- Email: [email protected]
Application of AC and DC magnetic field for surface wave excitation to enhance mass transfer
Journal Pre-proofs Application of AC and DC magnetic field for surface wave excitation to enhance mass transfer Mikus Milgrāvis, Andris Bojarevičs, Antra Gaile, Vadims Geža PII: DOI: Reference:
S0022-0248(19)30624-4 https://doi.org/10.1016/j.jcrysgro.2019.125409 CRYS 125409
To appear in:
Journal of Crystal Growth
Received Date: Revised Date: Accepted Date:
15 October 2019 30 November 2019 5 December 2019
Please cite this article as: M. Milgrāvis, A. Bojarevičs, A. Gaile, V. Geža, Application of AC and DC magnetic field for surface wave excitation to enhance mass transfer, Journal of Crystal Growth (2019), doi: https://doi.org/ 10.1016/j.jcrysgro.2019.125409
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Application of AC and DC magnetic field for surface wave excitation to enhance mass transfer Mikus Milgrvis∗, Andris Bojarevis∗, Antra Gaile∗, Vadims Gea∗ University of Latvia, Jelgavas iela 3, Riga, Latvia, LV-1004
Abstract Refining the metallic melts and removal of contaminants from the free surface may be sped up by increasing the surface area of mass exchange interface. It is relevant to both the case of volatile impurity evaporation in a vacuum as well as the case of chemical reactions when the continuous crust of reaction products should be interrupted. Previously proposed low-frequency AC magnetic field excitation of intense surface waves is limited by skin-effect. The induced signalternating forcing at high dimensionless frequency values becomes dominantly pulsing at considerably higher than unity values, delivering time-averaged stirring without intense surface waves. Superimposing DC magnetic field over AC one produces stronger alternating forcing with the frequency of the AC field. We are reporting an experimental setup which incorporates very high Amperewinding 50 Hz AC Bitter coil surrounded by a powerful permanent magnet system. Experiments demonstrating surface waves were done at room temperature with liquid Galinstan alloy in two crucibles, corresponding to the cases of relatively high and low skin-effect. In the following work proposed method will be tested in liquid silicon refining process from phosphorus and boron. Keywords: A1. Magnetic fields; A1. Induction; A1. Surface waves; A1. Refining; B1. Liquid metal;
1. Introduction Electromagnetically excited surface waves on the interface between liquid metal and other fluid have been extensively studied in SIMAP-EPM (Grenoble, France). The current work has been inspired by the long term collaboration with our French colleagues [1], [2]. In this study the aim is to develop a new technology to increase the efficiency of solar grade (SoG-Si) silicon refinement process. Mostly solar grade silicon is produced through Siemens process, but metallurgical route is a promising alternative with lower energy consumption, ∗ Corresponding
author Email address: [email protected] (Mikus Milgrvis)
Preprint submitted to ICCGE-19/OMVPE-19
December 7, 2019
yet many steps of the process should be improved. While most impurities are removed by a directional solidification process, to remove boron and phosphorus from silicon another treatment process is needed. In this study we are focusing on boron removal process, while phosphorus removal might be affected also. Reactive gas, such as hydrogen, is purged into the melting chamber to react with boron and to remove it. The challenge is to minimize energy consumption by minimizing heating time for boron removal. As boron removal process directly depends on the surface area of the melt, we propose to speed up the process by increasing the surface area of silicon with surface waves. In this work we present a laboratory scale experimental model for electromagnetically generated surface wave excitation on liquid metal surface. Melt in our physical model is chosen to be Galinstan instead of Silicon. Experimental system will be described using dimensionless parameters to later adapt the electromagnetic method for Silicon. It is known that gravity-capillary waves on a free surface can be achieved if the fluid is affected by alternating forcing, as described by W. Thomson [3]. For short waves when h · k >> 1 where h - depth of the liquid, k - wave number, formula (1) can be used, where ω - angular frequency, g - gravitational constant, α - surface tension and ρ - density: ω 2 = gk +
αk 3 ρ
(1)
By solving the equation for Silicon, the order of magnitude of typical wavelength at frequency of 10 - 50 Hz would be of 1 cm, thus fruiting potential to be used in the refining process. In general, if we consider liquid metal, the wavelength is highly affected by the oxide layer on the melt surface as it changes the surface tension. In this study we used Galinstan which is a liquid metal at room temperature. The surface tension of Galinstan varies in wide range from 0.3 to 0.7 N/m. Thus, if surface waves are generated by 50 Hz alternating force, the wavelength λ = 2Π k varies in range from 5 to 7 mm, see Figure 1.
