Pressure drop in geometrically ordered packed beds of spheres

Abstract

The pressure drop of water was measured when water flowed through a bed of stainless steel ball bearings packed in an ordered rhombohedral geometry. Experiments were carried out with eleven different packed beds, encompassing the entire range of the square‐base array, in the same 10.85 by 10.85 by 30‐in. rectangular test column in a forced circulation loop at modified Reynolds numbers up to 17,000. The test variables included water velocity, bed voidage, spacing between adjacent balls, ball diameter, and bed height. Curves of friction factor vs. Reynolds number are presented. An increase in the relative horizontal spacing between balls was found to have a more important effect than an increase in voidage in decreasing the pressure drop. A general correlation relating the mutual effects of bed voidage and ball spacing on pressure drop that would bring all the data points together, especially in the transition flow region, could not be found. As a result, the system appears to consist of two distinct parts separated at the minimum packing density. A correlation was found only for the first, but from a practical point of view more important, region. Data may be corrected for bed voidage, but only for small variations in ball spacing, by the ratios of (1 − ε)/ε³ at the two voidages. No entrance and exit effects could be measured beyond the first seven ball layers.