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... In spatially periodic domains (Agrawal et al., 2001;Igci et al., 2008;Jiang et al., 2020a;Liu et al., 2020b;Ozel et al., 2016;Radl and Sundaresan, 2014;Rauchenzauner and Schneiderbauer, 2022;Rubinstein et al., 2017;Tang et al., 2015;Zhou and Fan, 2015), the scale separation is implied such that the mesoscale behavior is independent of the macroscale flow/boundary con-straints, as indicated in Mouallem et al. (Mouallem et al., 2018) In other words, the mesoscale structure formed in the periodic domain is assumed to be typical of any fluidized bed with specific macroscale conditions. However, granular flows and gas-fluidized beds are basically far from equilibrium states and characterized by the lack of scale separation (Goldhirsch, 2003;Wang et al., 2018), although a near equilibrium state with scale separation is possible in certain simple granular systems (Ojha et al., 2004;Weinhart et al., 2013). ...

... where the averaged drag force (also referred to as the filtered drag force (Ozel et al. 2016 ...

... In both CFD-DEM and TFM simulations, the quantitative results are normally sensitive to the grid size. In CFD-DEM simulations, grids as small as 1.75 d p may be needed to get grid-independent statistics in very dilute suspensions (Capecelatro et al., 2014) and 3 d p is fine enough in cases at higher solids volume fraction (Ozel et al., 2016). In TFM simulations, the grid size achieving gridindependent results is commonly considered to be between 3 and 10 times the particle diameter (Agrawal et al., 2001;Jiang et al., 2020a;McCulloch and Pitts, 1943;Ouyang et al., 2021;Ozel et al., 2013;Parmentier et al., 2012;Sarkar et al., 2016). ...

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 gasphase,
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.

... It is widely reported that when multiphase models based on Kinetic Theory of Granular Flow (KTGF) (and the DDPM is one of them) are used with coarse grids, then using common homogeneous drag models leads to failure in the prediction of the multiphase flow hydrodynamics [42,43]. This failure is due to the unrealistic prediction of drag force caused by the inability of coarse grids to resolve mesoscale structures (such as particle strands in cyclones) [24,[42][43][44][45][46][47][48][49][50]. To overcome the deficiencies of homogeneous drag models for industrial-scale simulations heterogeneous drag models (also called sub-grid drag models) should be used to account for the effect of small mesoscale and heterogeneous structures on the drag correlations [24,[42][43][44][45][46][47][48][49][50]. ...

... This failure is due to the unrealistic prediction of drag force caused by the inability of coarse grids to resolve mesoscale structures (such as particle strands in cyclones) [24,[42][43][44][45][46][47][48][49][50]. To overcome the deficiencies of homogeneous drag models for industrial-scale simulations heterogeneous drag models (also called sub-grid drag models) should be used to account for the effect of small mesoscale and heterogeneous structures on the drag correlations [24,[42][43][44][45][46][47][48][49][50]. ...

... (2) to (11): 2)-(10)) [42]. Note that using sub-grid drag models constituted based on Eulerian-Eulerian simulations (such as the revised Sarkar et al. drag model) in an Eulerian-Lagrangian model (such as DDPM in present work) is an approximation as the particle information needs be mapped to the Eulerian grid before using the correlations [48,88]. An approximation of this kind is reasonable and the drag models deduced for Eulerian-Eulerian simulations can be used in Eulerian-Lagrangian simulations (such as DDPM and MP-PIC) and the other way around [48,88] (Particularly, the revised Sarkar et al. drag model has been used successfully in Eulerian-Lagrangian models in the literature [50,84]). ...

A hybrid multiphase model (Dense Discrete Phase Model, DDPM) coupled with an agglomeration model and a sub-grid drag model was developed for simulation of industrial-scale cyclones with high solid loading. The model is validated by experimental results of pressure drop and separation efficiency from a pilot-scale cyclone with a diameter of 1.6 m. Key trends such as improvement in separation efficiency and reduction in pressure drop of cyclone due to an increase in particle load are well captured by the model. It is concluded that including the agglomeration model is crucial in particular in cases involving very fine particles (d < 15 μm) for accurate predictions of pressure drop and separation efficiency, while using the sub-grid drag modification improves the prediction of separation efficiency.

... Therefore, either the need for grid size scaling or sub-grid corrections was recognized and pointed out [78][79][80], as a common requirement also for Eulerian-Eulerian and MP-PIC simulations on coarse grids (Figure 8a). For example, Radl and Sundaresan [78] examined the vertical upflow in periodic domains at different Reynolds' number and solids concentration, later focusing specifically on fluid and particle coarsening for parcel-based simulations [81]. Figure 8a shows graphically a typical effect of the use of coarse-grained parcels, which requires fluid grid coarsening. ...

... (a) Graphical example of the fluid-particle coarsening sequence leading to large cell sizes compared to the actual particles; (b) effect of the solid volume fraction ( = 1 − ) and number of particles per grain ( = in the present notation) on the normalized filtered drag coefficient . Reprinted from [81], with permission from Elsevier. ...

... Several periodic systems were investigated, mostly with the objective to improve understanding, characterize the influence of the coarse graining degree and grid size. Examples of such analyses are [68,78,80,81]. ...

In the last decade, a few of the early attempts to bring CFD-DEM of fluidized beds beyond the limits of small, lab-scale units to larger scale systems have become popular. The simulation capabilities of the Discrete Element Method in multiphase flow and fluidized beds have largely benefitted by the improvements offered by coarse graining approaches. In fact, the number of real particles that can be simulated increases to the point that pilot-scale and some industrially relevant systems become approachable. Methodologically, coarse graining procedures have been introduced by various groups, resting on different physical backgrounds. The present review collects the most relevant contributions, critically proposing them within a unique, consistent framework for the derivations and nomenclature. Scaling for the contact forces, with the linear and Hertz-based approaches, for the hydrodynamic and cohesive forces is illustrated and discussed. The orders of magnitude computational savings are quantified as a function of the coarse graining degree. An overview of the recent applications in bubbling, spouted beds and circulating fluidized bed reactors is presented. Finally, new scaling, recent extensions and promising future directions are discussed in perspective. In addition to providing a compact compendium of the essential aspects, the review aims at stimulating further efforts in this promising field.

... [41][42][43][44][45][46][47][48][49] It has to be noted that most of those models have been developed in the context of the Euler-Euler approach but it is agreed that these are also apply to Euler-Lagrange simulations. [40,50] Recently, we have presented a novel approach for deriving constitutive relations for the unresolved terms appearing in coarse grid simulations. Thereby, we advanced a spatially-averaged two-fluid model (SA-TFM), which is based on the concepts of turbulence modelling. ...

... [43,65] Euler-Lagrange methods commonly require at least a grid spacing, which is approximately 3-4 times the particle diameter. [38,50] It is, therefore, straightforward to apply coarse grids, which allow a considerable reduction of the computational effort. ...

... The solids phase is discretized by employing 3,636,983 parcels, while we use an average grid spacing of 0.1 to solve the gas-phase equations. This grid spacing is approximately 100 times larger than the resolution requirement for DDPM, [50] which implies a performance gain of about 4 orders of magnitude in the case of SA-DDPM. Figure 3 shows snapshots of the solids volume fraction. The figure clearly unveils that the bubbling/slugging regime, which is observed in the experiments, [68] is predicted by the SA-DDPM approach. ...

Detailed simulations of industrial‐scale fluidized beds such as the FINEX process are still unfeasible due to the wide range of spatial scales. Due to the computational limitations it is common to apply coarse grids, which do not resolve all relevant structures. In our previous study (Schneiderbauer, AIChE J., 63:3544‐3562, 2017), we have presented sub‐grid models, which enable the coarse grid simulation of dense large‐scale gas‐solid flows. In this paper, we apply these corrections to a parcel‐based the dense discrete phase model (DDPM), allowing to study the hydrodynamics of the FINEX® process. Furthermore, the parcel approach is augmented by an unreacted shrinking core model (USCM) to account for the direct reduction of the iron ore particles by the reducing agents of H2 and CO. This DDPM model is tested first for a cold pilot‐scale fluidized bed and second, the USCM approach is validated for the direct reduction in a lab‐scale fluidized. Finally, the model is applied to the FINEX process. The results show fairly good agreement with measurements of the average bed voidage and with experimentally determined particle size distributions. The results further indicate that fines are immediately reduced while the reduction of the largest ore grains takes considerably longer.
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... This is because, compared with TFM, CFD-DEM directly solves the motion and heat transfer of individual particles and hence produces more accurate results. Studies even show that CFD-DEM using a grid size around 3d p is able to obtain accurate results consistent with particle resolved-direct numerical simulation (PR-DNS), 35,36 where d p is the particle diameter. ...

... In this stage, the relevant contents related to the microscopic correlation such as two-point structure and the behavior at material front will be ana- A grid size of 2.5 d p is adopted since studies have shown that CFD-DEM using a grid size around 3d p is able to give grid-independent results. 35,36 With respect to the computational domain size, one can refer to Capecelatro et al., 38 which shows that more than 32 times the characteristic cluster length is needed in the gravity-aligned direction for obtaining domain size-independent statistics. However, in this work, as can be seen from Figure 1 For the discretization and solution method of the governing equations of the gas and solid phases, readers can refer to Yu et al. 39 The adopted domain-averaged solid volume fraction ⟨ϕ s ⟩ is 0.05, the particles are randomly distributed in the computational domain initially. ...

Computational fluid dynamics‐discrete element method is used to simulate gas‐solid flows with heat transfer. The strategy of repetitively resetting the gas phase temperature is adopted to maintain the temperature difference between the gas and solid phases. The difference between the heat transfer characteristics produced by this strategy and the traditional heat source method is analyzed. It is found that heat transfer in dense regions is artificially enhanced by the heat source method. Therefore, the results obtained by the temperature reset method are filtered to develop a three‐marker model for the filtered interphase heat transfer coefficient (IHTC). In the developed model, the filtered gas‐solid temperature difference is nondimensionalized by the average gas‐solid temperature difference in surrounding grids, which is shown to have an impact on the filtered IHTC. The developed model is demonstrated to be effective and accurate in both a prior and a posterior tests. This article is protected by copyright. All rights reserved.

... This necessitates the need for the coarsegraining of the standard CFD-DEM method to make it capable of simulating industrial systems. Over last 10-13 years, there has been a continued interest on the development of coarsegrained CFD-DEM methods [15][16][17][18][19][20][21][22][23][24]. In the coarse-grained CFD-DEM method, a specified number of original particles are represented by a relatively larger particle or parcel. ...

... This approach was later extended by Tauscendschon et al. [20] to model the fluidization of the cohesive particles in a fluidized bed dryer. Research work was also done on the development of appropriate interphase drag model for the coarse grained CFD-DEM method [21,22]. Coarse-grained CFD-DEM model was used to investigate the coal gasification [23] and biomass gasification [24] in a fluidized bed reactor. ...

