Incompressible Fluid Flow Through Pipes Packed With Spheres at Low Dimension Ratios

This technical note reports the results of the last of a series of three studies of the flow of incompressible fluids through pipes packed with spheres. In the first of these studies, published in the Journal of Fluids Engineering in 1987, it was shown that certain experimentally determined parameters which govern incompressible fluid flow through such packings are substantially independent of the dimension ratio, D/d, for D/d ≥ 40, where D and d represent the pipe and sphere characteristic dimensions (diameters), respectively. The second of the aforementioned studies, published in the Journal of Fluids Engineering in 1990, focused on the range 1.40 ≤ D/d < 40. In this range the flow parameters are functionally dependent upon D/d due to the so-called “wall effect.” The present investigation deals with the range 1.08 ≤ D/d ≤ 1.40, for which it is shown that the results are quite different from those obtained for higher D/d. Correlation equations are presented here by means of which the flow is characterized in the range 1.08 ≤ D/d ≤ 1.40. It is anticipated that this information will have practical applications, such as, for example, calculating the “cost,” in terms of pressure drop, of enhancing the rate of convection heat transfer in heat exchangers by packing the tubes of the heat exchangers with spheres.