Nozzle arc interruption in supersonic flow

Abstract

The general arc boundary layer equation is used to derive partial differential equations in arc radius and heat flux potential which account for the temporal and spatial variations of density,velocity, enthalpy, radiation, and electrical conductivity in a Laval nozzle. The model accounts for arc turbulence and permits the cooling "time constant" to vary with position and time. The model has been solved for linear current and voltage ramps subject to the conditions that the interrupting ability varies as (dI/dt) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> and that the nozzle flow is supersonic. Curves show the transient variations of arc radius, temperature, resistance, time constant and post arc current. The calculations indicate that a Cassie arc exists after current zero and that the Cassie-Mayr transition time can exceed 1 µ s.