OCR Text |
Show The reaction described in equation 15 is modeled by a conservation equation for the average carbon monoxide concentration, crco . Since the time scale of turbulence is comparable with the time scale of CO oxidation, the turbulent mixing affects the chemical rates controlling the oxidation of co. A transport equation describing the average co concentration is found by averaging the equations for the instantaneous reaction kinetics over a PDF to account for turbulence. Subsequently, average species concentrations for 02' CO2 ' H20, N2 , and fuel species are calculated using mf, mfr' crCO ' and the stoichiometric coefficients for conservation of species as defined in equations 14 and 15 . The following paragraphs describe the conservation equations and their source terms for homogeneous reactions . Fuel Mixture Fraction A conservation equation for fuel mixture fraction is solved. The source of fuel is calculated for each discrete-size group of coal particles and is accumulated over the entire particle size distribution . This source of fuel is expressed as: Ng 2 Sf -p ~ (r: Kd . . + Kjh) 1.J j i=l Fuel Remaining A conservation equation is solved for mfr with the source of fuel remaining given in the form: Sf r -= Sf - Min (R1 , R2 , ~) (18) (19 ) where the first term on the right side of the equation is the increase in fuel from devolatilization and char oxidation, while the second term is the decrease in fuel from combustion. Because the chemical reactions in most cases are very fast (compared with the rate of turbulent mixing), the rate of combustion will be determined by the rate of mixing on a molecular scale of the fuel and oxygen eddies. Accordingly, the fuel and oxygen appear as fluctuating intermittent quantities, and there will be a relationship between the fluctuations and the mean concentration of the species. Consequently, the rate of dissipation can be expressed by a mean concentration of the reacting species. In fuel-lean regions, the oxygen concentration is high, the fuel concentration is low (fuel is mostly intermittent), and the rate of combustion can be written as: (20) 11 |