Theoretical investigation of a 2 kA DC nitrogen arc in a supersonic nozzle

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.