Author : Andreas Cramer
Institution : HZDR, Germany
Fluid flow plays an important role in the recycling process of silicon contaminated with electrically non-conducting particles by electromagnetic separation (EMS) via applying Leenov-Kolin force (LKF). A too strong flow may inhibit EMS completely, whereas some flow is needed to transport the particles from the large bulk of the crucibles for directional solidification to the relatively thin regions at the side walls where the LKF is effective.
Intrinsically present temperature gradients ∇T will always force some natural or buoyant convection. Additional fluid flow may be induced by imposing alternating magnetic fields on the silicon melt. One first has to distinguish single-phase alternating magnetic fields (AMF), also known as pulsating magnetic fields, from travelling fields. The direction of movement of the field further distinguishes the latter into rotating magnetic fields (RMF) and linearly travelling magnetic fields (TMF). Each of them drives a characteristic fluid motion.
The primarily swirling flow driven by an RMF will most probably be of no benefit for the task formulation of removing the particles from the silicon melt. Depending on the direction of an axially applied TMF, the toroidal flow may support separation of the particles. The results from the project partner University of Greenwich, summarised in Deliverable 6.1 - Report on the software adjustments, show that an upwards travelling field is effective for separation by forcing flow towards the solidification front over a wide centrical region where the particles are captured in the bottom part early in the melt treatment phase. Whereas, if the TMF is travelling downwards, the contaminant particles are uniformly retained in the liquid bulk volume while solidifying with a similar cooling strategy.
An AMF will, in a manner of speaking, be intrinsic to achieve the objectives of SIKELOR. That is because the LKF is usually applied by means of an AMF. Besides establishing the electrophoretic separation, the relatively strong AMF needed to that will inevitably drive an accordingly vigorous flow. Studying the flow driven by this simplest among the alternating magnetic fields, a single-phase AMF, is thus the most prominent task in the physical modelling of fluid flow in SIKELOR.
A variety of magnetic systems are available at the HZDR to create RMFs and TMFs. They were not built in the course of the SIKELOR project, but rather in operation before the project was launched. Since also a TMF may become of interest for the project, the largest system providing amongst others a TMF and even AMFs is presented in the next section.
MULTIMAG is a MULTIpurpose MAGnetic field system for physical modelling in magnetohydrodynamics. It is a shell-like structure composed of, from the outer to the inner:
The Photo in Fig. 1 shows the coil system. If all the coils of MULTIMAG would be operated together at maximum current ratings, the related power would be about half a megawatt.
Fig. 1: Coil system of MULTIMAG.
The coil systems of MULTIMAG are driven by several power supplies. The biggest one is that usually taken for the DC field. It was custom made to fit the electrical characteristics of the big
outer solenoid. To have the maximum current of 1500 amps circulating through the solenoid, a voltage of 90 V is needed. This corresponds to an output power of 135 kilowatt. A specific feature of
the current source is the four-quadrant operation mode. This allows, in the frequency range up to 50 Hz, AC operation.
In the case that the innermost four cylindrical high-current coils are operated in DC mode, be that to boost the field of the big solenoid or to apply a cusp field, they are supplied by two DC sources. They are off-the-shelf devices having the electrical characteristics of 1000 A / 30 V and 1100 A / 35 V, respectively.
RMF and TMF are supplied by two identical custom made high-power 3-channel amplifiers. These amplifiers, developed and built by the project partner EAAT, are based on pulse-width modulation. Current setpoint and frequency are prescribed by frequency syntesizers connected to the inputs of the amplifiers. Such a concept allows a high degree of flexibility. The shift between the phases/ channels is not restricted to the usual 120°, it can be any value. Not only that the output current can be any other wave form than a mere sinus, e.g. sawtooth, triangular etc., it can be the superposition of two, three, or even a continuous spectrum of frequencies. In fact, the input can be any arbitrary wave form. That the wave form of the output current may not strictly follow the input wave form depends on the inductive load of the coils. The amplifiers work in a frequency range from DC up to 1 kHz; at half the maximum output current in the range from 0 to 10 Hz, and at full permanent output current above. The maximum output ratings per device are 3 × 160 Aeff / 340 V.
At the HZDR, three of these unique amplifiers are at disposal. The third one is foreseen to operate the four innermost cylindrical coils so as to produce an AMF of up to 1 kHz. Fig. 2 shows a photo of one of these amplifiers.
Fig. 2: 3 × 160 Aeff power amplifier.
