Abstract :
This paper transforms the equations for the dynamic arc radius R(x, t), obtained from a boundary layer analysis of a circuit breaker arc, into equations for the heat flux potential S(x, t). The key assumption underlying the transformation is that in the vicinity of current zero, the thermal storage in the arc column is controlled by changes in arc temperature rather than arc area. It is shown that the boundary layer theory of a circuit breaker arc can account for changes in arc temperature as well as arc area, and that boundary layer solutions for a linear current ramp are readily transformed into solutions for the heat flux potential approaching current zero. To apply these solutions, an order of magnitude analysis is made of a turbulence parameter. For a 100 ampere arc, calculations based on the analytical solutions show the effect of turbulence level oni the quasi-steady arc temperature, the time constant, arc conductance, voltage gradient, Reynolds number and the current zero temperature following a linear current ramp. Finally, the analytical solutions have been compared with exact numerical solutions of the boundary layer equations, and the analytical and numerical estimates of temperature, time constant, and voltage gradient have been correlated for a pressure of 10 atmospheres.