Figure 1: Wavelength of surface waves on liquid Galinstan surface created by 50 Hz alternating forcing in respect to surface tension
2
If a crucible with liquid metal is exposed to alternating magnetic field (henceforth AC field), eddy currents in the melt are generated. Eddy currents interact with the applied magnetic field, thus generating alternating force that excites waves on the free surface. Both Lorentz force distribution and the induced flow depends from AC field frequency and the geometry of the system. Skin-effect impact on the system can be described by dimensionless frequency Ωd = 2R2 /δ 2 or Ωd = σωµ0 R2 , where δ - skin-depth, σ - electrical conductivity of the melt, ω - the angular frequency of the AC field, µ0 magnetic permeability and R the radial dimension of the liquid metal region [4]. By increasing AC field frequency the electromagnetic forcing of the melt becomes more and more of pulsing type, delivering force that is dominantly directed inwards. While dimensionless frequency Ωd ≤ 1, the time averaged force comparing to force amplitude is relatively small. The time averaged component of electromagnetic force becomes dominant when Ωd > 1, delivering strongly pronounced liquid metal time averaged flow, but no surface waves. The electromagnetic force on the side surface of an axially symmetric liquid metal region is illustrated on left in Figure 2, according to an analytical solution of J. Krumins [5].
Figure 2: Force in the metal volume created by AC magnetic field (left) and force in the case of combined AC and DC magnetic fields (right)
As experiments in SIMAP-EPM has shown, by using high AC field amplitude and increasing the dimensionless frequency, liquid metal flows lead to surface deformations which are too intense to obtain surface waves. In our study we obtain a similar effect by increasing the dimensionless frequency by changing crucibles instead of frequency. In this study we propose to use combination of alternating and static magnetic field (DC field) to obtain surface waves on melt surface even when Ωd > 1. 2. Presentation of the problem In this study we focus on surface wave generation with a typical power supply frequency 50-60 Hz, as it is proposed to use the technology in industry. To
3
deal with the disadvantages in case of high intensity flows and to reduce the consumed electrical power for wave generation we propose to add a static magnetic field created by permanent magnets. Galinstan can be used to model liquid Silicon because both its density and electrical conductivity is three times higher than Silicon, thus keeping the ratio between electromagnetic and inertial forces approximately the same for both materials. Galinstan alloy (Ga-In-Sn) density is 6440 kg/m3, conductivity 3.46·106 S/m, kinematic viscosity 3.1 · 10−7 m2 /s. To probe surface wave dependency from dimensionless frequency a crucible with diameter 52.6 mm was used to achieve low skin-effect situation Ωd = 0.94 and 96.6 mm crucible with dimensionless frequency Ωd = 3.19 to obtain regime where skin-effect affects the system. We assumed that alternating electromagnetically induced forcing may be achieved by superimposing DC magnetic field of higher magnitude than the AC field (BDC > BAC ). DC field has to be perpendicular to the induced currents, so an axial DC field is chosen, thus letting DC field be parallel AC field. AC field serves mainly as the inducer of the AC current in the liquid conductor, but forcing dominantly results from the interaction of the induced current and the DC field see on right in Figure 2. By using a combination of magnetic fields, the characteristic alternating force frequency is approximately two times lower because the magnetic field with the highest intensity is not changing the direction in time. By not taking into account viscous and capillary forces, the velocity U for wave generation in the crucible can be evaluated by following Navier-Stokes equation (2), [6]: ρUω + ρ
U2 = σ(ωδBAC − UBDC )(BAC + BDC ) δ
(2)
Figure 3: Flow velocity in the melt volume which is affected by alternating and static magnetic field
The right side of the equation (2) describes electromagnetic forces. BAC 4
