Integral methods of analysing electric arcs: I. Formulation

Abstract

The equations of continuity, momentum and energy are derived for axisymmetric electric arcs in terms of overall radial integrals. The external flow is assumed to be adiabatic, reversible and one-dimensional, although compressibility and the possibility of time variation are included. The overall integrals define quantities with the dimensions of area when their integrands are normalized. Arc problems can then be solved in principle if relations between the area quantities can be guessed or found empirically, and a formal structure for such empiricism is suggested. It is shown that the enthalpy-flow model of Frost and Liebermann (1971) is equivalent to an integral method at a low level of approximation. The analyses of Topham (1971, 1972a, b) are related to the present general formulation.