Boundary Layer Analysis of an SF6 Circuit Breaker Arc

This paper covers the derivations of a hyperbolic partial differential equation for the dynamic arc radius in a circuit breaker nozzle. Starting at peak current, this equation is solved for a linear current ramp to determine the current zero arc radius. It is shown that axial convection cooling, augmented by radiation and diffusion, can produce a constricted arc radius of the order of 0.1 cm at current zero. Equations are derived, expressing the thermal time constant, at current zero as a function of the pressure, current derivative, arc length and gas properties. Finally, it is shown that the hyperbolic equation can be integrated to obtain a Cassie type equation for arc resistance during the pre-current- zero arcing period.