Extinction of surface stabilized gaseous diffusion flames: Part I Simplified numerical model and implications for solid fuels in fires

In this work a previously proposed empirical and analytical criterion for extinction is numerically extended and validated for varying fuel dilution, oxidant dilution, strain rate, and surface temperature. The output of this work is presented in two parts: the current Part I uses simple kinetics and constant thermal transfer properties and Part II uses detailed kinetics, varying thermal transfer properties, flame radiation feedback and flame suppression agents in order to demonstrate that conclusions from the simplified model are still valid. In addition this work goes beyond the concept of critical flame temperature or mass flux for extinction by including the influence of slow chemical kinetics through the Damkohler number which becomes even more important for commonly used fire retarded materials.Extinction of flames on solid fuels is modeled by decoupling the pyrolysis chemistry from the gas-phase combustion chemistry using the flame energy feedback versus pyrolysis rate curves and an energy balance at the surface. This approach has the advantage of identifying and deducing key materials properties for solid and gaseous phase from experiments. Simulations are performed in a planar stagnation-point flow diffusion flame configuration using one-step Arrhenius chemical kinetics and a simplified transport model with Lewis number equal to unity. Only quasi-steady conditions are considered for the gaseous phase even if the pyrolysis rate of the solid is transient because the response time for the solid phenomena is, in general, much larger than the response (diffusion) time for the gaseous phenomena.It is found that at high pyrolysis rates and low straining rates (infinitely fast kinetics regime) there is no leakage of oxygen to the surface of solid fuel. However, as the solid fuel extinction is approached, oxygen leakage occurs because the effective air to fuel mass stoichiometric ratio becomes less than one owing to fuel dilution near the surface. At high straining rates, solid combustion cannot be sustained at any pyrolysis rate. In the infinitely fast kinetics regime, an appropriate scaling has been developed which collapses the convective heat flux curves onto a single one. In general, the critical pyrolysis fuel mass flux exhibits a universal behavior for variation of various model parameters when plotted versus a modified Damköhler number, and becomes constant when the latter is sufficiently high. Comparison with experiments is discussed, and the implications of the criterion for characterizing ignition flammability properties of solid fuels are also discussed.