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Show r k2 Mt = pCy | (3) The standard k-e model proposed by Launder, et al. ' is used. Values of <J>, T , and S. are listed in Table 1 while the modeling constants are listed in Table 2. While this model has been widely applied, it suffers from some drawbacks such as underprediction of the size of wakes and recirculation (8)(9) zones . The currently applied model does not account for the effect of combustion on turbulence or the effect of particles on turbulence. Even with these drawbacks, this model was applied because it is well-documented and, unlike many other models, permits practical calculations with reasonable computational efficiency. Gas Phase Energy Equation. A conservation equation for stagnation enthalpy is solved for the gas phase. Again, Table 1 and Table 2 list the appropriate values of <£, T , and S and modeling constants, respectively. Sources of enthalpy arise from particle-to-gas and gas-to- gas radiation, and mass transfer from the particles. Gas Phase Chemistry. In diffusion flames, the fuel and air are initially separate, but mix and react upon entering the combustion chamber. The major heat-releasing reactions are physically controlled by the rate of turbulent mixing, since the time scale of turbulence, T , is much greater than the time scale of chemistry, x . Combustion is modeled by two equations with the form of Equation 1 using the assumptions of Bilger . The first equation represents the mean fuel mixture fraction, f. In PC combustion, the source of fuel results from devolatilization and subsequent char oxidation. In gas phase combustion alone, there is no source term. A second equation models the variance, g, in the fuel mixture fraction, f. The variance arises from the unmixedness of the fuel and oxidant, and is dissipated by the turbulent mixing. Although some investigators have questioned the use of the g-equation, this formulation seems to be the best solution at this stage of modeling. -5- |