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

Abstract

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.

Oxidation of UC: An in situ high temperature environmental scanning electron microscopy study

“…A correlation between the time needed for ignition to occur and oxygen partial pressure shown in Figure 7b is in agreement with a numerical prediction performed by Hughes et al 46 for a different system that considers competing exothermic and endothermic chemical reactions in parallel with water evaporation 46 . Their numerical prediction was performed by considering the simplest model where mass transport phenomena such as diffusion and advection are neglected as all gaseous and liquid phases are considered evenly distributed.…”

Semianalytical approach to criteria for ignition of excitation waves

“…For instance, combustion waves sometimes can propagate in oscillatory manner, i.e. as relative periodic orbits [52], which makes it plausible that the critical solution there also is a relative periodic orbit, and the transition to turbulence in shear flows, although exhibiting features of excitability, is in terms of models beyond reaction-diffusion even in the simplest phenomenological description [10].…”

“…For instance, combustion waves sometimes can propagate in oscillatory manner, i.e. as relative periodic orbits [52], which makes it plausible that the critical solution there also is a relative periodic orbit, and the transition to turbulence in shear flows, although exhibiting features of excitability, is in terms of models beyond reaction-diffusion even in the simplest phenomenological description [10]. Direct numerical simulations in this model are more difficult because in the standard finite-difference discretization, the critical nucleus solution, defined as an even, spatially nontrivial, stationary solution of the discretized equation, may not be unique and is stable, whereas in the differential equation it is unique and unstable.…”

Stabilization of combustion wave through the competitive endothermic reaction

“…[1] and references therein). By contrast, the competitive exothermic-endothermic reaction models have attracted less interest, despite the fact that these models can be appropriate for modelling pyrolysis [2] or decomposition [3] In this paper, we report results of a stability analysis of combustion waves in a model for the cases when the endothermic step plays a significant role in the reaction mechanism, and is shown to be able to limit or eliminate instabilities which may be inconvenient or even dangerous in practical applications. This is particularly relevant to the combustion of solid fuels, important in such applications as self-propagating high-temperature synthesis (SHS) [4], solid propellants [5], thermopower waves [6], etc.…”