Numerical Study of Supersonic Direct Current Plasma Nozzle Flow

Abstract

To address the problem of studying the complex e ow in dc supersonic plasma torches, an axisymmetric twodimensional numerical code is developed. Theaerodynamice elds are assumed to be expressed by a set of modie ed Euler equations in which heat conduction, generation, and radiative losses are included. A one-dimensional model is used for the nonequilibrium cathode sheath. The results for a 30-kW argon‐ hydrogen plasma are in good agreement with published experimental work. The theoretical results show that the structure of the e ow can be dividedradially inthreedistinctszoneswith specie ctransfermechanisms,clarifyingfundamentalquestionson this subject. The model results show signie cant improvement over simple engineering design methods for supersonic plasma jet nozzle. Nomenclature E = electric e eld, V/m e = specie c total internal energy, J/kg I = current intensity, A J = current density, A/m 2 Jr = radial current density, A/m 2 Jx = axial current density, A/m 2 k = thermal conductivity, W/m ¢K n = normal direction p = pressure, Pa R = radiative losses, W/m 3 Rc = cathode radius, m Rl = local radius of curvature, m r = radial position, m S = source term including radiative losses and Joule heating, W/m 3 T = temperature, K t = time, s u = axial velocity, m/s ut = tangential velocity, m/s v = radial velocity, m/s x = axial position, m q = mass density, kg/m 3 r = electrical conductivity, S/m v = electric potential, V