A detailed description of the MULTIMAG system is to be found in . References [2–18] are a selection of work conducted in this unique flow facility and smaller predecessor coil systems.
The flow measurements in an AMF reported in  were done in a smaller predecessor of MULTIMAG. As seen in the previous section, MULTIMAG allows to create a variety of AMFs differing in
geometry. The question thus may be posed why the physical modelling of the flow is not planned to be done in these experimental facilities. To give an answer, the experiments in  are
This work is among the few concerned with electromagnetic separation in a silicon melt. Although it is far removed from the geometric parameters of the demonstrators to be built in SIKELOR, it is
necessary to understand why these experiments were successful. This means in particular that the flow field has to be known so as to learn why it has not inhibited the separation process. Since
to date it is not possible to measure reliably the fluid velocities in a hot silicon melt, if it will ever be possible, meaningful model experiments have to be done in the reduced temperature
range accessible by the available measuring techniques. The experiments in  were conducted in a cylinder of radius R = 2 cm at 11 kHz. This corresponds to a
shielding parameter S = μσωR2, where μ is the permeability, σ the electrical conductivity, and ω = 2πf, of about 43. The model melt GaInSn has an about three times
higher conductivity, which means that a frequency of just under 4 kHz should be used if the container has the same size. Since the maximum frequency achievable with MULTIMAG is 1 kHz, R
might be doubled which would fit into this facility.
Remaining with the small scale and silicon, scratching along an S of 43 would not be enough. That the experiment in  was done with 11 kHz is most probably explained with a generator
having that frequency was available. It remains unclear whether the separation would not have been working even better at higher frequencies. A minimum of S = 100 should be reachable to
have a reasonable variation of parameters. As a container with an R of amply 8 cm would still easily fit into MULTMAG, there are other successful experiments on
In , frequencies of 3 kHz, 30 kHz, 80 kHz, and 200 kHz have been applied to an aluminium melt in a equal sized container. This corresponds to shielding parameters of 36, 360, 960, and 2400.
Separation was successful except at the lowest frequency. The authors explained the failure at S = 36 with the presence of a too strong fluid flow. It is worth noting that the
difference in S for 3 kHz and the experiment done on silicon is not that big, we do however not follow this interesting question here for the sake of compendiousness. Anyway, the
parameter range of  would by far be not accessible with an experiment based on the GaInSn melt. Even a container sized such that S = 360 would no longer fit into MULTIMAG.
Finally, the minimum reasonable scale of the Demonstrators is G2. Estimations of the LKF according to  yield a minimum frequency of 3 kHz for separation to be successful. This lower end of
minima results in S = 409. The iDSS furnace at the University of Padua to be used for Demonstrator II is presently designed for a special size crucible that would correspond to
G2.5. It is presently also not possible to operate the furnace at 3 kHz owing to vibrations. As higher frequencies are anyway desirable with respect to achievable LKF, 6 kHz are strived for. The
S for these parameters is 1643.
To physically model the flows in [19,20] and that to be expected in Demonstrator II, it is thus necessary to work at significantly higher frequencies as those provided by MULTIMAG. Two stages were planned to build up experiments reaching high S:
Both approaches are described in the next two sections.
The first approach has, of course, ab initio limitations. Variable frequency high-current sources are, in general, hardly available off-the-shelf. Hardly means either not (depending on
the current), or quite expensive up to simply unaffordable. Least of all if the required frequencies are high. The second limitation is that in a combination of highly specific equipment one
component will match to another in the scarcest cases. Only low field strength were thus expected, and it was not clear whether the resulting low fluid velocities can be reliably resolved with
the ultrasonic flow measuring technique.
Several isolation amplifiers of type HERO POWER® from Rohrer Mess- & Systemtechnik, München, Germany  are available in the labs of the Magnetohydrodynamics Department at the HZDR. They differ in their maximum voltage, current, and frequency ratings. All of them are capable of working at frequencies much higher than that needed to reach an S of several thousands. Given the inductances of available coil systems, the limitation showed up to be on the part of the output voltage. Thus, the model PFL 2250-28 having the highest maximum voltage of 410 V was selected. Its maximum current and frequency ratings are ±28 A/20 Aeff and 150 kHz.
Since the power source is an amplifier, a frequency synthesizer is needed to control the amplifier input. These devices are readily available off-the-shelf. In the first experimental setup, an
arbitrary waveform generator type 33220A from Keysight Technologies, Santa Rosa, CA, USA  was used.
