Models for turbulent transport

The multi-environment model for turbulent transport of the bi-variate moments in the absence of moment source terms has the form... 

In order to model turbulent reacting flows accurately, an accurate model for turbulent transport is required. In Chapter 41 provide a short introduction to selected computational models for non-reacting turbulent flows. Here again, the goal is to familiarize the reader with the various options, and to collect the most important models in one place for future reference. For an in-depth discussion of the physical basis of the models, the reader is referred to Pope (2000). Likewise, practical advice on choosing a particular turbulence model can be found in Wilcox (1993). 

A general overview of models for turbulent transport is presented in Chapter 4. The goal of this chapter is to familiarize the reader with the various closure models available in the literature. Because detailed treatments of this material are readily available in other texts (e.g., Pope 2000), the emphasis of Chapter 4 is on presenting the various models using notation that is consistent with the remainder of the book. However, despite its relative brevity, the importance of the material in Chapter 4 should not be underestimated. Indeed, all of the reacting-flow models presented in subsequent chapters depend on accurate predictions of the turbulent flow field. With this caveat in mind, readers conversant with turbulent transport models of non-reacting scalars may wish to proceed directly to Chapter 5. 

Give two frequently used models for turbulent transport in the environment and explain how they relate to the turbulent diffusion coefficient. 

The result of the mixing-length idea used to derive the expressions (16.56) and (16.57) is that the turbulent momentum and energy fluxes are related to the gradients of the mean quantities. Substitution of these relations into (16.46) leads to closed equations for the mean quantities. Thus, except for the fact that KM and Kr vary with position and direction, these models for turbulent transport are analogous to those for molecular transport of momentum and energy. 

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