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Supercritical water fluidized bed reactor (SCWFBR) is a novel concept for the gasification of coal and biomass to produce hydrogen. In this work, to enhance the mixing in the axial direction, an inclined distributor is introduced to optimize the flow dynamics in SCWFBR with partitioned fluid supply. Through numerical simulations based on the two fluid model (TFM), the effects of the inclined distributor structure and operating parameters on the solid distribution and the residence time are evaluated with the optimal values determined. Numerical results show that, area ratio = 2:1, SCW velocity ratio = 3:1, flow ratio = 3.36:1 and inclination angle = 20 ° are the optimal design in this paper. A predictive correlation of the minimum fluidization velocity for the improved SCWFBR is also proposed based on the numerical data. The average error between the correlation and numerical simulation results is approximately 1.4% which strongly demonstrates its capability. Finally, based on the optimal design, the lab-scale reactor is further scaled up and the studies about two scale-up rules are carried out. Only the cold flow is simulated in this study without considering chemical reaction which would be involved in future work.

Slugging represents one of the major regimes in fluidization, which occurs in small diameter beds with large bed height-to-diameter ratio or in large diameter beds with internals that resemble multiple small diameter fluidized beds. Slug types include round-nosed slug, wall slug and square-nosed slug. Studies of the slugs have been mainly focused on round-nosed or wall slugs known as half slug, typically occurring in Geldart group A particle fluidization. The square-nosed slug typically occurring for Geldart group D particles appears to be regarded as simple in its structure. The Electrical Capacitance Volume Tomography (ECVT) imaging of the square-nosed slugging phenomena conducted in this study reveals otherwise. That is the structure of the square-nosed slug is, in fact, complex, particularly with respect to its dynamic variation in fluidization. More broadly, this study examines experimentally the hydrodynamic characteristics of the square-nosed fluidization regime. Specifically, simultaneous measurements from multiple ECVT sensors provide non-invasive, continuous, 3-dimensional imaging of the entire flow region of the slugging bed and hence enabling the dynamic characterization of the evolution of the slugs. The analysis of the 3D images reconstructed for real-time gas–solid volume fraction profile of the slugging fluidized bed indicates that there are three different zones, namely, the bottom fluidization zone, the gas slug zone, and the solid slug zone, co-existing in the bed. The three zones present different hydrodynamic characteristics during the slug evolution. It is found that varying the gas velocity of the slugging bed mainly varies the maximum length of the gas slug zone, while it only has a minor effect on the lengths of the bottom fluidization zone and solid slug zone. It also has an insignificant effect on the solid volume fraction of the three zones.

Static electricity has an important effect on gas–solid fluidized bed reactor fluidization performance. In the process of fluidization, electrostatic interaction between particles will obviously accelerate particle agglomerate formation, which consequently reduces the fluidization performance. Pulsed gas flow injection is an efficient method to enhance particle mixing, thereby weakening the occurrence of particle agglomerate. In this study, the two-dimensional hybrid pulsed fluidized bed is established. The flow characteristics are studied by using the coupled CFD-DEM numerical simulation model considering electrostatic effects. Influences of different pulsed frequencies and gas flow ratios on fluidized bed fluidization performance are investigated to obtain the optimal pulsed gas flow condition. Results show that in the presence of static electricity, the bubble generation position is lower, which is conducive to the particle flow. Pulsed gas flow can increase the particle velocity and improve the diffusion ability. The bubble generation time is different at different frequencies, and the frequency of 2.5 Hz has the most obvious effect on the flow characteristics. Different gas flow ratios have significant impacts on the particle movement amplitude. When the pulse gas flow accounts for a large ratio, the particle agglomerate tends to be larger. Therefore, in order to improve the fluidization effect, the ratio of pulsed gas flow to stable gas flow should be appropriately reduced to 0.5 or less.

