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

publication date

  • December 2016

start page

  • 1010

end page

  • 1028


  • 6


  • 20

International Standard Serial Number (ISSN)

  • 1364-7830

Electronic International Standard Serial Number (EISSN)

  • 1741-3559


  • Frank-Kamenetskii"s analysis of thermal explosions is revisited, using also a singlereaction 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. There
    is a flameless slowly reacting mode for low wall temperatures or small vessel sizes,
    when the temperature rise resulting from the heat released by 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 other mode, the slow reaction rates occur only
    in an initial ignition stage, which ends abruptly when very large reaction rates cause a
    temperature runaway, or thermal explosion, at a well-defined ignition time and location,
    thereby triggering a flame that propagates across the vessel to consume the reactant
    rapidly. Explosion limits are defined, in agreement with Frank-Kamenetskii"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 subsequent long stage during which the temperature
    follows a quasi-steady balance between the rates of heat conduction to the wall and
    of chemical heat release. The changes in the explosion limits caused by the enhanced
    heat-transfer rates associated with buoyant motion are described in an accompanying


  • Mechanical Engineering


  • thermal explosion; reacting gases in vessels; flameless combustion