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.