Calculation of Laminar Flows of Plasma in the Channel of a Plasmatron with the Self-Adjusting Length of the Electric Arc

A simplified method is suggested for the calculation of the parameters of laminar flows of plasma in the channel of a plasmatron. A new analytical solution of the Elenbaas–Heller equation is derived, which generalizes the channel model of electric arc to the case when the volume radiation makes a significant contribution to the electric arc energy balance. Numerical calculations are performed in order to determine the electric field intensity, the longitudinal pressure gradient, and the heat transfer to the electric arc channel wall depending on the working parameters of the plasmatron in a laminar flow of gas in a stabilized section. In determining the arc length, it is assumed that the electric arc is shifted downstream of the flow and, at the same time, performs random walks over the channel cross section. The walks occur under the effect of vortexes whose characteristic size is of the order of the arc diameter.