Reactive mixing, Reynolds

The Eulerian (bottom-up) approach is to start with the convective-diffusion equation and through Reynolds averaging, obtain time-smoothed transport equations that describe micromixing effectively. Several schemes have been proposed to close the two terms in the time-smoothed equations, namely, scalar turbulent flux in reactive mixing, and the mean reaction rate (Bourne and Toor, 1977 Brodkey and Lewalle, 1985 Dutta and Tarbell, 1989 Fox, 1992 Li and Toor, 1986). However, numerical solution of the three-dimensional transport equations for reacting flows using CFD codes are prohibitive in terms of the numerical effort required, especially for the case of multiple reactions with... 

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. 

Turbulence models are generally limited to fully developed high-Reynolds number flows. Gas-phase flows are normally characterized by 5c 1, while for liquid phase flows, 5c > 1. The value of this Damkohler number indicates the relative rates of the mixing and chemical reaction rate time scales. Reactive flows might thus be divided into three categories Slow chemistry (Da/ -C 1), fast chemistry (Da/ 1), and finite rate chemistry (Da/ 1). 

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