There is often the notorious discussion on magnetic systems of a high number of turns/high voltage–low current vs. a low number of turns/low voltage–high current solution. Such discussions commence in the case of a DC magnetic system. In AC systems, the impedance becomes more and more problematic with increasing frequency. This seemingly favours a high–current solution, in particular for high frequencies. Examples of realisation are to be found in droves in industry; currents of several thousand amps circulate in induction heating/induction hardening facilities at frequencies from below 1 kHz up to a few hundred kHz. However, despite the relatively low inductance of induction coils, resonance circuits are used there to decrease the required generator output voltage. Since the frequency is fixed, a single resonance circuit is not the solution in a laboratory where, e.g., the dependence of a magnitude on S is a subject of investigation. As most of the installations at the HZDR tend to the high–current solution, it is always a compromise. For instance, the 160 Aeff in MULTIMAG are not really high compared to the kA in induction heating/hardening installations. Or compared to other magnetic systems at the HZDR—which has to be seen in conjunction with the voltage; the output voltage of MULTIMAG of 340 V is more than an order of magnitude above the 7 V required to have a current of 1.1 kA circulating through a compact solenoid. Also, the maximum frequency of 1 kHz of MULTIMAG is not what one would call a really high frequency—and, as described above, what is not sufficient to reach the high S aimed at.
The compromise matching best to the amplifier was the relatively large coil system depicted in Fig. 3. Four "coils" one on top of another can be seen on the photo, from which only the inner
both having a larger diameter are used. The smaller ones have distinctly higher number of turns, which, in conjunction with the smaller area, results in a too high impedance with respect to the
output voltage of the amplifier. They were not removed because of the effort this would have taken. "Coil" is put in quotation marks since what appears as a coil is in fact a package of two coils
one on top of another. From each of the packages, again due to impedance reasons, only those coils directed outwards with respect to the middle plane were used. In the case of no electromagnetic
coupling, the impedance Ltot of two coils L1 and L2 connected in parallel is given by 1/Ltot = 1/L1 + 1/L2. Consequently, if the
current is split in parallel to two coils, the lower total impedance demands less voltage to have the same total current circulating. Since, as said initially above, the limit is not the maximum
current rating of the amplifier but rather its maximum voltage, the parallel connection would allow a higher current. However, the close vicinity of the coils inside the package establishes a
strong electromagnetic coupling. It was verified by several experiments at different frequencies that, due to this mutual inductance, the reachable field strength is even slightly less in the
case that all four coils are used in parallel.
The parameters of the finally implemented system are:
Fig. 3: Photo of the first experimental setup realised with hardware previously existing at the HZDR. In the centre of the coil system, the cylindrical fluid vessel filled with the model melt is to be seen. The red arrow points at a 3–axes crossbar with which the ultrasonic transducer can be precisely positioned in the horizontal directions and lowered so as to touch the melt surface in kissing contact. The analog power amplifier is indicated by the green arrow.
The limitations discussed so far are not all the limitations, in particular with respect to potential effects to be modelled. For instance, the 9.15 A generating a magnetic field with
0.62 mT are an achievable current value for a reasonable range of S. With the container 180 mm in inner diameter to be seen in Fig. 3, an S of 200 can be reached
if the frequency is 960 Hz. As this container would fit into MULTIMAG without any problems and this facility has a maximum frequency of 1 kHz, it may be asked why the setup discussed
here was built. The problem may be seen as to be hidden behind what is frequently named "reasonable". A maximum S of 200 is not reasonable as becomes obvious from all the discussion
above. The bore diameter of MULTIMAG is 360 mm. Taking into account the container walls to keep the heavy liquid metal and some space around the cell for installation of the measuring
technique, the number not discussed so far above is a maximum of S = 370 which could be realised in MULTIMAG. This limitation, in conjunction with the quite high setting-up
time and effort, was the reason why any modelling in MULTIMAG was not taken into consideration.
It would not have been reasonable to start with a container of larger size. The price of the GaInSn alloy is about € 650 per kg. Given the density ρ = 6360 kg/m3, this corresponds to € 12,600 for a filling height of 120 mm. Not to think of the diameter of 240 mm and the corresponding filling height for the same aspect ratio that would fit into MULTIMAG. Only if there is some perspective it might be worth considering a larger container in terms of financial effort. Fortunately, S ≈ R2. Unfortunately, the cost-benefit ratio CBR remains poor, CBR ≈ R since costs ≈ R3. Before thinking of how costs might be reduced, and be that at the expense of measuring accuracy, the reasonableness of the 0.62 mT is considered.
