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Magnetohydrodynamics Processing and Modeling

  • Koulis A. Pericleous
  • Valdis Bojarevics
  • Georgi S. Djambazov
Chapter
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 273)

Abstract

Magnetohydrodynamics (MHD) is the scientific field devoted to studying the interaction between electric or magnetic fields and fluid flow in electrically conducting liquids. MHD phenomena appear in a wide range of metal processing applications, either as an unintended consequence of the presence of electric currents during processing or by the deliberate application of external magnetic fields or currents to a process. The allied field of Electromagnetic Processing of Materials (EPM) has many applications, ranging from melting, flow control, melt cleaning, stirring, arc processes (welding, AM, vacuum arc remelting) and electrolytic processes, including recently the field of liquid metal batteries for renewable energy storage. In terms of modeling and simulation, EPM remains a difficult task to master, since in addition to the usual flow, heat transfer, and solidification, one has to address the coupled electric and magnetic fields, often in a dynamic fashion. In this chapter, we divide applications in terms of applied current type, i.e. DC (aluminum electrolysis, vacuum arc remelting) or AC (EM levitation, induction crucibles, PV silicon kerf recycling and the contactless ultrasonic vibration of melts).

References

  1. 1.
    C.M. Hall, US patent 400664, Process of reducing aluminum from its fluoride salts by electrolysis, issued 1889-04-02Google Scholar
  2. 2.
    P. Héroult, French patent no. 175,711 (filed: 23 April 1886; issued: 1 September 1886)Google Scholar
  3. 3.
    Ferranti, British Patent 700 of 1887 on induction furnacesGoogle Scholar
  4. 4.
    H.K. Moffatt, On the suppression of turbulence by a uniform magnetic field. J. Fluid Mech. 28, 571–592 (1967)CrossRefGoogle Scholar
  5. 5.
    J. Sommeria, R. Moreau, Why, how, and when MHD turbulence becomes two-dimensional. J. Fluid Mech. 118, 507–518 (1982)CrossRefGoogle Scholar
  6. 6.
    G. Djambazov, V. Bojarevics, K. Pericleous, M. Forzan, Numerical modeling of silicon melt purification in induction directional solidification system. Int. J. Appl. Electromagn. Mech. 53(S1), S95–S102 (2017)CrossRefGoogle Scholar
  7. 7.
    H.K. Moffatt, A. Sellier, Migration of an insulating particle under the action of uniform ambient electric and magnetic fields. Part 1. General theory. J. Fluid Mech. 464, 279–286 (2002)CrossRefGoogle Scholar
  8. 8.
    S. Taniguchi, N. Yoshikawa, K. Takahashi, Application of EPM to the separation of inclusion particles from liquid metal, in The 15th Riga and 6th PAMIR Conference on Fundamental and Applied MHD, ed. by A. Alemany, (Salaspils Institute of Physics, Riga, 2005), p. 55Google Scholar
  9. 9.
    S. Asai, Overview of electromagnetic processing of materials, in Magnetohydrodynamics Historical Evolution and Trends, ed. by S. Molokov et al., (Springer, Berlin, 2007), pp. 315–317Google Scholar
  10. 10.
    P.A. Davidson, An Introduction to Magnetohydrodynamics (Cambridge University Press, Cambridge, 2001)CrossRefGoogle Scholar
  11. 11.
    O. Zikanov, A. Thess, Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number. J. Fluid Mech. 358, 299–333 (1998)CrossRefGoogle Scholar
  12. 12.
    K. Cukierski, B.G. Thomas, Flow control with local electromagnetic braking in continuous casting of steel slabs. Metall. Mater. Trans. B 39B, 94–107 (2008)CrossRefGoogle Scholar
  13. 13.
    H. Kobatake, H. Fukuyama, I. Minato, T. Tsukada, S. Awaji, Noncontact modulated laser calorimetry of liquid silicon in a static magnetic field. J. Appl. Phys. 104, 054901 (2008)CrossRefGoogle Scholar
  14. 14.
    A. Kao, J. Gao, H. Mengkun, K. Pericleous, D.V. Alexandrov, P.K. Galenko, Dendritic growth velocities in an undercooled melt of pure nickel under static magnetic fields: A test of theory with convection. Acta Mater. 103, 184–191 (2015)Google Scholar
  15. 15.
    C. Bailey, P. Chow, M. Cross, Y. Fryer, K. Pericleous, Multiphysics modeling of the metals casting process. Proc. R. Soc. A 452(1946), 459–486 (1996)CrossRefGoogle Scholar
  16. 16.
    S. Bounds, G. Moran, K. Pericleous, M. Cross, T.N. Croft, A computational model for defect prediction in shape castings based on the interaction of free surface flow, heat transfer, and solidification phenomena. Metall. Mater. Trans. B 31(3), 515–527 (2000)CrossRefGoogle Scholar
  17. 17.
    N. Urata, K. Mori, H. Ikeuchi, Behavior of bath and molten metal in aluminum electrolytic cell. Keikinzoku 26(11), 573–600 (1976)Google Scholar
  18. 18.
    G. Lossman, in Light Metals 1992, ed. by E. R. Cutshall, (The Minerals Metals and Materials Society, Warrendale, PA, 1992), pp. 441–447Google Scholar
  19. 19.
    C. Droste, M. Segatz, D. Vogelsang, in Light Metals 1998, ed. by B. Welch, (The Minerals Metals and Materials Society, Warrendale, PA, 1998), pp. 419–428Google Scholar
  20. 20.
    V. Bojarevics, J.W. Evans, Mathematical modeling of Hall-Héroult pot instability and verification by measurements of anode current distribution, in Proceedings of TMS Light Metals, (2015), pp. 783–788Google Scholar
  21. 21.
    V. Bojarevics, M.V. Romerio, Long waves instability of liquid metal-electrolyte interface in aluminum electrolysis cells: A generalization of Sele’s criterion. Eur. J. Mech. B Fluids 13(1), 33–56 (1994)Google Scholar
  22. 22.
    V. Bojarevics, K. Pericleous, Solutions for the metal-bath interface in aluminum electrolysis cells, in Proceedings of TMS Light Metals, (2009), pp. 569–574Google Scholar
  23. 23.
    R. Von Kaenel, J.P. Antille, Magnetohydrodynamic stability in alumina reduction cells. Travaux 23(27), 285–297 (1996)Google Scholar
  24. 24.
    B. Li, F. Wang, X. Zhang, F. Qi, N. Feng, Development and application of an energy saving technology for aluminum reduction cells, in Proceedings of TMS Light Metals, (2012), pp. 865–868Google Scholar
  25. 25.
    D. Leenov, A. Kolin, Theory of electromagnetophoresis. J. Chem. Phys. 22(4), 683–688 (1954)CrossRefGoogle Scholar
  26. 26.
    V. Bojarevics, A. Roy, Effect of magnetic forces on bubble transport and MHD stability of aluminum electrolysis cells. Magnetohydrodynamics 48(1), 125–136 (2012)Google Scholar
  27. 27.
    K. Pericleous, G. Djambazov, R.M. Ward, L. Yuan, P.D. Lee, A multiscale 3D model of the vacuum arc remelting process. Metall. Mater. Trans. A 44(12), 5365–5376 (2013)CrossRefGoogle Scholar
  28. 28.
    P. Chapelle, A. Jardy, J. Bellot, M. Minvielle, Effect of electromagnetic stirring on melt pool free surface dynamics during vacuum arc remelting. J. Mater. Sci. 43(17), 5734–5746 (2008)CrossRefGoogle Scholar
  29. 29.
    R.M. Ward, M.H. Jacobs, Electrical and magnetic techniques for monitoring arc behaviour during VAR of INCONEL1 718: Results from different operating conditions. J. Mater. Sci. 39, 7135–7143 (2004)CrossRefGoogle Scholar
  30. 30.
    R.M. Ward, B. Daniel, R.J. Siddall, Ensemble arc motion and solidification during the vacuum arc remelting of a nickel-based superalloy, in Proc. Int. Symp. Liquid Metal Processing and Casting, Santa Fe, (2005), pp. 49–56Google Scholar
  31. 31.
    W. Zhang, P.D. Lee, M. McLean, Numerical simulation of dendrite white spot formation during vacuum arc remelting of INCONEL718. Metall. Mater. Trans. A 33(2), 443–454 (2002)CrossRefGoogle Scholar
  32. 32.
    L. Yuan, P.D. Lee, A new mechanism for freckle initiation based on microstructural level simulation. Acta Mater. 60(12), 4917–4926 (2012)CrossRefGoogle Scholar
  33. 33.
    W. Wang, P.D. Lee, M. McLean, A model of solidification microstructures in nickel-based superalloys: Predicting primary dendrite spacing selection. Acta Mater. 51(10), 2971–2987 (2003)CrossRefGoogle Scholar
  34. 34.
    P.D. Lee, A. Chirazi, R.C. Atwood, W. Wang, Multiscale modeling of solidification microstructures, including microsegregation and microporosity, in an Al–Si–Cu alloy. Mater. Sci. Eng. A 365(1–2), 57–65 (2004)CrossRefGoogle Scholar
  35. 35.
    X. Xu, R.M. Ward, M.H. Jacobs, P.D. Lee, M. McLean, Tree-ring formation during vacuum arc remelting of INCONEL 718: Part I. Experimental investigation. Metall. Mater. Trans. A 33A(6), 1795–1804 (2002)CrossRefGoogle Scholar
  36. 36.
    J.C. Ramirez, C. Beckermann, Evaluation of a Rayleigh-number-based freckle criterion for Pb-Sn alloys and Ni-Base Superalloys. Metall. Mater. Trans. A 34A, 1525 (2003)CrossRefGoogle Scholar
  37. 37.
    T.M. Pollock, W.H. Murphy, The breakdown of single-crystal solidification in high refractory nickel-base alloys. Metall. Mater. Trans. A 27A, 1081 (1996)CrossRefGoogle Scholar
  38. 38.
    I. Egry, G. Lohofer, I. Seyhan, S. Schneider, B. Feuerbacher, Viscosity and surface tension measurements in microgravity. Int. J. Thermophys. 20(4), 1005–1015 (1999)CrossRefGoogle Scholar
  39. 39.
    H. Kobatake, H. Fukuyama, I. Minato, T. Tsukada, S. Avaji, Noncontact measurement of thermal conductivity of liquid silicon in a static magnetic field. Appl. Phys. Lett. 90, 094102 (2007)CrossRefGoogle Scholar
  40. 40.
    V. Bojarevics, K. Pericleous, Modeling electromagnetically levitated liquid droplet oscillations. ISIJ Int. 43(6), 890–898 (2003)CrossRefGoogle Scholar
  41. 41.
    K. Pericleous, V. Bojarevics, A. Roy, Modeling of EML in combined AC/DC magnetic fields as the basis for microgravity experiments. Int. J. Microgravity Sci. Appl. 30(1), 56–63 (2013)Google Scholar
  42. 42.
    J. Priede, Oscillations of weakly viscous conducting liquid drops in a strong magnetic field. J. Fluid Mech. 671, 399–416 (2010)CrossRefGoogle Scholar
  43. 43.
    V. Bojarevics, E. Beaugnon, Magnetic levitation of weakly conducting liquid droplets, in Proceedings of 9th Int. Conference MHD PAMIR, vol. 1, (University of Latvia, Riga, 2014), pp. 358–362Google Scholar
  44. 44.
    D.C. Wilcox, Turbulence Modeling for CFD, 2nd edn. (DCW Industries, California, 1998)Google Scholar
  45. 45.
    O. Widlund, Modeling of magnetohydrodynamic turbulence, Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden, ISSN 0348-467X, 2000Google Scholar
  46. 46.
    V. Bojarevics, K. Pericleous, Dual frequency AC and DC magnetic field levitation melting of metals. Int. J. Appl. Electromagn. Mech. 44, 147–153 (2014)Google Scholar
  47. 47.
    L. Rayleigh, On the capillary phenomena of jets. Proc. R. Soc. Lond. A 29, 71–97 (1879)CrossRefGoogle Scholar
  48. 48.
    E. Beaugnon, D. Fabregue, D. Billy, J. Nappa, R. Tournier, Dynamics of magnetically levitated droplets. Physica B 294–295, 715–720 (2001)CrossRefGoogle Scholar
  49. 49.
    S. Easter, V. Bojarevics, K. Pericleous, Numerical modeling of liquid droplet dynamics in microgravity. J. Phys. Conf. Ser. 327, 012027 (2011)CrossRefGoogle Scholar
  50. 50.
    H. Tadano, M. Fujita, T. Take, K. Nagamatsu, A. Fukuzawa, Levitational melting of several kilograms of metal with a cold crucible. IEEE Trans. Magn. 30(6), 4740–4742 (1994)CrossRefGoogle Scholar
  51. 51.
    T. Okumura, K. Yamamoto, M. Shibata, Large scale cold crucible levitation melting furnace with bottom tapping nozzle, in Proc. 6th Internat. Conf. Electromagnetic Processing Materials, (Forschungszentrum Dresden-Rossendorf, Dresden, 2009), pp. 521–524Google Scholar
  52. 52.
    E. Baake, S. Spitans, A. Jakovičs, New technology for EM levitation melting of metals, in The Proc. of Int. Conf. Heating by Electromag. Sources HES-13 – Padua, Italy, 21–24 May, (2013), pp. 1–8Google Scholar
  53. 53.
    L. Baptiste, N. van Landschoot, G. Gleijm, J. Priede, J. Schade van Westrum, H. Velthuis, T.-Y. Kim, Electromagnetic levitation: A new technology for high rate physical vapour deposition of coatings onto metallic strip. Surf. Coat. Technol. 202, 1189–1193 (2007)CrossRefGoogle Scholar
  54. 54.
    N. El-Kaddah, T.S. Piwonka, J.T. Berry US Patent Number 5033948, 1991Google Scholar
  55. 55.
    V. Bojarevics, K. Pericleous, M. Cross, Modeling the dynamics of magnetic semi-levitation melting. Metall. Mater. Trans. B 31, 179–189 (2000)CrossRefGoogle Scholar
  56. 56.
    V. Bojarevics, R.A. Harding, K. Pericleous, M. Wickins, The development and validation of a numerical model of an induction skull melting furnace. Metall. Mater. Trans. B 35B, 785–803 (2004)CrossRefGoogle Scholar
  57. 57.
    R.A. Harding, M. Wickins, G. Keough, K. Pericleous, V. Bojarevics, The use of combined DC and AC fields to increase superheat in an induction skull melting furnace, in Proc. 2005 Int. Symp. Liquid Metal Processing and Casting, (Santa Fe), pp. 201–210Google Scholar
  58. 58.
    B. Ceccaroli, E. Ovrelid, S. Pizzini (eds.), Solar Silicon Processes: Technologies, Challenges, and Opportunities (CRC Press, London, 2017)Google Scholar
  59. 59.
    SIKELOR, Silicon kerf loss recycling, www.sikelor.eu
  60. 60.
    F. Dughiero, M. Forzan, D. Ciscato, F. Giusto, Multi-crystalline silicon ingots growth with an innovative induction heating directional solidification furnace, in 37th IEEE Photovoltaic Specialists Conference, IEEE 978-1-4244-9965-6, (2011)Google Scholar
  61. 61.
    EAAT, Elektrische Automatisierungs- und Antriebstechnik GmbH Chemnitz, http://www.eaat.de/en/
  62. 62.
    G. Djambazov, V. Bojarevics, K. Pericleous, M. Forzan, Numerical modeling of silicon melt purification in induction directional solidification system. Int. J. Appl. Electromagn. Mech. 53(S1), S95–S102 (2017)CrossRefGoogle Scholar
  63. 63.
    G.I. Eskin, D.G. Eskin, Ultrasonic Treatment of Light Alloy Melts, 2nd edn. (CRC Press, Boca Raton, 2015)Google Scholar
  64. 64.
    T. Meek, X. Jian, H. Xu, Q. Han. Ultrasonic processing of materials, ORNL/TM-2005/125, 2006Google Scholar
  65. 65.
    I. Tzanakis, W.W. Xu, G. Lebon, D.G. Eskin, K. Pericleous, P.D. Lee, In situ synchrotron radiography and spectrum analysis of transient cavitation bubbles in molten aluminium alloy. Phys. Procedia 70, 841 (2015)CrossRefGoogle Scholar
  66. 66.
    D. Jarvis, V. Bojarevics, K. Pericleous, et al., European Patent 13756442.3-1373, 2016Google Scholar
  67. 67.
    V. Bojarevics, G. Djambazov, K. Pericleous, Contactless ultrasound generation in a crucible. Metall. Mater. Trans. A 46(7), 2884–2892 (2015)CrossRefGoogle Scholar
  68. 68.
    C. Vives, Crystallization of aluminium alloys in the presence of cavitation phenomena induced by a vibrating electromagnetic pressure. J. Cryst. Growth 158(1–2), 118 (1996)CrossRefGoogle Scholar
  69. 69.
    I. Grants et al., Contactless magnetic excitation of acoustic cavitation in liquid metals. J. Appl. Phys. 117, 204901 (2015)CrossRefGoogle Scholar
  70. 70.
    W.D. Griffiths et al., The use of positron emission particle tracking (PEPT) to study the movement of inclusions in low-melting-point alloy castings. Metall. Mater. Trans. B 43B, 370–378 (2012)CrossRefGoogle Scholar
  71. 71.
    C. Canuto et al., Spectral Methods in Fluid Dynamics (Springer, Berlin, 1998)Google Scholar
  72. 72.
    K. Pericleous, V. Bojarevics, Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications. Prog. Comput. Fluid Dyn. 7(2/3/4), 118–127 (2007)CrossRefGoogle Scholar
  73. 73.
    G. Djambazov et al., Staggered-mesh computation for aerodynamic sound. AIAA J. 38(1), 16–21 (2000)CrossRefGoogle Scholar
  74. 74.
    G.S.B. Lebon, K. Pericleous, I. Tzanakis, D. Eskin, A model of cavitation for the treatment of a moving liquid metal volume. Int. J. Cast Met. Res. 29, 324–330 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Koulis A. Pericleous
    • 1
  • Valdis Bojarevics
    • 1
  • Georgi S. Djambazov
    • 1
  1. 1.Centre for Numerical Modelling and Process AnalysisUniversity of GreenwichLondonUK

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