On the Modeling of Thermal Radiation at the Top Surface of a Vacuum Arc Remelting Ingot

Article
  • 13 Downloads

Abstract

Two models have been implemented for calculating the thermal radiation emitted at the ingot top in the VAR process, namely, a crude model that considers only radiative heat transfer between the free surface and electrode tip and a more detailed model that describes all radiative exchanges between the ingot, electrode, and crucible wall using a radiosity method. From the results of the second model, it is found that the radiative heat flux at the ingot top may depend heavily on the arc gap length and the electrode radius, but remains almost unaffected by variations of the electrode height. Both radiation models have been integrated into a CFD numerical code that simulates the growth and solidification of a VAR ingot. The simulation of a Ti-6-4 alloy melt shows that use of the detailed radiation model leads to some significant modification of the simulation results compared with the simple model. This is especially true during the hot-topping phase, where the top radiation plays an increasingly important role compared with the arc energy input. Thus, while the crude model has the advantage of its simplicity, use of the detailed model should be preferred.

References

  1. 1.
    L.A. Bertram, R.S. Minisandram and K.O. Yu: Modeling for casting and solidification processing, 1st, Marcel Dekker Inc., New York, NY, 2002. pp. 565–612.Google Scholar
  2. 2.
    A. Jardy and D. Ablitzer: Rare Met. Mater. Eng., 2006, vol. 35, pp.119–22.Google Scholar
  3. 3.
    K.M. Kelkar, S.V. Patankar, A. Mitchell, O. Kanou, N. Fukada and K. Suzuki: World Conf. Titanium, 11th, Kyoto, Japan, June, 3–7, The Japan Institute of Metal, Sendai, 2007, pp. 1279–82.Google Scholar
  4. 4.
    K. Pericleous, G. Djambazov, M. Ward, L. Yuan and P.D. Lee: Metall. Mater. Trans. A, 2013, vol. 44, no.12, pp. 5365–5376.CrossRefGoogle Scholar
  5. 5.
    A.S. Ballantyne: Proc. 2013 Int. Symp. on Liquid Metal Processing and Casting, Austin, TX, Sept. 22–25 2013, M.J.M. Krane, A. Jardy, R.L. Williamson, J.J. Beaman, 2013, pp. 253–59.Google Scholar
  6. 6.
    A. Anders and S. Anders: J. Phys. D: Appl. Phys, 1991, vol. 24, pp. 1986–1992.CrossRefGoogle Scholar
  7. 7.
    A.S. Ballantyne: Proc. 2015 Int. Symp. on Liquid Metal Processing and Casting, Leoben, Austria, Sept. 20–24, 2015, A. Kharicha, R.M. Ward, H. Holzgruber, M. Wu, 2015, pp. 244–54.Google Scholar
  8. 8.
    J. Sucec: Heat transfer, 1st ed., Simon & Schuster, New York, NY, 1975, 604 pp.Google Scholar
  9. 9.
    H. Leuenberger and R.A. Person: Am. Soc. Mech. Eng., 1956, Paper No. 56-A-144.Google Scholar
  10. 10.
    A.J. Buschman and C.M. Pittman: NASA, 1961, NASA-TN D-944.Google Scholar
  11. 11.
    H. Brockmann: Int. J. Heat Mass Transf., 1994, vol. 37, no. 7, pp. 1095-1100.CrossRefGoogle Scholar
  12. 12.
    H.W. Jensen, J. Arvo, P. Dutre, A. Keller, A. Owen, M. Pharr and P. Shirley: Monte Carlo Ray Tracing, 2003. http://www.cs.odu.edu/~yaohang/cs714814/Assg/raytracing.pdf.
  13. 13.
    J.J. Valencia and P.N. Quested: ASM Handbook, 2008, vol. 15, pp. 468-481.Google Scholar
  14. 14.
    M. Boivineau, C. Cagran, D. Doytier, V. Eyraud, M.-H. Nadal, B. Wilthan and G. Pottlacher: Int. J. of Thermophys., 2006, vol. 27, pp. 507-529.CrossRefGoogle Scholar
  15. 15.
    A. Jardy and D. Ablitzer: Mater. Sci. Technol., 2009, vol. 25, pp. 163-69.CrossRefGoogle Scholar
  16. 16.
    A. Patel, D.W. Tripp and D. Fiore: Proc. 2013 Int. Symp. on Liquid Metal Processing and Casting, Austin, TX, Sept. 22–25 2013, M.J.M. Krane, A. Jardy, R.L. Williamson, J.J. Beaman, 2013, pp. 241–44.Google Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2018

Authors and Affiliations

  • P.-O. Delzant
    • 1
    • 2
  • B. Baqué
    • 1
  • P. Chapelle
    • 1
  • A. Jardy
    • 1
  1. 1.Institut Jean Lamour, UMR 7198, Université de Lorraine/CNRS - LabEx DAMASNancy CedexFrance
  2. 2.TIMET SavoieUgineFrance

Personalised recommendations