Fluidized bed dryer often used in the pharmaceutical industry for drying of wet granules. Coupled computational fluid dynamics (CFD) – discrete element method (DEM) is frequently used to model the drying process because of its ability to obtain the relevant information at the particle level. However, it becomes almost impossible to model the industrial scale fluidized bed dryer using the coupled CFD-DEM method because of the presence of large number of particles \(\left(\sim {10}^{6-8}\right)\). To reduce the number of particles to be tracked in the simulation, coarse grained coupled CFD-DEM method was developed by researchers where a certain number of particles of the original system was represented by a relatively bigger particle in the coarse-grained system. The appropriate scaling of the particle–particle and particle–fluid interaction forces is necessary to make sure that the dynamics of the coarse-grained particles/parcels accurately represent the dynamics of the original particles. The coarse-graining of the drying process of pharmaceutical granules during fluidization needs systematic coarse-graining of the momentum, heat, and solvent vapor transfer process. A coarse grained coupled CFD-DEM method was used to model the momentum and heat transfer during the fluidization of pharmaceutical granules. It was shown that the heat transfer during the fluidization of large number of particles could be predicted by simulating a smaller number of bigger particles with appropriate scaling of particle–particle heat and momentum transfer, and particle–fluid heat and momentum transfer at significantly smaller computational time. This model can be further extended by including a coarse-grained moisture transport model in future.

... TFM simulations have difficulties resolving particle size distributions (PSD) and capturing the influence of particle shapes while the Euler-Lagrangian methods can directly resolve them 49 . Current research indicates that the sub-grid drag models are also important to the coarse-grained Euler-Lagrangian simulations 29,[50][51][52] . Similar to the filtering of fine-grid TFM, the filtered drag model can also be constructed from the filtering of fine-grid CFD-DEM simulations [53][54][55] . ...

... The sub-grid gas velocity was also reconstructed from the gridscale pressure balance equation according to weighted local porosities 56 or simplified momentum equations 54 . However, due to the limited research of filtered CFD-DEM drag models, many of the coarse-grained Euler-Lagrangian simulations are still using the drag models derived from fine grid TFM 51,57,58 . Recent research 59 showed that the filtered TFM drag model overcorrects the influence of sub-grid structures if used for simulations with only fluid coarse-graining. ...

The accuracy of coarse-grained Euler-Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved sub-grid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macro-scale markers using fine grid Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations. The traditional non-linear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen-Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R-squared values. The utilization of the gas inlet velocity as an additional macro-scale marker reduced the errors by up to 55.3% in the tested cases.

... However, DEM is not suitable for industrial systems, typically consisting of more than a billion particles because of high computational time. Several researchers worked on the coarse-graining of the DEM (and CFD-DEM) models to simulate the industrial systems relevant to different applications in a reasonable time [164][165][166][167][168][169][170] . In the coarse-grained CFD-DEM, a specified number of original particles are represented by a large particle or parcel [164][165][166][167][168][169][170] . ...

... Several researchers worked on the coarse-graining of the DEM (and CFD-DEM) models to simulate the industrial systems relevant to different applications in a reasonable time [164][165][166][167][168][169][170] . In the coarse-grained CFD-DEM, a specified number of original particles are represented by a large particle or parcel [164][165][166][167][168][169][170] . The parcel-parcel contact forces and the parcel-fluid interaction forces are modified to ensure that the coarse-grained system represents the original system. ...

The fluidized bed is an essential and standard equipment in the field of process development. It has a wide application in various areas and has been extensively studied. This review paper aims to discuss computational modeling of a fluidized bed with a focus on pharmaceutical applications. Eulerian, Lagrangian, and combined Eulerian-Lagrangian models have been studied for fluid bed applications with the rise of modeling capabilities. Such models assist in optimizing the process parameters and expedite the process development cycle. This paper discusses the background of modeling and then summarizes research papers relevant to pharmaceutical unit operations.

... By spatially averaging the highly resolved fine-grid simulation results, the constitutive relations used for coarse-grid simulations can be extracted. So far, numerous contributions [14][15][16][17][18][19][20][21][22][23][24][25] proposed a novel meso-scale drag model for coarse-grid E-L simulations. They indicated that the optimization of the viscous term is of importance for improving the predictability of the scaled drag force. ...

... Generally, the macroscopic phenomena are not sensitive to variations in Young's modulus commonly ranging from 10 6 to 10 9 Pa for cold-flow in the literature. 18,19,47,48 A sensitivity analysis of Young's modulus is included in the SI to evaluate the effect in a thermal gas-particle system. In order to ensure the accuracy of the generated model and to take into account the computational expenses, the Young's modulus is assigned to 10 8 Pa. ...

Accurately predicting the complex inhomogeneous heat transfer behavior in gas-solid fluidized beds is of fundamental importance. In this work, we constitute an enhanced filtered interphase heat transfer coefficient (IHTC) closure by systematically filtering the dataset from highly-resolved three-dimensional (3D) computational fluid dynamics-discrete element model (CFD-DEM) simulations. Particularly, effects of several potential filtered variable markers on filtered IHTC predictions are examined by statistical analysis. We reveal the formulated filtered IHTC correction closure manifests a systematic dependence on filtered interphase temperature difference as an additional marker. The proposed closure shows good agreement with the filtered fine-grid simulation data in an a priori analysis. Moreover, the difference of filtered IHTC corrections deduced from 3D Euler-Euler and Euler-Lagrange simulations is quantified. Finally, the comparative analysis between our proposed filtered IHTC formulation and those in literature is implemented. This work holds a potential to facilitate the development of thermal gas-solid flow modeling.

... Moreover, many articles have largely studied the influence of different drag models on direct macroscale flow parameters such as the gas/particle velocity and volume fraction (Xu et al., 2018;Bian et al., 2019Bian et al., , 2020 while relatively few studies have been focused on such influence on filtered mesoscale quantities such as filtered slip velocity, filtered correction factor and filtered mesoscale drag force (Zhou and Wang, 2014;Zhu et al., 2018). Besides, relatively few filtered SGM investigations have employed "more ideal" DNS-based HDCs as a sub-input in constructing filtered mesoscale drag closures (Radl and Sundaresan, 2014;Ozel et al., 2016). Radl et al. (2012) found that the microscopic HDCs of Wen and Yu (1966) and Beetstra et al. (2007) are of little impact on filtered drag predictions for dilute flows (εs≤0.15). ...

... (2) 16.32 and 10.44% for <εs>=0.25. Noting that Δgrid=~3ds was used in mesoscale modeling of inhomogeneous gas-particle flows in the literature, for example, Radl and Sundaresan (2014), Ozel et al. (2016) and Yu et al. (2020a). Therefore, the selection of Δgrid=3.3ds ...

Filtered mesoscale model can be formulated from highly-resolved continuum or discrete simulations. The embedded microscopic homogeneous drag closure (HDC) is of key importance in determining the reliability and accuracy of such simulations. This work investigates the effects of sub-input HDCs on filtered mesoscale predictions using highly-resolved simulations. Quantitative comparisons directly reveal that there are significant differences between the commonly-practiced Wen-Yu drag closure and the direct numerical simulation (DNS) based HDCs, especially for moderate and dense gas-particle flows. Moreover, the HDCs from DNS of static particles agree better with the benchmark data from DNS of dynamic gas-particle flows at very low Reynolds numbers for εs>0.05∼0.10 while Wen-Yu drag is more applicable for the remaining range. Regarding that DNS is commonly implemented over a specific range of operating conditions, an enhanced HDC via refitting more elaborate high-fidelity DNS data (εs=[0.01, 0.65], Res=[1, 1000]) from literature is proposed and analyzed.

... Although a smaller system relative to actual experimental system was simulated using the present coupled CFD-DEM model to avoid the difficulty due to the large number of particles, long duration of the complete drying process associated with the full experimental system, and smaller value of Δt DEM required to simulate the full experimental system because of smaller diameter of the actual granules, coarse graining of the present CFD-DEM model may in future allow us to simulate the full experimental system in a reasonable time duration. Coarse-grained CFD-DEM can considerably reduce the simulation time, and many researchers are working on this topic (45)(46)(47)(48). However, no work has been reported on the computational modeling of complete drying of wet granules in a fluidized bed dryer using coarse-grained CFD-DEM method till now to the best of our knowledge. ...

Drying of wet granules in a fluidized bed dryer is an important part of the pharmaceutical tablet manufacturing process. Complicated gas-solid flow patterns appear in the fluidized bed dryer, and interphase momentum, heat, and mass transfer happen during the drying process. A coupled computational fluid dynamics (CFD)-discrete element method (DEM)-based approach was used to model the drying process of pharmaceutical wet granules in a fluidized bed dryer. The evaporation of water from the surfaces of the particles and the cohesion force between the particles due to the formation of liquid bridges between the particles were also considered in this model. The model was validated by comparing the model predictions with the experimental data available from the literatures. The validated model was used to investigate the drying kinetics of the wet granules in the fluidized bed dryer. The results from numerical simulations showed that the dynamics and rate of increase of temperature of wet particles were considerably different from those of dry particles. Finally, the model was used to investigate the effects of inlet air velocity and inlet air temperature on the drying process. The model predicted increase in drying rate with the increase of inlet air velocity and inlet air temperature. This model can help not only to understand the multiphase multicomponent flow in fluidized bed dryer but also to optimize the drying process in the fluidized bed dryer.

... Analogous to the case of the heterogeneity index, ∇pg has also been recommended as an essential marker for correlating the drift velocity 37,38,51 ; it is hereinafter expressed as dg = dg ( s , slip , ∇ g )| Δ f =const . Ozel et al. 40 applied structural models and determined the drift velocity as functions of non-local coarse-grid quantities 26 . Recently, Rauchenzauner and Schneiderbauer 52 proposed a dynamic anisotropic spatially averaged TFM, where udg was closed by anisotropic components of the gas-phase turbulent kinetic energy and the scalar variance of the solid volume fraction. ...

Multiscale simulations of fluidized beds should account for the effect of sub-grid structures on drag. How to extract the features of these structures in the form of proper finite quantities, namely markers, has posed great challenges in mesoscale drag modeling. The choice of markers has seldom been investigated in terms of their rationality and adequacy. This paper introduces a two-step scheme that is applied in the classic experimental approach to reflect on the choice of markers. The steady-state definitional relations of the drag correction factor are deduced from force balance equations, with emphasis on the difference between definitional relations and constitutive relations. A comparison between common drag models obtained from fine-grid simulations and corresponding definitional relations shows that the challenge in developing a general mesoscale drag model cannot be circumvented by correlating the heterogeneity index or drift velocity with the solid volume fraction, slip velocity and gas-phase pressure gradient.

... Fluid transport through the airways was solved by the volume-filtered mass and momentum conservation equations (Anderson and Jackson, 1967;Capecelatro and Desjardins, 2013) implemented in OpenFOAM v2.2 (Weller et al., 1998). Particle and fluid phases were coupled through a version of the CFDEMcoupling platform (Kloss et al., 2012) modified to benefit from faster two-way coupling by Ozel et al. (2016). ...

For many of the one billion sufferers of respiratory diseases worldwide, managing their disease with inhalers improves their ability to breathe. Poor disease management and rising pollution can trigger exacerbations that require urgent relief. Higher drug deposition in the throat instead of the lungs limits the impact on patient symptoms. To optimise delivery to the lung, patient-specific computational studies of aerosol inhalation can be used. However in many studies, inhalation modelling does not represent situations when the breathing is impaired, such as in recovery from an exacerbation, where the patient’s inhalation is much faster and shorter. Here we compare differences in deposition of inhaler particles (10 and 4 micron) in the airways of three patients. We aimed to evaluate deposition differences between healthy and impaired breathing with image-based healthy and diseased patient models. We found that the ratio of drug in the lower to upper lobes was 35% larger with a healthy inhalation. For smaller particles the upper airway deposition was similar in all patients, but local deposition hotspots differed in size, location and intensity. Our results identify that image-based airways must be used in respiratory modelling. Various inhalation profiles should be tested for optimal prediction of inhaler deposition.

