Meso‐scale statistical properties of gas–solid flow—a direct numerical simulation (DNS) study

Statistical properties of particles in heterogeneous gas–solid flow were numerically investigated based on the results of a three‐dimensional large‐scale direct numerical simulation (DNS). Strong scale‐dependence and local non‐equilibrium of these properties, especially the particle fluctuating velocity (PFV) or granular temperature, were observed to be related to the effect of meso‐scale structures formed by the compromise in competition between fluid and particle dominated mechanisms. To quantify such effects, the heterogeneous structures were partitioned into a gas‐rich dilute phase and a solid‐rich dense phase according to the particle‐scale voidage defined through the Voronoi tessellation. Non‐equilibrium features, such as the deviation of PFV from Gaussian distribution and anisotropy, were found even in phase‐specific properties. A new distribution function for the PFV well characterizing these features was obtained by fitting the DNS results, which takes a typical bi‐disperse mode, with phase‐specific granular temperatures. The implications of these findings to the kinetic theory of granular flow and traditional continuum models of gas–solid flow were also discussed. © 2016 American Institute of Chemical Engineers AIChE J, 63: 3–14, 2017     

Bed Expansion – Extending Correlations for Fluidized Beds with Inserts to Open Fluidized Beds

Bed expansion occurs during the operation of gas‐fluidized beds and is influenced by particle properties, gas properties and distributor characteristics. It has a significant bearing on heat and mass transfer phenomena within the bed. A method of predicting bed expansion behavior from other fluidizing parameters would be a useful tool in the design process, dispensing with the need for small‐scale trials. This study builds on previous work on fluidized beds with vertical inserts to produce a correlation that links a modified particle terminal velocity, minimum fluidizing velocity and distributor characteristics with bed voidage in the relationship with P as the pitch between holes in the perforated distributor plate.     

A system‐size independent validation of CFD‐DEM for noncohesive particles

For the first time, CFD‐DEM simulations of small‐scale fluidized beds are quantitatively validated against large‐scale experiments. Such validation is possible via the identification of a measurement independent of system size, namely defluidization. CFD‐DEM inputs (particle properties and operating conditions) are measured directly. Sphericity is found to be critical, even for highly spherical particles. This size‐independent method of validation is valuable since it allows for validation of CFD‐DEM models without restrictions on system sizes or particle sizes. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4051–4058, 2015     

Method to estimate uncertainty associated with parcel size in coarse discrete particle simulation

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     

An efficient and reliable predictive method for fluidized bed simulation

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     

Particle scale study of heat transfer in packed and bubbling fluidized beds

The approach of combined discrete particle simulation (DPS) and computational fluid dynamics (CFD), which has been increasingly applied to the modeling of particle‐fluid flow, is extended to study particle‐particle and particle‐fluid heat transfer in packed and bubbling fluidized beds at an individual particle scale. The development of this model is described first, involving three heat transfer mechanisms: fluid‐particle convection, particle‐particle conduction and particle radiation. The model is then validated by comparing the predicted results with those measured in the literature in terms of bed effective thermal conductivity and individual particle heat transfer characteristics. The contribution of each of the three heat transfer mechanisms is quantified and analyzed. The results confirm that under certain conditions, individual particle heat transfer coefficient (HTC) can be constant in a fluidized bed, independent of gas superficial velocities. However, the relationship between HTC and gas superficial velocity varies with flow conditions and material properties such as thermal conductivities. The effectiveness and possible limitation of the hot sphere approach recently used in the experimental studies of heat transfer in fluidized beds are discussed. The results show that the proposed model offers an effective method to elucidate the mechanisms governing the heat transfer in packed and bubbling fluidized beds at a particle scale. The need for further development in this area is also discussed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Numerical study of particle mixing in bubbling fluidized beds based on fractal and entropy analysis

