On Flame Propagation Under Conditions of Stoichiometry

Source abstract

This paper contains a nonlinear analysis of flame front stability assuming stiochiometric composition of the combustible mixture. The constant-density model of a premixed flame is considered. An asymptotic nonlinear partial differential equation, which describes the evolution of the disturbed flame front,is derived: $$\Phi _\tau + 4\nabla ^4 \Phi + \nabla ^2 \Phi + \frac{1}{2}( \nabla \Phi )^2 = 0.$$ It is shown that a plane flame front is stable if the mean Lewis number of the reactants exceeds some critical value close to unity. If this condition does not hold the plane flame front is unstable, and numerical studies demonstrate that the flame assumes the form of a nonstationary cellular surface in a state of continual chaotic division and recombination of cells. A description is given of the effect of local violation of stoichiometry in the vicinity of the disturbed reaction zone, as a result of which the locally-excess component penetrates into the combustion product region. On the parts of the flame front which are convex toward the fresh mixture one observes an excess ofthe lighter component; on the concave parts there is an excess of the heavier component. After penetrating through the reaction zone of the premixed flame, the reactants burn out under conditions of diffusion combustion.