Aqueous solutions of very fine particles behave as non-Newtonian fluids and are used to fluidize heavy spherical particles creating large bed expansions and inhomogeneities similar to those observed in traditional fluidization of particles with Newtonian fluids. This study attempts to extend the validity of traditional computational fluid dynamics (CFD) models that are routinely used for gas-solids fluidization to non-Newtonian fluids. The modified model incorporates a shear-thinning power law viscosity for the non-Newtonian fluid and a recently published drag correlation derived from direct numerical simulation data of flow around randomly positioned spheres. This validation study compares numerical results obtained in 3D fluidized beds with two independent experimental bed porosity data sets for heavy steel and glass spherical particles. The current CFD results show a better agreement with experimental data obtained over a wide range of porosity and Reynolds number than a previously published semi-empirical correlation.

Numerical modelling offers the opportunity to better understand, predict, and optimise the behaviours of industrial systems, and thus provides a powerful means of improving efficiency, productivity and sustainability. However, the accurate modelling of industrial-scale particulate and particle-fluid systems is, due to the complex nature of such systems, highly challenging. This challenge arises primarily from three factors: the lack of a universally accepted continuum model for particulate media; the computational expense of discrete particle simulations; and the difficulty of imaging industrial-scale systems to obtain validation data. In recent years, however, advances in software, hardware, theoretical understanding, and imaging technology have all combined to the point where, in many cases, these challenges are now surmountable-though some distance remains to be travelled. In this review paper, we provide an overview of the most promising solutions to the issues highlighted above, discussing also the major strengths and limitations of each.

This study investigates, through numerical multiphase flow simulations, the deaeration (or defluidization) of aeratable glass particles of about 80 mu m diameter near minimum fluidization and bubbling conditions. First, the effects of plenum (also called windbox) are studied by using an idealized gas inlet condition with no windbox, then an empty and filled windbox are compared with experimental results at minimum fluidization velocity (Umf). Simulation results obtained using the discrete particle method (DEM) and the continuum two-fluid method (TFM) are compared with available experimental data for gas pore pressure decay during defluidization from minimum fluidization conditions. Second, the quantitative effects of cohesion and the presence of small clusters are included in the physical model to better understand the experimental results for deaeration from near minimum bubbling velocity (Umb).

This study compares the results of two commonly used computational fluid dynamics methods for fluidized bed simulation of smooth type-A monodisperse particles. One approach is based on the continuum assumption called the two-fluid-method (TFM), and one discrete particle method (DEM) based on a soft-sphere collision algorithm. Both DEM and TFM are coarsened by either lumping several particles in a parcel (CDEM) and/or by increasing the computational mesh size to achieve faster simulation speed. Simulations using both methods were conducted in a 3D periodic cylindrical riser domain in the core-annulus flow regime. Four different levels of coarseness were applied for each method with the finest simulations utilizing more than 200 M particles and 2.9 M computational cells. The finest DEM simulation is assumed to yield the most accurate results as attested in the literature. An error analysis shows that it is possible for CDEM to yield faster and more accurate results than TFM, although TFM is generally faster at the same coarseness level. For more complex cases involving particles with statical properties, such as size and density distributions, CDEM is anticipated to be a better choice for fluidized bed simulations.

This study focuses on simulating the formation and growth of granular jets under the impact of a heavy intruder on a bed of small particles. A discrete particle method to track the motion of 150 million individual particles in the bed, coupled with computational fluid dynamics to model the motion of the surrounding air, is used to obtain these predictions. The main idea of this research was to model the large impacting intruder by gluing together particles of the same size as those in the bed to approximate the form of a large sphere, which resulted in an efficient neighbor search and collision calculations. It also allowed a fine resolution of air flow. Our numerical results agreed with the experimental observation that the height of the jet diminishes from atmospheric to vacuum conditions. The effect of other parameters, such as initial intruder size and velocity, shows the same trends as those observed experimentally.

Coarse grained particle methods significantly reduce the computation cost of large‐scale fluidized bed simulation by lumping many real particles into a computation parcel. This research provides a method to estimate the errors associated with parcel size in large‐scale fluidized bed simulations. This uncertainty is first quantified in small scale domains by comparing results of discrete particle method with that employing coarse parcels of different sizes. Then, this uncertainty is correlated with parcel size and simulation domains consisting of a simple homogeneous cooling system and more complex bubbling and circulating fluidized beds. These correlations allow us to accurately estimate the uncertainty in large‐scale fluidized beds based solely on data obtained in smaller systems. The ability to estimate model‐related uncertainty in larger systems makes this method relevant for industrial applications. © 2018 American Institute of Chemical Engineers AIChE J , 64: 2340–2350, 2018

This chapter provides the full description of a coarse-grained discrete particle method based on a novel hard-sphere contact model for the simulation of industrial-scale fluidized bed reactors. This method is based on simple models that are easy to understand and implement in numerical codes. This technique is verified and validated for several small-scale fluidized systems where numerical data based on finer methods as well as experimental data are available. The speed of execution of this method is increased several orders of magnitudes compared to particle-based discrete methods, which allows for thousands of seconds of flow, heat, and mass transfer simulations of industrial reactors such as fluidized catalytic cracking regenerator, Methanol to Olefins reactor, and Rare Earth Elements leaching reactor, achieved in just few days using commonly available computer resources. It is now possible for the common engineer to conduct simulations of large-scale fluid-particle reactors to understand, design, and troubleshoot, as well as optimize the performance of these complex multiphase flow systems.

