Modelling and Analysis of Electrodes Erosion Phenomena of $SF_6$ Arc in a Laval Nozzle

The present work deals with the theoretical study of the effects of copper vapours resulting from the erosion of the electrodes on the properties of a SF6 arc in a Laval nozzle. Computations have been done for a DC arc of 1000A with upstream gas pressure of 3.75MPa. The arc plasma is assumed to be in local thermodynamic equilibrium(LTE). The sheath and non-equilibrium region around the electrodes are not considered in this model. However, its effects on the energy flux into the electrodes are estimated from some experimental and theoretical data. The turbulence effects are calculated using the Prandtl mixing length model. A conservation equation for the copper vapour concentration is solved together with the governing equations for mass, momentum and energy of the gas mixture. Comparisons were made between the results with and without electrodes erosion. It has been found that the presence of copper vapours cools down the arc temperature due to the combined effects of increased radiation and increased electrical conductivity. The copper vapour distribution is very sensitive to the turbulent parameter. The erosion of upstream electrode(cathode) has larger effects on the arc compared to the downstream electrode(anode) as the copper vapour eroded from the anode cannot diffuse against the high-speed axial flow.