Abstract. For arcs at atmospheric pressure which have cathodes that are thermionic emitters, it is possible to calculate the major properties of the arc and the electrodes as a function of current, by accounting for electrode shape and the heat transfer processes occurring at the surface of the electrodes. Such processes occur due to eleclron and ion emission and absorption and also from radiation emission and absorption. Electrical resistance of the plasma near the electrodes is calculated either by laking account of ambipolar diffusion or simply using the local plasma value, with mesh sizes sufficiently large to account for ambipolar diffusion. Derived temperature profiles are in fair agreement with experiment. Results of electrode temperatures and arc melting effects, including such phenomena as the transition from globular to spray modes in arc welding, are also in good agreement with experiment. Prediction of properties for non-thermionic cathodes still constitute a major problem. Approximate calculations indicate that electrons at the surface of the non-thermionic cathodes may be produced by photo ionisation of neutral atoms rather than by field emission.

A method is described to predict the two-dimensional distributions of temperature, velocity and potential of free burning arcs and their electrodes for cathodes of tungsten and thoriated tungsten. The effects of non-equilibrium due to the ambipolar diffusion of charged particles are included for the calculation of the plasma electrical conductivity. The electron diffusion current is explicitly included in the solution of the current continuity equation. The plasma for the arc and the electrode sheath regions is treated as a continuum, so that the thickness of the non-equilibrium regions near the electrodes is determined within the model, depending upon the arc current and the arc and electrode configuration. This new treatment allows the calculation of the negative anode fall that may occur across the anode sheath when the electron diffusion current near the anode surface becomes larger than the total arc current. For a thoriated tungsten cathode we take the work function for cooling by electron emission to be that of tungsten, as, for small percentages of thoria in tungsten, cooling effects from electrons passing through the interfaces for tungsten-thoria and then thoria-plasma will add up to be that of a tungsten-plasma interface. Calculations have been made for arcs in argon at currents between 2.5 A and 200 A. For currents above 120 A, we calculate the anode fall voltage to be negative, being -2 V at 200 A. For currents less than 50 A, non-equilibrium effects in the plasma extend across the whole arc and electron number densities can be several orders of magnitude below the values for local thermodynamic equilibrium. Calculated arc voltages, arc temperatures and electrode temperatures are in agreement with experimental measurements to within 20%.

A two-dimensional time-dependent model has been developed for the prediction of droplet formation in gas metal arc welding. The model is a unified treatment of the arc, the welding wire, taken as the anode, and the workpiece, taken as a plane cathode. Predictions are made of the formation and shape of the welding droplets as a function of time, accounting for effects of surface tension, gravity, inertia and magnetic pinch forces. The wire feed rate and gas flow rates are also incorporated into the model. Calculations are made of current densities, electric potentials, temperatures, pressures and velocities in two dimensions both in the arc and also within the molten drop and solid electrodes. For an arc in argon with a mild steel wire of 1.6 mm diameter and a current of 325 A or more, we predict the formation of small drops of diameter 1.2 mm or less and large drop frequencies consistent with the spray transfer mode observed in welding. At currents of less than 275 A, we predict large drop sizes of about 3.8 mm in diameter or more, consistent with the globular transfer mode in welding. At a current of 300 A, in a transition zone between the two modes, we predict the presence of both small and large drops.

A two-temperature, variable-density, arc model has been developed for description of high-current free-burning arcs, including departures from thermodynamic and chemical equilibrium in the plasma. The treatment includes the arc, the anode and the cathode and considers the separate energy balance of the electrons and the heavy particles, together with the continuity equations for these species throughout the plasma. The output includes a two-dimensional distribution for the temperatures and densities both of the electrons and of the heavy particles, plasma velocity, current density and electrical potential throughout the arc. For a 200 A arc in pure argon at 1 atm, we calculate large differences between the temperatures of the electrons and the heavy particles in the plasma region near the cathode tip, together with large departures from local chemical plasma equilibrium. In the main body of the arc at high plasma temperatures, we predict minor differences between the temperatures of the electrons and the heavy particles, which are inconsistent with recent measurements using laser-scattering techniques showing differences of up to several thousand degrees. However, we find that, for the region in front of the cathode tip, the ground-state level of the neutral atoms is overpopulated relative to the corresponding populations under conditions of LTE, in agreement with experimental observations. These departures from LTE are caused by the injection of a large mass flow of cold gas into the arc core due to arc constriction at the tip of the cathode.

A recently developed theory for predicting arc and electrode properties in gas metal arc welding (GMAW) has been generalized to include arc–electrode interfaces, variation of surface tension pressure with temperature, Marangoni forces and handling of weld pool development in stationary gas tungsten arc welding (GTAW). The new theory is a unified treatment of the arc, the anode, and the cathode, and includes a detailed account of sheath effects near the electrodes. The electrodes are included as dynamic entities and the volume of fluid method is used to handle the movement of the free surface of the molten metal at one electrode. Predictions can be made of the formation and shape of the welding droplets as a function of time in GMAW and also of weld pool development in GTAW, accounting for effects of surface tension, inertia, gravity, arc pressure, viscous drag force of the plasma, Marangoni effect and magnetic forces, and also for wire feed rate in GMAW. Calculations are made of current densities, electric potential, temperatures, pressures and velocities in two dimensions, both in the arc and also within the molten metal and solid electrodes. Calculations are presented for GMAW and GTAW for an arc in argon and the results are compared with experimental temperature measurements for the plasma and the electrodes.