A diffusion-flame analog of forward smolder waves: (I) 1-D steady structures

Abstract

A solid fuel may be viewed as a special kind of gas of vanishing molecular mobility. Accordingly, a forward smolder wave may be regarded as a special kind of diffusion flame with fuel Lewis number tending to infinity. Such a perspective is explored in this study to examine the structural characteristics of steady planar forward smolder waves, with particular emphasis placed on the heat loss effects. The problem is formulated by employing a diffusive-thermal model, in which the complex smolder reactions are modeled by a one-step exothermic char oxidation reaction. For both adiabatic and non-adiabatic cases, the reaction layer is analyzed by using the activation energy asymptotic method, which ends up with jump conditions connecting quantities across the reaction front. The asymptotic results indicate that adiabatic forward smolder waves do not have a blowoff limit in the small Damköhler number limit, whereas a quenching limit develops when heat loss effects are incorporated. For non-adiabatic forward smolder waves with a reaction trailing structure, the leakage of oxygen through the reaction layer vanishes to leading order, so the reaction zone is described by a structure that is essentially analogous to the premixed flame regime of diffusion flames. By contrast, in the presence of heat loss the reaction leading structure is characterized by O(1) leakage of both reactants, so the analogy is with the partial burning regime of diffusion flames. The description of these two distinct structures, however, can be unified through a common dimensionless parameter m, which is defined as the fraction of heat conducted to the fresh solid fuel side among the total amount of heat generated in the reaction zone.