The existence and spatial development of hydrocarbon cool flames in a spherical vessel under the influence of mass and thermal diffusion have been investigated by numerical methods. The purpose is to examine the nature of the interaction of the physics and chemistry that may drive an oscillatory reaction. The conditions correspond to those that would be experienced at zero gravity, as has been recently put to experimental test. Comparisons and contrasts with responses under perfectly mixed conditions are made. The numerical simulation was based on a skeleton thermokinetic scheme, derived from that of Yang and Gray, in a three-variable model representing two intermediate species and reactant temperature. Dirichlet and Neumann boundary conditions could be variously selected. The equations were cast in one dimension (spherical symmetry) and integrated using the numerical algorithm group routine D03PSF. The reactor surface was assumed to be inert. Both sustained oscillatory (i.e., multiple) and damped cool flames were predicted to exist under spatially uniform conditions resembling those reported in previous experimental studies. The phase relationship between the chemical species and temperature in sustained oscillation is demonstrated. There was strong evidence for the negative temperature-dependent features. No sustained oscillations were predicted to occur under the effect of diffusive fluxes, although highly damped oscillations were still able to exist. This is compatible with the initial experimental observations in microgravity conditions. The spatial development reveals the growth and decay of the reactive intermediate concentrations, with a corresponding expansion of a combustion front from the center of the reaction system to the edge. High concentrations of intermediates were sustained in the cooler periphery where reaction continued to be supported. Only at abnormally high mass diffusive fluxes could sustained oscillatory reaction be recovered. The dependence of oscillations on the magnitude of mass and thermal diffusion coefficients is explored.
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