On transition to cellularity in expanding spherical flames: Experiment and theoretical comparison

The transition to cellularity of the centrally ignited, positively stretched, outwardly propagating spherical flames was first experimentally determined for the near-equidiffusive flames of acetylene and non-equidiffusive flames of propane and hydrogen, recognizing that the former is subjected only to hydrodynamic instability while the latter experience diffusional-thermal instability as well. The experimentally measured critical radii of transition were then scaled by the laminar flame thickness determined from the calculated temperature profiles of the adiabatic laminar flames. The resulting critical Peclet numbers were found to assume an almost constant value of 350-375 for the diverse conditions investigated for the near-equidiffusion flames, being insensitive to variations of the equivalence ratio, pressure, and oxygen concentration. This insensitivity is anticipated from theoretical results. The corresponding values for the propane and hydrogen flames were found to respectively decrease and increase fairly linearly with equivalence ratio, in agreement with the decreasing and increasing trends of the global Lewis numbers of these flames. Comparison between the experimental critical Peclet numbers with those calculated from the theory, using locally evaluated fundamental flame parameters such as the global activation energy, yields not only trend-wise but also fairly close quantitative agreement.