Leaving aside a potential influence of the strength of the driving force on the flow structure, one remains with measuring resolution. Ultrasonic Doppler velocimetry was qualified to resolve
velocity differences of a mm/s and below at the HZDR in numerous investigations. So one needs to know which velocities will be reached for the 0.62 mT. To that, Alfvén's velocity
ua may be used to estimate the actual velocities. Under the assumption of equal magnetic and kinetic energy densities, solving for the velocity yields
ua = B / √(μρ), where B is the absolute value of the magnetic induction, μ the permeability, and ρ the density. Insertion of B
gives ua = 6.91 mm/s. As a rule of thumb, some ten percent of ua are reached in liquid metal MHD. There is no frequency f in the
equation. As is well known, characteristic velocities depend on f, they can be safely expected to be maximum below S = 200. At which S the velocities are
maximum is discussed controversially in the literature, it will be a result of the physical flow modelling in SIKELOR. Given all these uncertainties and estimates, the answer to the question
whether the flow can be measured can be only given by an experiment. One of the many results obtained so far is shown in Fig. 4.
Fig. 4: Contour plot of the time series over the height of the vertical velocity component uz at a shielding parameter S = 200. The measurements were taken in the centre of the container. Following the convention of the ultrasonic measuring device, which reports a positive velocity if the movement is directed away from the sensor, the red regions are those of a downstream and the fluid rises in the blue regions since the transducer was put at the melt surface so that the direction of the ultrasonic beam was downwards.
The measurement to Fig. 4 were intentionally not taken in a region where the highest velocity is to be expected. As the flow driven by an AMF is a recirculation with the driving force restricted to regions (i) at the rim/side wall and, (ii) at the top and at the bottom of the fluid volume (c.f. ), the more the higher S—and S = 200 is quite high, the highest velocity is consequently to be expected within kind of jets in those regions. A maximum absolute value of the velocity along the centre line of about 2 mm/s is thus in good agreement with the estimation based on Alfvén's velocity.
From the point of view of fluid flow the observed convective pattern is interesting. If the well-believed symmetric mean flow of two vortices one on top of another would have been observed, the plot should be symmetric in the vertical direction with respect to the horizontal centre plane (half the height of the container). Here, the upper vortex is much smaller, and the maximum velocity is about five times less compared to the lower vortex. Such asymmetry has never been reported in the literature before.
It is seen in particular from the temporal behaviour in the upper vortex that the flow is not stationary. With some allowance, the higher velocity of 2 mm/s in the lower vortex is considered
as the characteristic velocity uc. It is somewhere in between the velocity in the upper vortex and that at the rim. With that, the Reynolds number
Re = ucR/ν, where ν is the kinematic viscosity of 3.4·10-7 m2/s, calculates as 530. A flow at such a low
Reynolds number may not be considered turbulent. However, a glance at the lower part of Fig. 4 suggest, as good as it might be seen by the eye and by intention, that there are low frequency
oscillations with a period in the order of 10 seconds. Such oscillations were previously reported in [25–29]. The period of the oscillations was of the same order as observed here. In the
first of this series of publications from the same principal authors spanning a decade, it is stated that the low frequency oscillations are not what has to be considered as turbulence. This
statement was made for flows at quite high Reynolds numbers orders of magnitude above those considered here, i.e. those flows exhibit anyway developed turbulence. The striking result of the first
preliminary measurements in SIKELOR is that the low frequency oscillations occur at such low fluid velocities for which a flow is usually considered laminar.
It suggests itself from the temporal behaviour of the upper vortex that there are even oscillations at longer periods, say an order of magnitude above. These extremely slow oscillations were not observed in [25–29]. There, the low frequency oscillations were ascribed to oscillations of the mean flow eddies. What the authors meant by that becomes obvious from Fig. 5, which is reproduced here from one of their publications. The green arrows pointing radially inwards are drawn into the original figure to symbolise that, for whatever deformation of the mean flow eddies, the basic convective pattern of two vortices one on top of another with a common inwards directed flow between them is conserved. The preliminary measurements in SIKELOR show that this is, at least on the very long time scale, not always true. At the instances in time of around 270 s, between 500 and 550 s, between 830 and 900 s, and around 1050 s, the velocity in the upper part changes sign and becomes positive as in the lower part. This may mean that there might be only one eddy in the container spanning the full height from the bottom to the top. Attention is drawn to the fact that up to now only one velocity component uz along the vertical centre line is discussed. A minimum additional measurement to make a serious attempt describing the flow structure is that of uz along the side-wall close to the rim. Anyway, the extremely slow oscillations with a global modification of the flow structure exhibiting a unique sign of uz along the entire height is then then third observation having never been reported in the literature before.