... The time-to-solution can be further reduced by coupling GPU accelerations with coarse-grained simulations (Lu et al., 2016). As illustrated in Fig. 22, in coarse-grained CFD-DEM simulation, the fluid coarse-graining is the utilization of coarse CFD grid while the particle coarse-graining is the lumping of physical particles into numerical parcels (Ozel et al., 2016;Yu et al., 2020). To account for the unresolved sub-grid structures due to coarse-graining, the EMMS drag (Yang et al., 2003;Lu et al., 2017b) or filtered drag (Igci et al., 2008;Gao et al., 2018;Yu et al., 2020) was used. ...

In this research, a Graphical Processing Unit (GPU) accelerated Discrete Element Method (DEM) code was developed and coupled with the Computational Fluid Dynamic (CFD) software MFiX to simulate granular and multiphase flows. The Fortran-based CFD solver was coupled with CUDA/C++ based DEM solver through inter-process pipes. The speedup to CPU is about 130 to 243 folds in the simulation of particle packings. In fluidized bed simulations, the DEM computation time is reduced from 91% to 17% with a speedup of 78 folds. The simulation of Geldart A particle fluidization revealed a similar level of importance of both fluid and particle coarse-graining. The filtered drag derived from the two-fluid model is suitable for Euler-Lagrangian simulations with both fluid and particle coarse-graining. It overcorrects the influence of sub-grid structures if used for simulations with only fluid coarse-graining.

... Among all the proposed methods, two methods of Energy Minimization Multi Scale (EMMS) and filtering have attracted attentions of majority of the researchers. Gao et al. [132] classified the heterogeneous drag models into four types based on the derivation methods: -Heterogeneous drag models derived from fine-grid kinetic theory of granular flow in TFM simulations (such as [133][134][135]) -Heterogeneous drag models derived from fine-grid CFD-DEM simulations (such as [136,137]) -Heterogeneous drag models derived from particle-resolved direct numerical simulations (such as [138]) -Heterogeneous drag models derived from meso-scale structure-based methods such as EMMS (such as [139][140][141]) ...

Drag force models are one of the most important factors that can affect TFM and CFD-DEM simulation results of two-phase systems. This article investigates the accuracies, implementation issues and limitations of the majority of the drag models for spherical, non-spherical and systems with size distribution and evaluates their performance in various simulations. Around 1888 data points were collected from 19 different sources to evaluate the drag force closures on mono-dispersed spherical particles. The Reynolds number and fluid volume fraction ranges were between 0.01 and 10,000 and between 0.33 and 1, respectively. In addition, 776 data points were collected from seven different sources to evaluate the drag force closures on poly-dispersed spherical particles. The Reynolds numbers were between 0.01 and 500, fluid volume fractions between 0.33 and 0.9, and diameter ratios up to 10. A comprehensive discussion on the accuracy and application of these models is given in the article.

... [6][7][8] Such datasets are then applied to develop the filtered mesoscale correction to the microscopic closure. The developed correction considering the influence of mesoscale structures could be used to improve the predictions of coarse-grid simulations [9][10][11][12][13][14] . To acquire an understanding of the underlying physics from the filtered dataset, both the conventional modeling (i.e., data fitting via an algebraic function form) and artificial neural network (ANN) based data-driven modeling (DDM) can be adopted. ...

This study presents conventional and artificial neural network‐based data‐driven modeling (DDM) methods to model simultaneously the filtered mesoscale drag, heat transfer and reaction rate in gas‐particle flows. The dataset used for developing the DDM is filtered from highly‐resolved simulations closed by our recently formulated microscopic drag and heat transfer coefficients (HTCs). Results reveal that the filtered drag correction is nearly independent of filter size when including the filtered gas phase pressure gradient. We further find that the filtered HTC correction critically depends on the added filtered temperature difference marker while the filtered reaction rate correction shows weak dependence on the additional markers. Moreover, compared with conventional correlations, DDM predictions agree better with filtered resolved data. Comparative analysis is also conducted between existing HTC corrections and our work. Finally, the applicability of conventional and data‐driven models coupled with coarse‐grid computational fluid dynamics simulations for pilot‐scale (reactive) gas‐particle flows is validated comprehensively.

... Filtering analysis of fine-grid simulation data has access to both F d and F d , and so F d,sgs can be found at each location in the bed for the chosen filter size. It has been established previously that F d,sgs can be expressed as (Parmentier et al., 2012;Ozel et al., 2013Ozel et al., , 2016Ozel et al., , 2017Rubinstein et al., 2017;Cloete et al., 2018a;Neau et al., 2020;Jiang et al., 2020): ...

Simulations of large-scale gas-particle flows using coarse meshes and the filtered two-fluid model approach depend critically on the constitutive model that accounts for the effects of sub-grid scale inhomogeneous structures. In an earlier study (Jiang et al., 2019), we had demonstrated that an artificial neural network (ANN) model for drag correction developed from a small-scale systems did well in both a priori and a posteriori tests. In the present study, we first demonstrate through a cascading analysis that the extrapolation of the ANN model to large grid sizes works satisfactorily, and then performed fine-grid simulations for 20 additional combinations of gas and particle properties straddling the Geldart A-B transition. We identified the Reynolds number as a suitable additional marker to combine the results from all the different cases, and developed a general ANN model for drag correction that can be used for a range of gas and particle characteristics.

... In coarse grid simulation, the heterogeneous drag model should be used to account for the effect of the mesoscale structure. The heterogeneous drag model can be derived from fine grid two-fluid model simulations [31][32][33][34][35][36][37][38][39][40], fine grid CFD-DEM model simulations [41,42], particle-resolved direct numerical simulations (PR-DNS) [43], and mesoscale-structure-based methods. [44] In our previous work [36], a new filtered drag model was developed based on three-dimensional fine grid TFM simulations. ...

Computational fluid dynamics (CFD) is a powerful tool for prediction and analysis of complex multiphase flow hydrodynamics and residence time distribution (RTD) in chemical reactors. This study presented the validation and application of a filtered drag model for solid RTD prediction in a pilot-scale fluid catalytic cracking (FCC) circulating fluidized bed (CFB) riser with Geldart A particles. First, the filtered drag model implemented in the open-source MFiX-TFM solver was validated for flow hydrodynamics simulation in a FCC CFB riser. After that, the model was further employed to validate its ability for solid RTD prediction in the same riser by comparing the simulation results with the experimental data. The simulation with the filtered drag model well reproduced the tracer response experiment which is more accurate than that with the Gidaspow drag model. Simulations with both pulse and step tracer injection methods were compared, which reveals the limitation of solid RTD measurement using a pulse tracer injection method in the experiment.

... For each phase, a set of conservation equations are solved and closed with the stability condition. Both of these types of sub-grid scale model have been tested for use in gas-solid fluidized bed applications with Eulerian-Eulerian [7,8,57,58], CFD-DEM [59][60][61][62], and MP-PIC [30,34,35,63] In this work, our aim is to explore the validity of the DDPM with EMMS/bubbling drag for the two-dimensional (2D) hydrodynamic modeling of bubbling fluidized beds consisting of Geldart A, A/B, and B particles. The sensitivity of various modeling parameters (grid size, drag force, particle number per parcel, turbulence, and particleparticle restitution coefficients) and their effects on bubbling bed hydrodynamics are comprehensively investigated and validated using experimental measurements. ...

The fundamental problem encountered in the bubbling fluidized bed reactors is the presence of multiscale structures which cannot be resolved by the conventional drag models. In this study, a novel hybrid Eulerian-Lagrangian dense discrete phase model (DDPM) based on energy minimization and multiscale (EMMS) drag is proposed for the first time to analyze the hydrodynamics of bubbling fluidized bed reactors with Geldart A, A/B, and B particles. By comprehensive and comparative investigations of a number of key modeling parameters (grid size, drag force, particle number per parcel, turbulence, and particle-particle restitution coefficients), our proposed DDPM-EMMS model stands out of the currently-available counterparts in terms of improved grid-independency, multiscale structures resolvability with coarser grids, better parcel-independency, and better performance with laminar treatment against turbulence.

... The use of CFD-CGDEM inherently includes a coarsening of the mesh. This can result in unresolved flow features, which leads to an inaccurate drag prediction [73]. In analogy to MP-PIC and filtered-KTGF, the use of sub-grid drag models may improve the accuracy of CFD-CGDEM results in those cases. ...

Coarse‐Grained DEM is a relatively new, promising and, efficient method for the numerical simulation of particulate systems. The accuracy of the method relies on appropriate scaling rules for contact and fluid‐particle interaction forces. A variety of scaling rules is reported in the literature, including the additional use of drag correction models. To shed some light on the topic, different contact scaling rules are used and compared with DEM results regarding mean and RMS values of pressure drop and average particle height in a fluidized bed. The results indicated that in terms of averaged values as mean particle position and voidage profile the CFD‐CGDEM approach leads to accurate results for low scaling factors. With increasing scaling factors, deviations get higher. Regarding the particle dynamics, the approach leads to an underestimation of RMS values of particle position indicating a loss of particle dynamics in the system due to coarse‐graining. Furthermore, the results show that temporal discretization and contact scaling rule is not as important as expected. The impact of cell cluster size on drag force calculation is studied by comparing numerical results with experiments. The use of Energy Minimization Multi‐Scale drag correction is investigated, and a reduced mesh dependency and good accuracy are observed.

... Without taking into account the meso-scale structures, traditional drag models, such as Wen and Yu model [17] and Gidaspow model [2], overestimate the drag force [3]. By comparison, meso-scale drag models can be divided into two main groups according to their derivation method: EMMS drag model [18,19] based on meso-scale structure analysis and filtered drag model based on fine-grid two-fluid/ CFD-DEM simulations [20][21][22][23][24]. In this work we focus on EMMS-based method for MP-PIC simulations [11,12,25]. ...

To account for the sub-grid heterogeneity of bubbling gas-solid flows in the multi-phase particle-in-cell (MP-PIC) method, a bubble-based EMMS/DP drag model is proposed in this work by taking into account the particle/parcel position information. The local, inter-parcel porosity is calculated by using the method of smoothed particle hydrodynamics (SPH), while the intra-parcel porosity is closed by using the energy-minimization multi-scale (EMMS) model. The local velocities of gas phase and different solid parcels are determined by using the constraint of pressure drop balance between phases as in the EMMS/bubbling model. The drag force acting on each parcel is then determined with the sub-grid information of velocities and porosities. Two cases of bubbling fluidized bed are simulated to validate this drag model. And the results show good agreement with experimental data.

... This is of interest in the context of industrialscale fluidized beds, where applications of both fluid and particle coarsening are inevitable. An alternative to these kinds of models are the filtered drag models (31,33). These offer a correction to regular drag laws and are obtained by performing simulations of particles falling in a fluid on successively coarser grids for different flow conditions and solids-phase fractions. ...

