, are available. One of these devices developedby EAAT GmbH, Chemnitz, Germany [20] is depicted in Fig. 11.Fig. 12 shows their principle of operation, which, basically, is thatof an inverter (frequency converter): the mains’ 3 × 400 VAC arerectified and stored, intermediately, in a DC voltage link. In orderto reverse direction, a circuit called an H-bridge is used, whichis the electronic equivalent to a mechanical double-pole doublethrow switch. Switching circuits for high power are availablein MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor)and IGBT (Insulated Gate Bipolar Transistor) technology. MOSFETsoffer high switching speed and peak current capability renderingthem a good choice in power electronic design. These advantagesare partly mitigated by their conduction characteristics, whichare strongly dependent on temperature and voltage rating. Thisis, as the voltage rating goes up, the switching losses increase.IGBTs on the other hand have superior conduction characteristicswhile sharing many of the appealing features of power MOSFETs.However, the switching speed of an IGBT is inferior to that of powerMOSFETS. Since the speed of IGBTs is sufficient and the conductioncharacteristics of MOSFETs may pose a problem with respect to aprecise control of the output current, the decision for the AC powersupplies was to favour of IGBTs. In general, the switches in an H-bridgemust be protected from the voltage spikes caused by turningthe power off. This is usually done with catch diodes. Additionally,most H-bridges comprise logic to prevent a short circuit at a verylow level in the design. The required power or the effective voltage

Fig. 12. Principle of operation of the AC power supplies. The rectifier and thestorage are common to all three phases, whereas the IGBT power transistors, thecurrent control circuit, and the pulse width modulation are per phase.

output is finally realised by controlling the turn-on time of theswitcheswithin theH-bridge. This technique is termedpulsewidthmodulation (PWM).All said so far is state of the art and frequently implemented

in commercial applications, likely the most prominent of whichis the control of bipolar motors. The specific mode of operationis determined by the intended use. A variety of such operationalmodes is possible, for instance different (linear, quadratic,asymptotic or any combination thereof) characteristics of thedependence of the voltage on frequency while spinning up themotor. Another example is to keep constant momentum in alathe. The control of the switches in H-bridges is often done bya microprocessor in order to adapt to a specific application andto provide a high degree of flexibility, albeit analogue controlcircuits are commercially available. Whatever themodality, digitalor analogue, despite the perusal of quite a lot of technicaldocumentation and application notes it was not possible to find areadymade solution suitable for supplying the coils inMULTIMAG:a precisely controlled constant current taking into account theheating up of the coils was badly missing. In this respect, it isworth noting that EAAT GmbH [20] had developed the powersupplies of MULTIMAG’s smaller predecessor COMMA (cf. theAppendix) beforehand by means of modifying the firmware of acommercial inverter. Such software based solutions are, however,disadvantageous concerning speed, complying with a set-point,and quality of the wave form. Thus, the requirements specificationfor the power supplies to be developed for MULTIMAGwas, in firstplace, the avoidance of these drawbacks. In addition, the conceptof a most flexible flow control mentioned in Section 1 suggestedthe design of three-channel amplifiers instead of traditional powersupplies.From first principles, PWM can not exactly reproduce, e.g., a

sinusoidal wave form. Although the coils of MULTIMAG being aninductive load would certainly smooth the steep pulses more orless, a significant ripple remains. Thus, a first measure towardthe aimed at amplifier characteristic with an as low as possibledistortion factor was increasing the typical clock rate of 4 to 7 kHzto be found in motor inverters to 10 kHz.An anyway poor response time of software based solutions, in

combination with unpredictable runtime behaviour, was enoughreason to decide for a completely analogue current control. Therealisation is a lamp circuit: a limiting comparator is used forforming the rectangular control pulse of variable width switchingthe H-bridge, the one input of which comparator is suppliedwith a triangular pulse formed from the rectangular clock rateby a resistance–capacitor (RC) element. The other input of thecomparator is connected to a reference. In the simple case of a DCswitching power supplywherein the task formulation is to achievea duty cycle from 0% to 100%, this reference may be generated bya potential divider comprising an adjustable resistor. The variationrange of the comparison voltage is greater than the voltage changeof the triangular pulse, so that, in the one setting of the adjustingresistor, the comparison voltage exceeds the maximum value of

