Nonadiabatic combustion waves in a two-step competitive exothermic-reaction model

Abstract

We consider travelling front solutions of a one-dimensional reaction-diffusion system corresponding to two-stage competitively exothermic reactions. We suppose all reactions occurring during the combustion may be lumped together as two different paths. Both exothermic reactions compete for the same reactant. Properties of travelling wave fronts, particularly flame speed, are determined numerically by solving the governing partial differential equations. The flame speed is analysed for different values of the heat loss parameter. It is demonstrated that, as the heat loss coefficient increases, the flame speed decays gradually until the front ceases to exist due to insufficient energy being available to sustain the flame front. Earlier studies for the adiabatic case showed the existence of bi-stability (fast and slow waves co-exist for the same parameter values). We study how heat loss affects the size of the bi-stable region. Furthermore, we investigate how the extinction limit depends on the heat loss parameter as well as the parameter representing the ratio of the activation energy to the heat release of the second reaction. Numerical solutions show that there is no travelling front when these parameters are above threshold values. The dependence of flame speed on the temperature profile is also investigated. The bi-stability phenomenon is demonstrated by perturbing the temperature profile. References

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