Simulation by an analog computer of normal explosions and cool flames

This paper deals with the simulation of explosions and cool flames. First, for explosions, an analog computer is used to simulate a continuous branching chain reaction with an exothermic quadratic termination step. The use of an average temperature is justified, and a new approximation for the Arrhenius [2] law is employed. In this analysis the reactant consumption is taken into consideration. Without assuming any a priori critical condition it has been shown that the explosion limit is characterized by a sharp discontinuity in the development of every variable. Explosion limits so determined are compared with those obtained assuming zero reactant consumption. It is also shown that without reactant consumption the predicted critical temperature is half that predicted by Frank-Kamenetskii. The second part of the paper deals with the simulation of cool flames. If a termination step has a higher actication energy than that of the branching step, the scheme accounts for cool flames. The osciilations limits, the time dependence of parameters, and the influence of changes in activation energy or initial temperature are in good agreement with observations on cool flames in hydrocarbon oxidation.