J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251 249

the triangular pulse, and in another setting it is less than theminimum value of the triangular pulse.The means of complying to a set-point as well as of the widths

of the pulses conforming to an arbitrary DC input wave formare the same: the reference input of the comparator is to beconnected to the output of a differential amplifier, the inputsof which are either the set-point or the transient of the desiredwave form, respectively, and the measured actual value of theoutput of the H-bridge. The latter is either voltage or currentdepending on the operational mode (may be CC/CV = constantcurrent/constant voltage), and a mean value for conforming toa set-point or an averaged value for the amplifying mode ofoperationwith the integration time being adapted to the frequencyof the transient. In any case, the width of the control pulse isdirectly proportional to the deviation from the (instantaneous) set-point. In this respect, the AC power supplies of MULTIMAG operatein a CC amplifier mode with the effective output current beingcontrolled to the instantaneous set-point of the input wave form.As all the contemplation has so far been restricted to DC (unipolar)operation, the step to AC is straightforward: two comparators haveto be used, one for negative voltages and the other for positivevoltages of the input wave form, respectively, each controlling thecorresponding branch of, or better to say pathwithin, theH-bridge.To make this technique suitable for MULTIMAG’s power

supplies aiming at a low distortion amplifier mode, additionalmeasures were required. The generally lower switching speed ofIGBTs against MOSFETs remains being problematic with respectto the switch-off time even for lower frequencies, at which theyare otherwise quick enough. In order to understand how to copewith this difficulty, the principle of operation of an H-bridge isconsidered. Imagine the cross of the capital letter ‘‘H’’ being a coil(load), and the four upper/lower and left/right bars, respectively,representing the switching transistors of the bridge. Both upperends of the upper bars are connected to one pole of the DC link,and the lower ends of the lower bars to the other pole. Let ul,ur, ll, and lr denote the upper left, upper right, lower left, andlower right switches, which may be on or off, and, say, plus theupper and minus the lower pole of the DC link. Then, in onepolarity, electric current may flow via plus–ul–coil–lr–minuswhilethe current density is controlled with the duty cycle generated byswitching ul and lr simultaneously on and off. Reversal of polarityat the load is accomplished by using the path plus–ur–coil–ll-minus.A hazard of reversing is a condition frequently called shoot-

through. If the ur/ll pair is turned on before the ul/lr pair has fullyturned off, it creates a direct short circuit across the DC link. Sincean H-bridge must not be reversed while loaded, the switch-offtime1toff is taken into account by the manufacturers: the controlmodules delivered together with the transistor-bridges providethemeans for an appropriate delay of the switch-on time1ton afterreversing. 1ton is adapted to 1toff, which is often generous. Thishas to be seen in conjunction with another feature of the controlmodules. The ability of the driver stage to deliver a high pulsedensity current to the IGBTs allows one to speed up 1ton as wellas 1toff via a quick change of the charge of the gate capacity [21].However, in the standard application of driving motors, hardly thefull advantage is taken. For safety reasons taking time, the outputvoltage of the H-bridge is monitored to detect a potential shortcircuit. Moreover, some response time is to be planned, e.g. for asoft switch-off. The latter is a further delay of switching off whileinhibiting switching on for reversing to prevent the DC link fromhigh currents due to induction [22]. Unquestionably, the distortionfactor deteriorates as a consequence. The IGBT control modulesdeveloped for MULTIMAG make use of the fact that monitoringthe output current Iout is anyway precisely implemented for theamplifier operational mode [23]. Strict regulation of Iout to zerotoward an upcoming reversing renders all protective measures

described above superfluous, so that the maximum benefit fromthe quick change of the charge of the gate capacity is achieved.Notwithstanding the measures described above, the level of

