Clusters and particle segregation in gas-solids flow through a vertical tube through a vertical tube

Based on an analysis of hydrodynamic inter-particle interactions, a model describing particle clusters in two-phase, turbulent, gas-solid flow through vertical pipes is presented. The initial stage in the evolution of a cluster is the formation of a hydrodynamical aggregate of a small number of particles. This aggregate will then grow due to sedimentation aggregation. The growth law of clusters, i.e. the cluster size and velocity as functions of its age, is found using a ‘mean field theory’ approach. It is shown that clusters have large relative Reynolds numbers which leads to the formation of turbulent wakes behind them. Due to the complex turbulent flow structures, partially induced by the wakes of all clusters, the horizontal motion of a specific cluster can be considered to be a random walk. This horizontal motion eventually drives the cluster to the wall. The final stage is the destruction of the cluster due to a collision with the wall or with a high speed particle. It is shown that the former dominates the latter. Using this theory the cluster size distribution function and the mean cluster size are calculated. Theoretical predictions are compared to available experimental data and good agreement is found. Furthermore an expression is derived for the effective radial solid flux in terms of the intensity with which small hydrodynamical aggregates are formed. This then provides an explicit microscopic mechanism for the formation of a core-annulus structure in gas-solid flow through vertical pipes.