Some numerical solutions of the boundary layer equations for an SF6arc

An approximate integral formulation of the thermal boundary layer equation is derived for a steady arc in a nozzle. This differential equation defines the constriction of the arc radius in terms of a heat transfer parameter γ which represents the ratio of all radial heat losses to axial convection. These radial losses include both optically thin radiation and turbulent heat transfer as estimated from a mixing length model. Numerical solutions of the continuity, energy, and momentum equations have been obtained within an arc radius determined from the above equation. These solutions show the effects of various degree of arc constriction upon the velocity and temperature profiles and the arc time constant. The calculations make use of the thermodynamic, transport, and radiative properties of SF
6
evaluated for a throat pressure of 10 atm for temperatures up to 100 000°K. Solutions have been obtained for arc currents of 100 and 1000 A. It is found that a 100-A arc will have a time constant of several microseconds if the arc radius is of the order of 0.5 mm. Voltage gradients corresponding to this degree of constriction are approximately 200 V/cm.