Improvement of EMMS drag model for heterogeneous gas–solid flows based on cluster modeling

•Theoretical model of solid volume fraction in clusters is proposed and verified.•Theoretical model of cluster size is modified.•The EMMS drag model is modified by combining with the cluster sub-models.•The modified EMMS drag model is verified by CFD simulations of CFB.

Cluster sub-models are developed and combined with the Energy minimum multi-scale method (EMMS) drag model to improve drag predictions for heterogeneous gas–solid flows. Theoretical cluster sub-models are developed to relate the cluster parameters with the local solid volume fraction. The cluster sub-models are validated by experimental data in the literatures. Drag coefficients predicted by the modified EMMS model with cluster sub-models are much lower than previous EMMS results and agree well with the experiment-based model. At solid volume fractions between 0.1 and 0.15 the drag coefficient, β, reaches a minimum at a maximum for slip velocities and gradually increases towards both sides to that of uniform flow. The modified EMMS drag model is further verified by CFD simulations of gas–solid flows in a CFB riser by coupling with the two-fluid model. The verification of the modified EMMS model once again demonstrates the applicability of the cluster sub-models.