Fig. 5: Sketch of the low frequency oscillations of the mean flow eddies in an AMF-driven flow. The figure is reproduced here from .
With respect to measuring resolution, it can be said that this S of 200, which would be the maximum reachable in MULTIMAG with that size of the container, can be satisfactorily measured.
The situation will improve when moving the measuring position to the rim since the velocity should be higher there. Considering that the characteristic velocity may decrease when increasing
S, there will be certainly reserve to do this via the container size. Whether this can be done in the first setup beyond what would be possible in MULTIMAG will be discussed below, first
the flow at the rim is inspected.
Fig. 6: Contour plot of the time series over the height of the vertical velocity component uz at a shielding parameter S = 200. The measurements were taken close to the rim of the container. Note that, as in Fig. 4, positive velocity values represent regions of downstream.
If the global convective pattern were the well-believed double torus, what should be expected for the flow at the rim given the measurement in the centre in Fig. 4? In that figure, a small upstream region in, say, the top quarter of the height and a downstream region over the remainder of three quarters of the height below may be regarded as the mean/average flow structure. This would conform to the double torus. Heavily deformed, but even so. Consequently, at the rim one would expect the opposite; a downstream at the top and an upstream below. Figure 6 shows indeed a downstream region at the top, albeit it is quite small. Comparison of Fig.'s 4 and 6 shows that the duration of measurement was significantly longer in Fig. 6. And, indeed, some remarkable effect announces at around 900 s and becomes pronounced between 1100 and 1300 s and then once more between 1400 and 1600 s. Closer examination shows that it first appears, less long, at around 200 s. An attempt of explanation of this phenomenon will be given towards the end of this section, for the time being these four time periods are ignored.
Below this very short downstream region, an extended upstream region over most of the height of the container is to be seen in Fig. 6. If it permanently would extend up to the bottom, this would be the double torus; although, with the upper vortex even more deformed and smaller at the rim as it is the case in the centre. So, with some limited discretion, one might say that the formerly excluded regions are the normal case. This is however not so, most of the time there is again an upstream region at the bottom extending to about one third of the height. Figure 7 sketches a potential flow structure consonant with the measurements in Fig.'s 4 and 6; it is for the case of three vortices one on top of another at the rim persisting most of the time.
Fig. 7: Freehand sketch of a potential flow structure at S = 200 for certain instances in time according to the contour plots in Fig.'s 4 and 6. The figure shows a section through the left part of the fluid volume, the dash-dotted line to the right is the vertical centre line.The meaning of the coloured arrows is explained in the narrative.
In this freehand sketch, it was first drawn what is known from the measurements in the centre and at the rim. These are the upstream and downstream regions in blue and red, respectively, graphed
with solid lines. Blue and red arrows indicate the direction of motion of the melt. Then, since the flow is recirculating, i.e. the streamlines have to be closed, the most simple connection
between the known
parts are sketched with dashed lines. In agreement with the well-believed double torus, the flow at the melt surface is from the centre to the rim. This is indicated with the yellow arrow. With reference to Fig. 5, the common inwards directed flow between the upper and the lower torus is pointed out by
the green arrow. Because, in a manner of speaking, the upper vortex is heavily squeezed towards the surface, there is space below the lower one for a third vortex. It is an annular one since it does not penetrate the container up to the centre.
Besides that the four regions are excluded, the mean flow eddies are significantly deformed, and there is not such pronounced elongation and contraction of the mean flow eddies as suggested in
 (c.f. Fig. 5), the annular vortex at the bottom is the fourth finding in the preliminary measurements in SIKELOR conducted in the first simple setup which has never been reported in the
literature. At this stage, the flow structure as it was measured can be reported. Any attempt of explanation why the melt moved in that way it did has, inescapably, more or less the
character of speculation. From what is discussed so far, two observations are what might be termed actually striking:
It is now returned to the issue that the four time-periods, during which the annular bottom vortex disappears, have been excluded from the consideration of the mean flow structure in Fig. 7
above. Although the uppermost vortex is rather flat, in particular at the side-wall, the convective pattern is basically a double torus during these periods. Each of the two flow states, the
deformed double torus as well as the three vortices one on top of another, carries a particular energy. The energy minimum principle, in general, ensures that a system realises the state of
lowest energy. If, as it might be the case for the two differing flow structures, the energy contents is comparable, the system may switch between both states. Such mode switching is observed in
various branches within physics. The plot of the integral vertical kinetic energy along the measuring direction of the ultrasonic beam at the rim in Fig. 8 shows a distinct correlation with the
flow structure. Except in the spin-up phase from the rest state, the kinetic energy seems to be higher in the double toroidal flow.
