Eulerian simulation of heterogeneous gas–solid flows in CFB risers: EMMS-based sub-grid scale model with a revised cluster description

Gas–solid two-phase flow in CFB risers is characterized by the clustering of solid particles producing dynamical multi-scale structures, and how to quantify such heterogeneity is a critical yet unsolved issue. Recently, incorporating the energy minimization multi-scale (EMMS) model with Eulerian approach has obtained encouraging results for simulating the hydrodynamics in CFB risers. However, owing to the cluster diameter correlation used, the present model is still limited to the simulation of Geldart A particles. In this study, a stochastic geometry approach named doubly stochastic Poisson processes is used to analyze the fluctuation characteristics of solid concentration in CFB risers, which provides a mean to define the solid concentration inside clusters. The predicted results are validated by experimental data available in literature, and a revised cluster diameter correlation is then proposed for EMMS model previously developed for cocurrent-up gas–solid flow. Following our previous studies, the EMMS model thus improved is incorporated into an Eulerian–Eulerian description of gas–solid flow as a sub-grid scale model for inter-phase drag force, with which the hydrodynamics of both Geldart A and Geldart B particles in CFB risers are simulated. It is shown that the experimentally found S-shaped axial voidage profiles and the choking phenomenon can be well predicted. The computed one-dimensional slip velocities decrease toward the top of the risers and increase with decreasing cross-sectional averaged voidages. The experimentally found dependence of the root mean square of the solid concentration on its mean value at a given position is also well predicted.