stands for amplitude value. In the brackets the first part corresponds to the induced currents for flow generation, while the second part is the damping effect due to flows in a magnetic field. If the dimensionless frequency is above 1, the system should be described by using skin-depth value instead of using characteristic crucible radius R. By using static magnetic field, the induced flow velocity is greater than the flow damping effect, see Figure 3. If static magnetic field intensity is larger than 1 T, the damping force becomes more and more dominant and reduces the flow intensity. Even a slow flow with 5 cm/s is enough to stir the melt and obtain good mass transfer. Dimensionless parameters to predict the characteristic velocity are shown in table 1. formula 2 σ BDC N= ρ r ω σ Ha = Bδ r ρν δ Fr = ω g R A= h
explanation MHD interaction parameter Hartmann number Froude number
formula BAC BR = BDC Ωd = σωµ0 R2 Ca =
ρνωδ γ
explanation Ratio of magn. fields Dimensionless frequency Capillary number
Aspect ratio
Table 1: Main dimensionless parameters used in the evaluation of velocity
In our experimental system dimensionless frequency is chosen to show how strong skin-effect affects the system, while MHD interaction parameter N shows how system is affected by magnetic field (BDC > 0). Parameters A and Br are used to see how system geometry and magnetic field intensities affect the velocity and wave amplitude. Bond number similarly as Froude and Capillary number is used to measure the importance of gravitational forces compared to surface tension force - in the presented experiment both factors are important. By knowing the flow velocity the amplitude of waves can be evaluated, see Figure 4. Wavelength is not directly affected by magnetic field intensity, so the ratio between amplitude and wavelength increases by increasing field intensities. The schematic of the built experimental setup is shown in Figure 5. The whole setup is nearly axially symmetric. The crucible is located in the coil which is surrounded by a permanent magnet assembly. Experimental system is shown in Figure 6. AC field is produced by AC Bitter coil up to 50,000 Amper-windings may deliver up to 0.33 T AC field. The coil consists of 56 electric windings which are water-cooled from outer layer. DC field is produced by two radially magnetized Nd-Fe-B permanent magnet rings which create 0.428 T induction of an axial DC field on the axis. The concept of the permanent magnet system is based on Halbach array principle. Permanent magnet system consists of 192 permanent magnets which are set in ferromagnetic yoke. To avoid Joule heating of the magnets, the yoke is made
5
from eight 45 degree wide sectors and a layer of electric insulation between the magnets is used.
Figure 4: Wave amplitude and wavelength on the melt surface - with used assumptions only amplitude depends on applied field intensity
Figure 5: Scheme of experimental setup
Melt is located in the middle of the system so its free surface is where the intensity of both fields is the highest. Magnetic field is measured by Magnet-physics FH54 gauss meter. Measuring error for both AC and DC magnetic fields is below 1%, such error is neglected as magnetic field distribution from induction coil and permanent magnet system is not homogeneous, but it is not analyzed in this article. Experiments did not show significantly different wave pattern if the open surface of melt had been slightly offset from center. During experimental tests the free surface of the alloy was not free but covered by its oxide layer, resulting in unknown surface tension. To study wave pattern and formation we tried several measuring techniques. By taking high quality photos and processing them, wave-length was quantified. Full wave tracking was recorded with 960 fps camera. To avoid blur pictures and videos and reduce the error for wave-length detection short 1/4000 s exposure time is used. We were unsuccessful in measuring wave amplitude by a laser 6
distance sensor due to rapidly changing beam reflection angle. Thus, it was proposed to detect the amplitude by observing the dynamic of a laser beam reflection on a screen. In tests for the same field intensity we saw that reflection angle highly depends on the surface oxide layer. Oxide layer formation and how oxide layer affects light reflection cannot be easily predicted, so obtained results could give only magnitude estimation of wave amplitude.
Figure 6: Experimental setup - crucible is set in an induction coil which is surrounded by permanent magnet assembly
