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Accurate models to predict large-scale flame propagation are crucial to assessing the consequences of accidental explosions. A freely expanding spherical flame can experience significant acceleration due to the growth of the Darrieus–Landau instability, increasing the severity of the explosion hazard, and must be accounted for when modeling large-scale flames. Recent large-scale experiments have demonstrated an oscillatory rate of flame acceleration, consistent with self-similar flame propagation and the formation and growth of cells with discrete length scales. In this work, an analytical model describing the growth of multiple generations of cells on a flame surface is developed. Each generation is treated independently with a criteria for cell splitting based on a critical stretch rate. Superposition of the length scales is used to determine the global flame surface wrinkling and propagation velocity of the flame. The model is compared with experimental results and the effect of upstream flow disturbances on the development of the instability is also discussed. It is found that the model reproduces a number of features observed in the experiments, including the overall rate of flame acceleration and the frequency of oscillation. The model also captures the correct trends of flame behavior for the effect of elevated initial turbulence and the transition from positive to negative Markstein length. These results support the self-similar argument of spherical-flame acceleration and can be used in future studies to develop new models describing the behavior of large-scale flames.

In this work, the development of the Darrieus–Landau instability is examined at large scale using atmospheric-pressure methane-air flames in the presence of weak initial turbulence, as well as in quiescent conditions. In the absence of initial turbulence, the critical flame radius for the onset of instability is found to be on the order of 20–35 cm, increasing with methane concentration. In addition, an oscillatory flame acceleration is observed that is directly analogous to the behavior of propane-air mixtures seen in a previous study. Weakly-turbulent initial conditions lead to an earlier onset of flame instability that eliminates the rapid acceleration that occurs during global cell formation along with the oscillatory flame acceleration. It is also shown that weak initial turbulence does not significantly affect the burning velocity during the initial, laminar, flame propagation. Instead, initial turbulence triggers both an earlier onset of instability as well as an increase in the rate of flame acceleration. As a result, significant increases in overall flame velocity is observed in the presence of weak initial turbulence, and this difference increases with flame radius.

Large-scale experiments examining spherical-flame propagation of propane–air flames up to a diameter of 1.2 m were performed. Throughout these experiments, the growth of the Darrieus–Landau instability was directly observed and detailed measurements show that the increase of flame velocity follows a pattern of self-similar oscillatory growth that has not been previously reported. These oscillations are found to be the result of periodic growth and saturation of a narrow range of length scales that follows each generation of cell formation. Based on these observations, a new method to estimate the fractal-acceleration exponent is proposed based on the amplitude and frequency of these oscillations. Comparisons between the fractal exponents derived by this method and a direct power law fit show reasonable agreement with one another, as well as with values reported by previous studies.

Flame acceleration in tubes is studied. A tube filled with flammable mixture is closed at one end and open to the atmosphere at its second end. When ignition takes place near the closed end, it is well-known from experiments that the flame may accelerate, oscillate and eventually reach considerable speeds. A one-dimensional analysis is presented, based upon the assumption that the flame front propagates at a speed that is small compared to the speed of sound. The analysis leads to a construction of the complete unsteady solution. Results from the analysis and from a numerical simulation are compared. They are similar enough to validate the analysis. The tube acoustics are set in motion by the expansion of the fluid due to ignition at the closed end. Subsequently, both spectrum and amplitude evolve because of the motion of the temperature interface, and because of forcing by the flame front, which the analysis precisely quantifies. Oscillations in the front position are strong enough to result in flow reversal. In addition, the induced periodic acoustic acceleration of the temperature and density interface will periodically make the flame front Rayleigh–Taylor unstable, which should result in the dramatic increase in the propagation speed seen in experiments.