Lagrangian intermittent modelling of turbulent lifted flames

Abstract

Partially premixed combustion in turbulent non-premixed flames is studied. A possible way to describe these turbulent flames is to consider a transport equation for the probability density function (PDF) for all the fluctuating variables with a satisfactory representation of small-scale mixing phenomena influenced by chemical reactions. Here, a more tractable model based on a presumed joint PDF shape for both a mixture fraction variable and a progress variable is proposed. In this approach, the assumption of statistical independence between the two variables is avoided. On the contrary, a strong but clearly stated functional dependence between the two scalars is introduced. This allows us to express the higher probability that fluid particles have to burn for nearly stochiometric compositions. The effects of both non-infinitely fast chemistry and partially premixed combustion are taken into account by using a modified version of the MIL model (Modèle Intermittent Lagrangien) originally introduced by Borghi and Gonzalez. In the present modelling proposal, the MIL principles are essentially used as a way of distributing the mean chemical rate among a premixed and a diffusive contribution and the new formulation has the potentiality to take into account the essential features of the stabilization zone. Finally, the complete model has been used to simulate the turbulent non-premixed lifted methane–air flames studied by G. Mungal and his co-workers at Stanford University. With the proposed approach, a satisfactory agreement is obtained in terms of lift-off heights for a wide range of operating conditions.