An approximate model for high-current free-burning arcs

A single-dimensional model, based on an integral formulation of the conservation equations, has been developed which makes it possible to predict the behaviour of these arcs. The radial distribution of axial plasma velocity v 2 (r,z) is represented by a function v z (0,z)(1-(r/r a ) 2 ) n where r a is the arc radius and r and z are the radial and axial coordinates. The solution for n by by the use of radial integral of the axial momentum equation makes it possible to develop a simple but detailed picture of the axial velocity distribution in the arc column. A comparison of the axial distribution of plasma velocities with published experimental results shows that turbulent exchange processes are dominant for currents greater than about 500A.