In the present study, we develop a full second order model and a new flamelet closure relation for the mean chemical source term to describe turbulent reactive flows with premixed reactants. This description ensures that non-gradient and counter-gradient diffusion which can appear in such flames, are taken into account in 2-D or 3-D geometries. 2-D calculations are performed in the case of a confined turbulent premixed flame stabilized by a backward facing step, a configuration which reveals experimentally counter-gradient diffusion and combustion induced production of turbulence. Numerical results are found to be in excellent agreement with measurements of Shepherd et al. [Nineteenth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1982)]. The important influence of counter-gradient diffusion on first order quantities, i.e., mean velocity and length of the recirculation zone is shown.

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