Fluid–solid systems play a major role in a wide variety of industries, from pharmaceutical and consumer goods to chemical plants and energy generation. Along with this variety of fields comes a diversity in apparatuses and applications, most prominently fluidized and spouted beds, granulators and mixers, pneumatic conveying, drying, agglomeration, coating, and combustion. The most promising approach for modeling the flow in these systems is the CFD-DEM method, coupling computational fluid dynamics (CFD) for the fluid phase and the discrete element method (DEM) for the particles. This article reviews the progress in modeling particle–fluid flows with the CFD-DEM method. A brief overview of the basic method as well as methodical extensions of it are given. Recent applications of this simulation approach to separation and classification units, fluidized beds for both particle formation and energy conversion, comminution units, filtration, and bioreactors are reviewed. Future trends are identified and discussed regarding their viability.
Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 11 is June 8, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

... The specific calculation method is shown in Table 1. ② Surface force related to particle surface area [35], including drag and lift, etc.. Equivalent to the centroid of the particle, the surface resultant force A F and surface resultant torque A M are: ...

When the unresolved CFD-DEM (Computational Fluid Dynamics and Discrete Element Method) method is used to solve two-phase flow (composed of fracturing fluid and quartz sand) problems in a pipe, although the collision and accumulation of particles can be described in mesoscopic scale, the method has a serious shortcoming: the contradiction between computational efficiency and computational accuracy. In the current study, an improved CFD-DEM method based on time roundabout increment way is proposed. By improving the solution strategy of unresolved CFD-DEM in terms of time incremental way, the iterative convergence criteria and time advancement algorithm of fluid-particle coupling have been established. The improved CFD-DEM method can automatically adjust the CFD time steps according to the convergence criteria. At each time step, the particle iteration updates the force between the fluid and the particle. Also the fluid can be solved in a roundabout way based on the convergence criteria. A computational example is given by applying the improved CFD-DEM method to analyze a two-phase flow (fracturing fluid and quartz sand) in a contraction-expansion pipe. The result shows that the new method can simulate particle collisions efficiently, and calculate the pressure loss of the two-phase flow accurately. It is found that when the sand ratio is increased from 0 to 56%, the accumulation of particles at the outer edge of the sudden contraction/expansion section is more pronounced, while the force chain is much easier to be formed. When the diameter ratio increases from 0.3 to 0.7, the particle accumulation is weakened and the particle collision force chain is evenly distributed. Our research work provides a highly effective computational method for the solution of solid-liquid two-phase flow, and can be applied for coupled dynamic analysis of particles and fluids.

... While the heterogeneity based sub-grid models, such as EMMS [23,24], make some specific assumptions about the form of the unresolved clusters and streamers, the filtered approach aims to find appropriate constitutive relation for the unresolved terms appearing due to filtering of the balance equations. Closure models are commonly deduced from highlyresolved simulations (either Euler-Euler or Euler-Lagrange [25,26]), which are filtered using filters of different sizes. Different markers, such as solids volume fraction and slip velocity, are then used to classify the sub-filter scale state and averaged to obtain statistics of the filtered quantities. ...

Two different methods for closure modeling of the unresolved terms appearing in the filtered two-fluid model (fTFM) are discussed and compared. I) The spatially-averaged two-fluid model (SA-TFM) is based on generalizing the concepts of large eddy simulation to gas-particle flows. II) In the ADM-TFM approach the unresolved terms are modeled by an approximate deconvolution model, where an approximation of the unfiltered solution is obtained by repeated filtering. Finally, these models are applied to a lab-scale and a pilot-scale fluidized bed. Both approaches yield fairly good agreement with a highly resolved reference simulation as well as with experimental data. Additionally, both methods deliver reasonably grid independent solutions up to a grid resolution of 2 cm in the case of Geldart type A particles.

... We asses these (effectively two) different coarse-graining rules using fluidization of particles in a periodic domain as a test problem. As fluid grid resolution is known to have a large effect on predictions [36], we use the same fluid grid cell in the original and coarse-grained systems so that we can focus exclusively on particle coarsening. The CFD-DPM approach requires smoothing of exchange fields (e.g., particle volume fraction, drag force) that are projected on the fluid grid, since parcel size could become comparable to or even larger than a fluid cell depending on the degree of particle coarsening employed (when one chooses not to coarsen the fluid grid). ...

Although Euler-Lagrange simulations can be performed with millions of particles, particle coarsening where particles are replaced by parcels is necessary for simulation of large particulate and fluid-particle flows. The present study examines coarsening strategies for cohesive particles, where cohesion arises through either van der Waals interaction or liquid bridges between particles. In the latter case, the dynamics of liquid transfer between particles is also taken into account. Strategies based on matching dimensionless overlap, stress and effective coefficient of restitution are shown to lead to same coarse graining rules, while that based on matching the Bond number yields a different set of rules. Test simulations involving fluidization of cohesive particles reveal that the stress-based coarse graining rules provide better approximation of the average slip velocity between the gas and the particles.

... In the simulations, the modeling of particles phase is based on either the Eulerian formulation [2] or the Lagrangian methods such as the discrete element method (DEM) [3]. Regardless of advances in computational power to perform DEM simulations [4], its application is still limited to the simulation of small scale systems. Thus, the Eulerian approach is practically preferred and often used in simulations of fluidized beds. ...

In a fluidized bed system, mean trajectories of fuel particles within the bed of fluidized inert particles are governed by the associated drag forces and characterize hydrodynamic, chemical and thermal processes taken place in the system. A large particle size ratio between the bed material and the fuel particles affects the hydrodynamics of gas-solid multiphase flows via influencing the drag forces between solid phases. The present work focuses on the analysis of forces between the two solid phases with large size ratios using the Lagrangian simulations of discrete element method (DEM). The results are spatially averaged over variable control volume size for comparison to the continuum interphase momentum transfer model. Using our DEM simulation results, a correction factor of drag force is presented versus the size of averaging control volume usable in continuum models. In addition, the role of inhomogeneity of particles distribution within the averaging box is discussed.
https://authors.elsevier.com/c/1aZAl7QGmC1TJ

... A sophisticated filtered drag model was established in literature (Radl et al., 2012) for use in coarse-grid Euler-Lagrange simulations, highlighting the significant effect of particle clustering on the average slip velocity between particles and fluid and indicated how this clustering can be accounted for in unresolved EL-based simulations. The unclosed terms in the filtered model could also be constructed through a filtering operation of fine-grid resolved CFD-DEM simulations (Ozel et al., 2017(Ozel et al., , 2016. Ozel et al. (2017) performed Euler-Lagrange simulations of gas-solid flows in periodic domains to study the effective drag force model to be used in coarse-grained EL and filtered EE models. ...

In this paper a scaling method is proposed for scaling down the prohibitively large number of particles in CFD-DEM simulations for modeling large systems such as circulating fluidized beds. Both the gas and the particle properties are scaled in this method, and a detailed comparison among alternative mapping strategies is performed by scaling both the computational grid size and the riser depth. A series of CFD-DEM simulations has been performed for a pseudo-2D CFB riser to enable a detailed comparison with experimental data. By applying the scaling method, the hydrodynamic flow behavior could be well predicted and cluster characteristics, such as cluster velocity and cluster holdups agreed well with the experimental data. For a full validation of the scaling method, four mapping conditions with different ratios of the grid size and particle volume and of modified ratio of riser depth to particle size were analyzed. The results show that in addition to hydrodynamic scaling of the particle and fluid properties, scaling of the dimensions for the interphase mapping is also necessary. Keywords: Scaling method, CFB riser, CFD-DEM, Hydrodynamics, Clusters

... Finally, the prospects for future work are outlined as follows. (i) Coarse-grid and coarse-grained simulations (Sakai et al., 2014;Ozel et al., 2016;Chen and Wang, 2018) of thermal multiphase reactive riser flow systems (Gungor and Yildirim, 2013;Deen et al., 2014;Lane and Ryan, 2018;Zhu et al., 2019c) should be conducted in the near future. (ii) The current riser-only simulation allows us to focus on the dynamic behavior inside the riser through the feasible computer resource. ...

... However, as the simulations with the DEM are time consuming, the DEM is thus suitable for the simulation of small-scale fluidized beds or industrial scale fluidized beds with Geldart group D particles (Xu et al., 2011). Efforts have been directed to simplify the collision between particles and to reduce the number of particles by grouping them into parcels (Andrews & O'Rourke, 1996;Benyahia & Galvin, 2010;Hoomans et al., 1996;Lu, Gopalan, & Benyahia, 2017;Lu, Morris, Li, & Benyahia, 2017;Ozel, Kolehmainen, Radl, & Sundaresan, 2016;Snider, 2007). The lattice-Boltzmann method was coupled with the DE M to simulate the fluidized beds and some interesting results were reported in the literature (Third, Chen, & Müller, 2016;Xiong, Madadi-Kandjani, & Lorenzini, 2014). ...

A dense discrete phase model combined with the kinetic theory of granular flows was used to study the bubbling characteristics and segregation of poly-dispersed particle mixtures in a thin fluidized bed. Our simulations showed that in using the hybrid Eulerian–Lagrangian method, the common use of one computational cell in the thickness direction of the thin bed does not predict wall friction correctly. Instead, a three-cell discretization of the thickness direction does predict the wall friction well but six cells were needed to prevent overprediction of the bed expansion. The change in specularity factor (SF) of the model not only affected the predictions of the velocity of particles, but also had a considerable impact on their flow pattern. A decrease in SF, which decreases wall friction, showed an over-prediction in the size of bubbles, particle velocities, and void fraction of the bed, and led to a shift in the circulation center toward the bottom of the bed. The segregation of the Geldart B particles was studied in the narrow range from 400 to 600 μm with a standard deviation less than 10% of the average diameter. Simulations showed that large particles accumulated close to the distributor at the bottom of the bed and the center of the bed, but small particles moved towards the wall and top surface. The decrease in the mean particle size and spread in shape of the distribution improves mixing by up to 30% at a superficial gas velocity of around 2.5 times the minimum fluidization velocity. Log-normal mixtures with a small proportion of large particles had the most uniform distribution with a thin layer of jetsam forming at the bottom of the bed. Finally, experimental verification of the segregation and mixing of polydisperse particles with narrow size distribution is suggested.

The Dense Discrete Phase Model coupled with an agglomeration model is developed and validated for the simulation of industrial cyclones with high solid loads. The performance of the model is influenced by sub-models, model parameters, and numerical parameters. To optimize the performance of the present CFD model, an extensive sensitivity analysis was performed, varying one sub-model or parameter at a time, and systematically assessing the effect on the results through comparisons with measured pressure drop and separation efficiency of a highly loaded pilot-scale cyclone. The investigation shows that the turbulence model and particle-particle restitution coefficient have the strongest influence. This study concludes with the recommendation of a set of sub-models, model parameters, and numerical parameters providing the best prediction of the hydrodynamics of large-scale highly loaded cyclones. In addition, the impact of some operating conditions on the performance of a large-scale highly loaded cyclone were examined.

