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.

Analysis of the characteristics of DC nozzle arcs in air and guidance for the search of SF6replacement gas

“…Arc modelling at that time was mainly based on the integral method [5,[7][8][9]. This method of arc analysis has achieved considerable success in predicting the arc behaviour under steady state and for relatively high currents [5].…”

Electron Density Measurements in UV-Preionized XeCl and CO2 Laser Gas Mixtures

“…The integral equations are utilized in the formulation of Cowley (1974) with restriction to low-current DC arcs at low flow speeds by the omission of the magnetic pressure terms, the radiation losses and the kinetic energy terms. The equations are written in terms of the integral shape parameters and the thermal area 0,.…”

“…The shape factors, defined as follows, are taken at the second level of approximation of Cowley (1974), in which they are expressed in terms of standard shape factors and a velocity scaling parameter denoted by g. The shape factors then become…”

“…The required areas are as defined by Cowley (1974) with the reference conditions taken as the local free stream values.…”

“…Here a simpler case is examined in which attention is focused on the consequences of coupling between the energy balance of the arc column and an axial flow confined within a contoured nozzle. The analysis is based on the integral formulation of Cowley (1974) with the equations taken at the second level of approximation. The formulation allows for perturbations of the shear flow via the velocity scaling factor g; the mutual interaction of vorticity is however inhibited by the integral formulation.…”