‘LTE-diffusion approximation’ for arc calculations

Abstract

This paper proposes the use of the ‘LTE-diffusion approximation’ for predicting the properties of electric arcs. Under this approximation, local thermodynamic equilibrium (LTE) is assumed, with a particular mesh size near the electrodes chosen to be equal to the ‘diffusion length’, based on De/W, where De is the electron diffusion coefficient and W is the electron drift velocity. This approximation overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero, which makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity. Use of the LTE-diffusion approximation for a 200 A arc with a thermionic cathode gives predictions of total arc voltage, electrode temperatures, arc temperatures and radial profiles of heat flux density and current density at the anode that are in approximate agreement with more accurate calculations which include an account of the diffusion of electric charges to the electrodes, and also with experimental results. Calculations, which include diffusion of charges, agree with experimental results of current and heat flux density as a function of radius if the Milne boundary condition is used at the anode surface rather than imposing zero charge density at the anode.

Modelling of gas–metal arc welding taking into account metal vapour

“…The effects of the sheaths are simplified by using a mesh size of 0.1 mm at the electrodes, as recommended by Lowke and Tanaka [23]. The pressure is equal to atmospheric pressure.…”

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

“…This indicates that the electron pressure gradient plays a significant role in that region. Lowke and Tanaka [16] used one-temperature model with electron diffusion and found a need for field reversal near the anode to limit the electron flux and conserve the total current. Jenista et al [17] and Amakawa et al [18] also predicted a similar behavior of the electric potential drop near the anode using the generalized Ohm's law in diffuse and constricted electric arcs.…”

A Perspective on Arc Welding Research: The Importance of the Arc, Unresolved Questions and Future Directions

“…An alternative approach takes into account diffusion of electrons from the arc column into the sheath region, requiring an electron continuity equation to be solved within the sheath [31]. The two methods give very similar results for arc temperature distributions and heat flux to the anode for an argon TIG arc [30], demonstrating the value of the simple LTE-diffusion method in arc welding modelling. However, the influence of metal vapour, and of molecular gases, for which the anode attachment region may be much more constricted than for a pure argon arc, have not been taken into account.…”

“…Different methods have been used to circumvent this problem, some of which avoid modelling the sheath region, and some of which include a detailed treatment of the sheath. For example, the ''LTE-diffusion'' method [30] requires choosing the first mesh point in the plasma in the arc column outside the sheath region, thus avoiding the sheath completely. An alternative approach takes into account diffusion of electrons from the arc column into the sheath region, requiring an electron continuity equation to be solved within the sheath [31].…”