The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 1: transient analysis and explosion limit

Abstract

In this paper we revisit Frank-Kamenetskii’s analysis of thermal explosions, using also a single-reaction model with an Arrhenius rate having a large activation energy, to describe the transient combustion of initially cold gaseous mixtures enclosed in a spherical vessel with a constant wall temperature. The analysis shows two modes of combustion, including a flameless slowly reacting mode for low wall temperatures or small vessel sizes, when the temperature rise due to the reaction is kept small by the heat-conduction losses to the wall, so as not to change significantly the order of magnitude of the reaction rate. In the second mode of combustion the slow reaction rates occur only in the first ignition stage, which ends abruptly when very large reaction rates cause a temperature runaway, or thermal explosion, at a welldefined ignition time and location, which triggers a flame that propagates across the vessel to consume rapidly the reactant. We define the explosion limits, in agreement with FrankKamenetskii’s analysis, by the limiting conditions for existence of the slowly reacting mode of combustion. In this mode, a quasi-steady temperature distribution is established after a transient reaction stage with small reactant consumption. Most of the reactant is burnt, with nearly uniform mass fraction, in a second long stage, when the temperature follows a quasisteady balance between the rates of heat conduction to the wall and of chemical heat release. The changes in the explosion limits due to the enhanced heat transfer rates by the buoyant motion are described in an accompanying paper.