LES/FDF with laminar flamelet
I am modelling premixed turbulent combustion with LES, and I want to use a laminar flamelet approach to close the progress variable equation, whose source term depends hence on the mass fractions computed with detailed chemistry (on 1D laminar flows).
In RANS, since the computed variables have the meaning of statistical averages, I agree that the quantities calculated (a priori) with the laminar calculation must be convoluted through a PDF (presumed or calculated via transport equation). In analogy I expected that the same quantities should be filtered (with the same filter and filter width of your turbulent calculation) in LES context. Let's remind that in the turbulent calculation, the flame structure is hypothesized to behave locally laminar.
Nevertheless, I have heard and read that this approach is for some reason wrong, since it does not recover the correct filtered quantities, and I have to convolute the laminar quantities using the so called FDF (Filtered Density Functions) instead of the filter, which have a role of spatially statistical PDF I guess.
Can someone explain me why the filter approach is not valid and why the correct filtered value is recovered instead with a FDF??
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