On the Relation Between Presumed FDF, Subgrid Variance and Flame Speed in the Wrinkled Flamelet Regime: An A Posteriori Analysis

Abstract Presumed PDF/FDF approaches with dependency on second order moments of an appropriately defined progress variable are often used in combustion modelling, but they fail in predicting the limiting behaviour of burning speed when the latter approaches the laminar condition. In this work, we discuss a recently proposed correction for the burning speed in the context of presumed FDF approaches, and test its performance using large eddy simulation (LES). First, the correction model is discussed in relation to the interlink between filtered density function and second order moment (SGS variance in the LES case) from a theoretical point of view, and the further interlink with the LES filter size is discussed. In a second step, a propane flame in the wrinkled flamelet regime of the Borghi diagram is simulated a posteriori using two LES filter size resolutions. We firstly show that the increase of filter size leads to an overestimation of the burning speed. We then show how the incorrect estimation of burning speed with increasing filter size is corrected and how the correction affects the SGS variance. An extended correction model for partially-premixed combustion is also proposed.