Packed beds friction factor

In deriving expressions for the packed bed friction factor, three separate flow regimes are normally considered (see Figure 2.11) as follows. 

The packed bed friction factor,, is deflned by shear stress... 

The packed bed friction factor is shown in Figure 2.13 and applies to flow through random packing (e 0.4). 

At high Reynolds numbers the friction factor becomes nearly constant, approaching a value of the order of unity for most packed beds. In terms of S, particle surface area per unit volume of bed,... 

At low Reynolds numbers, the friction factor for flow in tubes is / = 16/Re. For packed beds, both / and V are adjusted by a tortuosity factor to account for the fact that a fluid element travels a longer distance (winding through the pore space) than bed length L. Empiricism has led to adjustments in either the tortuosity or the final equation or both (depending on the derivation) to yield a well-accepted result for... 

The latter equation is used to calculate the pressure drop through the bed and is named the Ergun equation [4]. The ps is the catalyst bulk density [kg/nfi), and / is a friction factor (—) for the packing. Ergun proposed the following parameterization for the friction factor ... 

Table 3-17 gives the Reynolds number, friction factor, and pressure drop of catalyst pellets of 0.25 inch and at different particle length. Table 3-18 shows a typical input data and computer output with PL = 0.25 inch. The simulation exercise gives a pressure drop of 68.603 Ib/in. The results show that the pressure drop in a packed bed depends on size and shape of the particles. 

Fanning friction factor, dimensionless fp, friction factor for packed bed... 

Koch [4] employed suspended rings and disks as inserts, as well as tubes packed with Raschig rings and round balls. The disks give maximum enhancement with moderate increases in friction factors, as indicated in Figs. 11.26 and 11.28 (curve d). Enhancement of heat transfer with rings and round balls is quite comparable to that with disks, but rings and balls increase the friction factor by more than 1600 percent (curves c and d). For further comments on packed tubes, see the chapter on heat transfer in fluidized and packed beds. 

Previously it was indicated that for noncircular conduits Fig, 6.10 (the friction factor plot) could be used if we replaced the diameter in both the friction factor and the Reynolds number with 4 times the hydraulic radius (HR). The hydraulic radius is the cross-sectional area perpendicular to flow, divided by the wetted perimeter. For a uniform duct this is a constant. For a packed bed it varies from point to point. But if we multiply both the cross-sectional area and the perimeter by the length of the bed, it becomes... 

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