The DEM–LES coupling method is used to study the mixing of mono-dispersed identical density particles in bubbling fluidized beds based on the fractal and entropy analysis. A dimensionless function is used to study the microscopic characteristics of mixing interface. A criterion for identification of the boundary of bubbles is proposed and used to investigate the effect of bubble on particle mixing characteristics. Moreover, the Shannon information entropy is used to evaluate the macroscopic level of mixing. It is found that both the mixing interface of particles and the boundary of bubbles in fluidized beds are fractal. The bubble boundary dimension decreases as the fluidization velocity increases. The fractal bubble boundary induces the inhomogeneous characteristics of mixing interfaces of particles. On the other hand, the radial distribution function indicates the universal and intrinsic characteristics of particle mixing, independent of the initial effects after a short segment of evolution. Moreover, the information entropy, which is defined based on the radial distribution function, increases as the fluidization velocity increases. The mean information entropy is a good indication and a credible evaluation on the macroscopic mixing levels under various operating conditions of the beds.     

Investigation of nonuniformity in a liquid–solid fluidized bed with identical parallel channels

Previous work has demonstrated that multiphase flow through identical parallel channels and multiple cyclones can give rise to significant nonuniformity among the flow paths. This article presents results from a study where the distribution of voidage and flux through parallel channels in liquid–solid fluidized beds is investigated. Experiments and computational fluid dynamics simulations were performed with 1.2 mm glass beads fluidized by water where a cross baffle divided a 191 mm diameter column into four identical parallel channels. Voidages were measured by optical fiber probes. Simulations from a three‐dimensional unsteady‐state Eulerian–Eulerian model based on FLUENT software showed good agreement with the experimental results. Despite the symmetrical geometry of the system, the average voidage and particle velocities in one channel differed somewhat from those in the others. Increasing the superficial liquid velocity could increase voidage greatly and affect the degree of nonuniformity in the four channels. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Fluidization Characteristics in Micro‐Fluidized Beds of Various Inner Diameters

The fluidization characteristics of quartz sand and fluid catalytic crack (FCC) catalyst particles in six micro‐fluidized beds with inner diameters of 4.3, 5.5, 10.5, 15.5, 20.5, and 25.5 mm were investigated. The effects of bed diameter (D_t), static bed height (H_s), particles and gas properties on the pressure drop and minimum fluidization velocity (u_mf) were examined. The results show that the theoretical pressure drops of micro‐fluidized beds deviated from the experimental values under different particles and gas properties. The possible reason is due to an increase in bed voidage under smaller bed diameters. The equations for conventional fluidized beds did not fit for micro‐fluidized beds. u_mf increased with decreasing D_t. When the ratio of H_s to D_t ranged from 1:1 to 3:1, u_mf was characterized by a linear equation with H_s, while the slope of the equation u_mf versus H_s decreased with increasing D_t. In this paper, D_t/d_p and H_s/d_p were defined as dimensionless variables and a new equation was developed to predict u_mf in micro‐fluidized beds under the present experimental conditions.     

Analysis and Interpretation of Multiple Radioactive Particle Tracking Data on Laboratory Scale Air/Polyethylene Fluidized Beds

Multiple radioactive particle tracking is a noninvasive technique used to study flow phenomena within gas‐solid fluidized beds. Five tagged polyethylene particles were added to a fluidized bed and tracked using two gamma cameras set perpendicular to one another. One camera collected x‐z particle locations and the other collected y‐z particle locations, while both cameras collected particle count rate values. The x‐z and y‐z particle movement information was combined to form three‐dimensional particle trajectories, and in turn used to calculate instantaneous flow information. The information from the five particles was then averaged and used to calculate three‐dimensional information regarding solid circulation parameters.     

