Modelling smothering extinction of buoyancy-driven smoldering combustion: Determination criteria and kinetic controlling mechanism

Modelling extinction of combustion is vital for understanding the extinction criteria and governing mechanism. However, it remains a challenging task for buoyancy-driven smoldering combustion because of dynamic transitions between kinetic and oxygen-transport limiting regimes and intricate couplings of buoyancy-driven air flow and smoldering combustion. In the present study, the kinetic/oxygen-transport limiting regime transitions are resolved with a minimum function between the Arrhenius kinetics and oxygen supply rate in oxidative source/sink terms. Besides, the global energy balance is improved for buoyancy-driven smoldering system to elucidate the interactions between buoyancy-driven air flow and smoldering combustion. The present model is validated by a variety of experiments on smoldering propagation until extinction of buoyancy-driven underground coal smoldering fires. Results show that the extinction of buoyancy-driven underground coal smoldering fires can be determined by two criteria: (1) the net energy rate < 0 with the global energy balance concept, and (2) the minimum oxygen supply rate < 0.48 g m² s⁻¹, which is about six times larger than that for peat smoldering with forced air flow. Under harsh conditions with limited oxygen supply, the coexistence of the local oxygen-transport limiting regime and the local kinetic regime is observed. If the extinction criteria are satisfied, this coexistence shifts to the local kinetic regime and leads to extinction, otherwise it shifts to the local oxygen-transport limiting regime and results in self-sustained smoldering propagation. It reveals the evolution of governing mechanism in smoldering combustion near extinction and provides solid evidence confirming the hypothesis that kinetic mechanism dominates the extinction.