On the transition from smoldering to flaming

Abstract

We consider the transition from smoldering to flaming. Though there have been numerous experimental studies of this topic, it has been virtually untouched theoretically. Rather than investigating the details of either the transition process or the subsequent flaming, we focus on determining the mechanism and the conditions that trigger the transition. We employ both computation and approximate analytical approaches. We consider a planar, forward smolder wave driven by a constant forced flow of gas containing oxidizer. The chemical kinetic scheme employed consists of three reactions, namely, pyrolysis, fuel oxidation, and char oxidation. There have been a number of speculations about the nature of the triggering mechanism, including the gaseous reactions, the char oxidation reaction, destruction of the porous matrix through which the smolder wave propagates, and others. However, no mechanism has, as yet, been theoretically demonstrated to be capable of acting as the triggering mechanism. We show that the char oxidation reaction hardly affects the characteristics of smolder wave propagation due to its small reaction rate, though under appropriate conditions, it can act as the trigger for the transition to flaming due to its ability to self-accelerate. Specifically, we introduce the concept of, and then compute, a quantity that we term the flaming distance, L F . This is the distance that a steadily propagating smolder wave initiated at the gas flux inlet travels inside the porous medium before the char oxidation reaction spontaneously self-accelerates, resulting in an eruption of the temperature at the smolder front. That is, the smolder wave propagates for a relatively long latent period of time until it reaches L F . A transition to flaming then occurs. The flaming distance L F depends on the physicochemical parameters of the fuel and the products as well as external parameters: the velocity and composition of the incoming gas, heat loss, etc. We show that smolder waves propagating in porous samples of length L do (do not) exhibit a transition to flaming if L F < L ( L F > L ).