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• Magnetic control on the generation of ferrofluid droplets from capillaries is realized. • A proposed correlation predicts the final volume of ferrofluid droplets grows in viscous fluids. • The impacts of magnetic force, viscous drag, and inertial forces on droplets' volume, deformation ratio, limit major axis, and neck breakup behavior are studied. • The rate of neck breakup of ferrofluid droplets is decelerated by viscous drag force. • Ferrofluid droplet necks exhibit self-similar breakup behavior at different magnetic Bond and Weber numbers. The controlled generation of droplets is crucial in bioassays, chemical analysis, and inkjet printing. Despite progress in droplet formation dynamics within liquid–liquid systems, improving the controllability and flexibility of manipulating droplets is still necessary. Here, we employ a non-uniform magnetic field for non-contact control of ferrofluid droplet generation in a vertical capillary. A correlation function predicts final ferrofluid droplet volumes with an average relative error of only 6.33%. Our study demonstrates that the magnetic field actively regulates droplets' volume, deformation, and generation period. In the final stages of droplet formation, we observe a unique neck rupture mechanism influenced by the viscosity of the continuous-phase fluid, distinct from observations in air. Scaling laws fit the minimum neck and position variations, revealing self-similar neck rupture behavior for droplets at different Bond and Weber numbers. These insights into droplet dynamics have potential applications across various technological domains. [ABSTRACT FROM AUTHOR]

Polydisperse gas-solid flows, which is notoriously difficult to model due to the complex gas-particle and particle-particle interactions, are widely encountered in industry. In this article, a refined kinetic theory for polydisperse flow is developed, which features single-parameter Chapman-Enskog expansion (the Knudsen number) and exact calculation of the integrations related to pair distribution function of particle velocity without any mathematical approximations. The Navier-Stokes order constitutive relations for multifluid modeling of polydisperse gas-solid flow are then obtained analytically, including the solid stress tensor, the solid-solid drag force, the granular heat flux and the energy dissipation rate. Finally, the model is preliminarily validated by comparing to the discrete element simulation data of one-dimensional granular shear flow and by showing that the hydrodynamic characteristics of gas-solid flows in a bubbling fluidized bed containing bidisperse particles can be successfully predicted. • A refined kinetic theory with C-E expansion is developed for polydisperse flow. • The complex integrals related to particle collision are calculated accurately. • Precise constitutive relations at Navier-Stokes order for multifluid model are obtained. • The model is preliminarily validated for a bidisperse bubbling fluidized bed. [ABSTRACT FROM AUTHOR]

[Display omitted] • Studying bubble effect on a batch-mode Li 2 SO 4 electrodialysis by a two-phase model. • Bubbles significantly raise the liquid velocity, inducing electrolyte circulation. • Bubble-induced circulation reduces concentration polarization, increasing ion flux. • Bubble impact on electrolyte potential depends on liquid flowrate and circulation. Electrodialysis (ED) of Li 2 SO 4 plays a crucial role in the closed-loop recycling of lithium-ion batteries. The enhanced flexibility and energy efficiency of batch-mode EDs highlight the significance of time-dependent models. The gaseous molecules evolved from electrochemical reactions induce localized turbulence, significantly impacting the velocity, potential, and concentration distributions. This study presents a two-phase model that analyzes the dynamic behaviour of a batch-mode Li 2 SO 4 ED and investigates the bubbles' impact employing an Euler-Euler model. The finite element method solves time-dependent hydrodynamic, mass conservation, and electrochemical equations. The model shows close agreement with experimental data, and incorporating the two-phase model reduces the concentration error from 20.6% to 10.3%. Bubbles-induced liquid circulation by buoyant and drag forces reduces concentration polarization, increasing transmembrane ionic fluxes and improving ED performance. Although bubbles increase ohmic overpotential, the enhanced ionic concentrations in concentrate channels due to bubble-induced liquid circulation reduce electrolyte resistance. Raising the inlet flowrate reduces the gas fraction and diminishes solution circulation. [ABSTRACT FROM AUTHOR]

• Counter-current liquid flow bubble column is investigated. • Experimental study of liquid and bubble velocity by shadow-imaging and PIV. • Numerical simulations using the Euler-Euler framework of the same column. • Comparison of different closure models for drag and lift. • Differences in flow structure for different bubble sizes are revealed. Bubble columns are gas–liquid contactors that are used in many process-engineering applications. A counter-current liquid flow is frequently imposed to adjust the bubbles' residence-time and thus optimize mixing and mass-transfer. The present work describes measurements in such a device together with corresponding computational fluid dynamics simulations based on the Eulerian two-fluid framework. Bubble-size and -velocity are measured by shadow-imaging for a large range of gas and counter-current liquid flow rates, as well as different nozzle sizes. The corresponding liquid flow-fields are characterized by Particle Image Velocimetry. From the large experimental database, a few cases are selected to analyze the flow structure and effects of the bubble-size. In the simulations, different models for the drag- and lift-force acting on the bubbles are evaluated. While good agreement between experiments and simulations could be achieved for the gas-fraction and gas-velocity, differences are found for the liquid-velocity, which is generally overestimated in the calculations. [ABSTRACT FROM AUTHOR]

Rotating Membrane Emulsification (RME) is a bottom-up emulsification technique developed to circumvent the significant energy requirements of conventional methods; however, its implementation has been hindered by low emulsion throughputs. This work presents a novel baffled-RME setup and investigates the potential improvement to emulsion throughput and droplet microstructure, whilst employing both surface-active and Pickering particle emulsifiers to assess whether any advantages are emulsifier-specific. Overall, baffle addition improves emulsion throughputs, however the droplet microstructure was positively influenced only when using surfactant-based emulsifiers. Positron Emission Particle Tracking (PEPT) was utilised to demonstrate that these advantages result from improved hydrodynamic conditions instigated by the break-up of streamlines, inducing higher turbulence near the membrane surface, and by increasing the transmembrane pressure drop and drag force through flow restrictions. Overall, by detailing the first baffled-RME setup and first application PEPT analysis to such equipment, this work lays the foundation for further optimisation of bottom-up emulsification approaches. • The use of baffles enhances rotating membrane emulsification (RME) throughput. • RME throughput enhancement persists regardless of emulsifier used. • The use of baffles influences emulsion droplet microstructure in RME. • Baffled-RME hydrodynamics can be assessed via positron emission particle tracking. [ABSTRACT FROM AUTHOR]

[Display omitted] • Two numerical models modified with empirical viscosity correlations are employed. • The dynamic and statistical forces exerted on particles are analysed. • The spatial distribution and flow behaviour of different particles are compared. • The underlying reasons for limited separation sharpness are revealed. • Novel insights into the classification process and principle are provided. The axial velocity fluctuation zone (AVFZ) characterizes the fluctuation range of the locus of zero vertical velocity, where the momentum transfer between the medium and solids is critical but has not been well revealed yet. Based on the viscosity-modified mixture and DPM models, this paper numerically investigated particles' motion behaviour, dynamic forces, spatial distribution, and flow characteristics. The results indicate that the particle size mainly influences drag force (F D) and has little effect on pressure gradient (F P) and centrifugal forces (F C), whereas the particle density affects F C / F P without changing F D. Due to the strong turbulence dispersion in the AVFZ, similar magnitudes of F D , F P , and F C cause prolonged residence time, higher accumulation rate, and higher circulation flow rate of near-cut-size particles, resulting in limited separation sharpness. Taking the AVFZ as a 'bridge', novel insights in the classification process along with the effects of main structural and operating parameters are provided. [ABSTRACT FROM AUTHOR]

