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Highlights • A comprehensive validation study of the developed model to its predictability is conducted. • The computed results accord with the experimental data well over various flow regimes. • The computation efficiency via the developed sub-grid model can be significantly improved. • To capture the macroscopic flow features reasonably, an additional wall correction is not needed for the developed model. Abstract Development and validation of sub-grid models are of pivotal importance for coarse-grid two-fluid modeling of gas-particle fluidization. In prior study (Zhu et al., 2018, Chem. Eng. Sci. 192, 759–773), we developed an effective three-marker sub-grid drag model to consider the local heterogeneity in gas-particle flows. In this study, we perform a comprehensive 3D hydrodynamic validation analysis of the developed model to its predictability. Specifically, the validation covers more flow situations with respect to rapid, turbulent and bubbling fluidization. Besides, we introduce a simplified wall correction factor for assessing how the bounding walls impact on flow hydrodynamics. Computational results accord well with the experimental data over various flow regimes. The developed model can adequately capture the macroscopic flow properties without an additional wall modification. Compared with the fine-grid two-fluid modeling using the uniform drag model for a lab-scale riser, approximately 44 times speedup in computational time is achieved via the developed model. A much more significant reduction in computational time can be consequently expected for industrial-scale reactors. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • An effective three-marker drag model is developed for considering the meso-scale effect on the hydrodynamic predictions. • The effect of uniform drag inputs on the derived three-marker drag correlation is quantified. • A comprehensive comparison between several typical sub-grid models and present work is implemented. • Coarse-grid validation reveals that the developed model can significantly improve hydrodynamic predictions. Abstract The effect of meso-scale structures on hydrodynamic predictions is not considered in the classically uniform drag models when the coarse grid is used. To address this issue, this study tries to develop an effective three-marker drag correlation via straightforward sub-grid modeling, which accounts for a parabolic spatial concentration distribution within a computational grid. The reliability and accuracy of the developed model is then assessed in detail. How the uniform drag inputs affect the derived sub-grid correction is quantified for the first time. Besides, a comprehensive comparison between several typical sub-grid models and present work is implemented. Results reveal a systematic dependence of our drag modification on the concentration gradient as an additional marker. Coarse-grid hydrodynamic validation shows that the developed model yields a fairly improved agreement with experiments under various operating conditions in a 3D turbulent fluidized bed. Furthermore, results demonstrate that the present model using different uniform drag inputs still can exhibit satisfactory performance. The developed model is able to resolve the heterogeneous flow behavior both cheaply and adequately, which is potentially applied for industrial reactor design and optimization. [ABSTRACT FROM AUTHOR]

• Applicability of different mesoscale drags for predicting hydrodynamics over all flow regimes. • Applying the optimal drag model to design bed internals and quantify bed size effects. • The proposed nature-inspired snowflake-type internal significantly improves fluidization quality. • Proposing a preliminary correlation to quantify the bed size-dependent effect. This work systematically investigates the applicability of our recently developed three mesoscale drag models for predictions of hydrodynamics over extensive flow regimes ranging from bubbling, turbulent, rapid to full-loop fluidization. Subsequently, we try to apply the suitable mesoscale model for designing bed internals and quantifying bed size effects in a dense turbulent fluidized bed reactor. It is found that the optimized nature-inspired snowflake-type internal scheme contributes to breaking up the bubbles effectively and thereby weakening the degree of the particle clustering near the wall significantly. This phenomenon can enhance the uniform solid hold-up distribution (A ∼25% reduction of its nonuniformity) and improve the fluidization quality. Moreover, the bed size evidently affects the gas–solid fluidization characteristics and we thereby propose a preliminary correlation to quantify this size-dependent effect. This work may contribute to facilitating the CFD design practice of multiphase reactors from an art to science. [ABSTRACT FROM AUTHOR]