Mixture fraction approach conservation

For complex chemistry, in many cases, a conserved scalar or a mixture fraction approach can be used, in which a single conserved scalar (mixture fraction) is solved instead of transport equations for individual species. The reacting system is treated using either chemical equilibrium calculations or by assuming infinitely fast reactions (mixed-is-reacted approach). The mixture fraction approach is applicable to non-premixed situations and is specifically developed to simulate turbulent diffusion flames containing one fuel and one oxidant. Such situations are illustrated in Fig. 5.6. The basis for the mixture fraction approach is that individual conservation equations for fuel and oxidant can be combined to eliminate reaction rate terms (see Toor, 1975 for more details). Such a combined equation can be simplified by defining a mixture... 

An alternative approach might be to address solely the mixture fraction / (mass of original fuel atoms per mass of mixture) since it has been established that there is a firm relationship between y, and/for a given fuel. Note that/moves from 1 to 0 for the start and end of the fire space and / is governed by Equation (12.45) for y, = 0. This then conserves the fuel atoms. Under this approach it is recognized that... 

Condensation of mixed vapors of immiscible liquids is not well understood. The conservative approach is to assume that two condensate films are present and all the heat must be transferred through both films in series. Another approach is to use a mass fraction average thermal conductivity and calculate the heat-transfer coefficient using the viscosity of the film-forming component (the organic component for water-organic mixtures). 

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