Temperature and velocity fields in a gas stream exiting a plasma torch. A mathematical model and its experimental verification

A mathematical model was developed to predict the velocity and temperature fields in a free plasma jet issuing from a D.C. plasma torch. It was assumed that the temperature and velocity at the torch nozzle were specified and the turbulent Navier-Stokes equations were solved in conjunction with a two-equation model of turbulence and the energy transport equation. The model was formulated in terms of the two-dimensional elliptic equations to facilitate its future extension to nonparabolic problems. The predictions of the model were compared with experimental measurements obtained from laser Doppler and spectroscopic techniques. Good overall agreement was found between the theoretical predictions and the experimental measurements for two sets of initial conditions corresponding to nitrogen/hydrogen and argon/hydrogen plasmas. Radiation was found to have a small effect on the overall heat transfer process, and it is suggested that the assumption of an optically thin radiation loss per unit volume is sufficiently accurate for most engineering applications. The significance of this work lies in the fact that, for the first time, it is possible to test the assumptions of the current model against a reliable set of experimental measurements.Notation C ₁,C ₂,C _D constants inK- turbulence model, Table III - C _P average specific heat of plasma at constant pressure - h ₁ length of integration region - h ₂ width of integration region - K turbulent kinetic energy per unit mass - P pressure - r radial coordinate - R ₀ internal radius of anode - S _K source term forK equation - S _R radiation loss per unit volume - S source term for equation - T ₀ temperature of plasma atz=0 - T temperature of plasma - T _a ambient temperature - u velocity inz direction - u ₀ velocity of plasma atz=0 - v radial velocity of plasma - z axial coordinate - dissipation rate of turbulence energy - , _eff, _t molecular, effective, and turbulent viscosities, respectively - density - _K, _T, Prandtl numbers forK, T, and, respectively