| OCR Text |
Show -5- The coupling terms in Eqs. (l)-(3) are only effective when the mean free path for photons is small. In general, the mean free path, or, equivalently the absorption capacity, would have to be determined from Mie theory, but we assume a grey medium so that much simpler approximations can be used. In particular, we assume that limitations to the photon mean free path arise from two contributions, particulate matter (excluding soot,) and molecular or atomic absorbers/ scatterers, and we compute these separately. In regard to the particulate interactions, we further assume that the characteristic wavelength of the photons is much less than the typical coal particle diameter, so that any photon that strikes a particle is absorbed. Then, the mean free path for photon absorption due to the presence of particles in a computation cell is X = -^ , (10) P N ' TT I M . r •_1 *- P- 1=1 1 where V is the volume of the computation cell, M. is number of coal particles in a parcel (see below) with radius r , and the summation is over all parcels in Pi the cell. The most important molecular absorbers of photons are C0_ and H_0 [5,6]. Gray, Kilham, and Miller [5] provide graphs of radiative eraissivity as functions of the temperature and the ratios of the partial pressures of water and carbon dioxide at atmospheric pressure. These data are tabulated in CONCHAS-SPRAY. For a grey medium the eraissivity e can be related to the extinction coefficient - [5] by 8 e = - exp (- y-) , (11) g where L is the mean beam length between the medium and the bounding surface of the reactor. Thus X = - -, rr^--r- . (12) g In (1 - e) Following Varma [6], we use a mean beam length L = 3.5 ^R/\ , (13) where V_ and A_ are the volume and internal surface area of the reactor. |
