53 Modeling Approaches

Several factors determine the extent of influence of turbulence on effective rates of chemical reactions, including:

• whether reactants are premixed or non-premixed;

• rate of chemical reactions relative to the rate of scalar mixing;

• turbulence length scales relative to size of a reaction zone;

• multiple reactions/order of reactions.

Chemical reactions may also affect turbulence by releasing energy and modifying the fluid properties locally. The influence can be quite significant in variable density flows (e.g. combustion). Nevertheless, in many computational models of constant density reactive flow processes, it is implicitly assumed that chemical reactions do not affect scalar mixing rates.

Available reactor models can be classified according to their assumptions about the relative magnitudes of characteristic time scales of mixing (micromixing and macromixing) and reactive flow process (chemical reaction time scale, ikin or residence time, t ). The relationship between suitability of different models and extent of macro- and micromixing is shown schematically in Fig. 5.5. When both, macro- and micromixing time scales are much smaller than the process time scale (high macro-and micromixing), ideal reactor models can safely be used (top right case in Fig. 5.5). When the rate of macromixing is slow but that of local micromixing is fast, the relevant mixing scale is intermediate between a micromixing scale and a reactor scale. Although reactants are locally mixed on a molecular scale, there is macroscopic segregation (top left case in Fig. 5.5). Cell balance models (Patterson, 1985; Middleton et al., 1986) can be used to simulate such reactive flow processes. In these models, no special modeling efforts are generally necessary except for the special treatment demanded by extra non-linearity (due to the reaction source) present in the reactive systems. The governing equations discussed in Chapter 2 can be used to simulate the behavior of such systems.

When local micromixing is slow compared to the reaction time scale and the macromixing time scale is smaller than the process time scale, the performance of a reactive flow process is controlled only by the micromixing. In such cases, though there is no macroscopic segregation, reactants are not mixed on a molecular scale (see the right bottom case of Fig. 5.5). Several micromixing models have been developed to simulate such reactive flow processes. Some of the widely used models are:

• 'Engulfment Deformation Diffusion (EDD)' model of Baldyga and Bourne (1984).

• 'Interaction by Exchange with the Mean (IEM)' model of David and Villermaux (1987).

• 'Engulfment (E)' model of Baldyga and Bourne (1989).

These models are not discussed here and the cited papers may be referred to for details of model equations. When macroscale and microscale segregation exist together (bottom left case of Fig. 5.5), none of the cited models are adequate. For such systems, it is necessary to include detailed interaction of fluid mechanics, mixing and reactions in the mathematical model. Various modeling approaches to simulate reactive flow processes with macro- and microscale segregation are discussed briefly below.

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