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The drag force model is vital for capturing gas–solid flow dynamics in many simulation approaches. Most of the homogeneous drag models in the literature are expressed as a function of phase fraction (ε) and particle Reynolds number (Res). In this work, we use a "big data" approach to analyze ~108 data points for drag coefficient (Fd) for Geldart Group A particles at atmospheric pressure and find that the contribution of Res on Fd is much less than ε based on the Maximal information coefficient analysis. Thus, these drag models are separately reduced to machine learning and conventional expressions only related to ε. The reduced models achieve almost the same predictive performance as the originals in bubbling, turbulent, and jet fluidizations. Moreover, the reduced models provide better numerical stability for coarse grid simulations. These findings provide new insights into the drag coefficient for Geldart Group A particles under full fluidization conditions. [ABSTRACT FROM AUTHOR]

The effect of fluid turbulence models on the coarse-grid simulation for the mesoscale gas-solid flow system is not as clear as that for gas-liquid/single flows. In this study, the effect of different turbulence models on predictions of riser-only, turbulent and bubbling flow hydrodynamics is quantified. Then the selected turbulence models are examined by coarse-grid simulations in a full-loop circulating fluidized bed (CFB) with a proposed hybrid drag model which integrates two SGMs and Hulin-Gidaspow model. Results show that the standard k -epsilon and k -omega models fail to capture a correct fluidization pattern in riser. Meanwhile, the RNG and realizable k -epsilon models and SST k -omega model enable satisfactory predictions which are highly comparable to discrete model predictions and experiments over different flow regimes. However, the realizable k -epsilon model produces more pronounced flow fluctuations causing computational instability. Using superior turbulence closures, full-loop simulations with the proposed hybrid model can predict desirable hydrodynamics. Unlabelled Image • A hybrid drag model is proposed for feasible coarse-grid full-loop CFB simulations. • Applicability of different turbulence models over various fluidization regimes. • Validated against the discrete particle model and experiments. • The RNG k -epsilon and SST k -omega are optimal for gas-solid flows. [ABSTRACT FROM AUTHOR]

Machine learning (ML) is experiencing an immensely fascinating resurgence in a wide variety of fields. However, applying such powerful ML to construct subgrid interphase closures has been rarely reported. To this end, we develop two data‐driven ML strategies (i.e., artificial neural networks and eXtreme gradient boosting) to accurately predict filtered subgrid drag corrections using big data from highly resolved simulations of gas‐particle fluidization. Quantitative assessments of effects of various subgrid input markers on training prediction outputs are performed and three‐marker choice is demonstrated to be the optimal one for predicting the unseen test set. We then develop a parallel data loader to integrate this predictive ML model into a computational fluid dynamic (CFD) framework. Subsequent coarse‐grid simulations agree fairly well with experiments regarding the underlying hydrodynamics in bubbling and turbulent fluidized beds. The present ML approach provides easily extended ways to facilitate the development of predictive models for multiphase flows. [ABSTRACT FROM AUTHOR]

In this work, a three-dimensional coarse-grid two-fluid model (TFM) simulation by varying granular properties like granular viscosity, frictional viscosity, and solids pressure has been performed. Simulated predictions were subsequently compared with experimental results in the case of Geldart A or B particles. Laminar flow behavior is also studied and coarse-grid simulation predictions were less realistic for laminar flow. This flow regime which although consumes less computational resources falls short for large-scale riser scale up. Flow regime in our simulation was fast fluidization and simulation predicts with minimum error near riser inlet. More specifically, granular viscosity, frictional viscosity and solids pressure for Type A particles predict with minimum error especially near riser inlet at a lower height. For Type B particles, these three solid properties correspond closely with experimental results near inlet at a lower height whereas, at a higher height, turbulence increases and simulation results deviate from experimental studies. Image 1 • A sub-grid drag model has been used. • Coarse-grid two-fluid simulation has been performed. • Laminar and turbulent flow behavior has been compared. • Granular property effect on flow behavior has been systematically assessed. [ABSTRACT FROM AUTHOR]

