A methodology termed the ''velocity-scalar filtered density function'' ͑VSFDF͒ is developed and implemented for large eddy simulation ͑LES͒ of turbulent flows. In this methodology, the effects of the unresolved subgrid scales ͑SGS͒ are taken into account by considering the joint probability density function ͑PDF͒ of the velocity and scalar fields. An exact transport equation is derived for the VSFDF in which the effects of the SGS convection and chemical reaction are closed. The unclosed terms in this equation are modeled in a fashion similar to that typically used in Reynolds-averaged simulation procedures. A system of stochastic differential equations ͑SDEs͒ which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These 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 by comparison with results obtained by a finite difference LES procedure in which the corresponding transport equations for the first two SGS moments are solved. The VSFDF results are compared with those obtained by the Smagorinsky model, 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 the values of both the SGS and the resolved components of all second order moments including the scalar fluxes are predicted well by VSFDF. The sensitivity of the calculations to the model's ͑empirical͒ constants are assessed and it is shown that the magnitudes of these constants are in the same range as those employed in PDF methods.

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An overview is presented of the state of progress in large eddy simulation of turbulent combustion via the filtered density function (FDF). This includes the formulations based on both the joint velocity-scalar FDF, and the marginal scalar FDF. In the former, the most up-to-date and comprehensive form of the model is presented along with its applications for LES of some relatively simple flows. In the latter, results are presented of the most recent LES of a complex turbulent flame. Both of the models are described in the context of a variable density flow via consideration of the filtered mass density function (FMDF).

This paper focuses on the application of the large eddy simulation (LES) technique to a swirling particle-laden flow in a model combustion chamber. A series of calculations have been performed and compared directly with detailed experimental measurements. The computational domain identically matches the laboratory configuration, which effectively isolates effects related to dilute particle dispersion and momentum coupling. Results highlight the predictive capabilities of LES when implemented with the appropriate numerics, grid resolution (as dictated by the class of models employed) and well-defined boundary conditions. The case study provides a clearer understanding of the effectiveness and feasibility of current state-of-the-art models and a quantitative understanding of relevant modeling issues by analyzing the characteristic parameters and scales of importance. The novel feature of the results presented is that they establish a baseline level of confidence in our ability to simulate complex flows at conditions representative of those typically observed in gas-turbine (and similar) combustors.

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