3. Results While affecting the liquid metal with AC field at Ωd = 0.94, concentric waves were observed (see Figure 7).
Figure 7: Surface wave structures dependency from magnetic field
At B = 25 mT the waves are similar over all of the diameter for both of the crucibles. When B = 35 mT in Ωd < 1 the waves are still concentric, but 7
for the Ωd > 1 a distinct meniscus has started to form, some surface waves are still visible on it. Judging from the contrast of the photo, the amplitude of the waves increases when AC field is increasing, but wavelength slowly decreases from 5 ± 0.5 mm to range of 2 ± 0.2 to 3 ± 0.3 mm. For B = 70 mT and Ωd = 3.19 we observed weak surface waves disrupted by a strong, unstable and turbulent time averaged flow that grew more intense as AC field amplitude was increased. Meniscus increased from 5 mm at BA = 50 mT to 15 mm at B = 90 mT . If Ωd was below 1, meniscus was not observed! For Ωd = 3.19 we saw that the meniscus of the free surface has two distinct regions the central one that has a chaotic surface deformation and the one on the perimeter where surface waves could be observed. We assumed the central meniscus to be a consequence of the time averaged meridional flow, but ultrasound Doppler anemometry measurements did not confirm this assumption. Measured flow intensity is too low to create such high surface deformation, thus inclining that another effect is not taken into account, also an increase in measured meniscus height does not correspond to an increase in measured velocity. As goes for the perimetral region, at low AC field values the surface waves are concentric, but as AC field value is increased they form curling structure around the edge of the crucible. Applying superimposed DC field at 0.146 T AC field magnitude resulted in a so strong free surface excitation that the liquid metal was splashed away as small droplets from the wave crests. We had to reduce drastically the AC magnetic field to perform the tests and we observed surface wave formation at significantly lower AC field values than in the case of only AC field excitation. First and foremost it can be seen that with AC and DC superposition the nonlinear waves are more intense even at lower AC field values (see Figure 8).
Figure 8: Surface wave structures dependency from magnetic field with superposition of AC/DC magnetic field
Similar wave intensity was obtained with 4 times lower AC field intensity, so energy saving in AC coil was up to 16 times. For both Ωd = 3.19 and Ωd 8
below 1 formation of meniscus was not observed and no meridional flow could be measured in AC and DC superimposition case. Wavelength is longer than in the case of only AC field, it is in the range of 5 to 7 mm as evaluated analytically. Analysis of 960 fps video revealed that the waves travels inward to the crucible center. The dominant frequency was roughly 4 times of the forcing frequency, both in the case of purely AC interaction and in case of superimposed AC/DC impact case, also other harmonics, such as f, 2f and 3f were observed. We have attempted laser measurements of the wave amplitudes, but the results are rather unsatisfying, amplitude of only 0.3 ± 0.1 mm at B = 20 mT , and 0.6 ± 0.2 mm at B = 40 mT seems contradicting to what we see. By using AC field only, the intense flows and meniscus were formed due to time average force which is directed to the system center. The meniscus in the center limits the surface wave traveling area, because waves can not travel up on the meniscus. By adding static magnetic field time average force comparing to only AC field impact is excluded, the meniscus is not formed and waves can travel all over the surface. The main factor in surface wave generation is alternating force amplitude - by adding static magnetic field it significantly increases (BDC > BAC ). 4. Conclusions An experimental study of liquid metal surface waves enhanced by AC magnetic field showed that wave amplitude is limited by intense liquid metal turbulent flow when the dimensionless frequency is above 1. By applying static magnetic field, the flow is partly damped and non-linear waves are obtained all over the surface - wave pattern is similar in both cases when dimensionless frequency is below and above 1. By applying DC field to the system, current in induction coil can be reduced 4 times to obtain similar wave intensity - energy consumption for AC field is reduced by 16 times! Acknowledgements The research is part of ERAF project: Refinement of metallurgical grade silicon using smart refinement technologies. Project number: Nr.1.1.1.1/16/A/097 [1] F. Debray, Y. Fautrelle, F. Dalard, Measurement of mass transfer across a moving mercury-electrolyte interface by an electrochemical method, Experiments in Fluids 19 (5) (1995) 353–358. doi:10.1007/BF00203422. [2] B. Saadi, A. Bojarevis, Y. Fautrelle, J. Etay, Contrle lectromagntique du transfert de masse aux interfaces liquides-liquides, Rcents Progrs en Gnie des Procd 92. [3] W. Thomson, 2. on the motion of free solids through a liquid, Proceedings of the Royal Society of Edinburgh 7 (1872) 384–390. doi:10.1017/ S037016460004222X. [4] H. K. Moffatt, Electromagnetic stirring, Physics in Fluids 3 (5) (1991) 1336– 1343. 9
[5] J. Krmi, Travelling magnetic field interaction with conducting media, Zintne (1969) 258–262. [6] A. Bojarevics, A. Cramer, Y. Gelfgat, G. Gerbeth, Experiments on the magnetic damping of an inductively stirred liquid metal flow, Experiments in Fluids 40 (2006) 257–266.
