On the Resistance Coefficient–Reynolds Number Relationship for Fluid Flow through a Bed of Granular Material

Abstract

The resistance coefficient–Reynolds number relationship for a bed of spherical particles, closely graded about a mean size, is considered and it is shown that this relationship correlates with that for a bed of non-spherical particles, provided a suitable allowance for particle shape is made. It is shown that for very large or very small values of the Reynolds number the co-ordinates of the resistance coefficient–Reynolds number curve fall closely about a mean line but for the transition-range the points suffer considerable scatter—probably due to the indeterminate nature of the flow in the pore channels for this range of the Reynolds number. Curves are given showing the frequency of occurrence of variations in the resistance coefficient, and an example of the practical application of these curves to a design problem is fully worked out. Curves relating the resistance coefficient to the Reynolds number for beds of particles of various degrees of angularity are put forward tentatively, these relationships being, as yet, not completely established.

A revisit of pressure drop-flow rate correlations for packed beds of spheres

“…In discussing the variations of his measurements from those of earlier studies, for example, Rose [15] noted that "These variations probably arise from the use of different bases for correction for the effects of walls and voidage variations by different workers, although this hypothesis cannot be easily verified because, in general, sufficient data are not published." One of the most comprehensive and wellknown studies based on past experimental data is that of Macdonald, El-Sayed, Mow and Dullien [32] who used six sets of data from the literature.…”

“…18). It may be noted that, in this particular paper, Rose [15] did not discuss the effect of porosity on pressure drop nor did he explicitly mention the fact that his equation is applicable only at ε = 0.4. Furthermore, the Rose equation has been occasionally quoted (e.g.…”

“…The notation Re 1 used in (Eq. (15)) is adopted from Richardson, Harker and Backhurst [4] who used it for packed beds and from Dharmarajah and Cleasby [7], Akgiray and Soyer [8] and Soyer and Akgiray [9] who employed it to correlate liquid-solid fluidization and sedimentation data. The pressure drop-flow rate correlations considered and tested in this work are listed in Table 1 in terms of f P and Re defined as above.…”

“…Rose [15] carried out a comprehensive analysis of data, including his own and those of other workers between 1922 and 1945. He proposed an empirical equation containing three terms (Eq.…”

“…Rose and Rizk [18] also provided sets of curves giving wall-effect correction as a function of the ratio d p /D and Re, where D is the column diameter. The following features of wall-effect curves stand out: (i) The mentioned curves were based on the earlier equation developed by Rose [15] (Eq. (18) in Table 1).…”