On transition to cellularity in expanding spherical flames

The instant of transition to cellularity of centrally ignited, outwardly propagating spherical flames in a reactive environment of fuel-oxidizer mixture, at atmospheric and elevated pressures, was experimentally determined using high-speed schlieren imaging and subsequently interpreted on the basis of hydrodynamic and diffusional-thermal instabilities. Experimental results show that the transition Péclet number, Pe_c = R_c/l_L, assumes an almost constant value for the near-equidiffusive acetylene flames with wide ranges in the mixture stoichiometry, oxygen concentration and pressure, where R_c is the flame radius at transition and l_L the laminar flame thickness. However, for the non-equidiffusive hydrogen and propane flames, Pe_c respectively increases and decreases somewhat linearly with the mixture equivalence ratio. Evaluation of Pe_c using previous theory shows complete qualitative agreement and satisfactory quantitative agreement, demonstrating the insensitivity of Pe_c to all system parameters for equidiffusive mixtures, and the dominance of the Markstein number, Ze (Le - 1), in destabilization for non-equidiffusive mixtures, where Ze is the Zel'dovich number and Le the Lewis number. The importance of using locally evaluated values of l_L Ze and Le, extracted from either computationally simulated one-dimensional flame structure with detailed chemistry and transport, or experimentally determined response of stretched flames, in the evaluation of Pe_c is emphasized.