Mesoscale bubbles exist inherently in bubbling fluidized beds and hence should be considered in the constitutive modeling of the drag force. The energy minimization multiscale bubbling (EMMS/bubbling) drag model takes the effects of mesoscale structures (i.e., bubbles) into the modeling of drag coefficient and thus improves the coarse-grid simulation of bubbling and turbulent fluidized beds. However, its dependence on the bubble diameter correlation has not been thoroughly investigated. The hydrodynamic disparity between homogeneous and heterogeneous fluidization is accounted for by the heterogeneity index, Hd, which can be affected by choice of bubble diameter correlation. How this choice of bubble diameter correlation influences the model prediction calls for further fundamental research. This article incorporated seven different bubble diameter correlations into EMMS/bubbling drag model and studied their effects on Hd. The performance of these correlations has been compared with the correlation used previously by EMMS/bubbling drag model. We found that some of the correlations predicted lower Hd by order of a magnitude than the correlation used by the original EMMS/bubbling drag. Based on such analysis, we proposed a modification in the EMMS drag model for bubbling and turbulent fluidized beds. A computational fluid dynamics (CFD) simulation using two-fluid model with the modified EMMS/bubbling drag model was performed for two bubbling and one turbulent fluidized beds. Voidage distribution, time averaged solid concentration and axial solid concentration profiles were studied and compared with the previous version of the EMMS/bubbling drag model and experimental data. We found that the right choice of bubble diameter correlations can significantly improve the results for CFD simulations.

The different carbon nanotube (CNT) particles (@A and @V) were bed materials in the pseudo-2D tapered fluidized bed (TFB) with/without a distributor. A detailed investigation of the motion mechanism of bubbles was carried out. The high-speed photography and image analysis techniques were used to study bubble characteristic and mixing behavior in the tapered angle of TFB without a distributor. The fractal analysis method was used to analyze the degree of particles movement. Results showed that an S-shaped motion trajectory of bubbles was captured in the bed of @V particles. The population of observational bubbles in the bed of @V particles was more than that of @A particles, and the bubble size was smaller in the bed of @V particles than that of @A particles. The motion mechanism of bubbles had been shown to be related to bed materials and initial bed height in terms of analysis and comparison of bubble diameter, bubble aspect ratio and bubble shape factor. Importantly, compared to the TFB with a distributor, the TFB without a distributor had been proved to be beneficial to the CNT fluidization according to the study of bubble characteristic and the degree of the particle movement. Additionally, it was found that the mixing behavior of @V particles was better than @A particles in the tapered angle of TFB without a distributor.

A modified wake model was proposed for the newly developed bubble-induced three-phase inverse fluidized bed (BIFB), by combining the generalized wake model and the gas-perturbed liquid model. On the basis of the modified wake model, the solids and liquid holdups and the complete fluidization gas velocity in BIFB system have been successfully predicted with two established correlations. The predictions achieved very good agreements with the experimental data.

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 with heat transfers and chemical reactions. The Fortran-based CFD solver was coupled with the CUDA/C++ based DEM solver through inter-process pipes. The speedup to the CPU version of MFiX-DEM is about 130–243 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.

Fluidization of non-spherical particles is widely practised in chemical engineering processes. In this work, the mixing and dispersion behaviours of non-spherical particles in a bubbling fluidized bed (BFB) are explored by a computational fluid dynamics-discrete element method (CFD-DEM) featuring a super-quadric model to describe particle morphology. After model validation, the general flow patterns, solid mixing, and solid dispersion of ellipsoid particles are studied, together with the discussion of the effect of aspect ratio (AR) on fluidization behaviours. The results show that minimum fluidization velocity increases with the aspect ratio. Bed permeability depends on bed porosity and particle shape. Bubbles place a significant role in determining flow patterns, which induce a double-recirculation pattern where particles mainly move from the wall region to the central region in the lower bed and oppositely in the upper bed. Ellipsoid particles with higher sphericity (e.g., AR = 0.75 and 1.5) show a smaller mixing index in the bed. The magnitudes of solid dispersion coefficients in x, y, and z directions are about ~10−3 m2/s, ~10−5 m2/s, and ~ 10−2 m2/s, respectively. Ellipsoid particles with higher sphericity show larger solid dispersion intensity. These findings shed light on the fundamental understanding of the particle shape on fluidization dynamics.

The magnetic stabilization flow regime could also be created for Geldart-B nonmagnetizable particles provided some magnetizable particles are introduced and the magnetic field is applied. This study aimed to explore the size (dpM) and density (ρpM) effects of magnetizable particles on its operating range. The upper limit (UmbH) could not be determined from the ΔPb–Ug↓ curve but could from analyzing the variation of ΔPb-fluctuation with increasing Ug. Due to the variation of UmfH (lower limit) with dpM and ρpM, both UmbH–UmfH and (UmbH–UmfH)/UmfH were used to quantify the operating range of magnetic stabilization. UmbH–UmfH varied hardly with dpM but increased significantly with decreasing ρpM. (UmbH–UmfH)/UmfH increased as dpM or ρpM decreased. It was more difficult for the nonmagnetizable particles to escape from the network formed by the smaller/lighter magnetizable particles. For the same magnitude of change, dpM had a stronger effect than ρpM on (UmbH–UmfH)/UmfH. Neither UmbH–UmfH nor (UmbH–UmfH)/UmfH varied monotonously with the minimum fluidization velocity of the magnetizable particles, indicating that no straightforward criterion for matching the magnetizable particles to the given nonmagnetizable particles could be established based on their minimum fluidization velocities to maximize the operating range of magnetic stabilization.

