Stability of flames in an exothermic-endothermic system

The propagation of a premixed laminar flame supported by anexothermic chemical reaction under adiabatic conditions butsubject to inhibition through a parallel endothermic chemicalprocess is considered. The temporal stability to longitudinalperturbations of any resulting flames is investigated. The heatloss through the endothermic reaction, represented by the dimensionlessparameter , has a strong quenching effect on wave propagation.The wave speed–cooling parameter (, c) curves are determinedfor a range of values of the other parameters. These curvescan be monotone decreasing or S-shaped, depending on the valuesof the parameters ß, representing the rate at whichinhibitor is consumed relative to the consumption of fuel, µ,the ratio of the activation energies of the reactants and theLewis numbers. This gives the possibility of having either one,two or three different flame velocities for the same value ofthe cooling parameter . For Lewis numbers close to unity, whenthere are three solutions, two of them are stable and one isunstable, with two saddle-node bifurcation points on the (,c) curve. For larger values of the Lewis numbers there is aHopf bifurcation point on the curve, dividing it into a stableand an unstable branch. The saddle-node and Hopf bifurcationcurves are also determined. The two curves have a common, Takens–Bogdanovbifurcation point.