Effects of cross-flow velocity, filtration pressure, and solid concentration on filter cake properties are studied by using a new filtration setup that allows performing filtration tests under a wide range of operating conditions. The main feature of this setup is that pressure and cross-flow velocity are decoupled, so it was possible to independently investigate the effect of these variables on filter cake properties. Filtration tests have demonstrated that particle invasion into filter media pores occurs initially, leading to the formation of an external filter cake. The increased cross-flow velocity creates an erosive shear stress at the surface of the external cake, which limits cake growth, indirectly maintaining a high filtrate flow rate. This high filtrate rate imparts a considerable drag force onto suspended particles, driving a high count into the porous substrate where these particles could deposit. Increasing pressure amplifies this internal particle deposition, particularly where there is no or limited external filter cake to limit filtrate drag and screen particles at the cake surface. The effect of cross-flow velocity on pore blocking and filter cake structure is observed and demonstrated by CT scanning and scanning electronic microscopy. • Initial filtration relies on standard blocking when particles are smaller than substrate pores. • Pressure and solid concentration affect steady state in cross-flow filtration. • Shear stress inhibits cake filtration. • Drag force linearly affects particle deposition and invasion in cross-flow filtration. [ABSTRACT FROM AUTHOR]

• A new immersed moving boundary is proposed for DPS with complex geometry. • Novel mapping technology for complex geometry into Cartesian grid. • GPU-based LBM-DEM-IMB model is implemented with high efficiency. • Proposed method is suitable for fast DPS of general particle–fluid two-phase flows. An immersed moving boundary (IMB) scheme in LBM-DEM is proposed for discrete particle simulation with arbitrarily complex geometry. Momentum exchange between fluid and unresolved particles can be exerted by a modified weighting function with drag force and a new solid operator in IMB, which can describe both particle–fluid interaction and complex geometry, and requires only local information in perspective of solution. Combined with stereolithography (STL) format for describing complex geometry, a GPU-based LBM-DEM-IMB is implemented, and its ability and accuracy for complex geometry from STL model is verified by simulating flow past a stationary sphere. Compared with CFD-DEM in discrete particle simulations of both fluidized bed with immersed tube and aerosol transporting in human nasal, proposed method has much higher efficiency and maintains comparable accuracy in dense and dilute particle–fluid systems with complex geometry, which demonstrates it to be a promising computational strategy for particle–fluid two-phase flows. [ABSTRACT FROM AUTHOR]

• Effects of bubble Reynolds number and grid-screen on bubble modification were studied. • Detailed bubble concentration and velocity were measured before and after a grid-screen. • Inverse correlation was found between screen size and centerline bubble concentration. • The centerline bubble concentration increased with increasing air discharge. • The threshold air discharge was measured for a wide range of grid-screen sizes. • The acting and resisting forces on air bubbles were calculated from measurements. • The drag force reduction was found to be correlated with the air discharge. Air injection through a single circular nozzle has been used for aeration enhancement, oxygen transfer, and mixing in natural lakes and reservoirs. A series of laboratory experiments with different hydrodynamic conditions was carried out to improve mixing capacity and entrainment in vertically discharged bubble plumes. Hydrodynamic modifications were performed by inserting a grid-screen with different openings and distances from the nozzle and hydrodynamic modifications were examined for different air discharges. Bubble plume characteristics such as bubble concentration and velocity were measured along the vertical axis of the plume using an accurate Refractive Bubble Index (RBI) probe. Utilizing bubble concentration and bubble velocity data, the hydrodynamic forces such as buoyancy, drag, added mass, and surface tension were calculated before and after the grid-screen to evaluate modification by a grid-screen. The bubble induced force acting on the grid-screen was then calculated by implementing the momentum transfer at the vicinity of the grid-screen. The effects of grid-screen openings, the location of grid-screen respect to the nozzle, and air discharge on the contributed forces were examined to design the optimum operation condition. The results indicated that the grid-screen size and its distance from the nozzle decreased the buoyancy and drag forces after the grid-screen by 49% and 42%, respectively. Non-linear correlations between the hydrodynamic forces and bubble Reynolds number were proposed indicating that all contributing forces increased with increasing bubble Reynolds number. Empirical models were also developed for prediction of surface tension and bubble induced forces on the grid-screen. [ABSTRACT FROM AUTHOR]

• An EMMS drag model was established for polydisperse flow. • Coupled EMMS drag model and multifluid model was used for CFD simulations. • The EMMS drag model predicted a better hydrodynamics and axial particle size distribution compared to Gidaspow drag model. • Both gas-particle and particle-particle drag models are important. • Particle phase stress has a minor effect on CFD results. Polydisperse gas–solid systems are more common in both industry and the natural world than their monodisperse counterparts. This paper aims to investigate the hydrodynamics of polydisperse gas–solid flow systems by extending the energy minimization multiscale (EMMS) drag model. The continuous particle size is discretized into several characteristic sizes, by which the polydisperse particles are classified into several discrete groups. A polydisperse EMMS drag model is then developed by treating these particle groups as solid phases. Finally, the proposed drag model is coupled with the multifluid model to simulate the hydrodynamics of polydisperse gas–solid flow in CFB risers. Extensive simulations are conducted to validate the effectiveness of the polydisperse EMMS drag model and investigate the effects of gas–particle drag models, kinetic theories, and particle–particle drag models on the simulation results. It was found that (i) the polydisperse EMMS drag model can predict the concentration and particle size distribution of polydisperse gas–solid flows better than the traditional drag model; (ii) the particle–particle drag force has an important influence on the mixing and segregation of different particles whereas the particulate phase stress has only a very minor effect, especially when the superficial gas velocity is low. The second finding highlights the need for a suitable particle–particle drag model that considers the effects of mesoscale structures, which will be the topic of our future study. [ABSTRACT FROM AUTHOR]

• We simulated a literature pseudo-2D spouted bed employing the CFD-TFM approach in Ansys Fluent 19.1. • We performed an extensive sensitivity analysis based on various sub-models and parameters. • Drag force and the definition of the granular phase have the greatest impact. • We included Di Felice's drag law through a User-Defined Function. • Based on the sensitivity analysis we optimized our model. A spouted bed has been simulated through a Computational Fluid Dynamic model using the Two Fluid Method and validated against experimental data. A sensitivity analysis has assessed the influence of the characteristic parameters on the solution. Among them, the accurate selection of the drag law seems to have the strongest influence on the results. In order to extend the capabilities of Ansys Fluent, Di Felice's drag law was also considered through a User Defined Function. The assessment of the granular phase and its kinetic, collisional and frictional forces, is highly relevant to achieve a correct prediction of the particle velocity profile. The specularity coefficient appears to be more influencing than the restitution coefficient, but both parameters are useful to optimise the model. Overall, the prediction of the particle vertical velocity is accurate whereas the height of the fountain is slightly over-predicted. [ABSTRACT FROM AUTHOR]

