The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 2: buoyancy-induced motion and its e ect on the explosion limits Articles uri icon

publication date

  • December 2016

start page

  • 1029

end page

  • 1045


  • 6


  • 20

International Standard Serial Number (ISSN)

  • 1364-7830

Electronic International Standard Serial Number (EISSN)

  • 1741-3559


  • This paper investigates the effect of buoyancy-driven motion on the quasi-steady slowly reacting' mode of combustion and on its thermal-explosion limits, for gaseous mixtures enclosed in a spherical vessel with a constant wall temperature. Following Frank-Kamenetskii's seminal analysis of this problem, the strong temperature dependence of the effective overall reaction rate is taken into account by using a single-reaction model with an Arrhenius rate having a large activation energy, resulting in a critical value of the vessel radius above which the slowly reacting mode of combustion no longer exists. In his contant-density, convection-free analysis, the critical conditions were found to depend on the value of a Damkohler number, defined as the ratio of the time for the heat released by the reaction to be conducted to the wall, to the homogeneous explosion time evaluated at the wall temperature.


  • thermal explosion; laminar reacting flows; buoyancy-induced flow; thermal-explosion; natural-convection; stability