distortion owing to PWM is still significant. Four switching modesof the H-bridge are considered so far: (i) ul = lr = on, whichis referred to as forward mode. (ii) Reverse mode, ur = ll = on.These are the usual operating modes. (iii) If all switches are open,e.g. during reversing, any (remaining) current flowing through theload will be working against the full DC link voltage plus the dropacross two catch diodes, so the current decays quickly. If the loadwere a motor, it would quickly coast to a stop. This mode, thuscalled fast decay or coasting mode, is used in MULTIMAGs powersupplies for safe reversing without load. (iv) Shoot-through withall switches on should be unconditionally avoided. Examinationof other switching states provides the clue to reduce distortion.The states termed slow decay aka dynamic braking and powerbraking within the realm of controlling motors would be beyondthe scope of the present paper. It is thus restricted to a statethat, interestingly, is also employed in high fidelity class D poweramplifiers. That is, basically, only one switch is used. Imagine thestate ul = lr = on with current flowing through the coil. Now,instead of switching a pair, only lr is switched off. Because thecatch diode built in ur provides an escape, the inductance of thecoilwill keep the current flowing. Fromone cycle of the clock it is tobe seen that discontinuities due to switching may be straightenedout. A useful mode implemented in MULTIMAG’s power supplyis keeping one switch on over a longer period while pulsing thediagonally opposing switch. What works nicely in high fidelityamplifiers continues to be true forMULTIMAG.Measurementswithone RMF coil showed that the current displayed on an oscilloscopeis not distinguishable from the input voltage sine wave with thenaked eye even at the maximum frequency of 1 kHz.The input wave form is freely programmable using an ADWin

Pro with the according DSP (digital signal processing) processorand analogue input/outputmodules [24]. 16-bit digital to analogueconverters, in combination with pre-calculated lookup tables,allow wave forms with negligible distortion factor (discretisationerror) in a frequency range exceeding that used for MULTIMAG byat least an order of magnitude. Concerning the overall accuracy,measurements showed that the AC power supplies are capablekeeping the final magnetic field strength constant to a set-pointbetter than 1% even if operated below5%of theirmaximumcurrentrating.The 1500 A/90 V power supply is a hybrid providing these

specifications in DC mode to feed the outermost solenoid, or in ACmode,wherein these numbers are peak values, to themultipurposecoils generating a PMFup to 70Hz. FormereDC operation, only onecontrol quadrant, whichmay be either forward or backwardmode,would have been needed. AC demands, at least, both quadrants.No use is made from the sophisticatedmodes described above, but,owing to the high power, power breaking is implemented. Thus,this PWM device may work in all four quadrants realised withIGBT H-bridges. It was also specifically developed for the needs ofMULTIMAG [25].A question left open in Section 4.4 was how to superimpose the

strong PMF produced by the 1500 A source with a DC magneticfield. Straightforwardly, the power supplies normally used to boostthe DC field of the outermost solenoid have to be exchanged withthe 1500 A source. The requirement of the relatively high voltageof 90 V of the outermost solenoid is, in parts, allowed for by twoalmost identical devices capable of output voltages of 30 and 35 V,respectively. The series connection of 75 V fits well to their max-imum current rating of 1100 A. Maximum achievable parametersare B = 179 mT and Ha = 1275, which is still quite much (cf. Sec-tion 3). Such devices are usually sold to the electro-plating indus-try, and are thus available off the shelf. Those used for MULTIMAGare based on IGBT technology, work in 1-quadrant mode, and may

250 J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251

be operated in both CC/CV control. High capacitances at the outputensure an acceptable level of the remaining ripple [26].

