Application of Steenbeck's minimum principle for three-dimensional modelling of DC arc plasma torches

In this paper, physical/mathematical models for the three-dimensional, quasi-steady modelling of the plasma flow and heat transfer inside a non-transferred DC arc plasma torch are described in detail. The Steenbeck's minimum principle (Finkelnburg W and Maecker H 1956 Electric arcs and thermal plasmas Encyclopedia of Physics vol XXII (Berlin: Springer)) is employed to determine the axial position of the anode arc-root at the anode surface. This principle postulates a minimum arc voltage for a given arc current, working gas flow rate, and torch configuration. The modelling results show that the temperature and flow fields inside the DC non-transferred arc plasma torch show significant three-dimensional features. The predicted anode are-root attachment position and the arc shape by employing Steenbeck's minimum principle are reasonably consistent with experimental observations. The thermal efficiency and the torch power distribution are also calculated in this paper. The results show that the thermal efficiency of the torch always ranges from 30% to 45%, i.e. more than half of the total power input is taken away by the cathode and anode cooling water. The special heat transfer mechanisms at the plasma-anode interface, such as electron condensation, electron enthalpy and radiative heat transfer from the bulk plasma to the anode inner surface, are taken into account in this paper. The calculated results show that besides convective heat transfer, the contributions of electron condensation, electron enthalpy and radiation to the anode heat transfer are also important (similar to30% for parameter range of interest in this paper). Additional effects, such as the non-local thermodynamic equilibrium plasma state near the electrodes, the transient phenomena, etc, need to be considered in future physical/mathematical models, including corresponding measurements.