Analysis of combustion waves arising in the presence of a competitive endothermic reaction

Abstract

We consider travelling wave solutions of a reaction-diffusion system corresponding to a single-step homogeneous premixed combustion scheme competitively coupled with an endothermic reaction. Properties of the travelling combustion fronts, such as the wave speed and the burnt temperature are derived numerically over a range of different parameter values, such as those describing the relative enthalpies, rates and activation energies of the endothermic and exothermic reactions. Unique combustion wave solutions are shown to exist for each distinct combination of the parameter values. These solutions are linearly stable if the heat release from the exothermic reaction is sufficiently large, otherwise the combustion waves develop pulsation. In particular, using a finite element package to numerically integrate the governing partial differential equations, period-1 and period-2 type oscillatory behaviour was observed prior to wave extinction.

Bistability of flame propagation in a model with competing exothermic reactions

“…Here, q is positive in contrast to [10,11], where the second reaction is endothermic and thus q was negative. Equations (2.1) are considered subject to the boundary conditions On the right boundary, we have a cold (u = 0) and unburned state (v = 1).…”

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

“…[11,12] and references therein); the case of competitive reactions, typical of decomposition or dissociation processes, has received much less attention. In recent papers [13][14][15], we have explored the behaviour exhibited by a model system in which a competitive endothermic reaction is regarded as a perturbation to a coexisting exothermic reaction having a lower activation energy. There we were concerned with the existence and stability of travelling reaction fronts in a spatially one-dimensional distribution of reactant material.…”

Stabilization of combustion wave through the competitive endothermic reaction

“…Arrhenius kinetics are assumed for both reactions. Following [15], the non-dimensional equations governing this process can be written as…”

“…The non-dimensional time and space coordinates used here, t and x, are related to the nondimensional variables, t and x from [15] via the equations t = t e β and x = x e β/2 . This additional scaling of time and coordinate is more convenient for the numerical analysis.…”

“…It is expected that interesting instability characteristics can occur for these different regimes. In [15], we have analysed the stability of combustion waves in the regime where the exothermic reaction is dominating over the endothermic step; it is the purpose of the current investigation to carry out a similar systematic stability analysis of combustion waves for the cases when the endothermic step plays a more significant role in the reaction mechanism. …”