Bistability of flame propagation in a model with competing exothermic reactions

Abstract

We investigate a diffusional-thermal model with twostep competitive exothermic reactions for premixed combustion wave propagation in one spatial dimension under adiabatic conditions. A criterion based on the crossover temperature notion was used to qualitatively predict the region in the space of parameters where three travelling combustion wave solutions coexist, which are further studied via numerical means. It is demonstrated that under certain conditions the flame speed is an 'S'-shaped function of parameters. The fast branch is either stable or is partly stable and exhibits the Andronov-Hopf (AH) bifurcation before the turning point is reached. The mid-branch is completely unstable. The slow solution branch is either unstable or partly stable and exhibits a single or a pair of AH bifurcations. The AH bifurcations are shown to be supercritical giving rise to stable pulsating waves. Bistability and hysteresis phenomena are also demonstrated.

Combustion waves in composite solid material of shell–core type

“…However, for intermediate parameter values, behaviour different from that predicted by Equations (15) [14], which is chemistry driven and is caused by the presence of two parallel reaction paths. Mathematically, the system of Equations (5)- (7) is also a set of three partial differential equations as in [14]; however, Downloaded by [New York University] at 06:53 01 June 2015 in the current model there is only a single reaction pathway. Nevertheless, multiplicity is possible even in such a situation.…”

“…s ∼ 1, the competition of the two flame propagation regimes may lead to the emergence of triple coexisting solutions, propagating with various flame velocities. This is a region of parameters where complex dynamical regimes such as flame hysteresis [14] can be expected to occur and we plan to investigate these scenarios in future work.…”

“…If α/s is small, Equations (14) tend to the ones describing the combustion of pure solid fuel, the distribution of temperatures θ 1, 2 (x) are monotonic functions close to each other, and the flame speed approaches the adiabatic combustion speed of the pure energetic component of the composite. In other words, the role of the heat conducting element becomes negligible.…”

On the route to extinction in non-adiabatic flames from competitive exothermic reactions

“…The competitive exothermic model examined in this study has practical application in simulating the combustion of MeCH 2 , where Me is either Zirconium or Titanium [12,13]. Towers et al [17] and Huang et al [8,9] have analysed this model for the adiabatic case and here we extend their study to take volumetric heat losses into consideration.…”

Stabilization of combustion wave through the competitive endothermic reaction

“…Significant attention has been paid to combustion systems with competitive exothermic reactions (e.g. [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.…”