• Drift velocity-based drag closures in filtered Two Fluid Models are considered. • Anisotropic closure complexity is increased by adding independent variables. • Minor improvement with increasing complexity in verification for different regimes. • Anisotropic closures are generally much more accurate than an isotropic closure. • Complex closures may not be necessary, but physical effects should be accounted for. Filtered Two Fluid Models (fTFMs) aim to enable accurate industrial-scale simulations of fluidized beds by means of closures accounting for the effects of bubbles and clusters. The present study aims to improve anisotropic closures for the drift velocity, which is the primary sub-grid effect altering the filtered drag force, by deriving increasingly complex closures by considering additional independent variables (markers). Three different anisotropic closures, as well as an isotropic closure, are evaluated. A priori tests revealed a significant increase in the predictive capability of the closures as the complexity, in terms of the number of markers considered, increases. However, this improvement is relatively small when compared to the effect of considering anisotropy. Next, a posteriori tests were completed by comparing coarse-grid simulations of bubbling, turbulent and core-annular fluidization against benchmark resolved TFM simulations. This analysis shows good performance of all anisotropic closures, with negligible to minor effects of increasing the drag closure's complexity by considering additional markers. On the other hand, the isotropic closure lacks generality and shows poor grid independence behaviour. It is therefore concluded that it is essential to include important physical effects, such as anisotropy, in fTFM closures, while complexity in terms of the number of markers considered is of lesser importance. [ABSTRACT FROM AUTHOR]

• The empirical cluster correlation can be replaced by a cluster evolution equation. • A general EMMS drag model is suggested for the overall fluidization regime. • The EMMS drag is used to simulate gas-solid turbulent beds and cocurrent downers. • The EMMS-based simulation shows better prediction than traditional CFD simulation. Eulerian-Eulerian models incorporated with the kinetic theory of granular flow were widely used in the simulation of gas-solid two-phase flow, while the effects of mesoscale structures such as particle clusters and gas bubbles could not be considered adequately if traditional homogeneous drag models were adopted in the coarse grid simulations. The energy minimization multiscale (EMMS) model has been proved to facilitate calculating a structure-dependent drag coefficient by considering particle clustering phenomena, which can be coupled with the two-fluid model (TFM) to improve the accuracy of coarse-grid simulation of gas-solid circulating fluidized beds. However, the original EMMS drag model cannot be further applied to the simulation of gas-solid fluidized beds with solids flow rate smaller than zero, e.g., turbulent fluidized beds and cocurrent downward flow, because the original cluster diameter correlation gives rise to a value smaller than single particle diameter or even negative value at extremely low solids fluxes or downward gas-solid flow. In this study, a new proposed cluster evolution equation is proposed by quantifying local clustering dynamics to replace the original cluster diameter correlation. The newly formulated EMMS drag model can be used to avoid a negative cluster diameter to be involved in calculating interphase drag force in the overall fluidization regime. The improved EMMS drag law is incorporated into the Eulerian-Eulerian model to simulate gas-solid turbulent fluidized beds and cocurrent downer reactors, since they both were widely used in many industrial processes. By analyzing local hydrodynamics as well as the axial and radial heterogeneous distributions in the two kinds of fluidized beds, it is clarified that the simulation using the improved EMMS drag model shows a better agreement with the experimental data than the computation using the homogeneous drag law. [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]

• The drag force of chain-like agglomerates in the Stokes region is investigated. • Drag correction coefficient linearly correlates with the chain's length ratio. • Two predictive drag models applicable to chain-like agglomerates are proposed. Particle agglomeration is common in various fields, such as pharmaceuticals, chemicals and energy. An accurate drag model for agglomerates is the key to analyzing their motion and agglomeration characteristics. However, the drag force of agglomerates has not been sufficiently studied, even for simple structures. In this study, the drag model of chain-like agglomerates (straight and curved chains) in the Stokes region was experimentally investigated. It was found that the straight-chain agglomerates had an excellent linear correlation between the drag correction coefficient and the particle number. Meanwhile, the curved-chain agglomerates were correlated with both the angle and the particle number. In addition, two predictive drag models applicable to chain-like agglomerates were proposed. Comparing the related drag models proposed in the literature, it was found that the models in this work were more accurate. [ABSTRACT FROM AUTHOR]

In Euler-Lagrange models for particulate systems, the information exchange of multiphase coupling terms, i.e. drag force, heat transfer, or mass transfer, is often smoothed from particles' location to nearby computational cells when the cell and particle sizes are comparable. The diffusion-based smoothing is among the most popular approach. However, when it comes to polydisperse systems, the state-of-the-art constant diffusivity approach does not consider variation in particle sizes, resulting in an even smoothing of exchanged information across all particles with different sizes. In this paper, a particle-size dependent smoothing scheme named "non-constant diffusivity approach" is proposed. This approach distributes the exchanged information based on the local Sauter diameter d 32 such that the area of influence per particle varies by size. The one-dimensional analytical solution of the non-constant diffusivity approach is first derived and two control parameters L ⁎ and S are identified, where L ⁎ determines the characteristic length of the diffusivity and S determines the magnitude of the diffusivity. Together they control the characteristic length scale ℓ ˜ c of the smoothing operation. In the one-dimensional study, it is found that the proposed smoothing method is most suitable for the dilute particulate regime. The investigation is extended to a three-dimensional dilute particle flow based on the experiment of the CRIEPI (Central Research Institute of Electric Power Industry) pulverized coal burner. It is shown that using the non-constant diffusivity smoothing, the prediction of the O 2 concentration is more accurate than when using the constant diffusivity smoothing approach, which assumes a universal smoothing length for all sizes of particles. The findings suggest that when it comes to polydisperse particulate systems, the area of influence per particle on the fluid depends on the particle size. The proposed non-constant diffusivity approach can describe that with the benefits of cheap computational cost, conservation of exchanged quantities, and easy-to-implement. • A novel particle-size dependent smoothing scheme for polydisperse Euler-Lagrange systems. • Characteristic smooth length connects with the local particle size. • Develop on the foundation of the state-of-the-art diffusion-based method. • Applicable in different particulate systems, from dilute to dense. [ABSTRACT FROM AUTHOR]

• A rigorous hydrodynamic model predicts a limiting gas fraction in two-phase systems. • Buoyancy force increase and constancy of the drag term explain the limiting value. • The hydrodynamic model can simulate experimental data for all gas fractions. • A simplified model agrees with the rigorous one under limiting operating conditions. The experimental evidence that a limiting value of gas fraction is achieved in a gas-liquid dispersion as the gas volumetric flow rate is increased is explained by means of a rigorous hydrodynamic model. The mathematical treatment, based on the Eulerian concept applied to each phase, considers a population balance with a range of bubble sizes allowing the coalescence and breakup between them; and it is implemented in the OpenFOAM framework. It is concluded that the limiting gas fraction is a consequence of the increase of the gas velocity and the constancy of the drag term of the interfacial exchange moment as the volumetric gas flow is enlarged. A simplified hydrodynamic model is also reported that closely matches both the rigorous one and the experimental results under limiting operating conditions. [ABSTRACT FROM AUTHOR]

• The EMMS drag was closed by the PBM to account for sub-grid corrections. • A CFD-PBM-EMMS model was formulated for bubbling fluidized beds. • The breakup and coalescence kernels were improved to achieve better versatility. • The bubble dynamics in 3D fluidized beds of Geldart A particles was captured. • The EQMOM was coupled with QMOM to reconstruct the NDF. The importance of bubble dynamics in fluidized beds is underscored by the efforts undertaken over the past decades through experimental and numerical studies. Nonetheless, the bubble dynamic evolution and its effects on sub-grid closures were neglected in previous coarse-grid CFD models, particularly for Geldart A particles. In this article, a population balance model with improved kernels was employed to describe the bubble dynamic evolution in three-dimensional bubbling beds, whereby the EMMS drag model was closedto be incorporated into an Eulerian continuum model. Furthermore, the Extended Quadrature Method of Moments (EQMOM) was utilized to reconstruct the number density function of bubble size once their lower moments were obtained. The simulation results showed that the hydrodynamics including bed expansion characteristics, solids concentration and bubble size distribution can be well predicted by the model, indicating its capability to capture the heterogeneous structures in three-dimensional bubbling beds of fine particles. [ABSTRACT FROM AUTHOR]

