OCR Text |
Show The reaction in equation 8 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 reaction of the form: 1 Kg fuel + r Kg oxidant > (1 + r) Kg products (10) Bilger (1980) and others have shown that species conservation equations can be written for the fuel, the oxidant and the products. Diffusion rates are assumed equal, and the reaction rates are related as follows: w w Transport of the fuel can then be modeled by a conservation equation for the fuel mixture fraction, nu. However, equation 1 is linear in nu, and the fuel mixture fraction is simply determined from the relationship: mr = m - m (12) f pm pmr v ' where the distribution of m and in is already known. pm pmr J The reaction described in equation 8 is modeled by a conservation equation for the fuel remaining, nL . 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. The reaction described in equation 9 is modeled by a conservation equation for the average carbon monoxide concentration, a m . Since the time scale of turbulence is much greater than the time scale of chemistry, the CO reaction rate is also controlled by the rate of turbulent mixing. A transport equation -8- |