Solutions of plasma arc equations by the orthogonal collocation method

Abstract

The orthogonal collocation method is applied to the study of wall-stabilised plasma arcs. The numerical implementation of this method is simpler and faster than that of finite difference methods of comparable accuracy. The solutions obtained agree with experiments and with previous finite difference calculations. For the steady-state DC case, radial temperature results are obtained for arcs in nitrogen and sulphur hexafluoride at atmospheric pressure. It is shown that the inclusion of radiative self-absorption in sulphur hexafluoride arcs leads to a reduction in the centre temperature, a broadening of the temperature distributions and a small decrease in the axial electric field. Solutions are obtained also for the time-dependent behaviour of a nitrogen arc following an abrupt current interruption. In this transient case, self-induced radial flow is considered, leading to the additional process of convective loss.

Anode Column Behavior of Long Vertical Air Arcs at Atmospheric Pressure

“…Lee [8], can be used for a free boundary problem, so the long computation times of our model can be avoided. Certainly the boundary problem requires further examination (see Appendix) for asymptotic behavior.…”

“…Matsumura et al [5], using a model by Hermann [6], show experimentally that models such as that of [4] may be applied to timedependent behavior of wall-stabilized arcs. Similar models have been used by Lowke [7] and Lee [8]. Jones and Freeman [9] give an analytic solution.…”

“…If the arc is very long, axial flow must be very small or absent, except close to the electrodes. The presence of the free boundary demands that radial velocity cannot be assumed zero everywhere, as in the steady-state wall-stabilized dc arc [8]. Because the velocity has no radius at which it is constrained, other than to be zero at the center of the arc, there is no characteristic radius useful in calculation.…”

A method for computing the radial temperature profiles in high-pressure, high-current arcs

“…The conductance appearing in the integral in equation ( 32) is approximated using a quadrature formula on the same basis function (Lee 1983):…”

“…The radial temperature distribution of an electric arc may be obtained by solving an energy balance equation, taking into account thermal conduction, emission and absorption of radiation, and Joule heating (Maecker 1963). In an earlier paper (Lee 1983) it was shown how the orthogonal collocation method could be used to provide accurate and efficient solutions of the energy balance equation in the case where the radiative term is treated as a known material function and tabulated as a net emission coefficient. However, this procedure represents only an approximation to the radiative energy transfer process, since it does not account accurately for the actual distribution of emission and absorption in the arc being studied.…”