Numerical simulation of flame balls with radiative reabsorption effects

The effects of reabsorption of emitted radiation on steady, source-free spherical premixed flames ("flame balls") were modeled using a time-dependent numerical code with detailed chemical, transport, and radiative emission-absorption models to establish the conditions for which radiatively-induced extinction limits of flame balls may exist independent of the system dimensions. A Statistical Narrow Band - Discrete Ordinates method was used to model radiative transport. Numerical solutions for the steady properties and stability limits of flame balls in lean H₂-air and H₂-O₂-CO₂ mixtures were obtained. It was found that reabsorption effects were moderate in H₂-air mixtures but dominant in H₂-O₂-CO₂ mixtures, due to the fact that in the former case the ambient mixture contains only radiatively inert gases whereas in the latter case CO₂, a strong absorber, is present in the unburned gas. It was found that reabsorption of emitted radiation led to substantially larger flame ball sizes and wider extinction limits than calculations using optically-thin radiation models. The effects of reabsorption were found to be much different for flame balls than for propagating premixed flames because of the much smaller thermal and composition gradients for flame balls. Numerical predictions were compared to recent Space Shuttle experiments. It was found that for H₂-O₂-CO₂ mixtures, the agreement between model predictions and experimental results was much close when reabsorption effects were incorporated. It is concluded that fundamental flammability limits of flame balls can exist due to radiative heat loss, but these limits are strongly dependent on the emission-absorption spectra of the reactant and product gases and their temperature dependence, and cannot be predicted using gray-gas or optically-thin model parameters.