10
Highlights
Electromagnetically excited surface waves on the liquid metal Combined magnetic fields create surface waves when skin-effect has significant By applying static magnetic field alternating field can be 4 times lower Static magnetic field damps intense liquid metal flows and surface deformation
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0022-0248(19)30624-4 https://doi.org/10.1016/j.jcrysgro.2019.125409 CRYS 125409
To appear in:
Journal of Crystal Growth
Received Date: Revised Date: Accepted Date:
15 October 2019 30 November 2019 5 December 2019
Please cite this article as: M. Milgrāvis, A. Bojarevičs, A. Gaile, V. Geža, Application of AC and DC magnetic field for surface wave excitation to enhance mass transfer, Journal of Crystal Growth (2019), doi: https://doi.org/ 10.1016/j.jcrysgro.2019.125409
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Application of AC and DC magnetic field for surface wave excitation to enhance mass transfer Mikus Milgrvis∗, Andris Bojarevis∗, Antra Gaile∗, Vadims Gea∗ University of Latvia, Jelgavas iela 3, Riga, Latvia, LV-1004
Abstract Refining the metallic melts and removal of contaminants from the free surface may be sped up by increasing the surface area of mass exchange interface. It is relevant to both the case of volatile impurity evaporation in a vacuum as well as the case of chemical reactions when the continuous crust of reaction products should be interrupted. Previously proposed low-frequency AC magnetic field excitation of intense surface waves is limited by skin-effect. The induced signalternating forcing at high dimensionless frequency values becomes dominantly pulsing at considerably higher than unity values, delivering time-averaged stirring without intense surface waves. Superimposing DC magnetic field over AC one produces stronger alternating forcing with the frequency of the AC field. We are reporting an experimental setup which incorporates very high Amperewinding 50 Hz AC Bitter coil surrounded by a powerful permanent magnet system. Experiments demonstrating surface waves were done at room temperature with liquid Galinstan alloy in two crucibles, corresponding to the cases of relatively high and low skin-effect. In the following work proposed method will be tested in liquid silicon refining process from phosphorus and boron. Keywords: A1. Magnetic fields; A1. Induction; A1. Surface waves; A1. Refining; B1. Liquid metal;
1. Introduction Electromagnetically excited surface waves on the interface between liquid metal and other fluid have been extensively studied in SIMAP-EPM (Grenoble, France). The current work has been inspired by the long term collaboration with our French colleagues [1], [2]. In this study the aim is to develop a new technology to increase the efficiency of solar grade (SoG-Si) silicon refinement process. Mostly solar grade silicon is produced through Siemens process, but metallurgical route is a promising alternative with lower energy consumption, ∗ Corresponding
author Email address: [email protected] (Mikus Milgrvis)
Preprint submitted to ICCGE-19/OMVPE-19
December 7, 2019
yet many steps of the process should be improved. While most impurities are removed by a directional solidification process, to remove boron and phosphorus from silicon another treatment process is needed. In this study we are focusing on boron removal process, while phosphorus removal might be affected also. Reactive gas, such as hydrogen, is purged into the melting chamber to react with boron and to remove it. The challenge is to minimize energy consumption by minimizing heating time for boron removal. As boron removal process directly depends on the surface area of the melt, we propose to speed up the process by increasing the surface area of silicon with surface waves. In this work we present a laboratory scale experimental model for electromagnetically generated surface wave excitation on liquid metal surface. Melt in our physical model is chosen to be Galinstan instead of Silicon. Experimental system will be described using dimensionless parameters to later adapt the electromagnetic method for Silicon. It is known that gravity-capillary waves on a free surface can be achieved if the fluid is affected by alternating forcing, as described by W. Thomson [3]. For short waves when h · k >> 1 where h - depth of the liquid, k - wave number, formula (1) can be used, where ω - angular frequency, g - gravitational constant, α - surface tension and ρ - density: ω 2 = gk +
αk 3 ρ
(1)
By solving the equation for Silicon, the order of magnitude of typical wavelength at frequency of 10 - 50 Hz would be of 1 cm, thus fruiting potential to be used in the refining process. In general, if we consider liquid metal, the wavelength is highly affected by the oxide layer on the melt surface as it changes the surface tension. In this study we used Galinstan which is a liquid metal at room temperature. The surface tension of Galinstan varies in wide range from 0.3 to 0.7 N/m. Thus, if surface waves are generated by 50 Hz alternating force, the wavelength λ = 2Π k varies in range from 5 to 7 mm, see Figure 1.
