Influence of bed size on the flow characteristics and porosity of randomly packed beds of spheres

Experiments were performed to investigate the flow characteristics and porosity of randomly packed beds of glass spheres for conditions where the bed size cannot be regarded as infinitely large compared with the sphere size. The operating conditions of the flow experiments extended over a Reynolds number range for which the flow was governed by the Forchheimer extension of the linear Darcy law. The influence of the bed bounding walls on the permeability, on the coefficient of the Forchheimer inertia term, and on the porosity, was studied by using beds of rectangular cross section. It was found that the permeability was not apparently influenced by the bounding walls when the equivalent diameter of the bed was greater than 12 times the sphere diameter, whereas the coefficient of the inertia term was affected by the presence of the walls for bed equivalent diameters as high as 40 sphere diameters. The porosity of the beds was not influenced by the bed size for values of the bed equivalent diameter greater than 15 sphere diameters. When the large-bed porosity value was used with the Carman-Kozeny relationship for the permeability as a function of sphere diameter, an excellent representation of accumulated experimental data was attained.