Highlights • Drag of steady flow through and around arrays of cylinders are numerically investigated. • A novel formula for the drag force is proposed. • Macroscopic permeability is estimated from microscopic flow results via Darcy's law. • Drag ratio computed is in a good agreement with previous porous media model results. Abstract The drag properties of flow through and around square arrays of 10 × 10 evenly spaced circular cylinders with a wide range of solid fraction ϕ from 9.69 × 10 - 11 to 0.785 and Reynold number of the array Re from 1 to 50 are investigated numerically. The purpose of the present study is to better understand the phenomena of flow through and around permeable bodies that appear in bioreactors and fluid–solid reactors, for example. Instead of using the semi-empirical porous medium model, the direct numerical simulation is employed in order to investigate the flow mechanism from a microscopic point of view. A peak in drag coefficient is observed for the range of ϕ investigated, which appears at a smaller ϕ as Re increases. Three flow regimes are identified based on the shape effects quantified via the averaged velocity within the array, and the drag property in each regime is analyzed. A novel drag formula is also found by investigating the dependence of drag on ϕ and R (Reynolds number based on the mean velocity within the array). Finally, the dimensionless macroscopic permeability Da is estimated via the Darcy's law. The drag ratio computed is in a good agreement with the previous results from porous media models. [ABSTRACT FROM AUTHOR]

Highlights • A lattice Boltzmann method is used to calculate the drag force acting on cubes. • The effect of solid volume fraction and Reynolds number on the drag force is studied. • Gluing together eight identical spheres cannot model accurately a super-quadric cube. • Drag force correlations for spheres under-predict the drag force acting on cubes. Abstract The accurate prediction of the drag force exerted by a fluid on assemblies of particles is critical to simulate key characteristics of gas-solid systems such as the bed expansion in fluidized beds. To this end, a lattice Boltzmann method has been applied to compute the drag force acting on assemblies of cubes for a wide range of Reynolds numbers, Re V = 0 - 200 , and solid volume fractions, ϕ = 0.1 - 0.45. The numerical data was used to propose a new drag force correlation for assemblies of cubes as a function of the Reynolds number and solid volume fraction. The new drag force correlation is expected to improve the accuracy of Euler-Euler and Euler-Lagrangian simulations of cubic particles. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Both hindering effect and wake accelerating effect were included in the drag correction. • Bubble columns (BCs) were simulated by CFD-PBM with the new drag model. • Drag correction should be based on both local gas holdup and bubble size distribution. • CFD-PBM with the new drag model can simulate BCs well at complex conditions. Abstract The underlying mechanism and the generality of the drag correction factor C D / C D0 , which was developed and applied in the simulation of bubble columns at elevated pressure in our recent work, was discussed in detail. With this drag model, numerical simulations of a bubble column were carried out by computational fluid dynamics (CFD) coupled with the population balance model (PBM). The complex variations of the drag correction factor and slip velocity with increasing local gas holdup were well predicted. The results confirmed that the drag correction should be based on the bubble size distribution and local gas holdup, instead of on the superficial gas velocity or overall gas holdup as commonly reported in the literature. The good predictions of the gas holdup and gas-liquid mass transfer in both water and high-viscosity liquids showed that the CFD-PBM model was powerful for the simulation of bubble columns under complex operating conditions. [ABSTRACT FROM AUTHOR]

In gas-solid flows, the drag force experienced by solid particles plays a significant role in determining the fluid dynamics of the system. Although several drag models have been proposed over the years, Gidaspow (1994) and Beetstra (2007) models are the ones that are still most commonly used. There is a lack of availability of work that gauges the capabilities of the newer models that have been developed over the past decade. Hence, this work utilizes three experimental configurations of fluidized beds to compare the performance of recent drag models proposed by Cello et al. (2010), Tenneti et al. (2011), Rong et al. (2013), Tang et al. (2016), and compares them with the drag models by Gidaspow (1994) and Beetstra et al. (2007). Euler-Euler (EE) or Two Fluid Model (TFM) simulations have been conducted for mono-disperse gas-solid fluidized beds containing Geldart-D particles corresponding to two experimental configurations and Geldart-B particles corresponding to one experimental configuration; all these configurations have been found in the literature. The temporal evolution of the ensemble-averaged particle height, time-averaged vertical particle velocity, temporal variation of the bubble diameter, time-averaged void-fraction distribution across the bed, and the time taken for computation are used as the variables for comparisons. It is observed that the drag models by Tenneti et al. (2011), Rong et al. (2013), and Gidaspow (1994) ensure appreciable performance for Geldart-D particles; for Geldart-B particles, the models by Tenneti et al. (2011) and Gidaspow (1994) exhibit satisfactory performance. The models by Beetstra et al. (2007) and Cello et al. (2010) are able to give appreciable performance only in predicting the bubble evolution, and even that at very early time instants, when the maximum solid volume fraction in the bed is about 0.60 (which is smaller than the maximum packing limit of 0.63). Taking both the computational time and solution accuracy into consideration, the model by Tenneti et al. (2011) seems to be the optimal choice for the considered cases, which is closely followed by the model of Gidaspow et al. (1994). The User Defined Functions (UDFs) and another code used for this work are included as Supplementary/Supporting Material. [ABSTRACT FROM AUTHOR]

The effects of the presence of the vertical internals of different sizes at a wide range of superficial gas velocity on the overall, local gas holdup distributions and their profiles have been studied and quantified in a 6-in. (0.14 m) Plexiglas® bubble column with air-water system using a non-invasive advanced gamma-ray computed tomography (CT) technique. In this study, two sizes of Plexiglas® vertical internals, having the same occupying area (∼25%) of the column's cross-sectional area (CSA) that represents those used in Fischer-Tropsch synthesis, have been used within a range of superficial gas velocities that cover bubbly and churn turbulent flow regimes (0.05–0.45 m/s). The reconstructed CT scan images revealed that the bubble columns equipped with or without internals displayed a uniform cross-sectional gas holdup distribution (symmetric) for all studied superficial gas velocities. However, the bubble column equipped with 1-in. vertical internals exhibited more uniform gas holdup distribution than the column with 0.5-in. internals. Also, the visualization of the gas-liquid distributions for bubble columns with and without internals reveal that the well-known phenomenon of the core-annular liquid circulation pattern that observed in the bubble column without internals still exists in bubble column packed densely with vertical internals. Moreover, a remarkable increase in the gas holdup values at the wall region was achieved in the churn turbulent flow regime based on the insertion of the vertical internals inside the column as compared with using a bubble column without obstacles. Furthermore, the values of the gas holdup in the core region of the bubble column with vertical internals are similar to those of the bubble column without vertical internals when they are operated at high superficial gas velocity (churn turbulent flow regime), based on the free cross-sectional area (CSA) for the flow. In general, the magnitude of the gas holdup increased significantly with increasing superficial gas velocity for the bubble columns with and without internals. However, the gas holdup profile was shaped like a wavy line in the bubble column with vertical internals, whereas it exhibited a parabolic gas holdup profile in the bubble column without obstacles. [ABSTRACT FROM AUTHOR]

