Counter-gradient in premixed turbulent flames

A new theory for premixed turbulent flames normal to the oncoming reactants is developed on the basis of the Bray-Moss-Libby model of premixed combustion and second-order closure. Gradient transport assumptions are carefully avoided. The final formulation focuses on the intensity of the fluctuations of the velocity component normal to the flame and on the mean flux of product. At low rates of heat release corresponding to small intensities of the density fluctuations the new theory is in agreement with our earlier theory based on gradient transport. However, as the heat release increases toward values of practical interest, counter-gradient diffusion, i.e., mean flux in the direction of increasing mean concentration, arises and is attributable to the differential effect of mean pressure gradient on cold reactants and hot products. The implications of these results are discussed.