A balance equation for the mean rate of product creation in premixed turbulent flames

Transport equations for reaction rate W and its Favre-averaged value W˜ are derived from first principle in the case of premixed turbulent combustion. The assumptions made for derivation hold for unity Lewis number premixed flames at least in the flamelet regime of turbulent burning. Analysis of the latter equation shows that it involves two dominant terms, but the difference between them vanishes if reaction zones retain the structure of the zone in the unperturbed laminar flame. However, in such a case, turbulent burning velocity cannot grow with time during interaction of an initially laminar flame with a turbulent flow. Therefore, the analysis indicates a vital role played by local perturbations of reaction zone structure in premixed turbulent combustion. The dominance of these two terms and the important role played by the difference between them are confirmed by analyzing three DNS databases associated with both the corrugated flamelets and thin reaction zones regimes of premixed turbulent burning. Moreover, the DNS data show that perturbations of local displacement speed due to perturbations of local flamelet structure are also of paramount importance for modeling transport of flame surface density even in weakly turbulent flows. Finally, by simulating curved and/or strained laminar premixed flames and integrating the transport equation for W across the flames, the integral is shown to depend linearly on the stretch rate even in highly perturbed flames, with results obtained from variously stretched flames being close to each other. Based on this finding, the difference between the two dominant terms in the transport equation for the mean rate W˜ is hypothesized to depend linearly on the stretch rate conditioned to the reaction zone. Application of this hypothesis to the DNS data associated with the corrugated flamelets combustion regime yields encouraging results, thus, confirming a crucial role played by local perturbations of reaction zone structure even in weakly turbulent flames.