Two-Dimensional Numerical Modeling of Direct-Current Electric Arcs in Nonequilibrium

  • J. Park
  • J. Heberlein
  • E. Pfender
  • G. Candler
  • C. H. Chang
Original Paper


A numerical model has been developed to analyze arc-anode attachment in direct-current electric arcs. The developed model fully couples a plasma flow with electromagnetic fields in a self-consistent manner. Electrons and heavy species are assumed to have different temperatures. Species continuities are taken into account to address the chemical nonequilibrium with the Self-Consistent Effective Binary Diffusion (SCEBD) formulation. Electric and magnetic field equations are determined with a newly developed Ohm’s law, an improvement over the conventional generalized Ohm’s law. The governing equations are discretized and solved using the Finite Volume Method (FVM) and Gauss–Seidel Line Relaxation (GSLR) method in a two-dimensional domain. The model is applied to a two-dimensional axisymmetric high-intensity argon arc. The results are compared favorably with experimental and other numerical data. A significant electric potential drop has been observed in the vicinity of the anode due to the thermal and chemical nonequilibrium effects.


Nonequilibrium Arc-anode attachment Species diffusion High-intensity arc Nonequilibrium boundary layer 



This work was supported in part by the National Science Foundation through grants CTS-9903950 and CTS-0225962.


