A structure-dependent multi-fluid model (SFM) for heterogeneous gas–solid flow

•A structure-dependent multi-fluid model (SFM) was proposed for gas–solid flow.•The SFM unifies the bubble-based and cluster-based EMMS models.•The SFM unifies the classic two-fluid model and EMMS models.•A new version of bubble-based EMMS model was validated for wide range of flow regimes.

For the heterogeneous gas–solid flow in a fluidized bed, meso-scale structures, such as bubble and cluster, have significant effects on the hydrodynamics, mass/heat transfer and reaction rate. These structures can be described with certain kinds of bimodal probability density distribution of solids concentration, i.e., the dilute-dense two-phase structures. To keep the physical nature of these meso-scale structures in mathematical formulation, a structure-dependent, multi-fluid model (SFM) was proposed. Then, the SFM was reduced to the conventional two-fluid model (TFM) as well as the hydrodynamic equations of the bubble-based and cluster-based EMMS (energy-minimization multi-scale) models by assuming different simplifications of structures. Thus, the SFM unifies these different models. A new version of bubble-based EMMS model was presented thereby and validated with comparison to experimental data. This bubble-based EMMS model was found to be applicable to wide flow regimes ranging from bubbling, turbulent to fast fluidization.