A probability model for predicting the slip velocity of large particles in vertical pipes

Abstract

The existence of the slip velocity has strong influence on the conveying efficiency in the hydraulic transportation process of mineral nodules. In the present work, a probability model is proposed to predict the slip velocity of large particles in vertical pipes. First, the uniform linear motion of one single particle in a turbulent upward flow is described by energy transfer from vortexes to particles. Second, the interaction is analyzed between a group of particles and turbulent flow. Third, the probabilities of particle-particle collision and particle-vortex collision are calculated to obtain the corresponding deceleration and acceleration rates. When the motion of particles remains stable, the deceleration and acceleration processes reach a dynamic equilibrium. Finally, a balance equation is established to solve the slip velocity of large particles. The validation of the present model is then carried out by comparing the predicted slip velocity with experimental data and empirical models available in the literature, confirming the superior accuracy of the present model. To acquire further knowledge of the transportation, effects of six parameters of the model are investigated in detail, including the fluid flow rate, the particle diameter, the volume concentration, the pipe diameter, the particle density, and the fluid density