A barrelledness criterion for C 0(E) by Mendoza J.

By Mendoza J.

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For the six possible regular packings of spherical particles, the voidage is only a function of packing arrangement. The voidage is also independent of the particle size. The six arrangements are cubic, two orientations of orthorhombic, tetragonal-spheroidal, and two orientations of rhombohedral. They are graphically presented in Fig. 2. Formulae for calculating the voidage of these six arrangements have been developed and the packing characteristics of these ordered arrangements are summarized in Table 1 (Herdan, 1960).

6 Modified Ergun Equation fp ¼ Gibilaro et al. (1985) modified the Ergun equation and proposed an alternative pressure drop equation on the basis of theoretical considerations: ! 17:3 r U2L ÁP ¼ þ 0:336 f ð1 À eÞeÀ4:8 ð77Þ ðReÞp dp The proposed equation compared well with published experimental data obtained from high-voidage fixed beds of spheres; it represented a significant improvement over that of Ergun. The equation is a combination of two equations, one for the laminar regime and the other for fully turbulent flow.

Both approaches gave reasonable predictions of pressure drop of flow through packed beds of spherical and near-spherical particles but were inadequate for beds with particles substantially different from the spheres. The pressure drop through the packed bed is due not only to the frictional resistance at the particle surface but also to the expansion and contraction of flow through the interstices among the particles The most popular approach is the pipe flow analogy model, also called the capillary tube model or channel model, which approximates the flow through the packed bed by the flow through a bundle of straight capillaries of equal size.

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