In dilute turbulent particle-laden flows, such as atmospheric dispersion of pollutants or virus particles, the dynamics of tracer-like to low inertial particles are significantly altered by the fluctuating motion of the carrier fluid phase. Neglecting the effects of fluid velocity fluctuations on particle dynamics causes poor prediction of particle transport and dispersion. To account for the effects of fluid phase fluctuating velocity on the particle transport, stochastic differential equations coupled with large eddy simulation are proposed to model the fluid velocity seen by the particle. The drift and diffusion terms in the stochastic differential equation are modelled using neural networks ('neural stochastic differential equations'). The neural networks are trained with direct numerical simulations (DNS) of decaying homogeneous isotropic turbulence at low and moderate Reynolds numbers. The predictability of the proposed models are assessed through a priori analyses and a posteriori simulations of decaying homogeneous isotropic turbulence at low-to-high Reynolds numbers. Total particle fluctuating kinetic energy are under-predicted by 40% with no model, compared to the DNS data. In contrast, the proposed model predictions match total particle fluctuating kinetic energy to within 5% of the DNS data for low to high-inertia particles. For inertial particles, the model matches the variance of uncorrelated particle velocity to within 10% of DNS results, compared to 60-70% under-prediction with no model. It is concluded that the proposed mathematical and computational framework is applicable for flow configurations involving tracer and inertial particles, such as transport and dispersion of pollutants or virus particles.

Computational fluid dynamics coupled with discrete element method (CFD‐DEM) has been widely used to understand the complicated fundamentals inside gas‐solid fluidized beds. To realize large‐scale simulations, CFD‐DEM integrated with coarse‐grain model (CG CFD‐DEM) provides a feasible solution, and has led to a recent upsurge of interest. However, when dealing with large‐scale simulations involving irregular‐shaped particles such as biomass particles featuring elongated shapes, current coarse‐grain models cannot function as normal because they are all developed for spherical particles. To address this issue, a CG CFD‐DEM for non‐spherical particles is proposed in this study, and the morphology of particles is characterized by the super‐ellipsoid model. The effectiveness and accuracy of CG CFD‐DEM for non‐spherical particles are comprehensively evaluated by comparing the hydrodynamic behaviors with the results predicted by traditional CFD‐DEM in a gas‐solid fluidized bed. It is demonstrated that the proposed model can accurately model gas‐solid flow containing non‐spherical particles, merely the particle dynamics are somewhat lost due to the scaleup of particle size. Finally, the calculation efficiency of CG CFD‐DEM is assessed, and the results show that CG CFD‐DEM can largely reduce computational costs mainly by improving the calculation efficiency of DEM. In general, the proposed CG CFD‐DEM for non‐spherical particles strikes a good balance between efficiency and accuracy, and has shown its prospect as a high‐efficiency alternative to traditional CFD‐DEM for engineering applications involving non‐spherical particles.

In dilute turbulent particle-laden flows, such as atmospheric dispersion of pollutants or virus particles, the dynamics of tracer-like to low inertial particles are significantly altered by the fluctuating motion of the carrier fluid phase. Neglecting the effects of fluid velocity fluctuations on particle dynamics causes poor prediction of particle transport and dispersion. To account for the effects of fluid phase fluctuating velocity on the particle transport, stochastic differential equations coupled with large-eddy simulation are proposed to model the fluid velocity seen by the particle. The drift and diffusion terms in the stochastic differential equation are modelled using neural networks ('neural stochastic differential equations'). The neural networks are trained with direct numerical simulations (DNS) of decaying homogeneous isotropic turbulence at low and moderate Reynolds numbers. The predictability of the proposed models are assessed against DNS results through a priori analyses and a posteriori simulations of decaying homogeneous isotropic turbulence at low-to-high Reynolds numbers. Total particle fluctuating kinetic energy is under-predicted by 40% with no model, compared to the DNS data. In contrast, the proposed model predictions match total particle fluctuating kinetic energy to within 5% of the DNS data for low to high-inertia particles. For inertial particles, the model matches the variance of uncorrelated particle velocity to within 10% of DNS results, compared to 60-70% under-prediction with no model. It is concluded that the proposed model is applicable for flow configurations involving tracer and inertial particles, such as transport and dispersion of pollutants or virus particles.

Accurate modeling and simulation of irregular shape sand particle fluidization are challenging as particle shape-resolved simulation is complex and time-consuming. In this study, the coarse-grained discrete element model (CG-DEM)-computational fluid dynamics (CFD) was adopted to improve the computational feasibility of traditional CFD–DEM and simplify the mathematical modeling by lumping a certain amount of physical particles into a numerical parcel. 3D CGDEM–CFD simulated the fluidization behavior of irregular shape sand particles in a fluidized bed, and several key parameters or model settings were assessed to identify critical model factors. Moreover, the impact of the model parameters on hydrodynamics was quantified by comparing the simulation results with the experimental data. The results demonstrate that applying a rolling friction model can increase the simulation accuracy of the fluidization behavior of non-spherical sand particles.

Different reaction technology determines different catalytic materials and solid density affects the hydrodynamics behavior in a fluidized bed. An efficient hydrodynamics study is, therefore, highly desirable, even for evaluating the assumptions through pilot-scale investigation. To develop new fluidized bed technology that requires low-density particles (e.g., the vapor-phase Beckman rearrangement to produce ε-caprolactam), the authors thoroughly studied the hydrodynamics of low-density particles (true density 750 kg/m³, packing density 450 kg/m³) in a turbulent fluidized bed. Pilot-scale cold experiments were conducted in an ∅800 mm column with optical fiber probes. The TFM was adopted, where the Wen&Yu model, EMMS model, and six filtered models were coupled, respectively. The solution of the EMMS model is often challenging because of the iterative solution of nonlinear equations. In this work, the calculation process of the EMMS model was optimized, saving one global search for every possible state solution, and a set of nonlinear equations can be linearized. Comparisons between experiment and simulation results revealed that the EMMS models gave the best prediction. This work can provide a research model and guidance for the design of industrial fluidized bed reactors using low-density particles.

Particle polydispersity is ubiquitous in industrial fluidized beds, which possesses a significant impact on hydrodynamics of gas–solid flow. Computational fluid dynamics-discrete element method (CFD-DEM) is promising to adequately simulate gas–solid flows with continuous particle size distribution (PSD) while it still suffers from high computational cost. Corresponding coarsening models are thereby desired. This work extends the coarse-grid model to polydisperse systems. Well-resolved simulations with different PSDs are processed through a filtering procedure to modify the gas–particle drag force in coarse-grid simulations. We reveal that the drag correction of individual particle exhibits a dependence on filtered solid volume fraction and filtered slip velocity for both monodisperse and polydisperse systems. Subsequently, the effect of particle size and surrounding PSD is quantified by the ratio of particle size to Sauter mean diameter. Drag correction models for systems with monodisperse and continuous PSD are developed. A priori analysis demonstrates that the developed models exhibit reliable prediction accuracy.

A coupled methodology was developed to model the fluidized bed coating process considering particle abrasion. Interactions of gas phase, particle phase and droplet phase were coupled with multiphase flow. Evaporation, coating and abrasion models were involved and verified by experimental data. The coupled method was evaluated by NaCl coating cases. Under the conditions of two experimental cases, quantitative proportion of the adhered precipitation abrased from the coated particle surface was obtained, which is attributed to frequent particle collisions. Another fluidized bed coating process, in-situ preparation of the Calcium-based supported sorbent for flue gas desulfurization, was simulated to validate the coupled model and investigate the effects of operating conditions on the net coating efficiency. When the nozzle was arranged near the dense phase zone, the conditions had little effect on the efficiency. Otherwise, higher efficiency can be achieved by increasing the bed inventory, droplet diameter, and droplet initial velocity. This research offers an efficient approach for modeling of fluidized bed coating process where particle abrasion is exigent, as well as providing guidelines for practical application of in-situ desulfurizer preparation.

Euler-Lagrange method is powerful for studying dense gas-solid flow, where the Eulerian grid is typically 3–5 times of particle diameter to ensure the accuracy of information mapping between gas and solid phases. This condition limits its applications in simulating reactors with complex geometries that require the use of Eulerian grids that are comparative to or smaller than particle diameter. In this study, eight methods for mapping discrete particle information to continuous fluid field were compared first via the simulation of a packed bed, their pros and cons were analyzed and discussed in detail; A kernel function method (the normalized kernel function method II, NKFMII) was then selected to simulate the hydrodynamics and heat transfer of gas-solid bubbling fluidized beds, the results not only validated NKFMII for interphase information mapping but also indicated that a grid-size-independent solution can be achieved; Finally, in order to balance the computational efficiency and accuracy a hybrid particle centroid method (PCM) and NKFMII method was proposed to achieve the interphase information mapping and then to simulate the hydrodynamics of a fluidized bed with immersed tubes, the ability of local grid refinement and the effectiveness of the coupled PCM and NKFMII method were demonstrated. This study proved that Euler-Lagrange simulation with local grid refinement is able to simulate gas-solid reactors with complex geometries.

Design, scale-up and operation of cyclone gas-solid separators are mostly based on simplified models and experience. Previous single-phase or one-way coupled simulations are not applicable to cyclones operating with relatively big particles and under high loadings, as used for example in circulating fluidized beds for the polymer and energy industry. Simulations based on the DEM-CFD allow for four-way coupled dense flow, including dissipation, friction, and rotational particle motions. However, the computational cost becomes easily prohibitive. Coarse-graining methods based on lumping smaller particles into parcels or grains have been recently proposed to reduce the number of elements and increase the time-step. Yet, much remains to be characterized in terms of accuracy vs. speed-up. In the present work, a coarse-grain DEM-CFD approach to simulate the two-phase flow in a Stairmand high-efficiency cyclone at gas velocities in the range 10-20 m/s and solid loading in the range 0.1% to 0.5%vol is investigated. In particular, the focus is on the effect that the coarse graining degree (up to 64 particles per coarse grain) exerts on the replicability of the results compared to pure DEM-CFD simulations. It is shown that the macroscopic quantities characterizing the cyclone performances, such as pressure drop, inner vortex length and collection efficiency, are generally maintained even with coarse graining degree up to 64, with an approximation that improves with the increase in the solids loading. However, detailed features of the gas and solids flow (e.g. strand formation) appear significantly affected by the coarse graining degree, already at coarse graining degree 8 and 27.

Most natural resources are processed as particle-fluid multiphase systems in chemical, mineral and material industries, therefore, discrete particle methods (DPM) are a reasonable choice of simulation method for engineering the relevant processes and equipment. However, direct application of this method is challenged by the complex multiscale behavior of such systems, which leads to enormous computational cost or otherwise qualitatively inaccurate description of the mesoscale structures. The coarse-grained DPM based on the energy-minimization multi-scale (EMMS) model, or EMMS-DPM, was proposed to reduce the computational cost by several orders while maintaining an accurate description of the mesoscale structures, which paves the way for its engineering applications. Further empowered by the highly-efficient multi-scale DEM software DEMms and the corresponding customized heterogeneous supercomputing facilities with GPUs, it may even approach realtime simulation of industrial reactors. This short review will introduce the principles of DPM, in particular, EMMS-DPM, and the recent developments in modeling, numerical implementation and applications of large-scale DPM which aims to reach industrial scale on one hand and resolves mesoscale structures critical to reaction-transport coupling on the other hand. This review finally prospects on the future developments of DPM in this direction.

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.

