Joint Velocity Scalar Filtered Density Function for Large Eddy Simulation of Turbulent Reacting Flows

The joint ``velocity-scalar' filtered density function (FDF) methodology is developed and implemented for large eddy simulation (LES) of turbulent reacting flows. In FDF, the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of the velocity and scalar fields. An exact transport equation is derived for the FDF in which the effects of SGS convection and chemical reaction are in closed forms. The unclosed terms in this equation are modeled by considering an equivalent set of stochastic differential equations (SDEs) which is similar to that typically used in Reynolds-averaged simulation (RAS) procedures. The SDEs are solved numerically by a Lagrangian Monte Carlo procedure in which the It^o-Gikhman character of the SDEs is preserved. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed. It is shown that the FDF results agree well with those obtained by a ``conventional' finite-difference LES procedure in which the transport equations corresponding to the filtered quantities are solved directly. The FDF results are also compared with those obtained by the Smagorinsky closure, and all the results are assessed via comparison with data obtained by direct numerical simulation of a temporally developing mixing layer involving transport of a passive scalar. It is shown that all the first twomoments including the scalar fluxes are predicted well by FDF. The predictive capabilities of the FDF are further demonstrated by LES of reacting shear flows. The predictions show favorable agreements with laboratory data, and demonstrate several of the features as observed experimentally