Abstract
Through the numerical solution of the Navier/Stokes equation, the energy transport equation, and the magnetic diffusion equation, a mathematical model has been developed to predict the velocity, temperature, and current density distributions in inert gas welding arcs. Although the model has one adjustable parameter, the cathode current density, it was found that a single value of this variable was sufficient to provide internally consistent results for a range of arc lengths and arc currents representative of welding. The computed temperature distributions in the arc were found to be in good agreement with spectroscopically measured temperatures taken from the literature, and similar agreement was obtained between the predicted and measured current density distributions at the surface of water cooled copper anodes. The mechanisms of heat and momentum transfer to the anode were investigated in the light of recent findings concerning the anode boundary layer and the presence of negative anode fall voltages. The predicted convective heat fluxes to the anode were found to be generally consistent with experimental data.
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Abbreviations
- B :
-
magnetic field vector
- B :
-
azimuthal component of magnetic field
- C p :
-
specific heat
- e :
-
electronic charge
- F :
-
Lorentz force per unit volume
- h :
-
plasma enthalpy
- / :
-
arc current
- J :
-
current density vector
- k B :
-
Boltzmann’s constant
- k :
-
thermal conductivity
- P :
-
pressure
- Q :
-
total heat flux to anode
- Q c :
-
convective heat flux to anode
- Q E :
-
electron heat flux at anode
- Q r :
-
heat flux at anode due to radiation from the arc
- r :
-
radial coordinate
- R c :
-
cathode spot radius
- S r :
-
radiation loss per unit volume from arc
- S t :
-
source term for energy equation
- T :
-
temperature
- u :
-
axial velocity
- v :
-
radial velocity
- V :
-
voltage
- z :
-
axial coordinate
- a :
-
Prandtl number
- μ :
-
viscosity
- μ o :
-
permitivity of free space
- p :
-
density
- σ :
-
electrical conductivity of plasma
- τ :
-
shear stress
- ϕ :
-
coefficient of thermal diffusion of electrons
- a :
-
anode or anode fall
- b :
-
edge of boundary layer in plasma
- c :
-
cathode or cathode fall
- e :
-
electron
- E :
-
electronic
- max:
-
maximum value on arc axis
- r :
-
the radial direction
- w :
-
work function
- z :
-
the axial direction
References
G. Oreper and J. Szekely:Jnl. Fluid Mech., in press.
M. Ushio, J. Szekely, and C. W. Chang:Ironmaking and Steelmaking, 1981, vol. 8, pp. 279–86.
J. W. McKelliget and J. Szekely:Jnl. Phys. D: Appl. Phys., 1983, vol. 16, pp. 1007–22.
J. Szekely, J. McKelliget, and M. Choudhary:Ironmaking and Steelmaking, 1983, vol. 10, pp. 169–79.
K. Hsu, K. Etemadi, and E. Pfender:Jnl. Appl. Phys., 1983, vol. 54, pp. 1293–1301.
K. Hsu and E. Pfender:Jnl. Appl. Phys., 1983, vol. 54, pp. 4359–66.
N. Tsai: Ph.D. Thesis, Dept. Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1983.
D. C. Evans and R.S. Tankin:Phys. Fluids, 1967, vol. 10, pp. 1137–44.
C. F. Liu: Ph.D. Thesis, Dept. of Mechanical Engineering, University of Minnesota, Minneapolis, MN, 1977.
K.C. Hsu and E. Pfender:Jnl. Appl. Phys., 1983, vol. 54, pp. 3818–24.
H. A. Dinulescu and E. Pfender:Jnl. Appl. Phys., 1980, vol. 51, pp. 3149–57.
N. A. Sanders and E. Pfender:Jnl. Phys., 1984, vol. 55, pp. 714–22.
W. M. Rosenhow and J.P. Hartnett:Handbook of Heat Transfer, McGraw-Hill, New York, NY, 1973, pp. 8–126.
W. Pun and D. B. Spalding: Report No. HTS/76/2, Heat Transfer Section, Imperial College, London, 1976.
O. H. Nestor:Jnl. Appl. Phys., 1962, vol. 33, pp. 1638–48.
H. Maecker:Z. Phys., 1955, vol. 141, pp. 198–216.
P. Schoeck and E. R. G. Eckert:5th Int. Conf. Phen. Ionized Gases, Munich, 1961, vol. 2, pp. 1812–29.
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McKelliget, J., Szekely, J. Heat transfer and fluid flow in the welding arc. Metall Trans A 17, 1139–1148 (1986). https://doi.org/10.1007/BF02665312
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DOI: https://doi.org/10.1007/BF02665312