As a subsequent paper for “type-A-choking-oriented unified model for fast fluidization dynamics”, the present work aims to provide more systematic mesoscale analyses on clusters. Starting from theoretical derivations on idealized flow patterns of gas and solids around a single falling cluster; the momentum consumption due to particle circulation in clouds and the modification of flows by the constraint of driving force available in the bed were addressed. Complete compensation of the pressure-drop driven percolated gas in clusters by the reversely-penetrating particles was used for the ultimate closure of the model. An important finding of the present work, different from most empirical correlations, but verified by Wei and Zhu's latest experimental data and others, is that the cluster diameter does not vary monotonically with the mean solids holdup of the bed, but has a maximum value in between. Demonstrative calculations show that it is easy for Group A particles to enter the flow regime of high-density fast-fluidization as the circulating solids flux increases continuously, while fast fluidization for Group B particles tends to be stopped at Type C choking in advance. Compared with Group A particles, the clusters for Group B particles are less dense, but the penetration velocities of particles are higher, resulting in much larger dimensionless diameters of clusters. Finally, issues of pseudo-2D fast-bed modeling were discussed, and modeling of fast-beds with uneven flow fields was outlook briefly.

A CFD-DEM coupled with a cohesive contact model is developed for simulation of a Wurster fluidized bed with heat and mass transfer. First, the water evaporation and cohesive contact sub-models are tested, respectively. Second, a Wurster fluidized bed with heating, drying, and wet particle fluidization is simulated. Results show that the particle temperature in the bottom and draft tube rises faster than that in the annular region, which leads to the probability density distribution of the particle temperature presents two peaks. The circulation pattern also has a significant effect on particle drying. Under conditions with a small amount of liquid injection, the water evaporates immediately and the particles are fluidized normally. Increasing the liquid injection rate, the stability of the particle circulation decreases. Under conditions with significant particle cohesion, large agglomerates are formed and the fluidization breaks down. The current study provides an effective method for studying hydrodynamics of Wurster fluidized beds with simultaneous processes of heating, drying, and wet particle fluidization.

Hydrodynamics in a newly invented bubble-induced inverse gas–liquid-solids three-phase fluidized bed has been studied via both experimental and numerical methods. With experiments in a 3.0 m column of 0.153 m in diameter, four fluidization regimes including a fixed bed regime, a bed expansion regime, a complete fluidization regime, and a freeboard regime have been identified with the increase in the superficial gas velocity. A three-phase Eulerian-Eulerian CFD model was developed to simulate the hydrodynamics in the inverse three-phase fluidized bed and the simulation results have a good agreement with the experimental data. The effects of the particle property and solids loading on the transitions across the flow regimes were numerically studied. A higher solids loading and/or a larger particle density are reported to contribute to an easier fluidization and a faster flow development to the complete fluidization regime. The radial flow structure becomes less uniform with increased inner circulation of the liquid after introducing more bubbles into the column.

Previous flow regime mapping work in both gas-solids (GS) and liquid-solids (LS) fluidization systems were carefully reviewed. A set of complete four-quadrant flow regime maps that unifies all the operating modes in both the GS and LS fluidization systems was proposed. The flow directions of the fluid and particle velocities were used as the abscissa and ordinate of the proposed four-quadrant regime map. All the fluidization systems then can be divided into four groups: cocurrent upward (Quadrant I) and downward (Quadrant III), counter-current fluid-down and solids-up (Quadrant II) and fluid-up and solids-down (Quadrant IV) in the regime map. The relative density between the particle and fluid was also selected as a parameter to differentiate operations of GS downer and LS inverse fluidized bed in Quadrant III. The transitions to and the limits of the flow regimes were discussed in detail. Some new flow regimes such as the GS circulating turbulent fluidization and the LS conventional circulating fluidization regimes were also outlined in the proposed regime map.

