Modeling extinction in forced opposed-flow smolder

We address a discrepancy between smolder extinction theory and experimental work regarding whether extinction can occur tinder oxygen-depleted conditions. Single heterogeneous (solid/gas) reaction models that model the complex reaction process of smoldering with a single reaction predict extinction for large head winds only when oxygen remains (fuel-limited smolder). Experimental evidence, however. shows that oxygen concentrations are essentially zero for smolder waves close to the extinction limit. We consider a two-step sequential reaction scheme in which the solid fuel is converted to char. which also reacts with oxygen to produce ash. This generic scheme leads to extinction with oxygen depletion. The model suggests that oxygen depletion is caused by the second reaction while extinction is driven by the first. Solid fuel must be completely converted to char for extinction to occur while oxygen consumption in the secondary reaction induces oxygen depletion. Spatial separation of the localized reactions is predicted to increase with head wind as a precursor to extinction.