A reduced model of smoldering-to-flaming (StF) transition

This study proposes a reduced model to predict the smoldering-to-flaming (StF) transition. Three chemical reactions, including surface and gas-phase reactions, are considered, coupled with heat and mass transfer between the surface and the gas phase. Unknown quantities, such as surface/gas-phase temperatures, reaction rates, and species concentrations, are solved simultaneously as part of the solution with pure smoldering, pure flaming, and combined cases, demonstrating the simplicity yet wide applicability of the model. Dimensionless parameters are first introduced to simplify the equations and to illustrate the nature of the model’s solutions. The results show an increase in temperature with the oxygen mass fraction, along with a higher surface temperature than the gas-phase temperature in smoldering mode and vice versa in flaming mode. The combined case predicts the shift from steady smoldering to steady flaming, indicating the critical temperature and species concentrations at the spontaneous StF transition. Combustion maps consisting of smoldering, bistable, and flaming regimes are constructed over a range of oxidizer flow rates. With an increase in oxidizer flow rate, the upper limit of oxygen mass fraction for smoldering and the lower limit of oxygen mass fraction for flaming initially decrease, reach a minimum, and then increase with oxidizer flow rate, while the lower limit of oxygen mass fraction for smoldering has a broader boundary and decreases with the oxidizer flow rate. These limits shift to higher oxygen mass fractions when increasing heat loss. The model is then validated against previous experimental data and applied to further investigate the effects of external radiant heat flux. The lower limit of oxygen mass fraction for flaming decreases with increasing external radiant heat flux, while the surface temperature remains within a certain range.