Reactive flow processes

Detailed modelling, or numerical simulation, provides a method we can use to study complex reactive flow processes (1). Predictions about the behavior of a physical system are obtained by solving numerically the multi-fluid conservation equations for mass, momentum, and energy. Since the success of detailed modelling is coupled to one s ability to handle an abundance of theoretical and numerical detail, this field has matured in parallel with the increase in size and speed of computers and sophistication of numerical techniques. 

In addition to an examination of length scales, it is useful to carry out quantitative examination of different relevant time scales of the mixing processes. Comparison of these time scales with the characteristic time scales of chemical reactions will be useful to determine the rate-controlling step in reactive flow processes. 

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. 

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 ... 

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. 

To make the matters worse, chemical reactions steepen scalar gradients and often, larger values of k ax need to be used. Since (kmax x max x k ax) values must be stored in the computer memory for each field for each time step, application of DNS to reactive flow processes is limited to moderate Reynolds numbers and Schmidt numbers near unity. The Damkohler number (ratio of charaeteristic time scales of small-scale mixing and chemical reaction, see Chapter 2) is generally limited to values less than 30 to 50. Even if huge computational resources are available, the DNS approach is difficult to apply to the realistic geometry of industrial chemical reactors. 

By far, the most widely employed models for reactive flow processes are based on Reynolds-averaged Navier Stokes (RANS) equations. As discussed earlier in Chapter 3, Reynolds averaging decomposes the instantaneous value of any variable into a mean and fluctuating component. In addition to the closure equations described in Chapter 3, for reactive processes, closure of the time-averaged scalar field equations requires models for (1) scalar flux, (2) scalar variance, (3) dissipation of scalar variance, and (4) reaction rate. Details of these equations are described in the following section. Broadly, any closure approach can be classified either as a phenomenological, non-PDF (probability density function) or as a PDF-based approach. These are also discussed in detail in the following section. 

RANS-BASED MODELS OF REACTIVE FLOW PROCESSES... 

Reynolds-averaged equations for momentum transport, are already discussed in Chapter 3. For modeling reactive flow processes, in addition to the solution of overall mass conservation equation described in Chapter 3, it is necessary to solve conservation equations for individual species. Following the practices of Reynolds averaging, an... 

Closure models for terms like the second term in the bracket of the right-hand side are vital to the modeling of turbulent reactive flow processes. It must be noted that as the chemistry becomes more complicated, several such terms will appear, which will make the task of modeling more difficult. Various methods have been used to develop such closure models. These methods are classified into two groups, namely conventional closure models with or without using probability distribution functions... 

There are a few other non-PDF approaches to simulating reactive flow processes (for example, the linear eddy model of Kerstein, 1991 and the conditional moment closure model of Bilger, 1993). These approaches are not discussed here as most of the engineering simulations of reactive flow processes can be achieved by the approaches discussed earlier. The discussion so far has been restricted to single-phase turbulent reactive flow processes. We now briefly consider modeling multiphase reactive flow processes. 

In general, multiphase reactive flow processes are classified into three types according to the location of the reaction zone ... 

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