Numerical simulation for large deformation problems of saturated soil poses an ongoing challenge since it requires the capabilities of modeling large deformations, interactions between solid skeleton and pore water, as well as fluidization behaviors. A hydro-mechanical coupled B-spline material point method is developed to simulate large deformations of saturated soils. Based on Biot's mixture theory, a single set of material particles is adopted to represent saturated soils where Darcy's law is employed to govern the motion of pore water and the momentum conservation of the mixture is used to govern the motion of solid skeleton. The convergence and effectiveness of the proposed method are examined by one-dimensional consolidation tests and quasi-static footing penetration into two-dimensional elastic saturated soils. The capability of simulating practical engineering for the proposed method is demonstrated by reproducing the dynamic process of three-dimensional saturated soil slopes with a strain-softening Drucker-Prager constitutive model. Results show that the coupled BSMPM well reveals the overall dynamic process of saturated soil slope involving evolution of shear bands, formation of graben and horst, and fluidization of progressive failures with improved computational accuracy and enhanced convergence, which demonstrates the proposed method is a promising approach for large deformation problems of saturated soils.

Gas fluidized beds with bi-dispersed particles of different sizes, densities, and shapes are encountered in many industrial processes spanning the manufacture of energy, material and resources to greenhouse emissions mitigation and renewable resources utilization. The design and operation of such systems heavily rely on the prediction of minimum fluidization velocity of the mixture (Umf(mixture)) to avoid particle segregation and maximize mixing. Many correlations exist for predicting Umf(mixture); however, they exhibit limitations in accuracy and/or applicability. The limitations of these correlations are often expressed in terms of particles properties (e.g. effective size and density), flow conditions, and solids composition. This study has critically assessed highly cited correlations, delivered a comparative analysis of their applicability and predictability against a large pool of experimental data, and deepened the understanding of parameters that affect the prediction of Umf(mixture) using different correlations.

Pressure fluctuation is commonly used to characterize the dynamic of fluidized bed, and bubble movements resulting in pressure fluctuations will seriously affect the stable operation of fluidized bed. This paper presents an extreme value statistical analysis model that uses generalized extreme value (GEV) distribution to analyze the pressure fluctuation time series, predict its future fluctuation state, and further provide risk warning for fluidized bed operation. The pressure fluctuation time-series for four mainly fluidization behaviors (single bubble, multiple bubble, exploding bubble and transport conditions) in an actual experiment were analyzed by the proposed method. The results show that the error rate of the proposed method in this paper is controlled within±10%, and the average error rate is controlled within −1.7%–3.7%. By analyzing the risk margin of the extreme pressure fluctuations of each flow regime, the risk margin of exploding bubble is the largest, and more stringent measures should be taken to ensure the stable operation of the fluidized bed in this flow state. In summary, the risk warning of the fluidized bed can be detected in the joint efforts of the confidence interval and the risk margin of the pressure fluctuation return level of each flow regime.

The present study evaluates elastic and inelastic contact forces in predicting the fluidization characteristics of irregularly shaped Titania nanoparticle agglomerates in a bench-scale conical fluidized bed. At first, experiments were performed to identify the mutual effects of gas velocity and agglomerate size on the instantaneous pressure, bed pressure drop and bed expansion ratio. Rigid complex-agglomerates (∼100−200 μm) were mainly formed in the partially fluidized regime, while soft simple-agglomerates (∼20−70 μm) were primarily formed in the spouting regime. The simulations were performed through the CFD-DEM approach. The error analysis of results in the partially fluidized regime revealed that the combination of Hertz-Mindlin and Johnson-Kendall-Roberts (HM + JKR) model led to a better prediction of the bed pressure drop and bed expansion ratio than the spring-dashpot (LSD) model. In the transition flow regime, the Hysteretic model led to better results of the instantaneous pressure values than those proposed for other flow regimes. In the spouting flow regime, the HM and Thornton models led to over-estimation of bed pressure drop when compared to the LSD model. The comparative results of this study provide promising new insights into the collision mechanism of polydisperse agglomerates in different flow regimes for industrial aspects.

