Simple convection-loss dominated model for optically thick SF6 arcs

A simplified analytical model of a high-current SF arc in an axial gas blast is presented. The model predictions of axially distributed temperature, radius and voltage are compared with experimental data for a particular interrupter geometry and static-pressure operating conditions. The equilibrium arc temperature is established by equating the optically thick radiation density to the total convection flux at any axial position z¿. This results in a simple graph of arc temperature as a function of the parameter M/z¿ where M is the local flow Mach number. The local arc radius and voltage are obtained by solving a total convection power balance equation that includes the kinetic-energy flux, but which neglects any radial-loss term. For set gas-flow conditions, the model predicts that the temperature, current density and voltage at fixed axial positions are independent of the arc current. The experiments confirm these results for the current range 3.5 kA to 17 kA. The experimental arc radius is about 10% smaller than the theoretical radius, but the calculated arc voltage falls within the range of measurement scatter. Taking into account a previously estimated 25% net heat loss to the thermal zone surrounding the arc gives good agreement between prediction and measurement.