VS-FMDF and EPVS-FMDF for Large Eddy Simulation of Turbulent Flows

The first part of this dissertation is concerned with implementation of the joint ``velocity-scalar filtered mass density function'' (VS-FMDF) methodology for large eddy simulation (LES) of Sandia Flame D. This is a turbulent piloted nonpremixed methane jet flame. In VS-FMDF, the effects of the subgrid scale chemical reaction and convection appear in closed forms. The modeled transport equation for the VS-FMDF is solved by a hybrid finite-difference/Monte Carlo scheme. For this flame (which exhibits little local extinction), a flamelet model is employed to relate the instantaneous composition to the mixture fraction. The LES predictions are compared with experimental data. It is shown that the methodology captures important features of the flame as observed experimentally. In the second part of this dissertation, the joint ``energy-pressure-velocity-scalar filtered mass density function'' (EPVS-FMDF) is developed as a new subgrid scale (SGS) model for LES of high-speed turbulent flows. In this model, the effects of compressibility are taken into account by including two additional thermodynamic variables: the pressure and the internal energy. The EPVS-FMDF is obtained by solving its modeled transport equation, in which the effect of convection appears in a closed form. The modeled EPVS-FMDF is employed for LES of a temporally developing mixing layer