The filtered density function (FDF) and its density weighted filtered mass density function (FMDF) have proven very effective for large eddy simulation (LES) of turbulent flows. The most sophisticated form of the model to-date is the joint frequency-velocity-scalar filtered mass density function (FVS-FMDF) and a simpler version (VS-FMDF) which does not include the subgrid scale (SGS) frequency. Hydro dynamic closure in incompressible, non-reacting flows has been achieved via the marginal velocity-FDF (V-FDF), and the one which considers only the species mass fraction field is the scalar-FDF (S-FDF and S- FMDF). The latter is the most elementary form of FDF and is currently the most widely used. The extension to include for exergy analysis is via Entropy FDF (En-FDF).
In almost all of the previous work, the FDF is considered for flows at low compressibility levels. In such flows, the effects of pressure fluctuations in the energy transport is negligible. In the present work, the FDF is extended to a “self-contained” format to include the SGS statistics of all of the hydro-thermo-chemical variables. These are the thermodynamic pressure, the specific internal energy, the velocity vector and the composition field. A transport equation is developed for the joint “pressure-energy-velocity-composition filtered mass density function” (PEVC- FMDF). In this equation, the effect of convection appears in a closed form. The coupling of the hydrodynamics and thermodynamics (and chemistry in reacting flows) is modeled. The consistency of the PEVC-FMDF formulation is established, and the overall predictive capability of the model is appraised via comparison with direct numerical simulation (DNS) data.