Velocity-scalar filtered mass density function for large eddy simulation of turbulent reacting flows

Abstract

A methodology termed the “velocity-scalar filtered mass density function” (VSFMDF) is developed and implemented for large eddy simulation (LES) of variable-density turbulent reacting flows. This methodology is based on the extension of the previously developed “velocity-scalar filtered density function” method for constant-density flows. In the VSFMDF, the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function of the velocity and scalar fields. An exact transport equation is derived for the VSFMDF in which the effects of SGS convection and chemical reaction are in closed forms. The unclosed terms in this equation are modeled in a fashion similar to that in Reynolds-averaged simulation procedures. A set of stochastic differential equations (SDEs) are considered which yield statistically equivalent results to the modeled VSFMDF transport equation. The SDEs are solved numerically by a Lagrangian Monte Carlo procedure in which the Itô-Gikhman character of the SDEs is preserved. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed. In nonreacting flows, it is shown that the VSFMDF 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 VSFMDF 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 of the first two moments including the scalar fluxes are predicted well by the VSFMDF. Moreover, the VSFMDF methodology is shown to be able to represent the variable density effects very well. The predictive capabilities of the VSFMDF in reacting flows are further demonstrated by LES of a reacting shear flow. The predictions show favorable agreement with laboratory data, and demonstrate several of the features as observed experimentally.