A methodology termed the ‘filtered mass density function’ (FMDF) is developed and
implemented for large-eddy simulation (LES) of variable-density chemically reacting
turbulent flows at low Mach numbers. This methodology is based on the extension
of the ‘filtered density function’ (FDF) scheme recently proposed by Colucci et
al. (1998) for LES of constant-density reacting flows. The FMDF represents the
joint probability density function of the subgrid-scale (SGS) scalar quantities and is
obtained by solution of its modelled transport equation. In this equation, the effect
of chemical reactions appears in a closed form and the influences of SGS mixing
and convection are modelled. The stochastic differential equations (SDEs) which yield
statistically equivalent results to those of the FMDF transport equation are derived
and are solved via a Lagrangian Monte Carlo scheme. The consistency, convergence,
and accuracy of the FMDF and the Monte Carlo solution of its equivalent SDEs
are assessed. In non-reacting flows, it is shown that the filtered results via the
FMDF agree well with those obtained by the ‘conventional’ LES in which the finite
difference solution of the transport equations of these filtered quantities is obtained.
The advantage of the FMDF is demonstrated in LES of reacting shear flows with
non-premixed reactants. The FMDF results are appraised by comparisons with data
generated by direct numerical simulation (DNS) and with experimental measurements.
In the absence of a closure for the SGS scalar correlations, the results based on the
conventional LES are significantly different from those obtained by DNS. The FMDF
results show a closer agreement with DNS. These results also agree favourably with
laboratory data of exothermic reacting turbulent shear flows, and portray several of
the features observed experimentally.
On Fokker–Planck Equations for Turbulent Reacting Flows. Part 2. Filter Density Function for Large Eddy Simulation