• Fluid-particle interactions in multiphase fluid flow are considered. • The effect of wettability on deformation is studied. • Various fluid properties are considered to quantify how they change the fluid distributions and deformations. • The results are compared with experimental studies and we found an excellent agreement. A key parameter with considerable influence on the spatial distribution of the fluid phases in porous media is the wettability. Understanding the effect of wettability on fluids' distribution in three-dimensional (3D) porous media is critical to any phenomenon that involves multiphase flow in such media. To address the problem, we have carried out extensive computer simulations of two-phase flow in a 3D granular packing of grains and studied the effect of the wettability by varying the contact angle. To this end, the Immersed Boundary and Volume-of- Fluid approaches are coupled with the discrete element method (DEM). Five contact angles, covering a full range of wettability, are considered. We find that the wettability affects particle dynamics, such as the displacement of the grains, the contact force, and fluid velocity, and that rupture of the fluid can also occur in the pore space. Our results indicate that the volume of invading fluid injected into the system, the pressure on walls, and the injection surface decrease for larger contact angles. Most importantly, increasing the contact angle reduces the inter-particle interactions, whereas the drag force exhibits an opposite trend, leading to larger displacement of the particles. We also demonstrate and emphasize that some aspects of the effect of the wettability can only be observed in the 3D models of porous media and, thus, 2D models are inadequate. [ABSTRACT FROM AUTHOR]

Recent studies have shown that the expanded bed heights of bubbling fluidized beds obtained from direct numerical simulations (DNS) are higher than those obtained from CFD-DEM method. In this study, we show that the consideration of the effect of either granular temperature using the model proposed by Tang et al. (AIChE Journal, 2016, 62: 1958–1969) or solid concentration fluctuation on the interphase drag force can significantly improve the agreement with the DNS results. This study highlights the importance of the fluctuation of state variables on the accurate CFD simulation of gas fluidization. [ABSTRACT FROM AUTHOR]

• The differences between realistic fluidized bed and periodic domain are highlighted. • Three force-balance relations in these two systems are identified. • Differences over force balance relations are analyzed on the micro-, meso - and macro- scales. To understand the effects of macroscale constraints on fluidization, we investigate the differences between the periodic domain and realistic bed by using fine-grid simulations. The differences in these two systems are highlighted by identifying three force-balance conditions with respect to the gas-phase, solid-phase and the mixture, respectively. Specifically, these three conditions are not satisfied at the microscale, but satisfied at the macroscale in both systems; Over the mesoscale, the gas-phase force balance is established in the periodic domain and in the fluidized bed at bubbling states, but not at turbulent states, whereas the solid-phase and the mixture force balance conditions are established only in the periodic domain, not in the realistic bed. The influence of the bounding wall can be implicitly included by introducing the gas-phase pressure gradient, turbulent kinetic energies (TKEs) of gas and solids phases, and drift velocity as the markers for the drag force. [ABSTRACT FROM AUTHOR]

• 10,400 irregular particles with Re numbers between 0.1 and 100 are simulated. • The ANN-based models predict flow fields and single drag force. • The PIEP method provides drag forces of the irregular particles with neighboring effects. This study applies machine learning-based approaches to develop a drag force model for irregular-shaped particles in incompressible flows. The particle-laden flows are studied through an in-house particle-resolved direct numerical simulation (PR-DNS) at low-intermediate Reynolds numbers (Re). We utilize the PR-DNS to obtain drag force coefficients and flow fields of single particles. A variational auto-encoder model is used to obtain latent vectors to represent the geometrical features of the particles, and artificial neural networks (ANN) are developed to predict drag force coefficients and flow fields of the single particles. This study applies a pairwise interaction extended point-particle (PIEP) model to obtain the coefficients assuming the flow fields of neighboring particles can be linearly superposed. The PIEP method shows significant improvement on prediction for a few neighbored particles. In addition, the results reveal R 2 scores of 0.56-0.62 and errors of 9.1-10.0 % for the dilute, polydispersed systems with a volume fraction of 0.5 %. [ABSTRACT FROM AUTHOR]

Gas–liquid–solid three phase flows are commonly found in (bio-)chemical processes, e.g. in bubble slurry columns in the Fischer–Tropsch process. In order to facilitate the rational scale-up and the design of such columns, a detailed understanding of the complex phase interactions is required. In this work, we focus on the effective drag acting on particles and bubbles, using Direct Numerical Simulations. We combined the Front Tracking method of Roghair et al. (2013b) and the second order implicit Immersed Boundary method of Deen et al. (2012) . The resulting hybrid Front Tracking Immersed Boundary method is able to simulate dense three phase flows and is used to study swarm effects in terms of drag. A correlation has been obtained for the drag coefficient for a system consisting of 2 mm bubbles and 1 mm particles at several phase volume fractions. In future research, the developed methodology can be applied to study the effect of the bubble and particle size and their ratio. [ABSTRACT FROM AUTHOR]

Fine-grid Euler–Lagrange simulations of gas-fluidization of uniformly sized particles have been performed in three-dimensional periodic domains. Snapshots obtained from these simulations have been systematically coarse-grained to extract filter size dependent corrections to the drag law that should be employed in coarse Euler–Euler (EE) simulations. Correction to the drag law that should be employed in Coarse Multi-Phase Particle-in-Cell (MP-PIC) model simulations is examined through a two-step process: separating the coarsening of the fluid and particle phases. It is found that the drag correction is almost entirely due to the coarsening of the fluid cells, with particle coarsening having only a weak effect. It is shown that drag correction for coarse EE and MP-PIC simulations are comparable. As a result, coarse drag models developed for EE simulations can serve as a good estimate for corrections in MP-PIC simulations, and vice versa. [ABSTRACT FROM AUTHOR]

The problem of a steady, axisymmetric, fully developed adiabatic bubbly flow in a vertical pipe is studied analytically with the two-fluid model. The exchange of momentum between the phases is described as the sum of drag, lift, wall and dispersion contributions, with constant coefficients. Under these conditions, we are able to express analytically the void fraction profile as a function of the liquid velocity and pressure profiles. This relation is valid independently of the Reynolds stress model in the liquid phase – and can serve as a verification case for multiphase flow codes. The analytical void fraction profile vanishes at the wall, as a result of the balance between dispersion and wall forces. It presents a peak near the wall for upward flows, whereas its maximum is reached in the center of the pipe for downward flows. This is illustrated by calculations performed for upward and downward bubbly flows with the NEPTUNE_CFD code. [ABSTRACT FROM AUTHOR]

Particle-resolved direct numerical simulation (PR-DNS) is used to quantify the drag force on clustered particle configurations over the solid phase volume fraction range of 0.1 ≤ ϕ ≤ 0.35 and the mean slip Reynolds number range of 0.01 ≤ Re m ≤ 50 . The particle configurations and flow parameters correspond to gas–solid suspensions of Geldart A particles in which formation of clusters have been reported. In our PR-DNS, we use clustered particle configurations that match cluster statistics observed in experimental studies. To generate the particle configurations, we perform discrete element method (DEM) simulations of homogeneous cooling gas (HCG) systems with cohesive and inelastic particles in the absence interstitial fluid. Clustered particle sub-ensembles are then extracted from HCG simulations to match the statistics of cluster size distributions observed in experiments. These sub-ensembles are used for PR-DNS. It is found that the mean drag on clustered configurations decreases when compared to the drag laws for uniform particle configurations. The maximum drag reduction is observed in the configuration with low solid-phase volume fraction ϕ = 0.1 in Stokes flow, and is about 35 % . The drag reduction reduces with increase in both ϕ and Re m . A clustering metric is introduced to explain the behavior of the drag reduction with respect to solid-phase volume fraction. Also the behavior of the drag reduction with mean slip Reynolds number is related to the Brinkman screening length. PR-DNS results are then used to propose a clustered drag model for the range of flow parameters considered in this study. This clustered drag model provides a smooth transition between the uniform and clustered states by means of a weighting function with two model parameters. [ABSTRACT FROM AUTHOR]

