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Three turbulent piloted methane jet flames with increasing levels of local extinction (Sandia Flames D, E and F) have been computed using Large Eddy Simulation. The smallest unresolved scales of the flow, in which combustion occurs, are represented using the filtered Probability Density Function method where the corresponding evolution equation is solved directly. A dynamic model for the sub-grid stresses together with a simple gradient diffusion approximation for the scalar fluxes is applied in conjunction with the linear mean square estimation closure for sub-filter scale mixing. An augmented reduced mechanism (ARM) derived from the full GRI 3.0 mechanism has is incorporated to describe the chemical reaction. The results demonstrate the ability of the method in capturing quantitatively finite rate effects such as extinction and re-ignition in turbulent flames.

A second-order, single-point closure model for calculating the transport of momentum and passive scalar quantities in turbulent flows is described. Of the unknown terms that appear in the Reynolds stress and scalar flux balance equations, it is those which involve the fluctuating pressure that exert a dominant influence in the majority of turbulent flows. A closure approximation (linear in the Reynolds stress) has been formulated for the velocity-pressure gradient correlation appearing in the Reynolds stress equation. When this is used in conjunction with previous proposals for the other unknown terms in the stress equation, the proposed model closely simulates most of the data on high Reynolds number homogeneous turbulent flows. For the fluctuating scalar-pressure gradient correlation appearing in the scalar flux equation, an approximation has been devised that satisfies the linear transformation properties of the exact equation. Additional characteristics of the fluctuating scalar field are obtained from the solution of modeled balance equations for the scalar variance and its ‘‘dissipation’’ rate. The resulting complete scalar field model is capable of reproducing measured data in decaying scalar grid turbulence and strongly sheared, nearly homogeneous flow in the presence of a mean scalar gradient. In addition, applications to the thermal mixing layer developing downstream from a partially heated grid and to a slightly heated plane jet issuing into stagnant surrounds result in calculated profiles in close agreement with those measured.

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The problem of modeling the velocity and acceleration of inertial particles in turbulent flows is discussed. Particular attention is focused on the modeling of the particle Lagrangian velocity increment, especially, but not exclusively, in the case in which only the low frequencies of the carrier turbulent flow field are available. The need for suitable models arises in the simulation of particle laden flows by the means of new computational techniques such as large-eddy simulation. For this, stochastic differential equations, sde, are often introduced, though there is a lack of clarity in how such models should deal with the experimental observed far from Gaussian statistics, intermittency, and heavy tailed probability density function for particle acceleration. It is well known that Langevin-type equations are not capable of reproducing such features. It is first shown how the stochastic model for the particle Lagrangian velocity increments is far from being a Langevin equation, and it is characterized by nonlinear drift and diffusion; the statistical characteristics of this first model are shown to be in qualitative agreement with experimental findings. These results suggest an improved model for the particle dynamics based upon a more general family of nonlinear sde; the family, which is generated by a single parameter, includes both the Langevin equation and the first model as special cases. An analysis of the statistical properties of the new sde shows that the model is capable of accurately reproducing the strong deviations from Gaussianity observed in recent experiments.