Turbulent reacting flow

DNS results are usually considered as references providing the same level of accuracy as experimental data. The maximum attainable Reynolds number (Re) in a DNS is, however, too low to duplicate most practical turbulent reacting flows, and hence, the use of DNS is neither to replace experiments nor for direct comparisons— not yet at least. However, DNS results can be used to investigate three-dimensional (3D) features of the flow (coherent structures, Reynolds stresses, etc.) that are extremely difficult, and sometimes impossible, to measure. One example of such achievement for nonreacting... 

Fox, R.O. (2003) Computational Models for Turbulent Reacting Flows, Cambridge University Press. 

Van Vliet, E., Derksen, J. J., and Van den Akker, H. E. A., Numerical Study on the Turbulent Reacting Flow in the Injector Region of an LDPE Tubular Reactor . Proceedings of the 12th European Conference on Mixing, Bologna, Italy, pp. 719-726 (2006). 

The NDF is very similar to the PDFs introduced in the previous section to describe turbulent reacting flows. However, the reader should not confuse them and must keep in mind that they are introduced for very different reasons. The NDF is in fact an extension of the finite-dimensional composition vector laminar flow where the PDFs are not needed, the NDF still introduces an extra dimension (1) to the problem description. The choice of the state variables in the CFD model used to solve the PBE will depend on how the internal coordinate is discretized. Roughly speaking (see Ramkrishna (2000) for a more complete discussion), there are two approaches that can be employed ... 

As a first example of a CFD model for fine-particle production, we will consider a turbulent reacting flow that can be described by a species concentration vector c. The microscopic transport equation for the concentrations is assumed to have the standard form as follows ... 

This book presents the current state of the art in computational models for turbulent reacting flows, and analyzes carefully the strengths and weaknesses of the various techniques described. The focus is on formulation of practical models as opposed to numerical issues arising from their solution. 

A theoretical framework based on the one-point, one-time joint probability density function (PDF) is developed. It is shown that all commonly employed models for turbulent reacting flows can be formulated in terms of the joint PDF of the chemical species and enthalpy. Models based on direct closures for the chemical source term as well as transported PDF methods, are covered in detail. An introduction to the theory of turbulence and turbulent scalar transport is provided for completeness. 

The choice of models to include in this book was dictated mainly by their ability to treat the wide range of turbulent reacting flows that occur in technological applications of interest to chemical engineers. In particular, models that cannot treat general chemical... 

In order to compare various reacting-flow models, it is necessary to present them all in the same conceptual framework. In this book, a statistical approach based on the one-point, one-time joint probability density function (PDF) has been chosen as the common theoretical framework. A similar approach can be taken to describe turbulent flows (Pope 2000). This choice was made due to the fact that nearly all CFD models currently in use for turbulent reacting flows can be expressed in terms of quantities derived from a joint PDF (e.g., low-order moments, conditional moments, conditional PDF, etc.). Ample introductory material on PDF methods is provided for readers unfamiliar with the subject area. Additional discussion on the application of PDF methods in turbulence can be found in Pope (2000). Some previous exposure to engineering statistics or elementary probability theory should suffice for understanding most of the material presented in this book. 

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). 

Notwithstanding the intellectual challenges posed by the subject, the main impetus behind the development of computational models for turbulent reacting flows has been the increasing awareness of the impact of such flows on the environment. For example, incomplete combustion of hydrocarbons in internal combustion engines is a major source of air pollution. Likewise, in the chemical process and pharmaceutical industries, inadequate control of product yields and selectivities can produce a host of undesirable byproducts. Even if such byproducts could all be successfully separated out and treated so that they are not released into the environment, the economic cost of doing so is often prohibitive. Hence, there is an ever-increasing incentive to improve industrial processes and devices in order for them to remain competitive in the marketplace. 

At first glance, the exclusion of premixed reactants and density variations might seem to be too drastic. (Especially if one equates turbulent reacting flows with combustion. 1)... 

In the remainder of this chapter, an overview of the CRE and FM approaches to turbulent reacting flows is provided. Because the description of turbulent flows and turbulent mixing makes liberal use of ideas from probability and statistical theory, the reader may wish to review the appropriate appendices in Pope (2000) before starting on Chapter 2. Further guidance on how to navigate the material in Chapters 2-7 is provided in Section 1.5. 

The FM approach to modeling turbulent reacting flows had as its initial focus the description of turbulent combustion processes (e.g., Chung 1969 Chung 1970 Flagan and Appleton 1974 Bilger 1989). In many of the early applications, the details of the chemical reactions were effectively ignored because the reactions could be assumed to be in local chemical equilibrium.26 Thus, unlike the early emphasis on slow and finite-rate reactions... 

Despite the progress in CFD for inert-scalar transport, it was recognized early on that the treatment of turbulent reacting flows offers unique challenges (Corrsin 1958 Danckwerts 1958). Indeed, while turbulent transport of an inert scalar can often be successfully described by a small set of statistical moments (e.g., (U), k, e, (, and (scalar fields, which are strongly coupled through the chemical source term in (1.28). Nevertheless, it has also been recognized that because the chemical source term depends only on the local molar concentrations c and temperature T ... 

For turbulent reacting flows, we are usually interested in chemical reactions involving multiple scalars. As for a single scalar, a histogram can be constructed from multiple scalar fields (Fig. 1.9). For example, if there are two reactants A and B, the samples will be bi-variate ... 

The relationship between the CRE approach and the FM approach to modeling turbulent reacting flows is summarized in Table 1.1. Despite the obvious and significant differences... 

Table 1.1. Relationship between the CRE andFM approaches for modeling the important physical processes present in turbulent reacting flows. 

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