This work extends filtered models to investigate the influence of particle polydispersity on the filtered fluid-particle drag and heat transfer behaviors based on well-resolved computational fluid dynamics-discrete element model (CFD-DEM) simulations. By systematically filtering the CFD-DEM simulation data, it is found that the markers used for the monodisperse systems, (i.e., the filtered slip velocity and the gas phase pressure gradient for the drag correction; the filtered interphase temperature difference for the heat transfer correction) are indispensable in the bidisperse systems. Furthermore, the dependence of the filtered corrections on the particle size ratio and volume fraction ratio is identified. The increase in the proportion of small particles generally corresponds to the reduction of drag and interphase heat transfer corrections. The Sauter mean diameter is applicable to quantify the effect of particle bidispersity. Eventually filtered models of fluid-particle drag and heat transfer corrections for the bidisperse systems are developed.

The coarse-grained discrete element method (CGDEM) is promising for its ability to reduce computational cost. However, compared with discrete element method (DEM), CGDEM often overpredicts the granular temperature in simulations of systems with frictional particles. This is partially due to the fact that traditional coarsening strategies only account for the correction to energy dissipation due to inelastic collisions. This work proposes two types of new coarsening strategies that also make the correction to energy dissipation caused by the frictional force between particles. CGDEM simulations of homogeneous cooling systems (HCSs) and two bubbling fluidized beds are executed to evaluate the performance of the proposed strategies. It is found that, relative to CGDEM with traditional coarsening strategies, CGDEM with the proposed strategies gives a more accurate prediction of the instantaneous granular temperature in HCSs. They also better reproduce the time-Averaged fields obtained by DEM simulations for the considered bubbling fluidized beds. This demonstrates the necessity of considering both inelastic and frictional origins of energy dissipation in the coarsening strategy.

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.

Coarse-grid Eulerian-Lagrangian approaches are promising for simulating fluidized gas-solid flows due to their ability to track the trajectories and collisions of individual particles. Like coarse-grid Eulerian-Eulerian methods, these approaches also require drag corrections to account for subgrid inhomogeneities. This work develops novel meso-scale models that make use of the detailed information of the resolved positions and velocities of the solid phase. Each coarse grid is divided into three-dimensional subgrids. The gas velocities at subgrids are computed using simplified mass and momentum conservation equations for the fluid phase. The viscous term representing the shear force between different subgrids are included in the momentum equation. Priori analysis shows that the proposed meso-scale models give significantly better predictions than the best available model designed for coarse-grid Eulerian-Eulerian methods. The effectiveness of the proposed models is also demonstrated by posteriori tests.

Residence time distribution of particles is a critical parameter for proper design of gas-solid fluidized beds, especially in many non-catalytic solid conversion processes where it is highly desirable to match the residence time of a particle and its complete conversion time to achieve the synchronized conversion of particles of different sizes. However, the requisite of considering particle polydispersity and the long residence time of particles required by reaction kinetics together pose a great challenge to the computational fluid dynamics study of such systems. To this end, a GPU-based, massively parallel coarse-grained CFD-DEM method-the EMMS-DPM method (Lu et al., 2014) was extended to simulate the residence time distribution of polydisperse particles in a continuously operated multiple-chamber fluidized bed with a calculation of physical time of up to one hour. It was shown that the experimentally measured pressure drop of the bed or the solid holdup can be predicted reasonably well by the ad hoc drag models of non-spherical and polydisperse particles proposed in present study; the residence time distribution of particles of whole system can also be predicted correctly; and finally, the ratio of the mean residence time of coarse particles to that of fine particles is about three, which is insufficient to achieve the synchronized conversion of particles of different sizes according to an ideally theoretical analysis, great effort is needed to get a better match between the residence time and the compete conversion time of particles.

Gas-solid fluidization technology has been commercialized in many industrial applications since its implementation in the fluid catalytic cracking process in the early 1940s, however, the understanding of the complex hydrodynamics of gas-solid flow inside fluidized beds is still far from satisfactory due to its dynamic and multiscale nature, especially, the critical role played by mesoscale structures. In recent decades, computational fluid dynamics (CFD) has become an important toolkit in understanding the physics of complex gas-solid flow and then for the scale-up, optimization and design of gas-solid fluidized bed reactors. This article presented a pedagogical and comprehensive review to the Navier-Stokes order continuum theory for CFD simulation of the hydrodynamics of gas-solid fluidization, without taking the effects of heat and mass transfer as well as chemical reactions into consideration. A concise introduction to the methods for multiscale CFD simulation of gas-solid fluidization was firstly provided, which include direct numerical simulation, (coarse-grained) discrete particle method, kinetic method, continuum method and mesoscale-structure-based multiscale method. The underlying postulates of homogeneous continuum theory that assume the structure inside each computational cell is (nearly) homogeneous were then examined, followed by an overview of the constitutive relationships available in literature, including the particle phase stress models, the interphase drag models and the models for particle-wall interactions. The importance of mesoscale structures that take the form of gas bubbles and/or particle clusters and streamers in the quantification of the hydrodynamics of gas-solid flows was then addressed, and the explicit resolution (or highly resolved) method and implicit modeling method for quantifying the effects of mesoscale structures in continuum modeling of gas-solid fluidization were highlighted. Coarse grid simulation of large scale fluidized beds with proper mesoscale, sub-grid scale or turbulent models for constitutive relationships were then reviewed, focusing on the filtered method, turbulence modelling and heterogeneity-based method where the energy-minimization multi-scale (EMMS) based method is a representative. Finally, the scope for the further research areas is described.

Due to the linear correlation between the subgrid drift velocity and the filtered drag force, modeling the drift velocity would be an alternative way to obtain the filtered drag force for coarse‐grid simulations. This work aims to improve the predictability of models for the drift velocity using a new effective marker, the filtered gas pressure gradient, which is identified by momentum balance analysis. New models are constructed based on conditional averaging of the results obtained from fine‐grid two‐fluid model simulations of three‐dimensional unbounded fluidized systems. A priori assessment is presented with the comparison between the proposed models and the best available Smagorinsky‐type model with dynamic adjustment technique proposed in the literature. Results show that the proposed models give satisfactory performance. More important, the proposed models are demonstrated to have a better adaptability for cases under various physical conditions than the Smagorinsky‐type model. This article is protected by copyright. All rights reserved.

The combined ion exchange-membrane filtration system, whereby an active filtration layer is formed using a slurry flow of resin beads and water, has the potential to reduce energy usage and increase the quality of purified wastewater. The hydrodynamic design of these systems is in its infancy and there is a need for numerical methods to analyze such systems. In this work, computational fluid dynamics coupled with the discrete element method (CFD-DEM) is utilized to analyse the hydrodynamics of the combined ion exchange-membrane filtration system, and the formation of the filtrating bed and the parameters affecting it are studied by varying the flow conditions. As a result, the details of the bed formation with insights on the parameters affecting these phenomena and suggestions for an improved hydrodynamic design of the combined ion exchange-membrane filtration system are presented.

The purpose of this paper is to present a new approach for the modelling of the fluctuating motion of particles in turbulent two-phase flows which takes the dragging by the fluid turbulence and the interparticle collision into account. This model is based on separate transport equations for the components of the dispersed Reynolds tensor and for the covariance between the fluctuating motions of the two phases. The proposed closure assumptions allow to compute dispersed dilute two-phase flow and lead to classical results derived by applying kinetic theory when interparticle collision is the dominating phenomenon.
In order to validate the numerical model and closure assumptions, computations have been carried out for axisymetric dilute particle-laden jet, and predictions were compared with experimental results. The model accounts for, among other phenomena, the influence of the radial r.m.s. velocity at the nozzle exit on particle dispersion and the high anisotropy of the particle fluctuating motion observed in the main flow.

This paper demonstrates that the setup of the fine grid two-fluid simulation considerably affects the statistics for the effective drag required for industrial scale coarse grid simulations. In particular, we investigate the impact of the frictional stress model, the superficial gas velocity, the value of the maximum packing ratio, the particle type and the as well as the geometrical configuration (full fluidized bed against periodic box) on the sub-grid drag modification. Our results clearly show that the type of fine grid simulation directly changes the functional form of the constitutive relation for the macro-scopic drag when using the filtered solids volume fraction and the filtered slip velocity as independent variables.

We present a multi-purpose CFD-DEM framework to simulate coupled fluid-granular systems. The motion of the particles is resolved by means of the Discrete Element Method (DEM), and the Computational Fluid Dynamics (CFD) method is used to calculate the interstitial fluid flow. We first give a short overview over the DEM and CFD-DEM codes and implementations, followed by elaborating on the numerical schemes and implementation of the CFD-DEM coupling approach, which comprises two fundamentally different approaches, the unresolved CFD-DEM and the resolved CFD-DEM using an Immersed Boundary (IB) method. Both the DEM and the CFD-DEM approach are successfully tested against analytics as well as experimental data.

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.

Many sub-grid drag modifications have been put forth to account for the effect of small un- resolved scales on the resolved meso-scales in dense gas-particle flows. These sub-grid drag modifications significantly differ in terms of their dependencies on the void fraction and the particle slip velocity. We, therefore, compare the hydrodynamics of a three-dimensional bub- bling fluidized bed computed on a coarse grid using the drag correlations of the groups of (i) EMMS, (ii) Kuipers, (iii) Sundaresan, (iv) Simonin and the homogenous drag law of (v) Wen and Yu6 with fine grid simulations for two different superficial gas velocities. Furthermore, we present an (vi) alternative approach, which distinguishes between resolved and unresolved particle clusters revealing a grid and slip velocity dependent heterogeneity index. Numerical results are analyzed with respect to the time averaged solids volume fraction and its standard deviation, gas and solid flow patterns, bubble size, number density and rise velocities.

This report describes the MFIX (Multiphase Flow with Interphase exchanges) computer model. MFIX is a general-purpose hydrodynamic model that describes chemical reactions and heat transfer in dense or dilute fluid-solids flows, flows typically occurring in energy conversion and chemical processing reactors. MFIX calculations give detailed information on pressure, temperature, composition, and velocity distributions in the reactors. With such information, the engineer can visualize the conditions in the reactor, conduct parametric studies and what-if experiments, and, thereby, assist in the design process. The MFIX model, developed at the Morgantown Energy Technology Center (METC), has the following capabilities: mass and momentum balance equations for gas and multiple solids phases; a gas phase and two solids phase energy equations; an arbitrary number of species balance equations for each of the phases; granular stress equations based on kinetic theory and frictional flow theory; a user-defined chemistry subroutine; three-dimensional Cartesian or cylindrical coordinate systems; nonuniform mesh size; impermeable and semi-permeable internal surfaces; user-friendly input data file; multiple, single-precision, binary, direct-access, output files that minimize disk storage and accelerate data retrieval; and extensive error reporting. This report, which is Volume 1 of the code documentation, describes the hydrodynamic theory used in the model: the conservation equations, constitutive relations, and the initial and boundary conditions. The literature on the hydrodynamic theory is briefly surveyed, and the bases for the different parts of the model are highlighted.

