On transition to self-similar acceleration of spherically expanding flames with cellular instabilities

The evolution of the self-acceleration of spherically expanding flames subjected to cellular instabilities was experimentally studied with H₂/O₂/N₂ mixtures over a wide range of Lewis numbers, flame thicknesses, and density ratios. Results show that the flames manifest a self-similar acceleration behavior, and the acceleration exponent, α, continuously increases and follows a power-law relation with the normalized Peclet number beyond a transition acceleration stage, which is different from the usually suggested self-similar propagation characterized by a constant α after the short transition acceleration period. The self-similar acceleration with reduced growth rate is found to be the results of the continuous extension of cellular spectrum on the long-wavelength side but the saturation of cellular spectrum on the short-wavelength side. The critical Peclet numbers associated with onset (Pe_cr) and transition (Pe_ct) of self-acceleration have a similar non-linear relationship with the Marksetin number, caused by the non-equal differential-thermal effects on the development of Darrieus–Landau (DL) cells for sub-unity (<1) and super-unity (>1) Lewis numbers. Based on the experimental Pe_cr and Pe_ct, a regime diagram is presented for the laminar premixed hydrogen flames with cellular instabilities, which consists smooth propagation, transition acceleration, and self-similar acceleration regimes. In addition, an empirical power-law correlation for the α is suggested to describe the whole self-acceleration process. This correlation is able to predict the present α as well as the experimental results of the previous work. The measured α in the range of present interpellation is smaller than 1.5, the suggested value for the flame self-turbulization. However, this value could possibly be attained at an extremely large Peclet number (or flame radius) based on the extrapolation of the present correlation.