Integral methods of analysing electric arcs. III. Shape-factor correlation for low radiation and laminar flow

Abstract

For pt.II see ibid., vol.7, p.2232 (1974). The energy equation for the core of axisymmetric electric arcs is de- rived in terms of radial integrals. The formulation includes terms to describe the diffusive heat flux at the core boundary and the work done against viscous stress there. When the shape factors derived in Part I are evaluated for a number of different arc situations from known differential solutions, they correlate well in terms of a non-dimensional form of the heat flux. This result suggests that arc behaviour can be predicted accurately by the overall integral equations of Part I and the core energy equation, together with empirical curves relating shape factors to non-dimensional heat flux, provided that the flow is laminar and there is negligible radiation.

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

“…The axial and radial components of are given by (9) For axisymmetric arc, the azimuthal magnetic flux density can be calculated by (10) where is the axial component of the current density and μ 0 the permeability of free space. The two components of Lorentz force are given by (11) The approximate radiation transport model of Zhang et al [10] is adopted to calculate the net radiation loss in the energy equation.…”

“…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].…”

“…For switching arc applications, it is important that a theoretical arc model should be able to predict satisfactorily the arc behaviour during the current zero period. The integral method of arc analysis is not successful when applied to the current zero period due to difficulties in finding adequate correlation between the required shape factors and arc characteristic quantities [9]. Thus, arc modelling up to this time was not able to answer the question why SF 6 gas has superior arc quenching capability in gas-blast circuit breakers.…”

The DC arc in a blocked nozzle

“…the electrode placed inside nozzle before the throat: in this case, expansion of equation ( 30) gives implying that M,CC({-Se) near the electrode. Thus the arc exhibits 'self-similar' behaviour near the electrode and g=2/0.5 (Chan 1976). The term 'self-similar' is used here to indicate that when the arc is subjected to a linear velocity gradient external flow, it has been found that all the arc '8' areas are constant.…”

Electrical breakdown in gases

“…Chan et el. (192,193) use integral methods to analyze axisymmetric arcs in laminar flow extinction gases. Arc behaviour is predicted in terms of density, velocity, enthalpy, and various shape factors.…”