Publication: The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 1: transient analysis and explosion limit
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2016-12-14
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Informa UK Limited
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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.
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Keywords
Thermal explosion, Reacting gases in vessels, Flameless combustion
Bibliographic citation
Liñán, A., Moreno-Boza, D., Iglesias, I., Sánchez, A. L., & Williams, F. A. (2016). The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 1: Transient analysis and explosion limits. In Combustion Theory and Modelling, 20(6), 1010–1028