  1. 1.
    Pfender E (1988) Thermal plasma processing in the nineties. Pure Appl Chem 60:591CrossRefGoogle Scholar
  2. 2.
    Pfender E (1999) Thermal plasma technology: Where do we stand and where are we going? Plasma Chem Plasma Proc 19:1CrossRefGoogle Scholar
  3. 3.
    MacRae DR (1989) Plasma arc process systems, reactors, and applications. Plasma Chem Plasma Proc 9:95SCrossRefGoogle Scholar
  4. 4.
    Fauchais P, Vardelle A (1997) Thermal plasmas. IEEE Trans Plasma Sci 25:1258CrossRefADSGoogle Scholar
  5. 5.
    Lancaster J (1986) The physics of welding. Pergamon, OxfordGoogle Scholar
  6. 6.
    Waymouth JF (1971) Electric discharge lamps. MIT Press, CambridgeGoogle Scholar
  7. 7.
    Leveroni E, Pfender E (1989) Electric probe diagnostics in thermal plasmas: double probe theory and experimental results. Rev Sci Instrum 60:3744CrossRefADSGoogle Scholar
  8. 8.
    Lowke JJ, Kovitya P, Schmidt HP (1992) Theory of free-burning arc columns including the influence of the cathode. J Phys D: Appl Phys 25:1600CrossRefADSGoogle Scholar
  9. 9.
    Scott DA, Kovitya P, Haddad GN (1989) Temperatures in the plume of a dc plasma torch. J Appl Phys 66:5232CrossRefADSGoogle Scholar
  10. 10.
    Butler GW, Kashiwa BA, King DQ (1990) Numerical modeling of arcjet performance. In: 21st Fluid dynamics, plasma dynamics, and lasers conference, AIAA 90–1472, Seattle, WA, 1990Google Scholar
  11. 11.
    Ramshaw JD (1993) Hydrodynamic theory of multicomponent diffusion and thermal diffusion in multitemperature gas mixture. J Non-Equilib Thermodyn 18:121MATHGoogle Scholar
  12. 12.
    Ramshaw JD, Chang CH (1996) Multicomponent diffusion in two-temperature magnetohydrodynamics. Phys Rev E 53:6382CrossRefADSGoogle Scholar
  13. 13.
    Chang CH, Ramshaw JD (1994) Numerical simulation of nonequilibrium effects in an argon plasma jet. Phys Plasma 1:3698CrossRefADSGoogle Scholar
  14. 14.
    Ramshaw JD, Chang CH (1996) Friction-weighted self-consistent effective binary diffusion approximation. J Non-Equilib Thermodyn 21:233MATHCrossRefGoogle Scholar
  15. 15.
    Dinulescu HA, Pfender E (1980) Analysis of the anode boundary layer of high intensity arcs. J Appl Phys 51:3149CrossRefADSGoogle Scholar
  16. 16.
    Lowke JJ, Tanaka M (2006) LTE-diffusion approximation’ for arc calculations. J Phys D: Appl Phys 39:3634CrossRefADSGoogle Scholar
  17. 17.
    Jenista J, Heberlein JVR, Pfender E (1997) Numerical mode of the anode region of high-current electric arcs. IEEE Trans Plasma Sci 25:883CrossRefADSGoogle Scholar
  18. 18.
    Amakawa T, Jenista J, Heberlein J, Pfender E (1998) Anode-boundary-layer behavior in a transferred, high-intensity arc. J Phys D: Appl Phys 31:2826CrossRefADSGoogle Scholar
  19. 19.
    George C, Pfender E, Candler G (1998) Forced diffusion effects in the simulation of a non-transferred DC arc. In: 36th Aerospace sciences meeting & exhibit, Reno, NVGoogle Scholar
  20. 20.
    Tanaka Y (2004) Two-temperature chemically non-equilibrium modelling of high-power Ar–N2 inductively coupled plasmas at atmospheric pressure. J Phys D: Appl Phys 37:1190CrossRefADSGoogle Scholar
  21. 21.
    Park J (2003) Three-dimensional nonequilibrium numerical modeling of arc-anode attachment in direct-current electric arcs. PhD thesis, University of MinnesotaGoogle Scholar
  22. 22.
    Ramshaw JD (1996) Simple approximation for thermal diffusion in ionized gas mixture. J Non-equilib Thermodyn 21:233MATHGoogle Scholar
  23. 23.
    Ramshaw JD (1996) Simple approximation for thermal diffusion in gas mixture. J Non-equilib Thermodyn 21:99MATHGoogle Scholar
  24. 24.
    Ramshaw JD, Chang CH (1991) Ambipolar diffusion in multicomponent plasmas. Plasma Chem Plasma Proc 11:395CrossRefGoogle Scholar
  25. 25.
    Ramshaw JD, Chang CH (1993) Ambipolar diffusion in two-temperature multicomponent plasmas. Plasma Chem Plasma Proc 13:489CrossRefGoogle Scholar
  26. 26.
    Frost LS, Phelps AV (1964) Momentum transfer cross sections for slow electrons in He, A, Kr, and Xe, from transport coefficients. Phys Rev 136:1538CrossRefADSGoogle Scholar
  27. 27.
    Hoffert MI, Lien H (1967) Quasi-one-dimensional, nonequilibrium gas dynamics of partially ionized two-temperature argon. Phys Fluids 10:1769CrossRefADSGoogle Scholar
  28. 28.
    Hirschfelder JO, Curtiss CF, Bird RB (1959) Molecular theory of gases and liquids. John Wiley & Sons, New YorkGoogle Scholar
  29. 29.
    MacCormack RW (1985) Current status of the numerical solutions of the Navier–Stokes equations. AIAA 85–0032Google Scholar
  30. 30.
    Candler GV (1988) The computation of weakly ionized hypersonic flows in thermo-chemical nonequilibrium. PhD thesis, Stanford UniversityGoogle Scholar
  31. 31.
    Chen DM (1980) Analytical modeling of two-temperature argon arc plasmas. PhD thesis, University of MinnesotaGoogle Scholar
  32. 32.
    Hsu KC (1982) A self-consistent model for the high intensity free-burning argon arc. PhD thesis, University of MinnesotaGoogle Scholar
  33. 33.
    Hartmann R, Heberlein JV (2001) Quantitative investigations on arc-anode attachments in transferred arcs. J Phys D: Appl Phys 34:2972CrossRefADSGoogle Scholar
  34. 34.
    Etemadi K (1982) Investigation of high current arcs by computer-controlled plasma spectroscopy. PhD thesis, University of MinnesotaGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • J. Park
    • 1
  • J. Heberlein
    • 2
  • E. Pfender
    • 2
  • G. Candler
    • 2
  • C. H. Chang
    • 3
  1. 1.Novellus Systems, Inc.San JoseUSA
  2. 2.University of MinnesotaMinneapolisUSA
  3. 3.Los Alamos National LaboratoryLos AlamosUSA

Personalised recommendations