Filtered mass density function for large-eddy simulation of turbulent reacting flows

A methodology termed the 'fiItered mass density function' (FMDF) is develop ed and implemented for large-eddy simulation (LES) of variable-density chem ically reacting turbulent hows at low Mach numbers. This methodology is bas ed on the extension of the 'fiItered density function' (FDF) scheme recentl y proposed by Colucci et al. (1998) for LES of constant-density reacting fl ows. The FMDF represents the joint probability density function of the subg rid-scale (SGS) scalar quantities and is obtained by solution of its modell ed transport equation. In this equation, the effect of chemical reactions a ppears in a closed form and the influences of SGS mixing and convection are modelled. The stochastic differential equations (SDEs) which yield statist ically equivalent results to those of the FMDF transport equation are deriv ed and are solved via a Lagrangian Monte Carlo scheme. The consistency, con vergence, and accuracy of the FMDF and the Monte Carlo solution of its equi valent SDEs are assessed. In non-reacting flows, it is shown that the filte red results via the FMDF agree well with those obtained by the 'conventiona l' LES in which the finite difference solution of the transport equations o f these filtered quantities is obtained. The advantage of the FMDF is demon strated in LES of reacting shear flows with non-premixed reactants. The FMD F results are appraised by comparisons with data generated by direct numeri cal simulation (DNS) and with experimental measurements. In the absence of a closure for the SGS scalar correlations, the results based on the convent ional LES are significantly different from those obtained by DNS. The FMDF results show a closer agreement with DNS. These results also agree favourab ly with laboratory data of exothermic reacting turbulent shear hows, and po rtray several of the features observed experimentally.