Continuum methods require the additional development of solids stress closures for polydisperse powders based on complex kinetic theories that are non-trivial to develop, code, and numerically converge for the wide range of fluidization regimes from very dilute to dense/frictional flow limit. On the other hand, it is straightforward to model the flow of polydisperse granular materials by treating particles as discrete rigid bodies that are tracked following simple physical laws of motion. The coarsening of these discrete methods by lumping several particles in a parcel alleviates the significant computational cost associated with these discrete methods while introducing some inaccuracies in the numerical results. In this research, we explore two different coarse graining methods that can be applied to polydisperse powders, namely the same statistic weight method (SSW) and the same size parcel method (SSP), and assess their accuracy by comparison with the finest simulation results obtained with a discrete element method (DEM). For Geldart group B powders fluidized at a relative low superficial velocity, the numerical results indicate that the SSW is more accurate than the SSP method. For type A powders fluidized at relatively high velocity, these two methods predict similar results. Interestingly, up to four times increase in the speed of simulation of the SSP method was obtained because the original polydisperse powder is scaled to a mono-disperse system in terms of particle-particle collision. These results suggest that the SSP method is more favorable for the simulation of fluidized beds due to its accuracy and efficiency while the SSW method may be used for granular flow and dense fluidized bed systems where capturing the size segregation of particles due to collision is important.

In past decades, the continuum approach was the only practical technique to simulate large‐scale fluidized bed reactors because discrete approaches suffer from the cost of tracking huge numbers of particles and their collisions. This study significantly improved the computation speed of discrete particle methods in two steps: First, the time‐driven hard‐sphere (TDHS) algorithm with a larger time‐step is proposed allowing a speedup of 20–60 times; second, the number of tracked particles is reduced by adopting the coarse‐graining technique gaining an additional 2–3 orders of magnitude speedup of the simulations. A new velocity correction term was introduced and validated in TDHS to solve the over‐packing issue in dense granular flow. The TDHS was then coupled with the coarse‐graining technique to simulate a pilot‐scale riser. The simulation results compared well with experiment data and proved that this new approach can be used for efficient and reliable simulations of large‐scale fluidized bed systems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5320–5334, 2017

In this paper, a bubbling fluidized bed is simulated with different numerical parameters, such as grid resolution and parcel size. We examined also the effect of using two homogeneous drag correlations and a heterogeneous drag based on the energy minimization method. A fast and reliable bubble detection algorithm was developed based on the connected component labeling. The radial and axial solids volume fraction profiles are compared with experiment data and previous simulation results. These results show a significant influence of drag models on bubble size and voidage distributions and a much less dependence on numerical parameters. With a heterogeneous drag model that accounts for sub-scale structures, the void fraction in the bubbling fluidized bed can be well captured with coarse grid and large computation parcels. Refining the CFD grid and reducing the parcel size can improve the simulation results but with a large increase in computation cost.

For a long time, salt tracers have been used to measure the residence time distribution (RTD) of fluidized catalytic cracking (FCC) particles. However, due to limitations in experimental measurements and simulation methods, the ability of salt tracers to faithfully represent RTDs has never been directly investigated. Our current simulation results using coarse-grained computational fluid dynamic coupled with discrete element method (CFD-DEM) with filtered drag models show that the residence time of salt tracers with the same terminal velocity as FCC particles is slightly larger than that of FCC particles. This research also demonstrates the ability of filtered drag models to predict the correct RTD curve for FCC particles while the homogeneous drag model may only be used in the dilute riser flow of Geldart type B particles. Thus, the RTD of large-scale reactors can be efficiently investigated with our proposed numerical method as well as by using the old-fashioned salt tracer technology.

Several discrete particle methods exist in the open literature to simulate fluidized bed systems, such as discrete element method (DEM), time-driven hard sphere (TDHS), coarse-grained particle method (CGPM), coarse grained hard sphere (CGHS), and multiphase particle-in-cell (MP-PIC). The main difference between these methods is in the treatment of particleparticle interactions: by calculating collision forces (DEM and CGPM), using momentum conservation laws (TDHS and CGHS), or based on the particle stress model (MP-PIC). Here, these methods are compared by simulating the same small-scale fluidized bed with the same open-source code MFIX. The results indicate that both modeling the particleparticle collision by TDHS and lumping a few particles in a parcel increase the computation speed with little loss in accuracy. However, the MP-PIC method predicts an unphysical particleparticle overlap, which results in incorrect overall bed hydrodynamics. These results suggest using the CGHS method for fluidized bed simulations owing to its accuracy and efficiency.