Gas-particle flows in circulating fluidized beds (CFB) with wide particle size distributions were simulated using the Eulerian-Eulerian approach to analyze the effects of the particle phase division and the applicability of the particle-particle drag model. The results indicate that the simulation is not accurate by just using a single average particle diameter when the particle size distribution includes a critical particle diameter. A binary particle phase division criterion was then developed to establish two particle phases representing two types of particles with different flow patterns. Coupling the Eulerian-Eulerian approach with the new criterion enabled accurate predictions of the pressures, particle volume fractions, and particle mass circulation rates that were in agreement with experimental data. The influences of different particle-particle drag models were also investigated to show that the simulation using the Syamlal model was not accurate due to the overestimated particle-particle drag, while the results without particle-particle drag and with the Manger model were similar and much more accurate. Moreover, the flow mechanism for the non-uniformity of particle circulation rates in the parallel circulating loops of the CFB boiler was revealed. This study improves the Eulerian-Eulerian simulations of fluidization with wide particle size distributions and further deepens the understanding of flow characteristics in CFB.

U-type reduction chamber plays a significant role in the suspension roaster which has been proven to be one of the most highly efficient and clean magnetization equipment to utilize complex refractory iron ores. In the present work, a hydrodynamic model has been developed for the operation that the materials in the fluidization chamber are fluidized while the particles in the supply chamber are in a moving packed bed. Through fluid dynamic analysis, a hydrodynamic model including four equations has been established, whose solution results in the solids concentration in the fluidization chamber and materials' height in the supply chamber. Meanwhile, the effects of operating conditions such as fluidizing gas velocity and delivery rate on solids concentration in the fluidization chamber and materials' height in the supply chamber were studied by a combination of model analysis and experiments. The experiments were carried out in a U-type reduction chamber cold test apparatus with alumina particles. The model predictions showed good agreement with the experimental data, giving average errors below 6.28% and 4.96% respectively.

The solid particle flow characteristics inside the cone valve were experimentally and numerically studied. The experiments were conducted at different valve sizes, valve opening positions, pressure drops, and fluidization velocities. Numerical simulation using the computational particle fluid dynamic method was also carried out over broader conditions. It is found that the solid particle flow inside the cone valve demonstrated the three-stage phenomena as the solid particle flew passing through two in-series connected orifice systems. The explanation of the three-stage phenomena of the solid particle flow rate to the valve opening was given according to the double-orifice flow model. Based on the physical nature of the solid particle flow characteristics, a semi-empirical model of the solid particle flow rate inside the cone valve was proposed. The model parameters, such as the saturated solid flow rate, the saturated valve opening, were determined using the experimental data and the existing knowledge of orifice systems. The model was then verified using the experimental data and presented acceptable prediction accuracy.

Background Inverse fluidized beds have been designed to control the fluidization of low-density particles in high-density of continuous fluid. Fluidization of a large quantity of low-density particles can be challenging to control in a classic inverse fluidized bed. A tapered inverse fluidized bed can assist in the better fluidization of wider particles size distribution as the cross-sectional area have been enlarged along with the bed height from the top to the bottom. Methods Here, a laboratory setup of a tapered inverse fluidized bed was used to examine the mean residence time characteristics and the dispersion coefficient. Additionally, a three-dimensional computational fluid dynamics (CFD) modelling was performed to examine the mass fraction of the tracer. The Eulerian-Eulerian approach and the kinetic theory of the granular flow model were used to analyze the liquid flow and solid materials behaviour, respectively. The dispersion coefficient obtained using CFD were compared and validated with the experimental results. Then, the CFD model was used to investigate the effect of liquid velocity, size and density of solid materials (i.e., lower density than the density of water) and two different bed angles (6.8o and 8o) on the mass fraction of tracer along the bed heights. Significant Findings It was found that the liquid tracer mean residence time and axial dispersion coefficient significantly depended on particle density, tapered angle of the column, and superficial liquid velocity. Based on the experimental data, an empirical correlation has been developed for the mean residence time of the tracer by using response surface methodology. The findings can assist in designing and operation a tapered inverse fluidized bed technology.

