Considering the multi-scale structure of the dense phase in the form of clusters and the dilute phase in the form of dispersed particles in the circulating fluidized bed

the relationship between accelerations and local structure parameters in the dense phase and dilute phase was established and the stability condition of the minimum energy dissipation by multi-scale drag force was proposed. Based on the bivariate extreme value theory

a cluster structure dependent (CSD) drag coefficient model was developed. Gas-solids flow behavior and cluster characteristics in risers were simulated using a two-fluid model. The concentrations of particles obtained by the CSD model showed better agreement with experimental results. Cluster diameter increased

reached a maximum and fell down to single particle diameter with increasing solids concentrations. In the simulation

the influence of accelerations of gas and particles could not be ignored because it appeared to be on the same order of magnitude as acceleration of gravity.