Cluster-based EMMS model

Here, Pc is the mixture density of the dense phase. U up i is defined by J Uf-U/), where Uf and U are mean velocities of the dilute and dense phases, respectively. This definition of mesoscale slip velocity differs a little bit from that in the cluster-based EMMS model, because the continuous phase transforms from the dilute phase to the dense phase. And their quantitative difference is l-f)PgUgc/Pc, which is normally negligible for gas-solid systems. Similarly, the closure of Fdi switches to the determination of bubble diameter. And it is well documented in literature ever since the classic work of Davidson and Harrison (1963). Compared to cluster diameter, bubble diameter arouses less disputes and hence is easier to characterize. The visual bubbles are normally irregular and in constantly dynamic transformation, which may deviate much from spherical assumption. Thus, the diameter of bubble here can also be viewed as drag-equivalent definition. 

From the above derivation, we can see that the SFM may revert to the cluster-based EMMS or bubble-based EMMS hydrodynamic models under different assumptions of structure parameters. Thus, SFM unifies these models. Indeed, the mesoscale structure has always been the critical part of the EMMS model. We may expect more variants of the EMMS model wiU be proposed because of different descriptions of the mesoscale structure (Hong et al, 2013). 

Figure 18 presents typical snapshots of solids distribution on the vertical plane for using both filtered drag and EMMS drag models. 2D results are also provided for comparison. Dense clusters are captured with both drags especially near the bottom zone. And the EMMS-based approach gives more pronoimced segregation of particles. 

WangJ, Ge W, LiJ Eulerian simulation of heterogeneous gas-sobd flows in CFB risers EMMS-based sub-grid scale model with a revised cluster description, Chem Eng Sci 63 1553-1571, 2008a. 

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