Fig. 8: Representative of the kinetic energy calculated as the sum of uz2 over all gates at the rim. To assess a potential correlation between the kinietic energy and the flow structure, the contour plot from Fig. 6 is underlaid semi-transparently.
The 9.15 amps at which the measurements presented up to now have been done are reachable at significantly higher frequencies. The maximum frequency is amply 5 kHz. A measurement at 5 kHz with the 180 mm in diameter container corresponds to S = 1044. Figure 9 shows the contour plot from a measurement at the rim.
Fig. 9: Contour plot of the time series over the height of the vertical velocity component uz at a shielding parameter S = 1044. The measurements were taken close to the rim of the container. Note that, as in Fig.'s 4 and 5, positive velocity values represent regions of downstream.
For that quite high S = 1044, which comes close to the parameter range of Demonstrator II, the flow structure does not basically change from that at S = 200. The annular bottom vortex seems less pronounced, however, this might also be due to the noisy measurement. As expected, the velocity has decreased significantly from S = 200 towards S = 1044. A comparison with Fig. 4 suggests that it is not the lower velocity in first place having impaired the measurement. More likely, although the sensor is based on emitting and receiving sound, it was electromagnetic interference (EMI) of the high frequency magnetic field which has coupled into the cable between the ultrasonic transducer and the data station. As of to date no measures have been taken against EMI, it may be reasonably expected that the noise can be reduced in the future.
It can be summarised for the first experimental setup composed from hardware having been available at the HZDR that reasonable measurements in AMF-driven flows can be conducted. More than
expected, interesting results have been found in the first tests that were initially only planned to investigate the feasibility of the assembled facility. The fluid velocities were in the
expected low range being prescribed by the limitations of the power supply. Despite of that, from the results it becomes obvious that one is not concerned with a boring laminar or even creeping
flow. Although the flow is not turbulent in the classical sense, it exhibits a plenty of phenomena being important for the design of Demonstrator II. It is planned to improve the setup and
continue the measurements in this facility even when the second setup described in the next section will be available. Due to high costs, the second setup will be limited in container size,
whereas relatively large ones fit in the first setup. Both facilities will be complementary to a certain extent.
The first measure to improve the first setup will be solving the EMI problems. Secondly, up to now no resonance circuits were used. It can be reasonably expected that a current approaching the maximum of 20 Aeff will be reached for shielding parameters exceeding 2000. Although it will not be a simple task, in particular not in combination with resonance circuits, two power amplifiers will be used feeding respectively one of the coils. As the characteristic velocity increases linearly with the strength of the magnetic field, finally four times higher fluid velocities are aimed at in the first setup.
The main limitation of the first experimental hardware is the limited fluid velocity accomplishable therein. It is discussed in detail in the previous section that increasing the field strength is compromised by a variety of factors and their relations. Just to repeat one of them, a high-current solution as implemented in industrial induction heating facilities would not allow to vary the frequency. Because the investigation of the dependence of the flow structure on S is the main task formulation in the workpackage on flow modelling, a widely variable frequency was the main design issue from the very beginning.
Since S depends on both frequency and dimension of the fluid container, the frequency range or better to say the maximum frequency fmax of the power supply to be
developed depends, firstly, on the size of the fluid volume. fmax depends however on a variety of other factors. For instance, an electric current of 1 A up to 500 kHz
is affordable, whereas a power supply capable of 50 A up to 10 kHz would cost a multitude of the first one. Thirdly, fmax depends on the inductance L of the coil.
L in turn depends on the number of windings n, which n influences the field strength accomplishable with a given current and the necessary output voltage of the power
To get started with solving all these compromises, those parameters have to be identified with should be fixed first. A high S in the range as it will be in Demonstrator II is mandatory.
