Stability analysis of combustion waves for competitive exothermic reactions using Evans function

Abstract

• Analysed a two-step adiabatic competitive exothermic reaction scheme. • Analysed the stability of the combustion waves using the Evan function method. • Determined the threshold values of parameters for the onset of pulsating behaviour. • Showed that the system exhibits pulsating and period-doubling behaviour. We consider travelling wave solutions of a reaction-diffusion system corresponding to an adiabatic two-step competitive exothermic reaction scheme. In such a scheme, a combustion process is assumed to be lumped into two different exothermic reactions. Although the rate constants of the reactions are distinct, both reactions occur simultaneously and feed on the same reactant. The travelling wave solutions are obtained via the shooting-relaxation method. The linear stability analysis is conducted using the Evans function technique and the compound matrix method. Further, threshold values of parameters corresponding to Hopf points are established. It is shown that the system exhibits pulsating behaviour when the parameter values are greater than the threshold values. The onset of instability is found for a broad range of parameter values. Two different numerical methods are then used to obtain solutions from the governing partial differential equations to validate the results.