Dynamical and statistical behavior of cellular premixed flame in a diverging Hele- Shaw channel

A detailed statistical analysis of experimental data on the propagation of a stoichiometric premixed propane-air flame in a diverging Hele-Shaw channel was conducted. The statistical structure of the flame front was determined, including the size distribution of cells, the lifetime statistics of cells due to their spontaneous division and absorption by larger neighboring cells. It is shown that the size distribution of flame front cells is described by a gamma distribution, and the cell lifetime is described by the law of radioactive decay. Statistical data are presented on the geometric characteristics of cells, including the aspect ratio and skewness. Cell splitting is considered in detail, with a probabilistic model for the division point position in the presence of a critical cell size below which no splitting occurs. The results obtained form a quantitative basis for the development of mathematical models of cellular front propagation, both quasi-two-dimensional and three-dimensional.