The Frank-Kamenetskii vortex

Abstract eng:
The effect of the buoyancy-driven motion on the quasi-steady “slowly-reacting” mode of combustion of a gaseous mixture enclosed in a spherical vessel with a constant wall temperature is addresed here. Following Frank-Kamenetskii’s (FK) analysis, combustion is modeled by an overall Arrhenius reaction with 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 buoyancy-free quasi-steady analysis the critical conditions were found to depend on the value of the Damk¨ohler number. For small values of Ra, temperature is given in the first approximation by the spherically symmetric FK distribution, involving an axisymmetric annular vortex determined at leading order. The analysis is extended to investigate the influence of convection on the resulting explosion limits through introduction of expansions for the flow variables in powers of Ra.

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