OCR Text |
Show fr 1-X s m. P(nu) dm. (29) fr f f A two parameter PDF was chosen. Shape parameters for the PDF using equations 28 and 29 were found with a Newton Raphson iteration. A triangular PDF was chosen because it is mathematically simple, is efficient and is without the computational overhead of a Gaussian distribution (Bilger, 1980). Once the shape of the PDF is known from equations 28 and 29, an average value, SCQ, can be determined from the global reaction proposed by Howard (see Bowman 1975). The instantaneous source term for the kinetic reduction of CO can be written: SCO = "p2 A W °H20 °02»^ eXP <"E/RT) (3°» Equation 26 can be used to determine the average source term for the conservation equation. ENERGY Smith and Smooth (1980) have defined an overall energy equation for the gas-particle mixture. The equation is listed in Table 1 and was derived subject to the assumptions: o particle and gas phase temperatures are equal o kinetic energy, viscous dissipation, gas compressibility and the effect of gravity are neglected The conservation equation for enthalpy is solved using inlet enthalpies defined for the incoming fuel and oxidant streams. Wall losses or gains affect the enthalpy equation as a source or sink of energy, and can be written q = h A (T - Tw) (31) -14- |