Dynamic behaviour of an a.c. arc column in a steady laminar accelerating flow

The a.c. arc in a laminar flow subjected to a linearly increasing pressure gradient has been studied theoretically by using simplified gas-property relations. The arc-conservation equations are solved numerically for sinusoidal current inputs by a full differential method, and, for comparison, by an approximate integral method. The dynamic behaviour of the arc is found to be fully determined by two nondimensional parameters: the product of the frequency and the time scale of the flow ¿F, and Z, which is proportional to the time scale of the flow divided by the square of the peak current. Of these, ¿F is the more significant, and controls the relative importance of the energy transport by thermal conduction and that by convection in the electrically conducting core of the arc around current zero. Compared with the differential method, the integral method predicts all the qualitative features of the arc behaviour, and good agreement is obtained for ¿F greater than one. At low frequencies, however, the integral method tends to predict lower electric fields near the current zero, and the reignition peak occurs at a later instant.