Figure 1: Wavelength of surface waves on liquid Galinstan surface created by 50 Hz alternating forcing in respect to surface tension
2
If a crucible with liquid metal is exposed to alternating magnetic field (henceforth AC field), eddy currents in the melt are generated. Eddy currents interact with the applied magnetic field, thus generating alternating force that excites waves on the free surface. Both Lorentz force distribution and the induced flow depends from AC field frequency and the geometry of the system. Skin-effect impact on the system can be described by dimensionless frequency Ωd = 2R2 /δ 2 or Ωd = σωµ0 R2 , where δ - skin-depth, σ - electrical conductivity of the melt, ω - the angular frequency of the AC field, µ0 magnetic permeability and R the radial dimension of the liquid metal region [4]. By increasing AC field frequency the electromagnetic forcing of the melt becomes more and more of pulsing type, delivering force that is dominantly directed inwards. While dimensionless frequency Ωd ≤ 1, the time averaged force comparing to force amplitude is relatively small. The time averaged component of electromagnetic force becomes dominant when Ωd > 1, delivering strongly pronounced liquid metal time averaged flow, but no surface waves. The electromagnetic force on the side surface of an axially symmetric liquid metal region is illustrated on left in Figure 2, according to an analytical solution of J. Krumins [5].
Figure 2: Force in the metal volume created by AC magnetic field (left) and force in the case of combined AC and DC magnetic fields (right)
As experiments in SIMAP-EPM has shown, by using high AC field amplitude and increasing the dimensionless frequency, liquid metal flows lead to surface deformations which are too intense to obtain surface waves. In our study we obtain a similar effect by increasing the dimensionless frequency by changing crucibles instead of frequency. In this study we propose to use combination of alternating and static magnetic field (DC field) to obtain surface waves on melt surface even when Ωd > 1. 2. Presentation of the problem In this study we focus on surface wave generation with a typical power supply frequency 50-60 Hz, as it is proposed to use the technology in industry. To
3
deal with the disadvantages in case of high intensity flows and to reduce the consumed electrical power for wave generation we propose to add a static magnetic field created by permanent magnets. Galinstan can be used to model liquid Silicon because both its density and electrical conductivity is three times higher than Silicon, thus keeping the ratio between electromagnetic and inertial forces approximately the same for both materials. Galinstan alloy (Ga-In-Sn) density is 6440 kg/m3, conductivity 3.46·106 S/m, kinematic viscosity 3.1 · 10−7 m2 /s. To probe surface wave dependency from dimensionless frequency a crucible with diameter 52.6 mm was used to achieve low skin-effect situation Ωd = 0.94 and 96.6 mm crucible with dimensionless frequency Ωd = 3.19 to obtain regime where skin-effect affects the system. We assumed that alternating electromagnetically induced forcing may be achieved by superimposing DC magnetic field of higher magnitude than the AC field (BDC > BAC ). DC field has to be perpendicular to the induced currents, so an axial DC field is chosen, thus letting DC field be parallel AC field. AC field serves mainly as the inducer of the AC current in the liquid conductor, but forcing dominantly results from the interaction of the induced current and the DC field see on right in Figure 2. By using a combination of magnetic fields, the characteristic alternating force frequency is approximately two times lower because the magnetic field with the highest intensity is not changing the direction in time. By not taking into account viscous and capillary forces, the velocity U for wave generation in the crucible can be evaluated by following Navier-Stokes equation (2), [6]: ρUω + ρ
U2 = σ(ωδBAC − UBDC )(BAC + BDC ) δ
(2)
Figure 3: Flow velocity in the melt volume which is affected by alternating and static magnetic field
The right side of the equation (2) describes electromagnetic forces. BAC 4
