COMBUSTION AND FLAME 59:17-30 (1985) 17 A Theoretical Study of the Ignition of a Reactive Medium by Means of an Electrical Discharge S. REFAEL and E. SHER Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel 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. INTRODUCTION The successful ignition of a mixture depends upon a large number of parameters, namely, the mixture compositon, the initial pressure and temperature, the oxidation kinetic, and the mode of introducing the required energy. It was experimentally observed that for a lean mixture at a given set of initial conditions the manner in which the electrical energy is released domi- nates the ignition process. Maly and Vogel [1] observed that the ignition and the subsequent flame propagation are controlled mainly by the amount of energy which is introduced in the breakdown phase of the spark establishment, and only to a moderate degree by the total energy. On the other hand, Ballal and Lefebvre [2] observed that the spark duration in the arc phase and the energy distribution with time have a profound impact on successful ignition. The theory behind these phenomena has not been entirely developed yet. Several works have been devoted to investigating the mechanism by which the energy of an electrical discharge is converted into activation energy; however, in most of them the role that plasma may play, and the importance of this role, in the ignition process has been oversimplified. Overly et al. [3] investigated the ignition of hydrazine vapor by using an unsteady-state laminar theory. The ignition source was modeled by a hot pocket of burned gases. This model assumed a rapid pocket formation during which the effects of thermal and mass diffusion were considered negligible. Akindale et al. [4] numerically solved a spherical spread of a thermal wave through a methane-air mixture. Here again, the spark kernel was considered as a hot pocket of nonreacting gases having initially a homogene- ous temperature of 10,000K. Kailasanath et al. [5] studied the ignition of a hydrogen-air mix- ture. The energy deposition in their model was assumed to be linear in time at a rate determined by a prescribed energy to be deposited in a Copyright © 1985 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue. New York, NY 10017 0010-2180/85/$03.00