OCR Text |
Show -12 NShD' oref 0.75 rln (1-zy . ) ob »m- d U f ) . (4) p \ ref The main difficulty in using equation (4) lies in determining the appropriate value for the Sherwood number. Daw and Krishnan review many of the current correlations developed for calculating the Sherwood number under various conditions. In general, the Sherwood number depends on four parameters; the particle Reynolds number, the Schmidt number, the Grashof number, and the flow field geometry (usually expressed as some dimensionless length ratio), The Grashof number is frequently not considered since it is only important where natural convection is significant relative to forced convection. Correlations of b c the general form Sh = 2.0 + a Re Sc have been successfully applied to a wide range of situations, including single particles, static beds, and fluidized beds. The main problem has been to account for the effect of void fraction and particle shielding in beds. This question is still unresolved, but Daw and Krishnan illustrate that the so-called Ranz-Marshall correlation (where a = 0.69, b = 1/2, and c = 1/3) seems to be satisfactory in some cases for fluidized beds. The limiting reaction rate for chemical control (regime I combustion) is typically evaluated from an expression of the form " i n R = A exp o, (5) where R is based on the effective external surface area of the particle and the partial pressure of oxygen is evaluated at the particle surface. For porous particle combustion, Daw and Krishnan (9) show that the pre-exponential factor, A, is often not constant but varies directly with the particle size. Thus equation (5) can be rewritten as R = A'd exp C P n 0, (6) It should be noted that equation (6) actually applies only over some limited range of particle sizes. Asymptotic rates are approached at upper and lower size limits where the effect of d on rate becomes P unimportant. It is also possible for the rate to vary due to changes |