4.6. Coolant loop and safety issues

A total power consumption of up to almost 12 MW requiresintense cooling. The 1500A and both 1100A sources are air-cooled,whereas the 160 A AC sources are water-cooled. Most crucial,because the majority of heat is dissipated there, are however thecoils. Each of the six RMF and TMF and the 4 multipurpose coils,respectively, and the outermost solenoid have their own coolingcircuit. Counting coils and power supplies, this sumsup to 20 loops,each of which is redundantly monitored by the flow rate and thetemperature drop across the load. In order to keep the risk ofdestroying any component as low as possible, monitoring is donevia according interfaces over the ethernet by a computer placed inanother room. A watchdog timer provides a high level of safety:the monitoring computer periodically sends an acknowledge to acontrol logic built into MULTIMAG. If this signal is missing, be thatbecause any of the operating conditions is critical or the computershuts down, MULTIMAG is switched off completely.In particular, the RMF and TMF coils pose an additional problem.

The five double-pancakes of the RMF coil shown in Fig. 6 arewoundfrom about 120 m of hollow conductor. While being electricallyconnected in series, this is not possible for the coolant becauseof the small diameter of 3 mm of the cooling channel. Thus, theparallel connection of the cooling loops shorts the voltage dropacross any pancake. Since the total drop across the coil may beas high as 1.5 kV, shorting 300 V is a severe danger also in thecase of water. As a consequence, the entire content of the coolingsystem is permanently de-ionised,which is additionallymonitoredby measuring the electrical conductivity. Extracting all ions is,in turn, also problematic with respect to the plumbing. Whereasthe natural content of oxygen might be beneficial with respect tocorrosion, even a much weaker concentration thereof renders thecoolingwater extremely aggressive. Thus, the oxygen also has to beremoved while the concentration needs frequent observation. Forthe reason of personal security, the residual current is monitoredper phase of any power supply and the respective earth leakagecurrent breaker is integrated into the safety control system (SCS) ofthe device. This SCS per power supply also monitors pressure andflow rate of the coolant, over-voltage in the DC link, and potentialshorting of the output. In addition, all power supplies are inter-locked: if one fails, the entire MULTIMAG is switched off. Thisinter-lock circuit provides a second independent security loop forthe whole facility in addition to the watchdog mechanism. A finalremark with respect to safety concerns switching off. Although apercentage fraction of energy is wasted, each single capacitor inthe series resonance circuits for the RMF and the TMF is shuntedout. In the case of a fault, the capacitors are discharged within amaximum of three minutes.

5. Experimental results

Since the completion of MULTIMAG, a variety of experimentswas performed with this flow device. The closing sectionexemplifies the capabilities with respect to a meaningful physicalmodelling at hand of three selected topics. These are thecombination of an RMF and a TMF, amplitude modulation of anRMF, and the superposition of an RMFwith both homogeneous andcusp DC magnetic fields.It is learned in Section 2 that an RMF as well as a TMF,

when operated separately, drive axisymmetric base flows. Thisis a general issue restricting a broad applicableness for stirringin industrial practice. Rotation and meridional/poloidal motionare relatively rigid two-dimensional flow structures providing

Fig. 13. Time series of the vertical velocity component for two different sets of themodulation parameters in a flow driven by an amplitude modulated RMF. The greycurve shows that the secondary flow temporarily changes direction.

only limited stirring efficiency. It is shown in [27,28] thatan RMF/TMF-combination may solve the task formulation. Fordifferent frequencies ωR of the RMF and ωT of the TMF so that1ω = |ωR − ωT | u/L, where L and u are the characteristiclength and fluid velocity, the Lorentz force becomes helical andtherewith three-dimensional. This is caused by the interactionof the eddy currents induced by the RMF with the TMF andvice versa, an effect which is no longer a linear superpositionof the single field types. In the investigated parameter range,these summands, which may be referred to as interaction terms,became predominant. For higher values of 1ω, the interactionterms oscillating with that frequency lose their influence on themelt flow because of inertia. In this case, both RMF and TMF forcessuperimpose linearly. While keeping the RMF constant, variationsof the poloidal TMF forcing may lead to an accumulation of swirlresembling features of tornado like flows [29].Amplitude modulation is also concerned with the matter of