Heat transfer within dynamically structured bubbling fluidized beds subject to vibration: A two-fluid modeling study

Bubbling fluidized beds are often used to achieve a uniform particle temperature distribution in industrial processes involving gas and particles. However, the chaotic bubble dynamics pose significant challenges in scale-up. Recent work (Guo et al., 2021, PNAS 118, e2108647118) has shown that using vibration can structure the bubbling pattern to a highly predictable manner with the characteristic bubble properties independent of system width, opening opportunities to address key issues associated with conventional bubbling fluidized beds. Herein, using two-fluid modeling simulations, we studied heat transfer characteristics within the dynamically structured bubbling fluidized bed and compared to unstructured bubbling fluidized beds and packed beds. Simulations show that the structured bubbling fluidized bed can achieve the most uniform particle temperature distribution because it can achieve the best particle mixing while maintaining a global heat transfer coefficient similar to that of a freely bubbling fluidized bed.     

循环流化床中宏观非均匀结构的计算机模拟

运用颗粒运动分解轨道模型模拟了循环流化床中的宏观非均匀结构,模拟结果给出了与实验结果相吻合的空隙率分布、颗粒速度分布及气体速度分布．因此,颗粒运动分解轨道模型能够用于循环流化床中的宏观非均匀结构的模拟。     

循环流化床中颗粒团聚物性质的PDPA测量

提出了一种利用相位多普勒粒子分析仪（PDPA）来测量气固循环流化床中颗粒团聚物性质的方法,并运用此方法初步考察了操作条件对循环流化床稀相区中颗粒团聚物性质的影响.在本实验操作条件下,颗粒团聚物的时间分率、频率、内部空隙率以及轴向速度等性质都存在轴径向的不均匀分布,具有较明显的环核特征;固体循环速率对颗粒团聚物性质径向分布影响不大,表观气速的变化可引起其轴向分布规律发生显著改变,但其径向的环核特性仍然存在.     

Influence of void fraction calculation on fidelity of CFD‐DEM simulation of gas‐solid bubbling fluidized beds

The correct calculation of cell void fraction is pivotal in accurate simulation of two‐phase flows using a computational fluid dynamics‐discrete element method (CFD‐DEM) approach. Two classical approaches for void fraction calculations (i.e., particle centroid method or PCM and analytical approach) were examined, and the accuracy of these methodologies in predicting the particle‐fluid flow characteristics of bubbling fluidized beds was investigated. It was found that there is a critical cell size (3.82 particle diameters) beyond which the PCM can achieve the same numerical stability and prediction accuracy as those of the analytical approach. There is also a critical cell size (1/19.3 domain size) below which meso‐scale flow structures are resolved. Moreover, a lower limit of cell size (1.63 particle diameters) was identified to satisfy the assumptions of CFD‐DEM governing equations. A reference map for selecting the ideal computational cell size and the suitable approach for void fraction calculation was subsequently developed. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2000–2018, 2014     

Monte Carlo modeling of fluidized bed coating and layering processes

A stochastic modeling approach based on a Monte Carlo method for fluidized bed layering and coating is presented. In this method, the process is described by droplet deposition on the particle surface, droplet drying and the formation of a solid layer due to drying. The model is able to provide information about the coating coverage (fraction of the particle surface covered with coating), the particle‐size distribution, and the layer thickness distribution of single particles. Analytical solutions for simplified test cases are used to validate the model theoretically. The simulation results are compared with experimental data on particle‐size distributions and layer thickness distributions of single particles coated in a lab‐scale fluidized bed. Good agreement between the simulation results and the measured data is observed. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2670–2680, 2016     

Fluidization of mixtures of two solids differing in density or size

The complex mechanism by which homogeneous mixtures of two solids achieve fluidization is subjected to theoretical analysis, to elaborate relationships capable to provide their “initial” and “final fluidization velocity” u_if and u_ff, i.e., the limits that encompass the suspension process. The article shows how the equation that describes the force equilibrium of fluidization can be rewritten in forms that account for the distribution of the components of density‐ or size segregating mixtures during the transition to the fluidized state. This approach leads to the theoretical expression of u_if and u_ff of either type of system, whose differences of behavior are correctly reproduced by accounting for the voidage reduction typical of beds of particles of different size. The comparison with experimental results at varying mixture composition demonstrates that the equations give a coherent interpretation of the dependence of the fluidization velocity interval of two‐solid mixtures on the principal variables of interest. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Particle attrition mechanism with a sonic gas jet injected into a fluidized bed

