Systematically reduced rate mechanisms and presumed PDF models for premixed turbulent combustion

The use of reduced kinetic mechanisms in models for turbulent premixed flames, at large but finite Damköhler numbers, is described. Taking as examples the two cases of hydrogen–air and methane–air systems for which there exist reduced kinetic schemes characterized by two independent scalar variables only, it is shown that the mean chemical production rate can be in a general way expressed as the product of a mixing factor, depending on the segregation of species due to turbulence, with a reaction rate factor. In this latter factor the probability density function (PDF) of the two scalars appears only as a constant integral quantity. The extension of this analysis to systems involving more than two independent scalars is envisaged. The general result is applied to the two specific cases of interior PDF’s modelled by (i) a single Dirac delta function and (ii) a laminar flamelet.