Since the electric power increases with the volume to be magnetised, in third power with the linear dimension, the fluid container should be made as small as the limitations with respect to
realisable frequencies allows. On the other hand, the project work demands that Demonstrators, and this should continue to be true also for physical modelling, is done on a reasonable scale. The
fluid container of 180 mm in inner diameter is in the order of G1 size, which was then initially regarded as a reasonable scale. With this decision, the size of the coil is also fixed; it
has to be the minimum larger so as to fit the measuring technique in between the outside of the container and the inner side of the coil. Since block casting of silicon is done in rectangular
crucibles, the decision was taken to build a quadratic coil. Besides the generic cylindrical fluid container presented in the previous section, a rectangular one is already built and ready to
The most serious compromises remaining are those between number of turns and electric current, and between number of turns and frequency. To solve these compromises, a somewhat praghmatic
decision was taken. The project partner EAAT has recently developed and established a technique for variable frequency power supplies based on affordabel IGBT technology, which works up to 16 kHz
and is easily scalable with respect to the maximum power rating. This frequency corresponds to S = 3380 in the 180 mm container. As this is significantly above above the 1643 estimated
for Demonstrator II in the previous section, the 16 kHz were decided to be the maximum frequency for another reason. Experiments should also be possible with smaller containers to save on effort
if, e.g., variation of the geometry (aspect ratio) is the subject of research.
Having fixed also the frequency, there seems only to be the compromise between number of turns and current left. In fact, it is not a compromise for the frequency chosen since the limiting factor is, again as in the previous section on the first setup, the maximum output voltage of the power supply. The 340 V are due to an affordable technical standard. Once affordable power IGBT transistors having been selected, the maximum number of turns is determined by the 340 V. The best cost-benefit ratio offered by 60 A modules therefore determine that the optimum coil has to have 12 turns.
The field strength achievable with these parameters calculates readily as 3 mT. Although this is significantly more than what can be reached with the first setup, it seems a little bit few
with respect to the velocities to be expected. The maximum achievable field strength was then a mere matter of financial effort. Finally, a two-channel system operating synchronously was built.
Thanks go to the Institute of Fluid Mechanics at the HZDR for covering the costs of 55,000 € that allow producing an AMF of 6 mT variable in frequency up to values exceeding by far the
mandatory S of Demonstrator II. Fig. 10 show a photo of the coil system, the parameters of which are described in more detail in the caption.
Fig. 10: Coil system of the second experimental hardware. It consists of two coils wound one into another in a bifilar manner. Because of the relatively high frequencies, litz wire was used for the conductor. A comparably large cross-section was chosen to allow permanent operation at maximum current rating without external cooling. The number of turns per coil is 12. The free space between a quadratic container with a side-length of 180 mm and a wall thickness of 10 mm is 50 mm.
Finally, in the last Figure 11 the power supply developed and built by the project partner EAAT is to be seen. It was shipped to the HZDR in early february. First tests have shown that it works out of specification even up to frequencies of 20 kHz. The current decreases to about 2 × 40 amps permanent operation at the highest frequency possible. Depending on the flow rate of the water cooling, the maximum current is possible for frequencies above 16 kHz for longer periods. After building the mechanical construction and support, the second experimental hardware for flow modelling in a high frequency alternating magnetic field will be available in march 2015.
Fig. 11: 2 × 60 Aeff power supply developed by EAAT. The two channels can be operated independently and allow synchronous operation even if the inductance of the load differs.
|||J. Pal, A. Cramer, Th. Gundrum, G. Gerbeth: "A MULTIpurpose MAGnetic system for physical modelling in magnetohydrodynamic". Flow Meas. Instrum. 20 (2009) 241–251|
