A simple model for the filtered density function for passive scalar combustion LES

LES models for turbulent non-premixed combustion usually require knowledge of the filtered density function of the conserved scalar, and we propose to use a simple top-hat function. Such top-hat distributions were developed as probability density functions for RANS applications in the 1970s but were soon surpassed by the function. We find that in the context of LES, the top-hat distribution provides an excellent alternative to the now much more common function. The top-hat function is assessed through a phenomenological analysis of Direct Numerical Simulation (DNS) data from a planar jet and of experimental data from a turbulent opposed jet. The approach is then tested a posteriori for a piloted diffusion flame (Sandia Flame D). Advantages of the top-hat function are the ease of implementation and the reduced dimensionality of look-up tables. The present paper also discusses inconsistencies of sub-grid -FDFs, the FDFs sensitivity on implicit filtering, and the regime in which a assumption can be a valid filtered density function for LES.