A cluster structure-dependent drag coefficient model applied to risers

Cluster structures affect macroscopic hydrodynamic behavior in gas–solid risers. The moment and energy balances for the dense phase and dilute phase are presented by the multi-scale resolution approach to investigate the dependence of drag coefficient on structure parameters. The modified model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD). Unlike previous works on CSD drag coefficient model, the modified CSD drag model takes wall friction into account. The closure for the drag coefficient depends not only on flow behavior of gas and particles but also on the wall friction. The structure-dependent drag coefficients calculated from the approach of the minimization of energy dissipation by drag force are then incorporated into the two-fluid model to simulate the behavior of gas–solid flow in a riser. The distributions of concentration and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature. The effect of the wall friction on flow behavior of particles is analyzed.