Direct Numerical Simulations of an igniting non-premixed flame are analysed in order to assess the accuracy of the gradient diffusion model for the conditional turbulent flux term in the context of the CMC equation. This term may become important in realistic combustion situations involving stabilisation, ignition and extinction. The results show that the edge flame probably cannot be treated with first-order CMC and that its stucture involves a balance between chemistry, molecular mixing, and spatial transport. The usual gradient diffusion approximation for the conditional turbulent flux seems to be adequate for high turbulence intensity relative to laminar burning velocity of a stoichiometric mixture, but there is strong conter-gradient transport at weak turbulence. An analysis of the major terms in the conditional scalar flux equation shows that the pressure fluctuation is mainly responsible for the counter-gradient transport.
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