Some aspects of presumed filtered density functions formulation in the context of large eddy simulation of turbulent reacting flows

In Large Eddy Simulations (LES) of turbulent flows, spatially-averaged versions of the Navier-Stokes equations are solved on a grid, which is coarse relative to the smallest turbulent length scales [1]. In order to couple the detailed chemistry and the computed flow field in LES of reacting flows, the so-called filtered density function-based approach for subfilter-scale modelling was suggested [2]. This approach was named as the laminar flamelet and allowed to link the complex chemistry to a single variable, i.e. mixture fraction. The mixture fraction is obtained by the solution of corresponding filtered transport equation and subgrid-scale (SGS) variance (the residual field) is usually modelled [3]. The objective of this article is to present in-depth analysis of filtered density functions (FDFs) by analysing experimental data obtained from two-dimensional planar, laser induced fluorescence measurements in isothermal swirling coaxial turbulent jets at a constant Reynolds number of 29000. The FDFs were analysed as a function of flow swirl number, spatial locations in the flow and were linked to the measured subgrid scale variance. In addition, presumed FDFs were also analysed and associated laminar flamelet solution integration errors were evaluated. It was experimentally found that the FDFs can become unimodal when SGS variance reaches a certain value. However, bimodal FDFs were observed in flow regions with high SGS variance. It was demonstrated that bimodality does not automatically result in large errors in resolved variables when top-hat FDF or -FDF formulations are used. It was suggested that possible source of errors in resolved variables could be linked to the SGS variance models rather than to the presumed FDF-based models.