Modeling of Combustion Reactions in Flowing Systems with Transport

Computer Modeling of Combustion Reactions in Flowing Systems with Transport 

Despite its title, and although it contains discussion of relevant numerical techniques, this article is not a comprehensive survey of the numerical methods currently employed in detailed combustion modeling. For that, the reader is referred to the reviews by McDonald (1979) and Oran and Boris (1981). Rather, the aim here is to provide an introduction that will stimulate interest and guide the enthusiastic and persistent amateur. The discussion will center mainly about low-velocity, laminar, premixed flames, which form a substantial group of reactive flow systems with transport. Present computational capabilities virtually dictate that such systems be studied as quasi-one-dimensional flows. We also consider two-dimensional boundary layer flows, in which the variation of properties in the direction of flow is small compared with the variation in the cross-stream direction. The extension of the numerical methods to multidimensional flows is straightforward in principle, but implementation at acceptable cost is much more difficult. 

Conservation or continuity equations, and other useful relations 

In order to analyze flames and other reacting systems in terms of basic flow principles and chemical kinetics, it is necessary to consider the conditions in a differential control volume within the reacting fluid. To this control volume we must apply the four fundamental conservation principles which are the basis of all physical and chemical problems conservation of mass, momentum, energy, and atoms. For each of these, the fundamental continuity equation for a volume element states that the rate of accumulation of the quantity within the element is equal to the rate of gain due to flow plus the rate of gain due to reaction, i.e., for a quantity denoted by the subscript /c, and referring to unit volume 

Volume element parallelepiped with sides Sx, 3y, 6z Flux components along axes F, Fy, F  

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Dixon-Lewis, G., "Computer modeling of combustion reactions in flowing systems with transport, in "Combustion Chemistry" (W. C. Gardiner, Jr., ed.). Springer-Verlag, New York, 1984. 

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