A numerical study of the nonlinear development of hydrodynamically unstable premixed flames

The nonlinear evolution of a perturbed premixed flame under the influence of the hydrodynamic instability, has been primarily studied in the literature within the context of the weakly-nonlinear Michelson-Sivashinsky equation. This equation is valid when the heat release relative to the thermal energy of the fresh mixture is relatively small, or σ - 1 ≪ 1. Although it provides valuable physical insight in the nonlinear development of the Darrieus-Landau instability, its application is limited by the fact that σ ∼ 5 ÷ 8 for real combustible gas mixtures. In this work we examine, within the context of a hydrodynamic model, the evolution of the flame front for finite amplitude disturbances and realistic values of a. This full nonlinear model elucidates the effect of thermal expansion on flame dynamics.