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Show PM m (12) The rate coefficient, R, is a function of the kinetic rate of the chemical reaction rate, Rch ' and the physical diffusion rate, ~h' of the oxidizer to the surface of the particle is written as: (13) HOMOGENEOUS CHEMISTRY The fuel is assumed to have the same elemental composition as the ash-free coal and is represented by a mixture of gases (CH 4 , C, C02' H20, S02' and N2 ) . Combustion of the fuel is characterized by a two-step process. In the first step, fuel is assumed to react with oxygen to form CO and other products as: Fuel + Oxidant => yCO + zH20 + ... (14) where y and z can be determined from an elemental balance. The second step involves kinetically controlled oxidation of the CO by the reaction: CO + Oxidant ~ CO2 + .. (15) The reaction in equation 14 is modeled with the fast chemistry assumption as described by Bilger (1980). Thus, when fuel and oxidant mix, they are assumed to react instantaneously and form products. Therefore, there can be only one of the following mixtures: fuel and products, oxidant and products, or products alone. The fast chemistry assumption reduces the first stage of combustion to a single, irreversible global r€action of the form: 1 kg fuel + ~ kg oxidant => (1 +~) kg products (16) Bilger (1980) and others have shown that species conservation equations can be reduced to a single conservation equation for the fuel, the oxidant, and the products. Diffusion rates are assumed equal, and the reaction rates are related as follows: W = fu ~x n - - (17) Transport of the fuel can then be modeled by a conservation equation for the fuel mixture fraction, mf, defined as a linear sum of fuel and product species: mf = mfr + mpr/(l+~). The reaction described in equation 14 is modeled by a conservation equation for the fuel remaining, mfr' The method proposed by Magnussen and Hjertager (1976) is used. This model is formulated by using the fast chemistry assumption and by further assuming that the rate of combustion is controlled by the rate of turbulent mixing. 10 |