The two-fluid model (TFM) has become a tool for the design and troubleshooting of industrial fluidized bed reactors. To use TFM for scale up with confidence, the uncertainty in its predictions must be quantified. Here, we study two sources of uncertainty: discretization and time-averaging. First, we show that successive grid refinement may not yield grid-independent transient quantities, including cross-section–averaged quantities. Successive grid refinement would yield grid-independent time-averaged quantities on sufficiently fine grids. Then a Richardson extrapolation can be used to estimate the discretization error, and the grid convergence index gives an estimate of the uncertainty. Richardson extrapolation may not work for industrial-scale simulations that use coarse grids. We present an alternative method for coarse grids and assess its ability to estimate the discretization error. Second, we assess two methods (autocorrelation and binning) and find that the autocorrelation method is more reliable for estimating the uncertainty introduced by time-averaging TFM data. © 2017 American Institute of Chemical Engineers AIChE J , 63: 5343–5360, 2017

Gas–solids flow in a three-dimension periodic domain was numerically investigated by direct numerical simulation (DNS), computational fluid dynamic-discrete element method (CFD-DEM) and two-fluid model (TFM). DNS data obtained by finely resolving the flow around every particle are used as a benchmark to assess the validity of coarser DEM and TFM approaches. The CFD-DEM predicts the correct cluster size distribution and under-predicts the macro-scale slip velocity even with a grid size as small as twice the particle diameter. The TFM approach predicts larger cluster size and lower slip velocity with a homogeneous drag correlation. Although the slip velocity can be matched by a simple modification to the drag model, the predicted voidage distribution is still different from DNS: Both CFD-DEM and TFM over-predict the fraction of particles in dense regions and under-predict the fraction of particles in regions of intermediate void fractions. Also, the cluster aspect ratio of DNS is smaller than CFD-DEM and TFM. Since a simple correction to the drag model can predict a correct slip velocity, it is hopeful that drag corrections based on more elaborate theories that consider voidage gradient and particle fluctuations may be able to improve the current predictions of cluster distribution.

The heat transfer in a gas-solids fluidized bed is simulated with computational fluid dynamic-discrete element method (CFD-DEM) and coarse grained particle method (CGPM). In CGPM fewer numerical particles and their collisions are tracked by lumping several real particles into a computational parcel. The assumption is that the real particles inside a coarse grained particle (CGP) are made from same species and share identical physical properties including density, diameter and temperature. The parcel-fluid convection term in CGPM is calculated using the same method as in DEM. For all other heat transfer mechanisms, we derive in this study mathematical expressions that relate the new heat transfer terms for CGPM to those traditionally derived in DEM. This newly derived CGPM model is verified and validated by comparing the results with CFD-DEM simulation results and experiment data. The numerical results compare well with experimental data for both hydrodynamics and temperature profiles. The proposed CGPM model can be used for fast and accurate simulations of heat transfer in large scale gas-solids fluidized beds. (C) 2017 Published by Elsevier Ltd.

Coupled discrete particle method - computational fluid dynamics simulations are carried out to demonstrate the potential of combined high-G-intensified gas-solids contact, gas-solids separation and segregation in a rotating fluidized bed in a static vortex chamber. A case study with two distinct types of particles is focused on. When feeding solids using a standard solids inlet design, a dense and uniform rotating fluidized bed is formed, guaranteeing intense gas-solids contact. The presence of both types of particles near the chimney region reduces, however, the strength of the central vortex and is detrimental for separation and segregation. Optimization of the solids inlet design is required, as illustrated by stopping the solids feeding. High-G separation and segregation of the batch of particles is demonstrated, as the strength of the central vortex is restored. The flexibility with respect to the gas flow rate of the bed density and uniformity and of the gas-solids separation and segregation is demonstrated, a unique feature of vortex chamber generated rotating fluidized beds. With the particles considered in this case study, turbulent dispersion by large eddies in the gas phase is shown to have only a minor impact on the height of the inner bed of small/light particles. (C) 2016 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

Most methods presented in the literature for estimation of discretization errors focus primarily on steady flows. The transport of error in strongly transient flow has not been adequately addressed. Issues related to transient error calculations are discussed and some methods that are viable for such applications are proposed. Examples are presented on simple flows such as transient Burgers equation followed by applications to more complex flows, e.g. two-phase gas-solid flow relevant fluidized beds. It is demonstrated that error estimation can be made with reasonable accuracy using a combination of various methods.

A coarse-grained-particle method (CGPM) that tracks fewer particles and their collisions by lumping several real particles into computational parcels is developed. We demonstrate that the accuracy of CGPM can be improved by properly selecting interpolation schemes used to compute flow variables at particle and computational grid locations. The computational speed of CGPM was shown to be similar to that of a widely used and less accurate particle in cell method (PIC). Finally, a chemical reaction mechanism based on rare earth elements (REE) leaching from coal byproducts was implemented with CGPM to study the effects of several flow and design parameters on the leaching process. A countercurrent reactor was studied and optimized to maximize the mass fraction of REE in the liquid solution. The CGPM can now be employed to cheaply and accurately solve industrial-scale problems containing millions of computational parcels.