• New analytical expression for particle (collision) speed in collision-dominated fluidized beds. • Combines kinetic theory of particle collisions with fluid-particle drag. • Accommodates collective/correlated particle motion in the bed. • Validated by comparing to computational fluid dynamics (CFD) - discrete element method (DEM) • Provides rapid prediction as well as a basis for understanding particle speed. The target of this method is gas–solid fluidized beds, in which the particles progressively become coated with liquid or generally become sticky for any reason. Previous studies have shown that the restitution coefficient of wet particle collisions depends on the speed at which the particles collide. Moreover, below a critical collision speed, the particles fail to rebound at all. Therefore, predicting particle collision speeds is important. Current methods to predict collision speeds are computationally expensive. The present method provides an analytical expression for particle collision speed, making it convenient for evaluating the potential for agglomeration. Moreover, it provides a basis for understanding the speed of particle motion in fluidized beds—usually only accessible through time-consuming numerical simulations—by anticipating the outcome of what is largely a repetitive computation of particle–particle collision and re-acceleration by the gas flow. The method combines the mean free time between inelastic particle collisions (with provision for collective particle motion), which cause them to lose kinetic energy, and the drag force by the turbulent gas flow on the particles, which accelerates them prior to their next collision. To validate the method, the results are compared to corresponding computational fluid dynamics (CFD) - discrete element method (DEM) calculations. [ABSTRACT FROM AUTHOR]

• A gravity-diffusion model for predicting water droplet concentration profiles in oil/water pipe flow was implemented. • In the model, the droplet size distributions could be replaced by the Sauter mean values without loss of accuracy. • The effect of turbulence of the droplet/fluid drag force was found to be important. • In general, a good match between the model predictions and data was found, although there was room for improvement for the lowest flow rates. A gravity-diffusion model was implemented for predicting water concentration profiles in dispersed oil-continuous oil–water flows. In this model, the measured droplet size distributions were used instead of a droplet size closure law. The turbulent diffusion was modelled assuming single-phase flow while the gravitational drift was based on closure laws from the literature, including hindrance effects. The results showed that including the effect of turbulence on the drag force was important, where the turbulent fluctuations cause an increase in the average drag because of the non-linearity of the drag law. The model yielded a good match with the experimental data reported by Gonzales et al. (Gonzalez et al., 2022), especially at the highest flow rates. We also concluded that the following model simplification could be introduced without changing the results significantly: 1) The droplet size distributions could be replaced by the Sauter mean droplet size. 2) The diffusivity profile model could be replaced by a uniform diffusivity model. [ABSTRACT FROM AUTHOR]

• A new gas–liquid model is developed for polydisperse turbulent bubbly flows. • The effect of virtual mass and model constants is investigated. • The effect of water flow rate is investigated. • The present model can significantly reduce the computational cost. We implement a new gas–liquid two phase model for the high-efficient prediction of polydispersed bubbly flows in a continuous casting mold. This model shares similarity with the Euler–Lagrange (E-L) method, in which the gas velocity is updated by bubble Lagrangian tracking, and with coupling the phase transport equation in Euler-Euler (E-E) method, thus, it is called the Quasi-Eulerian-Eulerian-IATE (Q-E-E-IATE) model. The local mean bubble size is obtained from solving the interfacial area transport equation (IATE). Various interfacial forces including drag force, lift force, virtual mass force, and turbulent dispersion force are incorporated in this model. This model is verified against published experimental data. Good agreement of gas volume fraction, flow field and bubble size distribution are obtained by adding the virtual mass force and adopting optimized IATE constants. The computational cost of the Q-E-E-IATE model is much lower compared to that of the traditional E-L and E-E models. [ABSTRACT FROM AUTHOR]

• A clouded bubble-based drag model is developed for bubbling fluidization. • The non-uniformity of drag force caused by bubble cloud is considered. • The feasibility of the clouded bubble-based drag model is validated. • Application of the modified drag model for Geldart A/B and A particle. A clouded bubble-based (CBB) drag model is developed in view of gas flow patterns around the clouded bubble. The bubble cloud is taken as the inter-phase between the bubble phase and emulsion phase based on the muti-scale resolution of the heterogeneous system. Moreover, the non-uniform distributions of drag force in the bubble crown and wake as well as the bubble sides are considered. The structure parameters are obtained by solving a series of equations including the mass conservation equations and empirical or semi-empirical correlations. The heterogeneous drag model is implemented into the two-fluid model (TFM) for 2D & 3D simulations of bubbling fluidized beds with Geldart A/B and A particles. The results demonstrate that the simulated results using the CBB drag model agree better with the experimental results compared to the homogeneous drag model and the structure-based drag model without the bubble cloud effect. [ABSTRACT FROM AUTHOR]

The dynamics of a bubble, initially stationary and spherical, rising in a viscous Newtonian liquid have been studied numerically using 3-D Volume-of-Fluid (VOF) method implemented in the Gerris flow solver. The study encompasses 8.7≤ Eo (= Δ ρ g D 2 / σ )≤641 and Re ≤151. Additionally, results published in the literature encompassing bubbles with lower values of E o numbers were also considered, such that the overall dependencies of bubble shape, wake characteristics, and drag coefficient over a large range of Eo and Re values can be identified. While it was found that the deformation of the bubbles as predicted through the numerical study can generally replicate experimental observations presented, several limitations were identified, such as in the representation of skirt formation behind a skirted bubble and the formation of satellite bubbles behind a bubble rising at high Reynolds numbers. The dependency of the bubble aspect ratio on the Weber and Morton numbers was confirmed for cases of spherical and ellipsoidal bubbles; whilst for spherical cap and skirted bubbles the aspect ratio was found to depend largely on the Reynolds and Capillary numbers, respectively. Finally, the expansion and formation of closed/open laminar wakes behind the rising bubble were analysed and was found to correlate well with the bubble Re and Eo numbers. [ABSTRACT FROM AUTHOR]

Cluster sub-models are developed and combined with the Energy minimum multi-scale method (EMMS) drag model to improve drag predictions for heterogeneous gas–solid flows. Theoretical cluster sub-models are developed to relate the cluster parameters with the local solid volume fraction. The cluster sub-models are validated by experimental data in the literatures. Drag coefficients predicted by the modified EMMS model with cluster sub-models are much lower than previous EMMS results and agree well with the experiment-based model. At solid volume fractions between 0.1 and 0.15 the drag coefficient, β , reaches a minimum at a maximum for slip velocities and gradually increases towards both sides to that of uniform flow. The modified EMMS drag model is further verified by CFD simulations of gas–solid flows in a CFB riser by coupling with the two-fluid model. The verification of the modified EMMS model once again demonstrates the applicability of the cluster sub-models. [ABSTRACT FROM AUTHOR]

