A theoretical study of the ignition of a reactive medium by means of an electrical discharge

A mathematical model is presented to simulate the evolution with time of a short segment of a spark channel in a methane-air mixture. The model assumes an axisymmetric cylindrical flame propagation and conducting column with moving boundaries in which local thermodynamic equilibrium exists at every point. The phenomena associated with the breakdown phase are considered as initial conditions. These are based on the experimental observations of other investigators. The radial profile of the time-dependent electrical energy input during the arc phase is determined by the computed plasma conductivity. The model employs a realistic equation of state, experimental transport coefficients at high temperatures, measured data for the mean emission coefficient for heat radiation, and a detailed chemical kinetics of a CH₄-air system. The evolution with time of the conductivity channel and the associated flow, temperature, and concentration fields are calculated by numerical integration of the relevant conservation equations in the one-dimensional Lagrangian coordinates.