stands for amplitude value. In the brackets the first part corresponds to the induced currents for flow generation, while the second part is the damping effect due to flows in a magnetic field. If the dimensionless frequency is above 1, the system should be described by using skin-depth value instead of using characteristic crucible radius R. By using static magnetic field, the induced flow velocity is greater than the flow damping effect, see Figure 3. If static magnetic field intensity is larger than 1 T, the damping force becomes more and more dominant and reduces the flow intensity. Even a slow flow with 5 cm/s is enough to stir the melt and obtain good mass transfer. Dimensionless parameters to predict the characteristic velocity are shown in table 1. formula 2 σ BDC N= ρ r ω σ Ha = Bδ r ρν δ Fr = ω g R A= h
explanation MHD interaction parameter Hartmann number Froude number
formula BAC BR = BDC Ωd = σωµ0 R2 Ca =
ρνωδ γ
explanation Ratio of magn. fields Dimensionless frequency Capillary number
Aspect ratio
Table 1: Main dimensionless parameters used in the evaluation of velocity
In our experimental system dimensionless frequency is chosen to show how strong skin-effect affects the system, while MHD interaction parameter N shows how system is affected by magnetic field (BDC > 0). Parameters A and Br are used to see how system geometry and magnetic field intensities affect the velocity and wave amplitude. Bond number similarly as Froude and Capillary number is used to measure the importance of gravitational forces compared to surface tension force - in the presented experiment both factors are important. By knowing the flow velocity the amplitude of waves can be evaluated, see Figure 4. Wavelength is not directly affected by magnetic field intensity, so the ratio between amplitude and wavelength increases by increasing field intensities. The schematic of the built experimental setup is shown in Figure 5. The whole setup is nearly axially symmetric. The crucible is located in the coil which is surrounded by a permanent magnet assembly. Experimental system is shown in Figure 6. AC field is produced by AC Bitter coil up to 50,000 Amper-windings may deliver up to 0.33 T AC field. The coil consists of 56 electric windings which are water-cooled from outer layer. DC field is produced by two radially magnetized Nd-Fe-B permanent magnet rings which create 0.428 T induction of an axial DC field on the axis. The concept of the permanent magnet system is based on Halbach array principle. Permanent magnet system consists of 192 permanent magnets which are set in ferromagnetic yoke. To avoid Joule heating of the magnets, the yoke is made
5
from eight 45 degree wide sectors and a layer of electric insulation between the magnets is used.
Figure 4: Wave amplitude and wavelength on the melt surface - with used assumptions only amplitude depends on applied field intensity
Figure 5: Scheme of experimental setup
Melt is located in the middle of the system so its free surface is where the intensity of both fields is the highest. Magnetic field is measured by Magnet-physics FH54 gauss meter. Measuring error for both AC and DC magnetic fields is below 1%, such error is neglected as magnetic field distribution from induction coil and permanent magnet system is not homogeneous, but it is not analyzed in this article. Experiments did not show significantly different wave pattern if the open surface of melt had been slightly offset from center. During experimental tests the free surface of the alloy was not free but covered by its oxide layer, resulting in unknown surface tension. To study wave pattern and formation we tried several measuring techniques. By taking high quality photos and processing them, wave-length was quantified. Full wave tracking was recorded with 960 fps camera. To avoid blur pictures and videos and reduce the error for wave-length detection short 1/4000 s exposure time is used. We were unsuccessful in measuring wave amplitude by a laser 6
distance sensor due to rapidly changing beam reflection angle. Thus, it was proposed to detect the amplitude by observing the dynamic of a laser beam reflection on a screen. In tests for the same field intensity we saw that reflection angle highly depends on the surface oxide layer. Oxide layer formation and how oxide layer affects light reflection cannot be easily predicted, so obtained results could give only magnitude estimation of wave amplitude.
Figure 6: Experimental setup - crucible is set in an induction coil which is surrounded by permanent magnet assembly