To enable the mechanistic description of the mixing of larger particles in gas-fluidized beds in models (e.g. fuel particles in combustors), knowledge about the rheology of the bed emulsion is required. Here, it is crucial to determine the drag on large fuel-alike particles. This work presents the experimental work on the fate of 13 different solid spheres falling or rising through a bed of air and glass beads at minimum fluidization. The trajectories of the tracer are highly resolved (sampling rate of 200 Hz) by means of magnetic particle tracking, this previously unmet accuracy allows disclosing the complex rheological behavior of gas-solids fluidized bed emulsions in terms of drag on immersed objects. The trajectories reveal that none of the tracers reach terminal velocity during their fall and rise through the bed. The shear stress is obtained through the drag force by solving the equation of motion for the tracer. The data reveal particularities of the bed rheology and clear differences of its effect on rising and falling particles. When studying the shear stress over the characteristic shear rate of each tracer, it can be seen that the stress of the bed on the tracers is dominated by a yield stress, with a somewhat smaller contribution of the shear stress. For rising tracers this last contribution is almost negligible. The falling tracers show strong interaction with the bed emulsion, resulting in a fluctuating shear stress, which increases with tracer size and density. The stagnation of some tracers at low shear rates reveals a viscoplastic behavior of the bed emulsion, exhibiting a typical yield stress that showing a clear dependence on the tracer diameter and buoyant density. The concept of yield gravity is used in order to introduce a normalized shear stress which provides additional verification of the experimental observations in relation to the influence of tracer size and relative density on the shear stress.

To actually describe the flow behaviors of particles in the liquid-solid fluidized bed, the effects of liquid film covered on the particles surface and the sphericity of particles need to be considered for quasi-spherical wet particles. Liquid-solid fluidization characteristics are predicted using a two-fluid model incorporating with the kinetic theory of rough spheres (KTRS) model. Simulation results show that the normal restitution coefficient for wet particles covered liquid film increases with an increase of the particles diameter. As for the sphericity of particles, a higher sphericity of particles gives rise to a lower granular temperature and higher solids pressure and viscosity. Also, the normal restitution coefficient of quasi-spherical particles is relatively small, compared with completely sphere. The simulation results obtained by the kinetic theory of rough spheres model for quasi-spherical wet particles are in satisfactory agreement with the experimental data from Lu et al.

A series of bed collapse tests were conducted for determining the dense fluidization flow rate of a gas-solid mixture in a micro-channel fluidized bed reactor, and a separate simulation was created for calculating the reactor conversion and temperature of the catalytic methane pyrolysis. The minimum fluidization and minimum bubbling flow rates were determined to be 3.04 and 8.07 sccm for a 2 × 4 mm2 reactor channel with an average voidage of 0.57; 6.21 and 15.9 sccm for a 4 × 6 mm2 channel with an average voidage of 0.42, respectively. By building a correlation between these critical velocities and the cross-sectional area of the fluidized bed reactor channel, the dense fluidization flow rate at the micro-/mini-channel level with an internal diameter range from 0.3 to 1 mm is predicted between 1.47 to 4.21 sccm. In the simulation, an internal diameter of 0.6 mm, a 10-kW solar input rate, and an initial gas flow rate from 0.08 to 0.23 sccm that expands to 1.5–4.3 ccm at the reaction temperature, are considered as the optimal conditions to maintain a reasonable conversion of methane pyrolysis and to keep the mixed fluid in the dense fluidization within the laminar flow range. The conversion of 79% under these conditions was calculated numerically and found to be promising compared to literature reports. An additional force analysis on a single carbon black particle is shown with different reactor orientations to validate the experimental data and simulation results.

The flow dynamics and attrition characteristics of three air reactor designs are investigated using an Eulerian-Eulerian kinetic theory model. The hydrodynamics of these reactor designs are analyzed to identify the flow regimes in which the particles evolve. The investigated designs, which differ in the configuration of the secondary flow ports, exhibit bubbling and turbulent fluidization regimes in similar spatial regions. The most substantial differences in the hydrodynamics was in the turbulent fluidized regions near the secondary inlets. The mechanical stressing environments undergone by the particles were analyzed using the collision energy spectra, reconstructed using the local flow field properties (i.e. granular temperature and particle number density). The spectra show that the increase in the specific collision power is associated with the regions near the secondary injector ports, which are in a turbulent fluidization regime. A simple analysis relying upon a partitioning of the energy spectrum, showed that attrition rate may be reduced by about 34% over the original design.

