Metallurgical and Materials Transactions B

, Volume 35, Issue 2, pp 363–372 | Cite as

Mathematical modeling of a direct current electric arc: Part I. Analysis of the characteristics of a direct current arc

  • Marco Ramírez
  • Gerardo Trapaga
Article

Abstract

A mathematical model is used to describe fluid-flow, heat-transfer, and electromagnetic phenomena in the arc region of a direct current electric arc furnace (DC EAF). Based on those model results, a detailed physical analysis of the arc was performed, where the numerical computations help to explain the arc structure, its behavior, and the highly coupled relationship among their main physical variables. This analysis leads to the conclusion that the arc behaves in such a way that all the arc characteristics are controlled by the expansion of the arc, which is the main feature used to physically describe the arc behavior. The arc expansion is evident from the arc shape, which is defined as the region where conduction of electricity takes place. The arc shape is clearly seen in several contour fields presented in this work, such as the current density, the magnetic flux density, the electric conductivity, the electric potential, and the temperature fields. The results of this article focus on process analysis, to provide insight into the inter-relationship among the arc variables, and to establish physical grounds to subsequently explore dimensionless analytical representations to describe the arc behavior.

Keywords

Material Transaction Bath Surface Current Density Vector Magnetic Flux Density Field Electromagnetic Body Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

#x004A-0304;

current density vector (A/m2)

\(\bar B\)

magnetic flux density vector (Tesla)

\(\bar V\)

velocity vector (m/s)

BΘ

azimutal magnetic flux density (Tesla)

Jr

radial current density (A/m2)

Jz

axial current density (A/m2)

vz

axial velocity (m/s)

vr

radial velocity (m/s)

r

radial position (m)

Jc

current density at the cathode spot (A/m2)

L

arc length (m)

σ

electric conductivity (Θ−1 m−1)

φ

electric potential (V)

μo

magnetic permeability (henry/m)

vt

kinematic viscosity (m2/s)

k

turbulent kinetic energy (J/Kg)

ε

energy dissipation rate (W/Kg)

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References

  1. 1.
    Crude Steel Production 1999, International Iron & Steel Institute, Brussels, Belgium.Google Scholar
  2. 2.
    P. Greis: MPT Metall. Plant Technol. Int., 1998, vol. 4, pp. 84–88.Google Scholar
  3. 3.
    J. Szekely and G. Trapaga: Metall. Plant Technol. Int., 1994, vol. 4 pp. 30–47.Google Scholar
  4. 4.
    M. Ushio, J. Szekely, and C.W. Chang: Ironmaking and Steelmaking, 1981, vol. 6, pp. 279–86.Google Scholar
  5. 5.
    J. Szekely, J. McKelliget, and M. Choudhary: Ironmaking and Steelmaking, 1983, vol. 10, pp. 169–79.Google Scholar
  6. 6.
    F. Qian, B. Farouk, and R. Mutharasan: Metall. Trans. B, 1995, vol. 26B, pp. 1057–67.Google Scholar
  7. 7.
    W. Hu and J.D. Lavers: IEEE Trans. Magn., 1997, vol. 33 (2), pp. 1726–29.CrossRefGoogle Scholar
  8. 8.
    S. Pai and H.D. Nguyen: Int. J. Heat Mass Transfer, 1995, vol. 38 (7), pp. 1161–71.CrossRefGoogle Scholar
  9. 9.
    H.L. Larsen and J.A. Bakken: TPP-4, 1996, pp. 837–44.Google Scholar
  10. 10.
    J. Alexis, M. Ramírez, G. Trapaga, and P. Jonsson: Iron Steel Inst. Jpn. Int., 2000, vol. 40, pp. 1089–97.Google Scholar
  11. 11.
    M. Boulos, P. Fauchais, and E. Pfender: Thermal Plasmas—Fundamentals and Applications, Plenum Press, New York, NY, 1994, vol. 1, pp. 452–53.Google Scholar
  12. 12.
    G.R. Jordan, B. Bowman, and D. Wakelam: J. Phys. D: Appl. Phys., 1969, vol. 3, pp. 1089–99.CrossRefGoogle Scholar
  13. 13.
    B. Bowman: J. Phys. D: Appl. Phys., 1972, vol. 5, pp. 1422–32.CrossRefGoogle Scholar
  14. 14.
    M. Ramirez: Ph.D. Thesis, MIT, Boston, MA, 2000, p. 68.Google Scholar
  15. 15.
    A.B. Murphy: Plasma Chem. Plasma Process., 1995, vol. 15 (2), pp. 279–307.CrossRefGoogle Scholar
  16. 16.
    B. Bowman: 52th Electric Furnace Conf. Proc., ISS, Warrendale, PA, 2000, pp. 111–20.Google Scholar

Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 2004

Authors and Affiliations

  • Marco Ramírez
    • 1
  • Gerardo Trapaga
    • 2
  1. 1.the Graduate Center in MetallurgyInstituto Technológico de MoreliaMorelia, Mich.México
  2. 2.CINVESTAV-IPN Unidad QuerétaroQuerétaro, Qro.México

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