Developing premixed turbulent flames: Part I. A self-similar regime of flame propagation

Contrary to numerous models addressing hypothetical, fully-developed premixed turbulent flames, the focus of this work is placed on the behavior of the developing flames, because they occur in most laboratory and industrial burners. By analyzing the available experimental data, the following trends are emphasized: (1) spatial profiles of the progress variable, presented in the dimensionless form by using the mean turbulent flame brush thickness, are collapsed to a universal curve well approximated by the complementary error function under a wide range of conditions; (2) the development of flame thickness, delta (t)(t), is well approximated by the turbulent diffusion theory in a range of t/tau (t); and (3) the development of flame speed, S-t(t), and thickness are qualitatively different. Based on these trends, a self-similar regime of turbulent flame development is defined and its consequences for mean heat release models are considered. The ability of various models to describe this regime and, in particular, to yield the qualitatively different time-dependencies of the normalized S-t(t) and of delta (t)(t), indicated by experimental data, is assessed both analytically and numerically. It is shown that only time-dependent closures of the mean heat release rate can lead to the substantial difference between the development of the normalized flame speed and thickness. The numerical results indicate that the emphasized difference is a challenge for many current combustion models, but the so-called Flame Speed Closure model is well tailored to simulate it and other emphasized trends of turbulent flame development.