Stochastic characterisation of unstable lean hydrogen–air annular premixed flames

Abstract

This study is devoted to the characterisation of lean premixed hydrogen–air laminar flames stabilised on an annular burner. The flames studied are chosen to lie close to the lean flammability limit, spanning a range of Damköhler and Reynolds numbers, and correspond to situations where instabilities arise. The experimental characterisation is achieved by examining the statistical moments of the flame hydroxyl radical (OH*) chemiluminescence and schlieren. The standard deviation and the skewness, that are needed to fully characterise the measured probability density functions, are shown to exhibit a non-monotonic behaviour with the distance from the burner surface, first increasing, then decreasing downstream the flame tip. An exponentially modified Gaussian distribution model is proposed to describe the skewed schlieren fluctuations probability density function. This model is closed by developing relations for the probability density function parameters based on the Damköhler and Reynolds numbers, and then used to describe the OH* stochastic behaviour. The relation between the distribution parameters and the transport equation of a reactive scalar gradient is addressed also.