• A material-property-dependent sub-grid drag modification is developed. • The newly constituted correction model is verified by highly-resolved simulation results. • Results reveal an essential dependence of sub-grid drag correction on material properties. • Hydrodynamic validation predictions achieve good accordance with various experiments. Developing, verifying and validating sub-grid methods is of crucial significance for enabling accurate coarse-grained two-fluid modeling of rapid gas-fluidized flows. However, very few studies in the literature so far have been focused on how the sub-grid modification depends on material properties. As an extension of previous sub-grid efforts, this fundamental investigation attempts to derive a material-property-dependent drag modification based on generated data from an initially homogeneous state of periodic gas-particle suspensions. The newly constituted model is then verified by highly-resolved two-fluid simulation results. We further validate the accuracy of model predictions via systematic assessments to experimental results that encompass a wide variety of material properties in five three-dimensional large-scale circulating fluidized bed (CFB) risers. Besides, we introduce a deviation index (DI) to quantify the predictive capability of the extended model. Computational results demonstrate an essential dependence of drag correction on material properties as an additional factor. Hydrodynamic validation predictions achieve satisfactory accordance with experiments. The current model is potential to serve as a more general tool for efficiently reducing the number of pilot-scale tests and effectively designing and controlling industrial process devices. [ABSTRACT FROM AUTHOR]

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]

In this work, a three-dimensional (3-D) filtered two-fluid model (TFM) was developed to describe the gas–solid flow behavior in a large-scale methanol-to-olefins (MTO) fluidized bed reactor (FBR). The cold-model flow behaviors were characterized successfully via the filtered TFM with a coarse grid. A coarse-grid sensitivity test was first carried out, and the filtered model was testified using predictions from classical models and the experimental data. Moreover, four drag models have been incorporated into the TFM for evaluating the effectiveness of these models at the same coarse-grid condition. Subsequently, the effects of some important model parameters including solid stresses, wall corrections and filter size on the flow behaviors were also investigated numerically. Finally, the filtered model was applied to predict the effects of the operating gas velocity, distributor shape and solid particle size. The results suggested the effectiveness of the sub-grid models for simulating large-scale MTO FBRs at coarse-grid conditions. This study further confirmed that the filtered drag coefficient correlation plays a significant role in capturing flow behaviors and the filter size is nearly independent on the grid size when the filter size is larger than or equal to twice the grid size. The simulation results by coarse-grid also show that the catalyst particles are easier to be fluidized with the increase of the operating gas velocity. It is also found that a triangle-shaped distributor strengthens the mixing behaviors and weakens the clustering of the near-wall regions. Additionally, our study indicates that the clustering phenomena near the wall regions are more obvious with the decrease of the catalyst particle size. [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]

The gas-solid fluidized bed is a complex multiscale system with diverse mesoscale structures such as bubbles and particle clusters. The Euler-Euler two-fluid model is one of the most popular methods in simulating this kind of system. However, when using coarse grids, the mesoscale structures involved can hardly be characterized. In this study, a new quasi-three-phase method was proposed to properly account for the mesoscale structures by using three phases (bubble phase/solid phase/emulsion phase) to represent the gas-solid fluidized bed, and comparative simulations were performed under different gas velocities. It was found that the simulation could reasonably predict the flow changes from bubbling fluidization to turbulent fluidization. The predicted gas velocity at the flow pattern transition is close to that calculated by the empirical equation concerning the bed pressure fluctuation, and the predicted solids fraction distribution fits well with the experimental data in the literature. [Display omitted] • Both bubbles and particle clusters are considered simultaneously. • Application of three-fluid model in gas-solid two-phase flow is feasible. • Three-fluid model reveals well the flow pattern transition of FBR. • The simulation using the classical drag model can match the experimental data. [ABSTRACT FROM AUTHOR]