RT Journal Article
T1 The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 2: buoyancy-induced motion and its effect on the explosion limits
A1 Sánchez Pérez, Antonio Luis
A1 Iglesias Estradé, María Inmaculada
A1 Moreno Boza, Daniel
A1 Liñán Martínez, Amable
A1 Williams, Forman Arthur
AB 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 enclosedin a spherical vessel with a constant wall temperature. Following Frank-Kamenetskii’s seminalanalysis of this problem, the strong temperature dependence of the effective overall reactionrate is taken into account by using a single-reaction model with an Arrhenius rate havinga large activation energy, resulting in a critical value of the vessel radius above which theslowly reacting mode of combustion no longer exists. In his contant-density, convection-freeanalysis, the critical conditions were found to depend on the value of a Damk¨ohler number,defined as the ratio of the time for the heat released by the reaction to be conducted tothe wall, to the homogeneous explosion time evaluated at the wall temperature. For gaseousmixtures under normal gravity, the critical Damk¨ohler number increases through the effect ofbuoyancy-induced motion on the rate of heat conduction to the wall, measured by an appropriate Rayleigh number Ra. In the present analysis, for small values of Ra, the temperatureis given in the first approximation by the spherically symmetric Frank-Kamenetskii solution,used to calculate the accompanying gas motion, an axisymmetric annular vortex determinedat leading order by the balance between viscous and buoyancy forces, which we call the FrankKamenetskii vortex. This flow is used in the equation for conservation of energy to evaluatethe influence of convection on explosion limits for small Ra, resulting in predicted criticalDamk¨ohler numbers that are accurate up to values of Ra on the order of a few hundred.
PB Informa UK Limited
SN 1364-7830
YR 2016
FD 2016-12-14
LK https://hdl.handle.net/10016/35476
UL https://hdl.handle.net/10016/35476
LA eng
NO This work was supported by the Spanish MCINN through project # CSD2010-00010. FAW is supported by the US National Science Foundation through award#CBET-1404026.
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RD 27 jul. 2024