• CFD-DEM simulation of particle drying processes. • Immersed boundary method for handling complex geometries. • Stefan flow has no effect on simulation results. • Development of particle drying model for discrete simulation. A great deal of industrial processes involves drying processes that removes water from the surface and interior of particles, where knowing the flow behavior, mass and heat transfer is crucial for proper design and optimization of industrial dryers. This work developed a CFD-DEM method for the simulation of particle drying processes, where the immersed boundary method (IBM) was used to handle the no-slip boundary condition of gas phase at the wall of complex geometries. The model was validated by comparing the numerical results to the experimental data of particle moisture and gas (particle) temperature in the dense bubbling bed and dilute pneumatic conveying bed, respectively. Compared with the experimental results, the maximum relative errors of outlet gas temperature, particle temperature and water content in the pneumatic conveying bed are 2.2%,2.2% and 7.9%, respectively. It was also found that considering the effect of Stefan flow on the drag correction did not affect the studied particle drying processes. Present study proved that CFD-DEM-IBM method is powerful for simulating the fluid flow, mass and heat transfer in gas-fluidized beds. [ABSTRACT FROM AUTHOR]

• Characterize a rotating packed bed by a new numerical model developed in OpenFOAM. • Equipped the new model with new features, including relative resistance formulation. • The verified and validated OpenFOAM model competes with commercial software, like Ansys-Fluent. • Parametric analysis with the new model. Computational fluid dynamics (CFD) simulation is an effective tool to study the flow characteristics of a rotating packed bed (RPB) in comparison with the corresponding complicated, time-consuming, and expensive experiments. Detailed flow characterization of RPB enables the optimization of micromixing efficiency, thus its overall performance. Among various CFD models, the reliable proficiency of Euler-Euler model in describing the two-phase flow behavior of a packing media has been demonstrated. It is less computationally expensive and sensitive to the size and mesh resolution than other CFD models, such as volume of fluid (VoF) and Euler-Lagrangian models. In addition, the interfacial mass and momentum transfers between phases are considered without resolving the interface characteristics in this model. These features make the Euler-Euler model a suitable choice for large-scale and 3D simulations of an RPB. The primary purpose of this work is to develop a new Euler-Euler model in OpenFOAM to characterize two-phase flow behavior of RPBs. A new two-phase porous media model is coupled with the Euler-Euler model in OpenFOAM to properly predict drag forces between liquid–solid and gas–solid phases. The numerical model was verified and validated by two sets of global and local hydrodynamic experimental data collected from the literature. The new OpenFOAM model demonstrates a promising capability in adequately describing principal hydrodynamic parameters of RPBs, including the liquid holdup, velocity, and pressure drop. Parametric analyses with the aid of the developed numerical model delineated the effects of main operating parameters, such as rotating speed, liquid and gas volumetric flow rates, gas to liquid filling ratio, and packing/bed diameter ratio, on the hydrodynamics of an RPB. Performances of two and three-dimensional numerical models in hydrodynamic predictions of an RPB were also studied. [ABSTRACT FROM AUTHOR]

• The reduction of drag force caused by Stefan flow decreases as Re increases. • The thickened boundary layer is suppressed by the surrounding inert particles. • The drag force reduction is non-negligible even at higher solid volume fraction. • A drag correlation is proposed based on the simulation results. Single reactive particle is generally surrounded by a sea of inert sand particles in thermo-chemical conversion process of solid fuels inside fluidized bed reactors. The drag force of the reactive particle under such special condition is affected by the combination of Stefan flow from the reactive particle, particle Reynolds number (Re), and solid holdup (c). This work quantifies this combinational effect via particle-resolved direct numerical simulations. It is found that the outward Stefan flow weakens the drag force, while the inward Stefan flow strengthens the drag force. The effect of Stefan flow becomes weak as c or Re increases. The variation of Re has negligible effect on the reduction of the drag force when c is relatively high. Finally, a drag correlation considering the joint influences of Stefan flow, Re and c is proposed based on the simulation data. [ABSTRACT FROM AUTHOR]

[Display omitted] • Empirical correlations were assessed with an established database of U mf. • The limited applications of empirical correlations were disclosed. • Four modified formulae of correlations were developed for the prediction of U mf. • A general correlation of U mf based on direct numerical simulations was proposed. As one of the most significant parameters in fluidized beds design and operation, the minimum fluidization velocity (U mf) has received utmost attention since 1940s. As an effective reference for evaluating the fluidization characteristic, U mf is conventionally predicted using the empirical correlation developed based on experiments for the specified gas-solid system. Despite more than 100 correlations proposed in the literature, these correlations show great diversity in either the applicable regimes or the mathematical formulae. Thus a general correlation for accurately determining U mf is highly desired. In this work, with a recently established database of U mf mined from published papers, the empirical correlations with four different formulae were first assessed for Geldart Groups A, B, and D particles, respectively. In view of the application limitations, modifications to different formulae of empirical correlations have been made to achieve satisfactory performances in predicting U mf for either Geldart Groups A, B, or D particles. Note that U mf is essentially determined by the balance between the gravitational force and drag force for a gas-solid system, a new formula based on a fluidized bed drag correlation derived from direct numerical simulations (DNS) was proposed. By using this formula, we developed a general correlation for U mf in gas-fluidized beds, which exhibits the best performance for all Geldart Groups A, B, and D particles when compared with empirical correlations reported in the literature. [ABSTRACT FROM AUTHOR]

• Two-level averaging approach is proposed and the unified EMMS drag is defined. • The unified EMMS drag is determined by performing a series expansion. • The fluctuation terms are closed by EMMS approach and validated by fine-grid simulation. • The unified EMMS drag is validated by CFD simulations covering multiple flow regimes. Gas-solid fluidization is characterized by pervasive, dilute-dense two-phase flow structures, which need mesoscale drag modeling to account for their subgrid effects. The classic formulation of the energy-minimization multi-scale (EMMS) drag modeling requires a semi-empirical correlation of cluster diameter. To avoid using such a phenomenological description of mesoscale structures, in this work, we propose a two-level averaging approach: First, the mean drag in a fine-grid cell is defined as a weighted sum of the drag force in both the dilute and dense phases; Then, the second-level averaging is performed at the coarse-grid scale, where the unified EMMS drag is defined, and determined by performing a series expansion with respect to the phase-mean points of both the dilute and dense phases, respectively. The unified EMMS drag is validated with comparison to fine-grid simulation in a periodic domain and coarse-grid simulation of realistic fluidized beds, both showing fair agreement. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann method has been used to compute the drag force acting on assemblies of approximately cubic particles constructed from eight spheres for a wide range of Reynolds numbers. Based on the simulation data we propose a new drag force correlation for assemblies of approximately cubic particles. We have compared the drag force obtained with that predicted by the correlation proposed by Beetstra et al. (2007) , originally proposed for spheres, by considering either the drag acting on individual spheres or the drag acting on an approximately cubic particle composed of eight spheres. The comparisons showed that Beetstra׳s correlation cannot predict the system well. The correlation proposed in this paper enables Euler–Euler and Euler–Lagrangian simulations of approximately cubic particles, allowing the influence of the solid volume fraction in these models to be assessed. [ABSTRACT FROM AUTHOR]

Fluidized gas-particle systems are inherently unstable and they manifest structures on a wide range of length and time scales. In this article we present for the first time in the literature a coarse-grained drag force model for Euler-Lagrange (EL) based simulations of fluidized gas-particle suspensions. Two types of coarse graining enter into consideration: coarse fluid grids as well as particle coarsening in the form of parcel-based simulations where only a subset of particles is simulated. We use data from well-resolved EL simulations to assemble a model for the filtered drag force that examines fluid and particle coarsening separately. We demonstrate that inclusion of correction to gas-particle drag to account for fluid coarsening leads to superior predictions in a test problem. We then present an ad hoc modification to account for particle coarsening, which improves accuracy of simulations involving both fluid and particle coarsening. We also identify an approximate characteristic length scale that can be used to collapse the results for different gas-particle systems. [ABSTRACT FROM AUTHOR]

