The arc conservation equations based on laminar flow and on the boundary layer assumption have been solved for a 2 kA DC nitrogen arc burning in a supersonic nozzle at a stagnation pressure of 23 atm. An approximate radiation transport model is used to account for the emission and absorption of radiation. The computed results are in good agreement with experiments. A hybrid approach (i.e. a combination of integral and differential methods) is used to predict the pressure in the nozzle in the presence of the arc. It has been found that isothermal external flow provides the best agreement between the calculated and the measured pressures. The relative importance of radiation transport, convection (both enthalpy and kinetic energy) and thermal conduction is discussed. It has also been found that in the region upstream of the nozzle throat there is a radial inflow heated up by strong radiation absorption while in the supersonic region this flow changes its direction. The outward radial flow provides the energy source for the arc to expand axially in the thermal layer. Viscous stresses play a very small role in momentum balance and axial velocity profiles are typical of those of inviscid fluid flows.

Recent experimental results (Smith et. al., 1980 and New land et. al., 1982) indicate that nozzle wall ablation can occur even before the arcing current reaches its thermal blocking limit. The wall ablation is caused by intense arc radiation. The evaporated wall material forms an ablation layer which reduces the effective flow area for the arc quenching gas. A theoretical model is established to study the complicated interaction between the ablation layer, the external gas flow and the arc. It has been found that for arcs burning in affinely related nozzles the arc behaviour is controlled by two nondimensional parameters, one of which is similar to the nozzle coefficient (Fang et al, Cowley and Chan). The other nondimensional coefficient, which characterises the effect of wall ablation, is determined by the thermodynamic properties of the nozzle material, the characteristic quantities of the gas and the radiation coefficient for a given upstream electrode material. Three nozzle materials, steel, copper and PTFE, have been studied and two arc quenching gases, SF6 and air, examined. It has been found that wall ablation greatly reduces the thermal blocking current but only has a marginal effect on the voltage-current characteristics. A comparison with the recent test results (Smith et al, New land et al) indicates that the theoretical model can adequately describe the nozzle arc behaviour in the presence of wall ablation.

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