Initiation and propagation of combustion waves with competitive reactions and water evaporation

We use a one-dimensional model to present numerical and analytical results on the propagation of combustion waves, driven by competing exothermic and endothermic chemical reactions in parallel with water evaporation. The research was motivated by the phenomenology of emulsion explosives comprising a mixture of fuel and an ammonium nitrate (AN)-water solution. An extensive programme of computational modelling has covered a range of important physical influences, particularly the water fraction and the ambient pressure, on which the endothermic effect of evaporation is critically dependent. A substantial, and not immediately obvious, influence of the evaporation, through its effect on the temperature, is on the fraction of the AN consumed, respectively, by the competing exo- and endothermic reactions, which are controlled by differing, temperature-sensitive kinetics. Self-sustaining travelling combustion waves are initiated for a wide range of parameter values. They are usually oscillatory, regular for small water content and become highly irregular, sometimes causing extinction for larger water content. The numerics are complemented by a brief theoretical analysis, which throws light on the complex and subtle interplay of the two chemical reactions and the evaporation, expressed in the form of a highly convoluted integral over the whole time and space extent of the process.