Stabilization of combustion wave through the competitive endothermic reaction

Abstract

In this paper, we numerically investigate the stability of propagating combustion waves in the competitive exothermic-endothermic reaction model. The analysis is based on the Evans function method and direct numerical integration of the governing partial differential equations. The critical conditions for the onset of instability are found for a broad range of parameter values of the model. It is demonstrated that for the parameter values for which the combustion wave is unstable in the one-step reaction model, the inclusion of the endothermic step can lead to flame stabilization.

One-Dimensional Chaotic Laminar Flow With Competitive Exothermic and Endothermic Reactions

“…The multiplicity of the parameter space within which the phenomenology exists has meant that any initial exploration of this kind is partly haphazard, usually guided by existing knowledge of simpler situations, and our case here is no exception. Consequently, we have sought to link our methodologies and results with those for uniform well-mixed flows with competitive reactions (see, for example, [6,7,20]) and with those for chaotically advected flows with single reactions [11]. In the first case, we find in Section 5 that the addition of chaotic mixing to the endothermic-exothermic system described by Sharples et al [20] has a destabilizing effect, in which the stable steady state loses stability at a lower exothermicity.…”

“…However, the results are in qualitative agreement. When r = 1, the endothermic reaction is activated and plays a quenching effect as mentioned by Gubernov et al [6] and Hamaidi et al [9]. However, here we are principally concerned with the effect of the strained flow, and Figures 6 and 7 show that there is a critical value of the Damköhler number, Da crit , above which there are two solutions, one stable and one unstable, and below which the only solution is the trivial solution (u = u a and c = 1).…”

“…So far, we have set Θ = 1 in order to stress the effect of chaotic mixing on competitive exothermic-endothermic reactions. We note that without chaotic mixing, the model describing competitive exothermic-endothermic reactions exhibits oscillatory behaviour for large values of the Lewis number and Θ, as shown in [6,20]. Here we wish to investigate whether or not oscillatory behaviour remains possible with the strained flow represented by equations (2.2) and (2.3).…”

“…In earlier papers we have explored the rich phenomenology of combustion fronts driven by two reactions, either parallel, in which each reaction feeds on its own distinct reactant, or, more interestingly, competitive, in which reactions "compete" for the same fuel [2,6,7,9,20]. In this earlier research we have assumed that the various constituents and products of the process have been well mixed, with any spatial inhomogeneity confined to thin reactive regions (for example, combustion fronts), within which more specialized modelling (for example, coordinate stretching) is required.…”