Effect of Thermal Expansion on the Stability of Plane, Freely Propagating Flames

Much of the previous effort on the stability of plane, freely propagating flames to short-wave perturbations is based on the constant-density approximation (CDA). Such a treatment achieves analytical simplicity at the expense of ignoring thermal expansion. It is valid only when the heat release is small, either due to weak exothermicity or scarcity of reactants, hardly the state of affairs in real flames. This paper treats the stability question without invoking the CDA, and finds that when thermal expansion is taken into account, the Lewis-number stability band disappears. In the limit of long-wave perturbations, the present results agree with those obtained recently by several authors by means of the Slowly-Varying-Flame approach.