OCR Text |
Show and 89 micron sizes are the lower and upper limits of the size distribution considered. The particles do not necessarily follow the gas streamlines. The radial motion of the particles is primarily due to turbulent dispersion. As seen in Fig. 3, small particles when injected near the primary-tube wall may be entrained into the recirculation zone. If the fraction of these particles is large, this may have a significant effect on the mean particle residence time. For each particle size dj and starting location Yi, there is also a corresponding discrete residence time identified by trG, i). Such a residence time matrix for a given particle size and injection location distribution was ~extracted from computer simulations for each test case. A probability density function (pdf) was defined by Particle mass flux with residence time between t k -ot/2 and tk +ot/2 Total mass flux of particles (3) based on the mass fraction of particles. Pm represents the probability that a particle which enters the reactor at t = tk - ot/2leaves the reactor within the time interval tk - Bt/2 and tk + ot/2. The mean particle residence time was then determined from (4) The cumulative probability distribution was calculated from k Fm (ta:) = L Pm (tk) 1 (5) A mean particle residence time (t 50), defined such that 50 percent of the particles on a mass basis have residence times less than or equal to this time, was used for the present correlations. This residence time was obtained by taking the residence time corresponding to Fm (tk ) = 0.50. t 50 was preferred to tpr calculated from Eq. (4) for the reasons -6- |