Because of the enormous range of length and time scales present in practical reacting flow devices, the governing equations cannot be solved directly, and models are introduced. Among the simplifications commonly made is that the thermochemical state may be parameterized by a small number of parameters called reaction variables. Then, transport equations are solved for the reaction variables and mixing models are employed to approximate the unresolved (or subgrid) distribution of the reaction variables. This study uses Direct Numerical Simulation (DNS) of simple reacting jets to evaluate the performance of several common mixing and reaction models.; Significant improvements to the characteristic boundary conditions for compressible, reacting flow are presented in this work. The improvements proposed herein allow flames to pass through computational boundaries without disturbing the solution. This was not possible with previous boundary condition treatments. The improved boundary conditions facilitate the spatially evolving DNS studies considered in this work.; A new method has been proposed to quantify the amount of differential diffusion occurring in a nonpremixed system. This method is based on a generalized transport equation for the mixture fraction which makes no assumption regarding the diffusive fluxes of individual species. Results show that differential diffusion can be very important in nonpremixed systems. This has direct implications for modeling efforts, since many modeling approaches assume that the mixture fraction is a conserved scalar, which may only be true in the absence of differential diffusion.; A new general technique is proposed which allows the ideal performance attainable by a reaction model to be defined. Comparing this with the actual performance of a model provides a quantitative basis for evaluating reaction model performance. This analysis is applied to three DNS simulations for three different choices of reaction variables. One outstanding issue remains the selection of optimal reaction variables in low-dimensional manifold methods. A new method is proposed that may aid in selection of optimal reaction variables for use in low-dimensional manifold methods.; Also considered is the performance of coupled mixing and reaction models. Two presumed-shape PDF mixing models are considered in this work: the beta-PDF and the clipped-Gaussian PDF. Results indicate that the reaction model is a larger source of error than the presumed-shape mixing models. Furthermore, it appears that the clipped-Gaussian and beta-PDFs give virtually indistinguishable results.
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