Particle-resolved direct numerical simulations of a 3-D liquid-solid fluidized bed experimentally investigated by Aguilar-Corona (2008) have been performed at different fluidization velocities (corresponding to a range of bed solid volume fraction between 0.1 and 0.4), using Implicit Tensorial Penalty Method. Particle Reynolds number and Stokes number are O(100) and O(10), respectively. In this paper, we compare the statistical quantities computed from numerical results with the experimental data obtained with 3-D trajectography and High Frequency PIV. Fluidization law predicted by the numerical simulations is in very good agrement with the experimental curve and the main features of trajectories and Lagrangian velocity signal of the particles are well reproduced by the simulations. The evolution of particle and flow velocity variances as a function of bed solid volume fraction is also well captured by the simulations. In particular, the numerical simulations predict the right level of anisotropy of the dispersed phase fluctuations and its independence of bed solid volume fraction. They also confirm the high value of the ratio between the fluid and the particle phase fluctuating kinetic energy. A quick analysis suggests that the fluid velocity fluctuations are mainly driven by fluid-particle wake interactions (pseudo-turbulence) whereas the particle velocity fluctuations derive essentially from the large scale flow motion (recirculation). Lagrangian autocorrelation function of particle fluctuating velocity exhibits large-scale oscillations, which are not observed in the corresponding experimental curves, a difference probably due to a statistical averaging effect. Evolution as a function of the bed solid volume fraction and the collision frequency based upon transverse component of particle kinetic energy correctly matches the experimental trend and is well fitted by a theoretical expression derived from Kinetic Theory of Granular Flows.

In particulate flow devices particles acquire electric charge through triboelectric charging, and resulting electrostatic forces can alter hydrodynamics. To capture this effect, the electrostatic force acting on individual particles in the device should be computed accurately. We present a hybrid approach to determine the electrostatic force, which finds the long-range contribution to the electric field by solving the Poisson equation, estimates the short-range contribution through truncated pairwise sum and adds a correction to avoid double counting. Euler-Lagrange simulation of flows incorporating this hybrid approach reveals that bed height oscillations in small fluidized beds of particles with monopolar charge decreases with increasing charge level, which is related to lateral segregation of particles. A ring-like layer of particles, reported in experimental studies, forms at modestly high charge levels. Beds with equal amounts of positively and negatively charged particles are fluidized in a manner similar to uncharged particles.

In Part I, simulations of strongly coupled fluid-particle flow in a vertical channel were performed with the purpose of understanding, in general, the fundamental physics of wall-bounded multiphase turbulence and, in particular, the roles of the spatially correlated and uncorrelated components of the particle velocity. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions were presented, and the unclosed terms that are retained in the context of fully developed channel flow were evaluated in an Eulerian–Lagrangian (EL) framework. Here, data from the EL simulations are used to validate a multiphase Reynolds-stress model (RSM) that predicts the wall-normal distribution of the two-phase, one-point turbulence statistics up to second order. It is shown that the anisotropy of the Reynolds stresses both near the wall and far away is a crucial component for predicting the distribution of the RA particle-phase volume fraction. Moreover, the decomposition of the phase-average (PA) particle-phase fluctuating energy into the spatially correlated and uncorrelated components is necessary to account for the boundary conditions at the wall. When these factors are properly accounted for in the RSM, the agreement with the EL turbulence statistics is satisfactory at first order (e.g., PA velocities) but less so at second order (e.g., PA turbulent kinetic energy). Finally, an algebraic stress model for the PA particle-phase pressure tensor and the Reynolds stresses is derived from the RSM using the weak-equilibrium assumption.

Simulations of strongly coupled (i.e., high-mass-loading) fluid-particle flows in vertical channels are performed with the purpose of understanding the fundamental physics of wall-bounded multiphase turbulence. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions are presented, and the unclosed terms that are retained in the context of fully developed channel flow are evaluated in an Eulerian–Lagrangian (EL) framework for the first time. A key distinction between the RA formulation presented in the current work and previous derivations of multiphase turbulence models is the partitioning of the particle velocityfluctuations into spatially correlated and uncorrelated components, used to define the components of the particle-phase turbulent kinetic energy (TKE) and granular temperature, respectively. The adaptive spatial filtering technique developed in our previous work for homogeneous flows [J. Capecelatro, O. Desjardins, and R. O. Fox, “Numerical study of collisional particle dynamics in cluster-induced turbulence,” J. Fluid Mech. 747, R2 (2014)] is shown to accurately partition the particle velocityfluctuations at all distances from the wall. Strong segregation in the components of granular energy is observed, with the largest values of particle-phase TKE associated with clusters falling near the channel wall, while maximum granular temperature is observed at the center of the channel. The anisotropy of the Reynolds stresses both near the wall and far away is found to be a crucial component for understanding the distribution of the particle-phase volume fraction. In Part II of this paper, results from the EL simulations are used to validate a multiphase Reynolds-stress turbulence model that correctly predicts the wall-normal distribution of the two-phase turbulence statistics.

Euler-Lagrange simulations of fluidized beds of Geldart Group A particles containing different levels of fines are performed in periodic domains with various domain-averaged solid volume fractions. Bubble-like voids readily form when no fines are added. Introducing fines does not reduce bubble sizes if van der Waals force between particles is not accounted for. In contrast, the addition of van der Waals force produces significant changes. With no fines, bubbles are found to be suppressed at sufficiently high solid volume fractions, corresponding to the expanded bed regime for Group A particles. With the addition of fines, bubbles can be suppressed at lower solid volume fractions. With more fines added, bubbles can be suppressed at even lower solid volume fractions. When bubbles are suppressed, the system is found to be in a stable solid-like regime. In this regime, forces on each particle are balanced, and the particle velocity fluctuations are dampened. This article is protected by copyright. All rights reserved.

Simulations of wet fluidized beds of particles in small periodic domains have been carried out using a CFD-DEM approach. A liquid bridge forms upon particle-particle collision, which then ruptures when the particle separation exceeds a critical distance. The simulations take into account only the surface tension force of attraction due to the liquid bridge. Increasing the strength of cohesion leads to larger agglomerates, and correspondingly, higher gas velocities are required to fully support the particles. The slip velocity results from the simulations have been correlated in terms of a Bond number characterizing the strength of cohesion, volume of liquid in the bridge, and particle volume fraction. The CFD-DEM results are systematically coarse-grained to expose the dependence of the filtered drag coefficient on Eulerian filter size, surface tension forces, liquid loading, and solids loading in wet gas-solid fluidized beds.

In a fluidized bed, the drag force acts to oppose the downward force of gravity on a particle, and thus provides the main mechanism for fluidization. Drag models that are employed in large-scale simulations of fluidized beds are typically based on either fixed-particle beds or the sedimentation of particles in liquids. In low-Reynolds-number (
$Re$
) systems, these two types of fluidized beds represent the limits of high Stokes number (
$St$
) and low
$St$
, respectively. In this work, the fluid–particle drag behaviour of these two regimes is bridged by investigating the effect of
$St$
on the drag force in low-
$Re$
systems. This study is conducted using fully resolved lattice Boltzmann simulations of a system composed of fluid and monodisperse spherical particles. In these simulations, the particles are free to translate and rotate based on the effects of the surrounding fluid. Through this work, three distinct regimes in the characteristics of the fluid–particle drag force are observed: low, intermediate and high
$St$
. It is found that, in the low-
$Re$
regime, a decrease in
$St$
results in a reduction in the fluid–particle drag. Based on the simulation results, a new drag relation is proposed, which is, unlike previous models, dependent on
$St$
.

Useful as a reference for engineers in industry and as an advanced level text for graduate engineering students, Multiphase Flow and Fluidization takes the reader beyond the theoretical to demonstrate how multiphase flow equations can be used to provide applied, practical, predictive solutions to industrial fluidization problems. Written to help advance progress in the emerging science of multiphase flow, this book begins with the development of the conservation laws and moves on through kinetic theory, clarifying many physical concepts (such as particulate viscosity and solids pressure) and introducing the new dependent variable-the volume fraction of the dispersed phase. Exercises at the end of each chapterare provided for further study and lead into applications not covered in the text itself.

Granular flow of three experiments are predicted by a computational particle fluid dynamic CPFD numerical scheme in three-dimension using the true particle size distribution. The experiments are simple which show the distinct characteristics of particle flow which differs from fluid flow. The experiments are flow of particles in sedimentation, a U-tube and from a hopper. The CPFD method models the fluid as a fluid and models the particles as discrete particles (material description). The CPFD method is a form of discrete element method, where each particle has three dimensional forces from fluid drag, gravity, static-dynamic friction, particle collision and possibly other forces. However, unlike DEM models which calculate particle-to-particle force by a spring-damper model and direct particle contact, the CPFD method models collision force on each particle as a spatial gradient. The CPFD numerical method predicts all three experiments.

Predictions of simulations based on filtered Two-Fluid Models (TFMs) with constitutive relations for filtered fluid–particle drag coefficient and filtered stresses proposed by Igci and Sundaresan [Ind. Eng. Chem. Res. 50 (2011) 13190–13201] and Milioli et al. [AIChE J. 59 (2013) 3265–3275] were compared against experimental data from a bubbling fluidized bed challenge problem put forward by the National Energy Technology Laboratory and Particulate Solids Research Inc. It is found that the most important correction to filtered models is a modification to the drag, and filtered stresses play a secondary role at best. As expected, coarse grid simulations using the kinetic-theory based TFM over-predicted the gas–particle drag force, yielding unphysical bed expansion. The filtered fluid–particle drag model proposed by Igci and Sundaresan that classifies the inhomogeneity in sub-filter scale flow structures using filter size and filtered particle volume fraction as markers also predicted unphysical bed expansion. Refined filtered drag models proposed by Milioli et al. based on filtered fluid–particle slip velocity as an additional marker led to good agreement with experimental data on bed expansion and the time-averaged gas pressure gradient. It was also observed that inadequate grid resolution in the region between gas distributor and the adjacent cylindrical wall of the test unit could lead to spurious asymmetric gas–particle flow predictions. With the inclusion of adequate inflation layer elements in that region, flow predictions became nearly symmetric with little to no effect on bed expansion predictions. However, it dramatically and qualitatively altered the details of gas–particle structures in the bed.

Significance
The quantitative ability of a kinetic‐theory‐based, two‐fluid model is demonstrated in a clustering (unstable) gas‐solid system via highly resolved simulations. Unlike previous works, this assessment is validated against ideal computational fluid dynamics‐discrete element method data to minimize sources of discrepancy. Overall, good agreement in mean‐slip velocities is observed with relative errors less than 20% over a mean solids concentration range of 0.02–0.25. Local concentration gradient distributions are also studied, showing a distinct shift toward higher gradients at higher mean solids concentrations which is proposed as the bottleneck in obtaining grid‐independence rather than the cluster length scale. © 2015 American Institute of Chemical Engineers AIChE J, 62: 11–17, 2016

In this work, we present the development of an open-source software for modeling granular material by means of the Discrete Element Method. LIGGGHTS (www.liggghts.com) stands for 'LAMMPS Improved for General Granular and Granular Heat Transfer Simulations' and is based on LAMMPS ('Large-Scale Atomic/Molecular Massively Parallel Simulator'), a successful open source Molecular Dynamics code written and distributed by Sandia National Laboratories for massively parallel computing on distributed memory machines. We first give a brief overview of implemented models and features. These comprise CAD geometry import, features for particle insertion and packing, contact models, wallstress analysis and wear prediction, moving mesh capability, a 6 DOF feature and non-spherical particle handling. Finally, we would like to focus on the simulation of coupled granular-fluid systems with the CFD-DEM approach.

