Semiempirical Model of the Drag Force Acting on an Obstacle in Downward Dense Particle Flows as per the Flow-Around Behavior

Abstract

Determination of the flow-around drag force acting on an internal when particles downwardly flow around the internal is important for the safety of internals in the downward particle flow channel. In this study, the flow behaviors of particles downwardly flowing around different obstacles were investigated and a semiempirical drag force model was proposed based on the characteristics of the flow patterns. The proposed model was validated and key coefficients were correlated using the experimental data. The results indicate that there were three featured flow zones when particles downwardly flowed around an obstacle: the flow stagnant zone (disappear for triangular/conical obstacle), the slip-shear flow zone, and the flow separation zone. The stagnant zone angle and the flow separation angle were proposed to depict transition points of three flow zones when particles flowed around a cylindrical/spherical obstacle, and the two angles were found independent of the flow condition. A drag force model as per the flow patterns was proposed. The model decomposed the drag force into the compression force, the shear force, and the confinement force. The expressions of the compression stress, the shear stress, the effective area, and the confinement force were given. The mathematical form of the proposed model was validated and key coefficients in this model were also correlated using the experimental data. The average error of the drag force model was ±7.6% while the maximum error was within ±15%.