Fluid flowing through packed beds of multi-sized spheres is studied by a parallel lattice-Boltzmann (LB) model. The packed beds are generated by means of the discrete element method. First, the LB model is used to study the effects of size ratio and volume fraction on the fluid flow and quantify the drag forces on binary mixtures of particles. Typical flow behaviours are identified in relation to pore geometries. The results suggest that the polydispersity in particle size enhances local structure heterogeneity and flow non-uniformity, resulting in distributed fluid-particle interaction forces. Then, based on the simulated data, a new equation is formulated to calculate the mean individual drag force. The equation is extended to multicomponent mixtures of particles. The results show that the new equation is more accurate and reliable than those in the literature, and can be generally used in the modelling of particle-fluid flows. [ABSTRACT FROM AUTHOR]

• A novel 3D Eulerian porous medium model is developed for the gas–liquid flow in a RPB. • The sensitivity of the capillary pressure and mechanical dispersion models is analyzed. • The effect of liquid dispersion under different design and operational parameters are obtained. • The established model paves the way for simulating a 3D full scale RPB effectively and accurately. Liquid dispersion is very important for the modelling of liquid flow in a rotating packed bed (RPB) when an Eulerian porous medium approach is employed. For investigating the effect of the liquid dispersion in a practical RPB, a 3D Eulerian porous medium model has been established coupled with the appropriate interfacial, drag and dispersion forces formulations. The sensitivity of the parameters employed in these formulations has been thoroughly analyzed. New forms of the porous resistance model and the effective interfacial area correlation have been developed for the non-uniform two-phase flows. The simulation results show that the effect of the capillary pressure and mechanical dispersion forces on the liquid flow distribution and holdup in the RPB is clear and important. In addition, the effects of the dispersion force on the liquid holdup under different design and operational parameters have been thoroughly analyzed and it is found that the effect of the dispersion forces on the liquid holdup is almost the same for different nozzle widths and the porosities of the packing investigated. The investigation demonstrates that utilizing the Eulerian method can substantially reduce the simulation time and efforts when compared to the pore resolved method, such as the Volume of Fluid method without loss in accuracy. This provides a feasible approach to simulate RPBs in full 3D and for RPB technology scaling up and optimizations. [ABSTRACT FROM AUTHOR]

• Molecular dynamics simulation is performed to study droplets in rotating gas. • The droplet trajectories in forced vortexes are observed. • A droplet trajectory model based on drag force is proposed. • Droplet collisions in forced vortexes are studied. Molecular dynamics simulations of droplets in gas forced vortexes by applying a virtual rotational potential were presented. The result showed that the flow field scale of the simulation performed can reflect the macroscopic characteristics. The trajectories of water droplets are longer than that of oil droplets within a certain radius of flow field. A droplet trajectory model was proposed to predict droplet behavior. The study continued to investigate droplet collisions. It was observed that the large oil droplet and the downwind small water droplets produced near head-on, highly off-centre and scraping-adhering collisions, forming stable two-phase interfaces. The slight changes of the interfaces between water and oil droplets under the action of rotating flow field can be reflected by van der Waals interaction. The intermolecular hydrogen bonds form when two water droplets collide. Our study provides a new idea for further understanding of droplet collision in gas flow field. [ABSTRACT FROM AUTHOR]

• 3-D, full loop, LES of a circulating fluidized bed are conducted using EE approach. • Effects of drag and sgs turbulence models are investigated. • Results are validated against measurements from an in-house pilot-scale model. • The influence of change in the riser diameter is more pronounced for EMMS models. • The hybrid EMMS drag model and sgs -TKE model made the most accurate predictions. Large eddy simulation is performed on a circulating fluidized bed (CFB) based on an Eulerian-Eulerian approach. The riser of the CFB has two axial sections of different diameters joined by a diffuser. The effects of drag and subgrid-scale models are examined on hydrodynamic parameters, such as solids volume fraction (ε s), solids circulation rate (G s), and full loop pressure profiles. A hybrid energy minimization multi-scale (EMMS) drag model is applied that combines EMMS drag models for the bubbling and the fast fluidized bed regimes. Experiments are conducted on a pilot-scale CFB model, and numerical results are validated against the experimental measurements of pressure and G s. The change in the riser diameter has a significant influence on axial- and radial profiles of ε s , particularly in the upper riser section. The hybrid EMMS drag model and the sgs -TKE turbulence model give the best agreement to the experimental data. [ABSTRACT FROM AUTHOR]

[Display omitted] • A general gas–solid turbulence model is validated for different flow regimes. • Model parameters can be determined through a dynamic adjustment procedure. • Meso-scale production of variances in the solids volume fraction due to clustering. • Wall boundary conditions for the turbulent kinetic energy are derived. • Dynamic adjustment procedure yields grid-size independent results. The Spatially-Averaged Two-Fluid Model (SA-TFM) is a functional multiphase turbulence model aimed at predicting the influence of unresolved meso-scale structures on the macro-scale flow properties in coarse-grid simulations of gas-particle flows. In this study, we highlight the general applicability of the SA-TFM model due to the dynamic estimation of the model coefficients through test-filters, the anisotropic treatment of the Reynolds-stresses and the drag force correction, and additional wall-friction boundary conditions for the particle-phase velocity, Reynolds-stress and turbulent kinetic energy. The dynamic approach derives information on the unresolved meso-scale flow properties from the resolved macro-scale variables without the need for any intensive prior considerations of the specific flow structure. Thereby, the drift velocity, a measure for the drag-reduction due to the presence of meso-scale structures is estimated from the turbulent kinetic energies of the phases and the variance of the solids volume fraction. We validate the dynamic anisotropic SA-TFM against highly resolved fine-grid Two-Fluid Model simulation data and experimental measurements of Geldart type A and B particles in bubbling to turbulent flow regimes. In the course of this extensive study, we find that the predictions for the macro-scale flow properties, such as slip-velocity, bed expansion, volume fraction distribution, and mass-flux, are in good agreement with the experimental and fine-grid simulation data in a vast number of cases, ranging from unbound fluidization to pilot-scale fluidized beds, thus, implying a wide applicability of the dynamic model independent of the underlying grid-size. [ABSTRACT FROM AUTHOR]

• An agglomeration evolution model based on the formation-fragmentation competition mechanism was proposed. • A simulation method of fluidization with wet agglomerates was proposed with the combination of particle agglomeration mechanism and EMMS model. • The vertical solid velocity simulated by CFD was in good agreement with the PIV measurement results. • The influence of different liquid holdup on the agglomeration and fluidization behaviors of wet agglomerates was explored.. When the liquid is injected into a gas-solid fluidized bed, particles are easily wetted and prone to form liquid bridges among them, further leading to particle agglomeration. Wet particle agglomeration induced by liquid bridge is dynamic and unstable, and its evolution behavior affects the stable operation of fluidized bed reactor. Therefore, based on the formation-fragmentation competition mechanism, a wet agglomeration evolution model is proposed to predict the evolution characteristics of wet agglomerates under different conditions. Furthermore, a modified drag force model which attributed the effect of wet agglomerates into the drag force was established and applied to the CFD simulation of a fluidized bed with wet agglomerates under the liquid spray-evaporation equilibrium state. Meanwhile, the particle image velocimetry (PIV) technology is applied in this work, and it was found that the vertical solid velocity simulated by CFD is in good agreement with the PIV measurement results. [ABSTRACT FROM AUTHOR]