To improve the adaptability of fluidized beds for fine coal separation, a new type of liquid–solid fluidized bed was constructed, i.e., the inflatable-inclined liquid–solid fluidized bed (IILSFB). A combination of simulation analysis and separation experiments was used to analyze the fluidization characteristics and separation performance of the IILSFB. The results showed that there was upflow and downflow in the fluidized bed. The upflow was mainly composed of water flow, followed by light and heavy particles; on the other hand, the downflow was caused by the backflow of heavy particles that settled at the inclined section. In addition, the light particles that settled at the inclined section could return to the rising water flow under the action of secondary airflow. As the water velocity, separation time, and secondary gas velocity increased, the comprehensive separation efficiency of fine coal in the fluidized bed improved, while the value decreased as the feed quantity increased. This also indicated the order of importance for these four factors, i.e., water velocity, separation time, feed quantity, and secondary gas velocity, on fluidisation. Furthermore, the comprehensive separation efficiency of 0.1–1 mm fine coal varied significantly with various factors, while that of ∼0.1 mm and 1–3 mm fine coal was always at a low value. In the latter case, the classification process of the size fraction was significantly better than the separation process in the fluidized bed. Under optimal working conditions, an IILSFB was used to separate the fine coal (0.1–1 mm). The yield of clean coal was 37.95% with an ash content of 12.11%, and the possible error was 0.085 g/cm3, indicating that the IILSFB had good separation performance for 0.1–1 mm fine coal.

Hydrodynamics of fluidization of hydrophilic titanium nanoparticles with vibration was investigated through pressure fluctuations using recurrence quantification analysis. The bed expansion revealed that the bed operates in the ABF regime. The standard deviation of the pressure fluctuations indicated that vibration reduces the minimum fluidization velocity. Hydrodynamic structures were defined using the wavelet transform analysis of pressure fluctuations and the effect of vibration was investigated through the energy of the pressure signal and the recurrence analysis. It was shown that the agglomerates have the most impact on the fluidization of the nanoparticles and vibration has a significant effect on this structure. Using the energy of the signal and recurrence analysis, characteristics of the vibration on the fluidization were defined. The energy of finer structures is higher in the vibrated bed, indicating a more stochastic pattern in this case. The recurrence rate showed the dynamic behavior of formation and breakage of agglomerates in the bed.

Particle velocity measurement based on cross-correlation algorithm is used widely in various multiphase flow systems. In this study, an optical fiber probe, i.e. Labasys® 100 from MSE Meili was used to systematically compare the qualities of its measured particle velocities in a pair of hydrodynamically distinct regimes, i.e. a fast fluidized bed (FFB) and a bubbling fluidized bed (BFB). Compared to FFBs, the measured particle velocities in BFBs show lower data repeatability, higher percentage of invalid data and higher sensitivity to the selection of the threshold value of maximum cross-correlation coefficient, which corresponds to much lower measurement qualities in this regime. Comparatively, higher measurement qualities were observed in the FFB based on the same evaluating methods. The highest measurement qualities appear in the core region of the riser and under high superficial gas velocities. A matchup relationship between the measurement quality and the shape of the probability density function (PDF) curves of maximum cross-correlation coefficient is found. Narrower PDF curves correspond to higher measurement quality and vice versa.

The modeling of the fluidization or sedimentation velocity of a suspension of solid particles is revisited by examining experiments conducted in either a liquid or a gas. A general expression is found in the case of negligible fluid inertia, i.e. at low Reynolds or Archimedes number. It is built as the product of the velocity of an isolated particle by three non-dimensional corrections that each takes into account a specific physical mechanism. The first correction reflects the variation of the buoyancy with the particle concentration. The second correction describes how the drag force increases with the concentration in case of negligible particle inertia. The third one accounts for the further increase of the drag when the particle inertia is increased. Remarkably, each correction only relies on a single of the three independent non-dimensional groups that control the problem: (1) the particle volume fraction Φs; (2) the ratio Φs/Φpack where Φpack is the bed packing concentration; (3) the Stokes number S t 0 , which characterizes the inertia of the particles and controls their agitation. Moreover, the onset of the instability that separates the homogeneous regime from the heterogeneous one is found to be controlled similarly by the Stokes number. Empirical expressions of the corrections are given, which provide a reliable tool to predict fluidization and sedimentation velocities for all values of the three non-dimensional numbers. The present results emphasize the crucial role of particle inertia, which is often disregarded in previous modeling approaches, such as that of Richardson and Zaki.

