A re-evaluation of design equations for the established flow region of vertical dilute-phase pneumatic conveyors

Abstract

An analysis of data sets from the literature was completed for particle velocities of granular material in vertical, dilute-phase pneumatic conveyors. The generally accepted equation of motion used to describe such velocity data incorporates the solids friction factor, a variable term based on the additional pressure drop due to solids. The analysis determines that rather being a variable, the term is a constant related to the physical properties of the particle that influence its bouncing behaviour as it progresses along the pipeline. In addition, the analysis reveals that particle drag coefficients determined from the particle velocity data differ significantly from values taken from the standard drag coefficient curve. This observation was confirmed by drag coefficient measurements reported in the literature and made using particle-elutriating equipment. The drag coefficients from the pneumatic conveying experiments and the test equipment were determined under turbulent conditions, which is considered to account for the difference in values from the standard curve determined under quiescent conditions. Relationships are presented that predict the turbulence-influenced drag coefficients and the particle velocity data with good accuracy. These relationships are used to predict pressure drops for two data sets presented with the particle velocity data. The single-term pressure drop equation is used and predicts with good accuracy as well as producing the trough-shaped curve characteristic of the measured pressure drops.