stirring. The first example has addressed the domain of mixingand homogenisation, whereas the application of magnetic fieldmodulation may be sought in the realm of solidification. Overthe past years, it became well known that RMF stirring maybe beneficial to directional solidification with respect to grainrefinement and promoting a columnar to equiaxed transition(cf. [30] and references therein). The drawback, on the other hand,is often a centre-macrosegregation owing to the secondary flowproduced by the RMF. No matter whether the primary swirl is inthe clockwise or counter-clockwise direction, the mean secondaryflow at the solidification front is from the rim toward the centre.A desirable flow control thus aims at either suppressing thesecondary flow as well as possible or influencing its direction. Thelatter may be achieved with a sinusoidal or a pulse modulationof the RMF. Local velocity measurements with ultrasonic Dopplervelocimetry presented in Fig. 13 show that reversals of themeridional flow are accomplishable for certain combinations ofthemodulation parameters amplitude, offset, and frequency. Moreresults and details of the parametric studies are to be foundin [31–33].The last example is engaged with temperature fluctuations in

Czochralski crystal growth processes, in which fluctuations maybecome detrimental with respect to a mono-crystalline growth.It is shown in [3] that an RMF is capable of damping suchtemperature oscillations. The studies in [34,35] expand this workto higher values of the buoyancy relatedGrashof number and to thesuperposition of static magnetic fields in both homogeneous andcusp configuration for different aspect ratios. A distinct transitionof the flow from a turbulent large-scale low-frequency buoyantconvection to a turbulent small-scale RMF-driven convection with

J. Pal et al. / Flow Measurement and Instrumentation 20 (2009) 241–251 251

a higher frequency of the oscillations was identified, and a furthersignificant reduction of the amplitude of temperature fluctuationswas observed.

6. Summary

Model experiments using low melting point alloys are oftenthe only means to gather information from the flow field presentin industrial processes in the areas of metallurgy and crystalgrowth via the similarity criteria. A comparison of MULTIMAG toexisting flow devices shows that liquid metal models have beenwell established over the past decades and the relevant magneticsystems became state of the art. Hitherto, only a few attemptswere however made toward tailored solutions for specific heatand mass transfer problems frequently to be found in industrialpractice. With this in mind, MULTIMAG is the first embodimentof a flexible flow facility for magnetohydrodynamics to the bestof our knowledge. It offers true linear superposition of a rotating,a travelling, a single-phase alternating, a static homogeneous,and a static magnetic field in cusp configuration. Moreover,the use of amplifiers instead of conventional power suppliesfor the alternating field types allows complex spatio-temporaldistributions of the magnetic induction in a large experimentalvolume. With regard to the maximummagnitude of the similaritycriteria, MULTIMAG is well-placedwithin existing flow devices. Anexcerpt of a fewexperiments performed so far proves the industrialrelevance of the results on key fields such as homogenisation ofmelts, solidification, and crystal growth.

Acknowledgement

This work was financially supported by ‘‘Deutsche Forschungs-gemeinschaft’’ in the framework of the Collaborative ResearchCen-tre SFB 609.

Appendix. Overview on technical specifications

The table below compares MULTIMAG with its smaller prede-cessor COMMA. Geometrical data are in mm, frequencies f in Hz.Electric current I in A and induction B inmT are true rms. Values arecalculated for the properties of GaInSn at 50 Hz and are maximumratings, if applicable. The lower values for the PMF are in the fre-quency range up to 1 kHz, whereas the higher ones are limited to70 Hz. Permanent operation of the cusp field is possible at 1100 A.The higher value in braces is limited to about 10 min.

MULTIMAG COMMA

Bore height 400 220Borediameter

365 100

f 0–1000 10–400BRMF 12 23IRMF 160 100Ta 2.3× 1011 1.3× 109BTMF 15 37ITMF 160 100F 4.5× 1011 8.3× 109k 13.96 26.74BPMF 8/52 (one coil) –

23/141 (four coils) –IPMF 160/1061 –BDC, homogeneous 244+ 147 –IDC, homogeneous 1500+ 1100 –IDC, cusp 1100 (1500) –

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