Some Conditional Statistics in a Turbulent Premixed Flame Derived from Direct Numerical Simulations

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Abstract
The conditional moment closure (CMC) method constitutes an alternative approach in the modelling of turbulent reacting systems. In the present study, the CMC formulation is introduced for turbulent premixed combustion and the transport equation for the conditional mass fraction is derived. It appears that the key points for these methods consist in the modelling of the conditional scalar dissipation rate and mean velocity. In order to provide information concerning these two quantities, an existing data base for direct numerical simulations (DNS) of three-dimensional turbulent premixed flames is used. From the DNS, the effects of the Damköhler and Lewis numbers on the conditional means are presented and discussed. It appeal's that the conditional mean scalar dissipation remains unaffected by the turbulent mixing in the reaction zone. However, at low Damköhler numbers, the gradients of the mean progress variable are steeper in the preheat zone of the instantaneous flame fronts leading to a higher dissipation rate. The conditional mean velocity is found to evolve almost linearly through the turbulent flame brush, as expected from the mean pressure gradient that arise from the overall heat release. A noticeable negative slip velocity associated with the wrinkling of the turbulent flame is observed in the simulations. It is also found that there is no significant change in the axial velocity through the instantaneous flame front. This suggests that the flame adjusts itself so that it can provide dilatation without axial acceleration in the instantaneous flame front. The probability density function of the progress variable exhibits a strongly bimodal shape, but the peak corresponding to the fresh gas side is broader. Turbulent fluxes for the mean progress variable are derived from the DNS and, contrary to previous studies, no counter-gradient diffusion is observed in these simulations.