High velocity gas jets in fluidized beds provide substantial particle attrition: they are used industrially to control the particle size in fluid bed cokers and to grind products such as toner, pharmaceutical or pigment powders. One method to control the size of the particles in the bed is to use an attrition nozzle, which injects high velocity gas and grinds the particles together. An important aspect of particle attrition is the understanding and modeling of the particle breakage mechanisms. The objective of this study is to develop a model to describe particle attrition when a sonic velocity gas jet is injected into a fluidized bed, and to verify the results using experimental data. The model predicts the particle size distribution of ground particles, the particle breakage frequency, and the proportion of original particles in the bed which were not ground. It was found that the particle breakage frequency can be used to predict the attrition results in different bed sizes. A correlation was also developed, which uses the attrition nozzle operating conditions such as gas density and equivalent speed of sound to predict the mass of particles broken per unit time.     

Magnetic Resonance Imaging of fluidized beds

This paper reviews recent developments in Magnetic Resonance Imaging (MRI) which enable it to follow particle motion in fluidized beds. Imaging with a spatial resolution of 400 μm and a temporal resolution of 1 ms is now feasible; particle velocities of order 1 m/s can be measured with good accuracy. The technique provides voidage fractions on a motion-picture basis and particle velocity fields. Limitations are: (i) the particles must contain appropriate atoms e.g. C or H; and (ii) currently the fluidized bed diameter cannot exceed 50 mm, though measurements from larger units will doubtless become available. MR studies on fluidized beds are described: results are reported for (i) air jets entering the bed (ii) bubbling and slugging beds and (iii) dispersion in a bubbling bed. The data are consistent with published measurements. Study (i) helps to resolve the longstanding puzzle about the behaviour of an air jet entering a fluidized or partly-fluidized bed, answering the question: does the entering air form bubbles or a continuous jet?     

Effective particle diameters for simulating fluidization of non‐spherical particles: CFD‐DEM models vs. MRI measurements

Computational fluid dynamics—discrete element method (CFD‐DEM) simulations were conducted and compared with magnetic resonance imaging (MRI) measurements (Boyce, Rice, and Ozel et al., Phys Rev Fluids. 2016;1(7):074201) of gas and particle motion in a three‐dimensional cylindrical bubbling fluidized bed. Experimental particles had a kidney‐bean‐like shape, while particles were simulated as being spherical; to account for non‐sphericity, “effective” diameters were introduced to calculate drag and void fraction, such that the void fraction at minimum fluidization (ε_mf) and the minimum fluidization velocity (U_mf) in the simulations matched experimental values. With the use of effective diameters, similar bubbling patterns were seen in experiments and simulations, and the simulation predictions matched measurements of average gas and particle velocity in bubbling and emulsion regions low in the bed. Simulations which did not employ effective diameters were found to produce vastly different bubbling patterns when different drag laws were used. Both MRI results and CFD‐DEM simulations agreed with classic analytical theory for gas flow and bubble motion in bubbling fluidized beds. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2555–2568, 2017     

鼓泡流化床离散模拟中的一个局部空隙率模型

气固流化床离散颗粒模拟中通常采用面积加权平均法计算局部空隙率,不能较好地反映流化床中显著的非均匀结构特性.为了考虑非均匀结构对局部空隙率的影响,文中提出一个适用鼓泡流化床的局部空隙率模型.将流场划分为稀区(气泡区)和密区(乳相区);非均匀结构对密区局部空隙率的影响通过引入局部空隙率下限和非均匀影响系数描述;将提升管流动...