Eddy Break-Up model

The quantitative description of such phenomena is commonly done by solving the averaged transport-equations for momentum, enthalpy and species-concentration. The calculation of the averaged source-term due to chemical reaction is usually based on various assumptions. E. g., the assumption of infinite fast chemistry in premixed configurations leads to the so called Eddy-Break-Up-model. An other example is the assumption of flame-sheet combus-... 

The rate of combustion of hydrogen was assumed to be infinite. Combustion reactions are relatively fast so that micro-mixing limitations have to be accounted for. The Eddy Break-Up model [Spalding, 1972], presented in Section 12.5.3.2, was applied. Using (12.2-4) with a value for Cy of 4, the following mixing rates were obtained for the combustion reactions 1, 2, 3 ... 

If the chemical reactions are very fast compared to the mixing rate, it may be assumed that any mixed reactants are immediately reacted. No rate expression is therefore necessary. The simplest model to represent such cases is called the eddy break up (EBU) model (Spalding, 1970 Magnussen and Hjertager, 1976). In the EBU model, the effective rate of chemical reactions is equated to the smaller of rate calculated based on kinetic model and that based on the eddy break-up rate. The eddy breakup rate is defined as the inverse of a characteristic time scale kle. Therefore, for fast reactions, the rate of consumption or formation is proportional to the product of density, mass fraction and the eddy break-up rate elk). The model is useful for the prediction of premixed and partially premixed fast reactive flows. EBU, however, was originally developed for single-step chemical reactions. Its extension to multiple step reactive systems should be made with caution. 

The Eddy Break-Up (EBU) model considers either micro-mixing or the reactions to be rate-determining. The micro-mixing rate and the intrinsic reaction rate, i.e.. 

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