Model of cellular instability of flames of ternary mixtures

A simple phenomenological diffusive-thermal model of cellular instability of premixed flames of ternary mixtures is developed and presented. The model shows that preferential diffusion can alter stoichiometry of the mixture, i.e., the ratio of the fuel and oxidizer concentrations, and also its effective dilution by an inert. Key parameters of the model are estimated using numerical modeling of burning velocities. Laminar burning velocities are calculated for hydrogen-oxygen-nitrogen, methane-oxygen-nitrogen, and propane-oxygen-nitrogen mixtures. Conditions for the appearance of cellular instability in ternary mixtures are determined and compared with experiments. In good agreement with experimental observations, the diffusive-thermal instability is predicted in hydrogen flames with equivalence ratios $\varphi\lesssim$ 1.45, in lean methane flames with $\varphi\lesssim$ 1.02, and in rich propane flames with $\varphi\gtrsim$ 1.03. The magnitude of the change in the local flame velocity due to preferential diffusion is evaluated. It is demonstrated that nitrogen diffuses faster than oxygen in hydrogen-air and methane-air flames, while oxygen diffuses faster than nitrogen in flames of propane and other heavier hydrocarbons. In mixtures of air with propane or heavier hydrocarbons, the transition between stable and unstable regimes is predicted in mixtures that are leaner than the mixture corresponding to the peak of the burning velocity curve, in agreement with experimental observations.