Flow Through Granular Media

Abstract

Abstract Ever since Darcy’s (1) basic work on the mechanics of filtration, flow through porous media has been the object of repeated research. Numerous and most valuable data on filtration coefficients have been gathered (2), the approach in recent years having been broadened by invoking the principle of dynamic similitude (3). So far, however, no general picture has been disclosed, such for example as made available for pipes by Osborne Reynolds and his successors. Systematic research was initiated accordingly at the fluid-mechanics laboratory of Columbia University with the object of possibly obtaining a comprehensive view of the phenomenon as a whole. This paper summarizes the results of the first series of experiments, which deal with flow through media composed of uniform spherical bodies, for which lead shot varying in diameter from 0.0377 in. to 0.361 in. was used. The device used permitted resistance slopes over 7 : 1, and the Reynolds’ characteristics were extended to the unprecedented range of nearby 1.8 × 103. Under such conditions the whole series of the successive flow forms became evident. The initial Darcy type of flow with resistance proportional to the first power of the velocity was superseded by a zone where losses rapidly grew on an increasing power of the velocity Un, until in the higher ranges once more an apparently stable pattern with a constant exponent n = 1.8 was reached. A simple method based on dimensional considerations and which takes into account the varying porosities was used to reduce experimental data to a unified basis. In terms of a proper Reynolds characteristic, the generalized resistance coefficient in a quadratic formula presented itself in the form of a unified continuous outline. The possible mechanism of resistance in the different flow forms is discussed in the condensed survey of the dynamics of the case preceding the description of the experiments. The unwarranted analogy with laminar and turbulent flow in pipes is substituted by an interpretation invoking a parallel with the Stokes type of flow and with the customary “form” resistance of spheres. At the close a comprehensive expression is given to the Darcy filtration coefficient taking account of the porosity and the viscosity of the fluid, with only one dimensionless empirical parameter, the numerical value of which assumedly is a constant for a certain shape.