Stability of combustion waves in the Zeldovich–Liñán model

In this paper we investigate the stability of the premixed combustion waves in the Zeldovich–Liñán model in the adiabatic limit in two spatial dimensions. It is shown that either wave or cellular instabilities emerge for the Lewis number for fuel greater or smaller than one respectively. On the Lewis number for fuel vs activation energy parameter plane, the critical parameter curve for wave (cellular) instability is a monotonically decaying (increasing) function, which tends to one for large values of activation energies and grows infinitely (vanishes) as the activation energy is decreased to some critical value (zero). Decreasing the recombination parameter, which corresponds to the relation between the characteristic times of the branching and recombination reactions, makes the combustion waves more stable by increasing the region of parameter values for stable traveling wave solutions. Increasing the ambient temperature is demonstrated to have similar stabilizing effect on combustion waves. The effect of the varying the Lewis number for radicals is shown to be more complex and depends on the regime of recombination. It is demonstrated that as the critical parameter values for the onset of instability are crossed, either pulsating or cellular two-dimensional solutions emerge. The properties of these solutions are studied. A comparison of the results of this paper with known data from the literature for deflagration of hydrogen–oxygen mixtures is made.