3. Results While affecting the liquid metal with AC field at Ωd = 0.94, concentric waves were observed (see Figure 7).
Figure 7: Surface wave structures dependency from magnetic field
At B = 25 mT the waves are similar over all of the diameter for both of the crucibles. When B = 35 mT in Ωd < 1 the waves are still concentric, but 7
for the Ωd > 1 a distinct meniscus has started to form, some surface waves are still visible on it. Judging from the contrast of the photo, the amplitude of the waves increases when AC field is increasing, but wavelength slowly decreases from 5 ± 0.5 mm to range of 2 ± 0.2 to 3 ± 0.3 mm. For B = 70 mT and Ωd = 3.19 we observed weak surface waves disrupted by a strong, unstable and turbulent time averaged flow that grew more intense as AC field amplitude was increased. Meniscus increased from 5 mm at BA = 50 mT to 15 mm at B = 90 mT . If Ωd was below 1, meniscus was not observed! For Ωd = 3.19 we saw that the meniscus of the free surface has two distinct regions the central one that has a chaotic surface deformation and the one on the perimeter where surface waves could be observed. We assumed the central meniscus to be a consequence of the time averaged meridional flow, but ultrasound Doppler anemometry measurements did not confirm this assumption. Measured flow intensity is too low to create such high surface deformation, thus inclining that another effect is not taken into account, also an increase in measured meniscus height does not correspond to an increase in measured velocity. As goes for the perimetral region, at low AC field values the surface waves are concentric, but as AC field value is increased they form curling structure around the edge of the crucible. Applying superimposed DC field at 0.146 T AC field magnitude resulted in a so strong free surface excitation that the liquid metal was splashed away as small droplets from the wave crests. We had to reduce drastically the AC magnetic field to perform the tests and we observed surface wave formation at significantly lower AC field values than in the case of only AC field excitation. First and foremost it can be seen that with AC and DC superposition the nonlinear waves are more intense even at lower AC field values (see Figure 8).
Figure 8: Surface wave structures dependency from magnetic field with superposition of AC/DC magnetic field
Similar wave intensity was obtained with 4 times lower AC field intensity, so energy saving in AC coil was up to 16 times. For both Ωd = 3.19 and Ωd 8
below 1 formation of meniscus was not observed and no meridional flow could be measured in AC and DC superimposition case. Wavelength is longer than in the case of only AC field, it is in the range of 5 to 7 mm as evaluated analytically. Analysis of 960 fps video revealed that the waves travels inward to the crucible center. The dominant frequency was roughly 4 times of the forcing frequency, both in the case of purely AC interaction and in case of superimposed AC/DC impact case, also other harmonics, such as f, 2f and 3f were observed. We have attempted laser measurements of the wave amplitudes, but the results are rather unsatisfying, amplitude of only 0.3 ± 0.1 mm at B = 20 mT , and 0.6 ± 0.2 mm at B = 40 mT seems contradicting to what we see. By using AC field only, the intense flows and meniscus were formed due to time average force which is directed to the system center. The meniscus in the center limits the surface wave traveling area, because waves can not travel up on the meniscus. By adding static magnetic field time average force comparing to only AC field impact is excluded, the meniscus is not formed and waves can travel all over the surface. The main factor in surface wave generation is alternating force amplitude - by adding static magnetic field it significantly increases (BDC > BAC ). 4. Conclusions An experimental study of liquid metal surface waves enhanced by AC magnetic field showed that wave amplitude is limited by intense liquid metal turbulent flow when the dimensionless frequency is above 1. By applying static magnetic field, the flow is partly damped and non-linear waves are obtained all over the surface - wave pattern is similar in both cases when dimensionless frequency is below and above 1. By applying DC field to the system, current in induction coil can be reduced 4 times to obtain similar wave intensity - energy consumption for AC field is reduced by 16 times! Acknowledgements The research is part of ERAF project: Refinement of metallurgical grade silicon using smart refinement technologies. Project number: Nr.1.1.1.1/16/A/097 [1] F. Debray, Y. Fautrelle, F. Dalard, Measurement of mass transfer across a moving mercury-electrolyte interface by an electrochemical method, Experiments in Fluids 19 (5) (1995) 353–358. doi:10.1007/BF00203422. [2] B. Saadi, A. Bojarevis, Y. Fautrelle, J. Etay, Contrle lectromagntique du transfert de masse aux interfaces liquides-liquides, Rcents Progrs en Gnie des Procd 92. [3] W. Thomson, 2. on the motion of free solids through a liquid, Proceedings of the Royal Society of Edinburgh 7 (1872) 384–390. doi:10.1017/ S037016460004222X. [4] H. K. Moffatt, Electromagnetic stirring, Physics in Fluids 3 (5) (1991) 1336– 1343. 9
[5] J. Krmi, Travelling magnetic field interaction with conducting media, Zintne (1969) 258–262. [6] A. Bojarevics, A. Cramer, Y. Gelfgat, G. Gerbeth, Experiments on the magnetic damping of an inductively stirred liquid metal flow, Experiments in Fluids 40 (2006) 257–266.
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Highlights
Electromagnetically excited surface waves on the liquid metal Combined magnetic fields create surface waves when skin-effect has significant By applying static magnetic field alternating field can be 4 times lower Static magnetic field damps intense liquid metal flows and surface deformation
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: