Skip to main content

Modeling the dynamics of magnetic semilevitation melting

Abstract

In semilevitation melting, a cylindrical metal ingot is melted by a coaxial a.c. induction coil. A watercooled solid base supports the ingot, while the top and side free surface is confined by the magnetic forces as the melting front progresses. The dynamic interplay between gravity, hydrodynamic stress, and the Lorentz force in the fluid determines the instantaneous free surface shape. The coupled nonstationary equations for turbulent flow, heat with phase change, and high-frequency electromagnetic field are solved numerically for the axisymmetric time-dependent domain by a continuous mesh transformation, using a pseudospectral method. Results are obtained for the two actually existing coil configurations and several validation cases.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    E. Okress, D. Wroughton, G. Comenetz, P. Brace, and J. Kelly: J. Appl. Phys., 1952, vol. 23 (5), pp. 545–52.

    Article  Google Scholar 

  2. 2.

    A. Gagnoud and J.P. Brancher: IEEE Trans. Magn., 1985, vol. 21 (6), pp. 2424–27.

    Article  Google Scholar 

  3. 3.

    C.H. Winstead, P.C. Gazzerro, and J.F. Hoburg: Metall. Mater. Trans. B, 1998, vol. 29B, pp. 275–81.

    Article  CAS  Google Scholar 

  4. 4.

    T.P. Felici: J. Fluid Mech., 1995, vol. 302, pp. 1–28.

    Article  Google Scholar 

  5. 5.

    E. Schwartz, J. Szekely, O.J. Ilegbusi, J.-H. Zong, and I. Egry: MHD in Process Metallurgy, TMS, Warrendale, PA, 1991, pp. 81–87.

    Google Scholar 

  6. 6.

    J. Szekely and E. Schwartz: Int. Symp. Electromagn. Process. Mater., ISIJ, Nagoya, 1994, pp. 9–14.

    Google Scholar 

  7. 7.

    A. Muhlbauer, A. Muiznieks, and A. Jakowitsch: Industrielle Electrowarme, 1991, vol. B3, pp. 130–41.

    Google Scholar 

  8. 8.

    H. Tadano, M. Fujita, T. Take, K. Nagamatsu, and A. Fukuzawa: IEEE Trans. Magn., 1994, vol. 30(6), pp. 4740–42.

    Article  Google Scholar 

  9. 9.

    J.R. Bhamidipati and N. El-Kaddah: MHD in Process Metallurgy, TMS, Warrendale, PA, 1991, pp. 69–74.

    Google Scholar 

  10. 10.

    S.P. Song and B.Q. Li: Trans. ASME, J. Heat Transfer, 1998, vol. 120, pp. 492–504

    CAS  Google Scholar 

  11. 11.

    J.D. Lavers and M.R. Ahmed: Casting of Near Net Shape Products, TMS, Warrendale PA, 1988, pp. 395–410.

    Google Scholar 

  12. 12.

    A.J. Mestel: J. Fluid Mech., 1982, vol. 117, pp. 27–43.

    Article  Google Scholar 

  13. 13.

    A.D. Sneyd and H.K. Moffatt: J. Fluid Mech., 1982, vol. 117, pp. 45–70.

    Article  CAS  Google Scholar 

  14. 14.

    H. Fukumoto, Y. Hosokawa, K. Ayata, and M. Morishita: MHD in Process Metallurgy, TMS, Warrendale, PA, 1991, pp. 21–26.

    Google Scholar 

  15. 15.

    R. Kageyama and J.W. Evans: Metall. Mater. Trans. B, 1998, vol. 29B, pp. 919–28.

    Article  CAS  Google Scholar 

  16. 16.

    B.Q. Li: Int. J. Engg. Sci., 1994, vol. 32(8), pp. 1315–36.

    Article  CAS  Google Scholar 

  17. 17.

    W. Rodi: J. Geophys. Res., 1987, vol. 92, (C5), pp. 5305–28.

    Article  Google Scholar 

  18. 18.

    C.-J. Chen and S.-Y. Jaw: Fundamentals of Turbulence Modeling, Taylor & Francis, Philadelphia, PA, 1998.

    Google Scholar 

  19. 19.

    B.E. Launder and D.B. Spalding: Comp. Meth. Appl. Mech. Eng. 1974, vol. 3, pp. 269–89.

    Article  Google Scholar 

  20. 20.

    K. Heyerichs and A. Pollard: Int. J. Heat Mass Transfer, 1996, vol. 39 (12), pp. 2385–2400.

    Article  CAS  Google Scholar 

  21. 21.

    P.A. Durbin: AIAA J., 1995, vol. 33(4) pp. 659–64.

    Article  Google Scholar 

  22. 22.

    J. Meyer, F. Durand, R. Ricou, and C. Vives: Metall. Trans. B, 1984, vol. 15B, pp. 471–78.

    Google Scholar 

  23. 23.

    W.R. Smythe: Static and Dynamic Electricity, 3rd ed., Hemisphere, New York, NY, 1989, p. 408.

    Google Scholar 

  24. 24.

    B.Q. Li: Int. J. Engg. Sci., 1993, vol. 31(2), pp. 201–20.

    Article  Google Scholar 

  25. 25.

    D.J. Moore and J.C.R. Hunt: Metallurgical Applications of Magnetohydrodynamics, The Metals Society, London, 1984, pp. 93–107.

    Google Scholar 

  26. 26.

    N. El-Kaddah and J. Szekely: J. Fluid Mech., 1983, vol. 133, pp. 37–46.

    Article  Google Scholar 

  27. 27.

    V. Bojarevics, K. Pericleous, and M. Cross: Modeling of Casting, Welding and Advanced Solidification Processes—VIII, TMS, San Diego, CA, 1998, pp. 1007–14.

    Google Scholar 

  28. 28.

    V. Bojarevics, K. Pericleous, and M. Cross: Transfer Phenomena in Magnetohydrodynamic and Electroconducting Flows, Kluwer Academic Publishers, Dordrecht, 1998, pp. 345–57.

    Google Scholar 

  29. 29.

    V.R. Voller, M. Cross, and N.C. Markatos: Int. J. Numer. Meth. Eng., 1987, vol. 24, pp. 271–84.

    Article  Google Scholar 

  30. 30.

    S.H. Seyedein and M. Hasan: Int. J. Heat Mass Transfer, 1997, vol. 40, pp. 4405–23.

    Article  CAS  Google Scholar 

  31. 31.

    J.R. Bhamidipati: Ph.D. Thesis, University of Alabama, Tuscaloosa, AL, 1995.

    Google Scholar 

  32. 32.

    C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang: Spectral Methods in Fluid Dynamics, Springer, Berlin, 1988.

    Google Scholar 

  33. 33.

    J. Happel and H. Brenner: Low Reynolds Number Hydrodynamics, Prentice-Hall, New York, NY, 1965.

    Google Scholar 

  34. 34.

    J.P. Boyd: Chebyshev & Fourier Spectral Methods, Springer, New York, NY, 1989.

    Google Scholar 

  35. 35.

    F.N. Fritsch and J. Butland: SIAM J. Sci. Stat. Comput., 1984, vol 5, pp. 300–04.

    Article  Google Scholar 

  36. 36.

    R.A. Harding and X.R. Zhu: Proc. Int. Congr. Electromagnetic Processing of Materials, Centre Francais de l’Electricite, Service Diffusion de la Documentation, Paris, 1997, vol. 1, pp. 165–70.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bojarevics, V., Pericleous, K. & Cross, M. Modeling the dynamics of magnetic semilevitation melting. Metall Mater Trans B 31, 179–189 (2000). https://doi.org/10.1007/s11663-000-0143-7

Download citation

Keywords

  • Free Surface
  • Material Transaction
  • Liquid Metal
  • Magnetic Levitation
  • Coil Design