A discrete particle model for flows of Group A particles in Geldart's classification is studied. In general, Group A particles are fine and light, so that the adhesion force has a strong effect on their fluidization behavior. Inter-particle adhesion force of Group A particle was measured first. Secondly, the DEM–CFD coupling simulation with the measured adhesion force was performed, and the simulated results were compared with the experimental data about a small-scale fluidized bed for verification of the simulation. It was found from the results that there were considerable differences between their flow patterns. In order to reveal the cause of the differences, the effect of the adhesion force in the contact force model was studied on the motion of a single particle colliding with a wall.

CFD calculations for multiphase gas-particle flows would benefit from a multiphase turbulence theory which would allow the direct calculation of an average solution. A slightly truncated form of the two fluid equations, which are the basis of the MFIX code, have been formally averaged, introducing Favre-like averages for the phasic velocities. This process results in a set of equations which can be solved directly for the average variables describing the flow. This equation set has significantly fewer closure terms than would have occurred using standard Reynolds averaging. The full set of required closure relations is enumerated. Some simple forms for these closures are suggested, although no attempt is made to establish their validity.

In this study a prismatic spouted bed was characterized experimentally and modelled by means of 3D CFD-DEM simulations. The main focus was on the investigation of the influence of the gas flow rate on the bed dynamics and spouting stability. Pressure drop time series obtained at different gas velocities were used for the identification of flow regimes by means of the frequency domain and of chaotic properties such as the correlation dimension and Kolmogorov entropy. The gas and particle dynamics were investigated through simulations of different operational regimes: the spouting onset, as well as stable and instable regimes. A 3-D bed behaviour, typical for slot-rectangular beds, was found. A good agreement between simulations and experiments in the particle flow patterns, bed expansion and dynamics of characteristic gas pressure fluctuations was achieved. The particle dynamics as a function of the gas velocity was investigated for the entire bed. For one of the stable regimes, the bed regions showing different particle dynamics (spout, fountain and annulus) were characterized in detail. A regime map showing the stable operational window in dependence on an inlet-to-bed size ratio and gas velocity is also provided.

Coarse-grid simulations of gas-solids flows are common practice with continuum-based models, which is necessary to obtain numerical results quickly enough to be useful. Such coarse-grid simulations are able to qualitatively resolve large-scale behaviors, such as bubbles and large clusters of solids that have been observed experimentally. It is well known that the continuum approach fails to capture the small-scale heterogeneous flow structures unless very high grid resolutions are employed. Such grid refinement studies have also led to the development of sub-grid models that can be used with coarse-grid continuum simulations and result in faster simulations of gas-solids flows [1, 2].
Discrete particle models that track the trajectory and collisions of every particle are more accurate than continuum models but are not economical for many practical gas-solids flow systems due to the large amount of particles involved. A more affordable discrete technique, called multiphase particle-in-cell (or MP-PIC) is based on lumping many particles together in a parcel in order to track fewer particles and replaces the collisional interactions with a continuum pressure gradient [3]. The MP-PIC technique still requires coarse computational grids so that fewer parcels can be used and the computational cost remains affordable. In this study we examine if the MP-PIC approach, when applied over coarse grids, requires similar sub-grid corrections as continuum models.
To address this issue, we have conducted continuum and MP-PIC simulations of gas-particle flows in a 2D periodic domain at several grid resolutions. The simulations assumed that the particles were all of the same size. The constitutive models for the continuum approach was chosen to match those employed in the MP-PIC approach; specifically, both of these modeling approaches used the same solids pressure model and the Wen & Yu [4] drag law. Both continuum and MP-PIC simulations using coarse grids manifested nearly homogeneous flows where the domain-average slip velocity was essentially the same as that for homogeneous flow. When the grid was refined, the numerical results for both approaches manifested heterogeneous flow structures that increased the domain-average gas-particles slip velocity to 2.5-3 times that for homogeneous flow; importantly, both approaches manifested very similar flow structures and yielded essentially the same domain-average slip velocity. These results confirm the inherent equivalence between the two approaches. From a practical point of view, our study indicates that the sub-grid models that are being developed for the continuum approach can (and should) be imported to the MP-PIC approach.
References: [1] Andrews, A. T.; Loezos, P. N.; Sundaresan, S. Coarse-grid simulation of gas-particle flows in vertical risers. Ind. Eng. Chem. Res. 2005, 44, 6022. [2] Igci, Y.; Andrews, A. T.; Sundaresan, S.; Pannala, S.; O'Brien, T. Filtered two-fluid models for fluidized gas-particle suspensions. AIChE J. 2008, 54, 1431. [3] Snider, D.M. An incompressible three-dimensional multiphase particle-in-cell model for dense particle flows. J. Comput. Phys. 2001, 170, 523549. [4] Wen, C. Y.; Yu, Y. H. Mechanics of Fluidization. Chem. Eng. Prog. Symp. Ser. 1966, 62, 100-111.

The thirteen chapters of this book are introduced by a preface and followed by five appendices. The main chapter headings are: motion and forces at a point of contact; line loading of an elastic half-space; point loading of an elastic half-space; normal contact of elastic solids - Hertz theory; non-Hertzian normal contact of elastic bodies; normal contact of inelastic solids; tangential loading and sliding contact; rolling contact of elastic bodies; rolling contact of inelastic bodies; calendering and lubrication; dynamic effects and impact; thermoelastic contact; and rough surfaces. (C.J.A.)

We present an Eulerian-Lagrangian numerical simulation (LNS) scheme for particulate flows. The overall algorithm in the present approach is a variation of the scheme presented earlier. In this numerical scheme we solve the fluid phase continuity and momentum equations on an Eulerian grid. The particle motion is governed by Newton’s law thus following the Lagrangian approach. Momentum exchange from the particle to fluid is modeled in the fluid phase momentum equation. Forces acting on the particles include drag from the fluid, body force and the interparticle force that prevents the particle volume fraction from exceeding the close-packing limit. There is freedom to use different models for these forces and to introduce other forces. In this paper we have used two types of interparticle forces. The effect of viscous stresses are included in the fluid phase equations. The volume fraction of the particles appear in the fluid phase continuity and momentum equations. The fluid and particle momentum equations are coupled in the solution procedure unlike an earlier approach. A finite volume method is used to solve these equations on an Eulerian grid. Particle positions are updated explicitly. This numerical scheme can handle a range of particle loadings and particle types. We solve the fluid phase continuity and momentum equations using a Chorin-type fractional-step method. The numerical scheme is verified by comparing results with test cases and experiments.

Starting from a kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-averaged (RA) equations are derived for the particle phase in a collisional fluid particle flow. The corresponding equations for a constant-density fluid phase are derived from a model that includes drag and buoyancy coupling with the particle phase. The fully coupled macroscale/hydrodynamic model, rigorously derived from a kinetic equation for the particles, is written in terms of the particle-phase volume fraction, the particle-phase velocity and the granular temperature (or total granular energy). As derived from the hydrodynamic model, the RA turbulence model solves for the RA particle-phase volume fraction, the phase-averaged (PA) particle-phase velocity, the PA granular temperature and the PA turbulent kinetic energy of the particle phase. Thus, unlike in most previous derivations of macroscale turbulence models for moderately dense granular flows, a clear distinction is made between the PA granular temperature Theta(p), which appears in the KT constitutive relations, and the particle-phase turbulent kinetic energy k(p), which appears in the turbulent transport coefficients. The exact RA equations contain unclosed terms due to nonlinearities in the hydrodynamic model and we briefly discuss the available closures for these terms. Finally, we demonstrate by comparing model predictions with direct numerical simulation results that even for non-collisional fluid particle flows it is necessary to provide separate models for Theta(p) and k(p) in order to correctly account for the effect of the particle Stokes number and mass loading

We present a computational study of cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. A separation of length scales must be established when evaluating the particle dynamics in order to distinguish between the continuous mesoscopic velocity field and the uncorrelated particle motion. To accomplish this, an adaptive spatial filter is employed on the Lagrangian data with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The method is used to investigate, for the first time, the properties of a statistically stationary gravity-driven particle-laden flow, where particle–particle and fluid–particle interactions control the multiphase dynamics. Results from fully developed CIT show a strong correlation between the local volume fraction and the granular temperature, with maximum values located at the upstream boundary of clusters (i.e. where maximum compressibility of the particle velocity field exists), while negligible particle agitation is observed within clusters.

New constitutive relations for filtered two‐fluid models (TFM) of gas‐particle flows are obtained by systematically filtering results generated through highly resolved simulations of a kinetic theory‐based TFM. It was found in our earlier studies that the residual correlations appearing in the filtered TFM equations depended principally on the filter size and filtered particle volume fraction. Closer inspection of a large amount of computational data gathered in this study reveals an additional, systematic dependence of the correction to the drag coefficient on the filtered slip velocity, which serves as a marker for the extent of subfilter‐scale inhomogeneity. Furthermore, the residual correlations for the momentum fluxes in the gas and particle phases arising from the subfilter‐scale fluctuations are found to be modeled nicely using constitutive relations of the form used in large‐eddy simulations of single‐phase turbulent flows. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3265–3275, 2013

This paper aims at investigating the capability of numerical models to ac- curately capture the physical characteristics of particle clustering in vertical risers. Within the energy sector, particle clustering in vertical risers of circu- lating fluidized bed reactors are known to play a key role in the multiphase dynamics as well as secondary processes such as catalytic conversion and heat transfer. Recent experiments suggest that particle clustering is most significant in the fully developed flow region of the riser, hence this study focuses on this region. To explore such flows, a high-fidelity large-eddy sim- ulation framework is combined with a Lagrangian particle tracking solver to simulate statistically stationary gravity-driven risers in vertical pipes for a large range of Archimedes numbers. The walls of the reactor are modeled using a conservative immersed boundary scheme integrated with the La- grangian particle tracking framework. A structure tracking algorithm akin to particle image velocimetry is used to accumulate statistics on individual clusters. Cluster descent velocities display excellent agreement with experi- mental measurements for the range of flow conditions considered. Predicted volume fraction fluctuations and mean solid concentration within the clusters also match experimental correlations. The probability distribution function of solid concentration and radial distribution function provide insight on the degree of clustering and the characteristic cluster length scale. The degree of particle clustering is found to be independent of the Archimedes number, and models for the volume fraction distribution are discussed. Statistics on the solid concentration and phase velocities for two- and three-dimensional configurations are compared, and the ramifications of simulating risers in two dimensions are discussed.

Two different approaches to constitutive relations for filtered two-fluid models (TFM) of gas- solid flows are deduced. The first model (Model A) is derived using systematically filtered results obtained from a highly resolved simulation of a bubbling fluidized bed. The second model (Model B) stems from the assumption of the formation of sub-grid heterogeneities inside the suspension phase of fluidized beds. These approaches for the unresolved terms appearing in the filtered TFM are, then, substantiated by the corresponding filtered data. Furthermore, the presented models are verified in the case of the bubbling fluidized bed used to generate the fine grid data. The numerical results obtained on coarse grids demonstrate that the computed bed hydrodynamics is in fairly good agreement with the highly resolved simulation. The results further show that the contribution from the unresolved frictional stresses is required to correctly predict the bubble rise velocity using coarse grids.