Extinction of opposed flame spread over thin paper

Opposed flame spread is a classic fundamental fire research problem that is controlled by the simultaneous interactions of heat transfer, chemical kinetics, and fluid dynamics mechanisms. Although the problem has been widely studied before, there is still a need for more fundamental research particularly at limiting conditions, such as near extinction in non-standard atmospheres such as those expected in future spacecraft and habitats. The determination of the extinction of a material is often based on the oxygen volume fraction below which the material does not burn. and is referred to as the limiting oxygen index, or concentration (LOI or LOC). This extinction limit depends on the fuel properties and environmental conditions. This work presents a simplified analytical model of the oxygen volume fraction (LOC) leading to the extinction of opposed flame spread over thin combustible materials. The analysis predicts two oxygen volume fraction boundaries for extinction: a “heat transfer” boundary and a “chemical kinetics” boundary. The former is given by the conditions needed to heat the solid to its pyrolysis temperature, and the latter by the conditions needed for the gas phase reaction to be maintained. The combination of the two boundaries provides an overall boundary for the oxygen volume fraction for extinction as a function of material properties, gas flow velocity, ambient pressure, gravity level, and external heating. The results are compared with available experimental data for the LOC of thin paper sheets under different environmental variables to provide relevant information about the material flammability at near extinction conditions, particularly in spacecraft environments.