Reactive mixing Reynolds number

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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