OCR Text |
Show multiple mixture fractions should be considered in future modeling efforts for the various stages of volatile release and for char oxidation. Use of a separate mixture fraction for char oxidation is particularly important for low volatile coals in which the release of carbon is much slower than the lighter, hydrogen-containing, volatile species. The homogeneous reaction of the gaseous fuel is characterized by a twostep process: Fuel + Oxidant => CO + H20 The first reaction is very fast in comparison with the second reaction and with the time scale of turbulence. This permits use of a fast chemistry approximation (Bilger, 1980) in which the kinetic reactions proceed infinitely fast, and that the reaction is controlled mainly by the rate of turbulent mixing. The second reaction is described by the global reaction rate proposed by Howard, et ale (1972). In this case, the reaction time scale is comparable with the time scale of turbulent mixing. The impact of turbulent fluctuations on temperature and species concentrations is considered by integrating the instantaneous reaction rate over a probability density function (PDF) to determine the local average rate of CO oxidation. Approximations for the instantaneous concentrations of CO and 02 and the instantaneous enthalpy of the mixture are used to simplify the complex integrations. Governing Equations for Advection-Diffusion of Gas-Particle Species The concentrations of gas and particle species are represented by a Favre average, general convective transport equation which can be written for a Cartesian geometry as follows: axa . CpuJ. +) __axa _. r-• aa+x . = s+ J J J (1) where + is the Favre average species mass fraction, E. is the effective diffusion coefficient, and S is the time mean source of • per unit volume. The index-j in equation 1 d:notes summation over the three coordinate directions. Conservation equations for gas or particle species can be combined to reduce the total number of equations, provided that the effective diffusion coefficients are the same. New variables are then introduced which represent a linear combination of the gas or particle species concentrations. Conservation equations similar to equation 1 can also be written for mass, three components of momentum, and energy (Fiveland and Wessel, 1988). These equations are mathematically elliptic. Boundary conditions are prescribed around the computational domain and consist of prescribed values of ~ or its derivative. 6 |