Analysis of Forced Flow of Granular Materials in Vertical Pipes without and with Air Permeation

The problems associated with grain elevation and conveying under forced flow in vertical pipes are discussed. Based on experimental results, a theory is presented to describe forced flow with varying degrees of air permeation up to and just beyond the fluidization point. The theory takes into account the boundary and internal frictional properties, the degree of consolidation of the bulk granular material, and the stress fields that occur during forced flow. The force to elevate grain in a vertical tube is shown to be composed of two components, one to overcome Coulomb friction and initiate motion, and the other a time-dependent component that depends on the stiffness and damping characteristics of the granular material. The Coulomb friction component increases approximately exponentially with column height due to the positive feedback effect of the shear stresses at the pipe wall opposing the motion. Air permeation is shown to significantly reduce this component of the conveying force by reducing both the internal friction and the apparent bulk specific weight, the latter being the actual bulk specific weight less the air pressure gradient. Air permeation has a very significant effect on reducing both the bulk stiffness and, particularly, the damping characteristics, thereby reducing the time-dependent component of the conveying force.