|||A. Cramer, C. Zhang, S. Eckert: "Local flow structures in liquid metals measured by ultrasonic Doppler velocimetry". Flow Meas. Instrum. [Special issue, M.L. Sanderson (Ed.): Ultrasonic flowmetering] 15:3 (2004) 145–153|
|||A. Cramer, K. Varshney, Th. Gundrum, G. Gerbeth: "Experimental study on the sensitivity and accuracy of electric potential local flow measurements". Flow Meas. Instrum. 17 (2005) 1–11|
|||J. Stiller, K. Fraňa, A. Cramer: "Transitional and weakly turbulent flow in a rotating magnetic field." Phys. Fluids 18 (2006) 74105|
|||A. Cramer, J. Pal, G. Gerbeth: "Experimental investigation of a flow driven by a combination of a rotating and a traveling magnetic field". Phys. Fluids 19:11 (2007) 118109|
|||A. Cramer, J. Pal, G. Gerbeth: "Electromagnetic stirring with superimposed travelling and rotating magnetic fields". Przegląd Elektrotechniczny 84:11 (2008) 144–148, ISSN 0033-2097|
|||X. Zhang, A. Cramer, A. Lange, G. Gerbeth: "Model experiments on macroscopic thermoelectromagnetic convection". Magnetohydrodynamics 45:1 (2009) 25–42|
|[8[||A. Cramer, X. Zhang, G. Gerbeth: "Macroscopic thermomagnetic convection: A more generic case and optimization". Magnetohydrodynamics 45:4 (2009) 505–510|
|||A. Cramer, X. Zhang, G. Gerbeth: "Thermoelectromagnetic stirring in metallurgy". Proc. 54th IWK Internationales Wissenschaftliches Kolloqium, invited lecture, Ilmenau, Germany (2009)|
|||A. Cramer, M. Röder, J. Pal, G. Gerbeth: "A physical model for electromagnetic control of local temperature gradients in a Czochralski system". Magnetohydrodynamics 46:4 (2010) 353–361|
|||A. Cramer, J. Pal, K. Koal, S. Tschisgale, J. Stiller, G. Gerbeth: "The sensitivity of a travelling magnetic field driven flow to axial alignment". J. Cryst. Growth 321 (2011) 142–150|
|||A. Cramer, J. Pal, G. Gerbeth: "Turbulence measurements in a rotating magnetic field driven flow". Phys. Fluids 24 (2012) 045105|
|||A. Cramer, S. Eckert, G. Gerbeth: "Flow measurements in liquid metals by means of the ultrasonic Doppler method and local potential probes". Eur. Phys. J.-Spec. Top. 220 (2013) 25–41|
|||J. Stiller, K. Koal, W. Nagel, J. Pal, A. Cramer: "Liquid metal flows driven by rotating and travelling magnetic fields". Eur. Phys. J.-Spec. Top. 220 (2013) 111–122|
|||A. Cramer, J. Pal, G. Gerbeth: "Model experiments for the Czochralski crystal growth technique". Eur. Phys. J.-Spec. Top. 220 (2013) 259–273|
|||A. Cramer, J. Pal, G. Gerbeth: "Ultrasonic flow measurements in a model of a Czochralsi puller". Flow Meas. Instrum. 37 (2014) 99–106|
|||J. Pal, A. Cramer, G. Gerbeth: "Experimental investigation on the electromagnetically controlled buoyancy-induced flow in a model of a Czochralski puller". Int. J. Appl. Electrom. 44 (2014) 163–170|
|||A. Cramer, K. Varshney, G. Gerbeth: "Investigation of the fluid flow driven by a pulsating magnetic field with ultrasound Doppler velocimetry". In S. Lupi, F. Dughiero (Eds.): Proc. Int. Symposium on Heating by Electromagnetic Sources, S.G.E. Publishing, Padua, Italy (2004) 413–420|
|||M. Kadkhodabeigi, J Safarian, H. Tveit, M. Tangstad, S.T. Johansen: "Removal of SiC particles from solar grade silicon melts by imposition of high frequency magnetic field". Trans. Nonferrous Met. Soc. China 22 (2012) 2813–2821|
|||K. Takahashi, S. Taniguchi: "Electromagnetic separation of nonmetallic inclusion from liquid metal by imposition of high frequency magnetic field". ISIJ Int. 43 (2003) 820–827|
|||S. Makarov, R. Ludwig, D. Apelian: "Electromagnetic separation techniques in metal casting. I. Conventional methods. IEEE T. Magn. 36:4 (2000) 2015–2021|
Rohrer Mess- & Systemtechnik, München, Germany.
Keysight Technologies, Santa Rosa, CA, USA
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||E. Baake, B. Nacke, A. Jakovičs, A. Umbrasko: "Heat and mass transfer in turbulent flows with several recirculated flow eddies". Magnetohydrodynamics 37:1-2 (2001) 13–22|
||E. Baake, B. Nacke, A. Umbrasko, A. Jakovičs: " Large eddy simulation modeling of heat and mass transfer in turbulent recirculated flows". Magnetohydrodynamics 39:3 (2003) 291–297|
||A. Umbrashko, E. Baake, B. Nacke, A. Jakovičs: "Modeling of the turbulent flow in induction furnaces". Metall. Mater. Trans. B 37 (2006) 831–838|
||A. Kirpo, A. Jakovičs, E. Baake, B. Nacke: "Analysis of experimental and simulation data for liquid metal flow in a cylindrical vessel". Magnetohydrodynamics 43:2 (2007) 161–172|
||M. Ščepanskis, A. Jakovičs, E. Baake, B. Nacke: "Analysis of the oscillating behaviour of solid inclusions in the induction crucible furnace". Magnetohydrodynamics 48:4 (2012) 677–686|