CRE approach

In hindsight, the primary factor in determining which approach is most applicable to a particular reacting flow is the characteristic time scales of the chemical reactions relative to the turbulence time scales. In the early applications of the CRE approach, the chemical time scales were larger than the turbulence time scales. In this case, one can safely ignore the details of the flow. Likewise, in early applications of the FM approach to combustion, all chemical time scales were assumed to be much smaller than the turbulence time scales. In this case, the details of the chemical kinetics are of no importance, and one is free to concentrate on how the heat released by the reactions interacts with the turbulent flow. More recently, the shortcomings of each of these approaches have become apparent when applied to systems wherein some of the chemical time scales overlap with the turbulence time scales. In this case, an accurate description of both the turbulent flow and the chemistry is required to predict product yields and selectivities accurately. 

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

In the remainder of this section, we will review those components of the CRE approach that will be needed to understand the modeling approach described in detail in subsequent chapters. Further details on the CRE approach can be found in introductory textbooks on chemical reaction engineering (e.g., Hill 1977 Levenspiel 1998 Fogler 1999). 

One of the early successes of the CRE approach was to show that RTD theory suffices to treat the special case of non-interacting fluid elements (Danckwerts 1958). For this case, each fluid element behaves as a batch reactor. 

Note that all terms in (1.37) can be directly extracted from DNS data for turbulent-scalar mixing. Thus, unlike the CRE approach, the FM approach allows for the direct validation of micromixing models. 

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... 

Until 10 to 15 years ago the combined approach of macromixing and micromixing models was very widely used in the field of CRE but gradually CFD-based strategies have replaced the first mentioned strategy. In this respect it should be noted that this change also introduced big conceptual differences because the traditional CRE approach is usually formulated in the age space of fluid parcels whereas in CFD approaches a Eulerian framework is often adopted. Subsequently a brief overview of CFD-based approaches for reacting flows is presented and the current limitations are also indicated. 

Given their complexity and practical importance, it should be no surprise that different approaches for dealing with turbulent reacting flows have developed over the last 50 years. On the one hand, the chemical-reaction-engineering (CRE) approach came from the application of chemical kinetics to the study of chemical reactor design. In this approach, the details of the fluid flow are of interest only in as much as they affect the product yield and selectivity of the reactor. In many cases, this effect is of secondary importance, and thus in the CRE approach greater attention has been paid to other factors that directly affect the chemistry. On the other hand, the fluid-mechanical (FM) approach developed as a natural extension of the statistical description of turbulent flows. In this approach, the emphasis has been primarily on how the fluid flow affects the rate of chemical reactions. In particular, this approach has been widely employed in the study of combustion (Rosner 1986 Peters 2000 Poinsot and Veynante 2001 Veynante and Vervisch 2002). 

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