Gluten is produced from wheat grains and is used in the food industry as an improver in flour baking properties. On the basis of a comparative analysis of the methods of dehydration of frozen granules of wheat gluten with a surface dry crust, a rational method of drying them in a fluidized bed has been selected. In the process of calculating units with a fluidized bed, its hydrodynamic parameters have been determined: loss of the pressure of the fluidizing agent; the speed at the transition of the bed from the state of rest to the pseudo-boiling mode; layer porosity; the rate of entrainment of particles in unrestricted conditions roughly corresponding to the rate of soaring, at which a single particle is in equilibrium in the gas flow. During the dewatering operation, the rate of entrainment of the granules varies; therefore, it is advisable to use the passing fluidization mode depending on the decrease in their moisture content. In the variant of the active hydrodynamic regime in the drying unit, the dehydration procedure is intensified without a noticeable decrease in the economic efficiency of its functioning and high quality indicators of the finished product with the given final moisture are provided, which is due to the specific conditions of contact of the granules with the coolant. For granules with a moisture content of 0.19 kg/kg, the values of hydrodynamic characteristics have been determined: the area of critical pseudo-boiling rates is 4.1-5.5 m/s; the carryover rate of the fines is 12.5-14.5 m/s. As a result of the study, the choice has been substantiated in favor of drying the studied granules in a fluidized bed due to the prevalence of its advantages over the dehydration of the object in drum dryers.

A common scientific problem is that the monographs of leading scientists provide very modest recommendations for the calculation and design of gas distribution devices in fluidized bed apparatus. So, in the monograph of P.G. Romankov and N.B. Rashkovsky, hydraulic resistance of the switchgear is advised to be taken equal to half the hydraulic resistance of the fluidized bed. This recommendation does not take into account such factors as: the specific gravity of the fluidized product, the rate of fluidization and removal of small particles of the product, and the geometric parameters of the gas distribution device. In the monograph of B.S. Sazhin, it is recommended that a pressure drop on the gas distribution device is taken not less than 1000 Pa. What parameters should induce such a pressure drop is not specified. In the work of V.M. Marchevsky and R.N. Zherebkina, the dependence connecting the hydrodynamic stability of the fluidized bed with the area of the "living" section of the openings in the gas distribution device and with the parameters of the velocity regime of the fluidized bed was obtained experimentally. The value of the hydrodynamic stability was taken as the difference in the bed heights at which the fluidization of the higher layer ceased. The obtained dependence allows calculating the cross-sectional areas of the openings for the passage of the coolant, but does not allow calculating the design of the gas distribution device: in particular, the configuration and number of openings, their location, pitch and hydraulic resistance. Experimental studies are needed for their calculation. The unsolved part of the scientific problem is that it is not possible to find an exact theoretical definition of the hydraulic resistance coefficients; their values can be found only experimentally. Experiments and literature data show that the hydraulic resistance coefficient does not depend on numbers Re ≥ 1000. The main factor influencing the value of the hydraulic resistance coefficient is the ratio F / F1, where F is the cross-sectional area of the lattice holes and F1 is the cross-sectional area of the apparatus. Analysis of the parameters presented in this paper confirms that the value of the hydraulic resistance coefficient increases with increasing according to the linear law . Segment 0 - 1, which cuts off the approximating line on the y-axis, reflects the hydraulic resistance coefficient of the columnar grid. The obtained equation describes with sufficient accuracy the dependence of the hydraulic resistance coefficient on the parameter in the range of . The standard deviation of the experimental values of the hydraulic resistance coefficient from the calculated one is σ = 0.075. It is established that the main factor influencing the value of the hydraulic resistance coefficient is the relative area of the "living" cross-section of the openings in the gas distribution device.

The main objective of this study is to verify different (semi)empirical formulas used to predict hydrodynamic parameters of a fluidized bed against CFD simulations. The hydrodynamic parameters investigated include minimum fluidization velocity, bed voidage at minimum fluidization condition, bubble diameter, and bubble velocity. All simulations were completed using a 3D Euler-Euler-based model available in ANSYS Fluent 19.2. The study of solid volume-averaged velocity inside the bed revealed a minimum fluidization velocity of 0.194 m/s, which was in agreement with the result obtained when the pressure drop in a fluidized bed was set equal to that in a fixed bed. The time-averaged solid volume fraction showed that the constant value of 0.476 (with the assumption of the uniform cubic mode of packing) was a good estimation for bed voidage at minimum fluidization condition. The study of air turbulent viscosity demonstrated high air turbulence above the bed and inside large bubbles within the bed. Higher mean bed heights and higher levels of air circulation were observed at higher air flowrates. The analysis of different formulas predicting bubble diameter and bubble velocity at different bed heights and air flowrates showed that Yasui-Johnson's formula for estimating the bubble diameter could produce results in good agreement with our CFD simulations for the tested geometry and initial conditions.

This work aimed to solve the controversies about defining and determining the minimum fluidization velocity (Umf) in the magnetized fluidized bed (MFB). It should be defined rigorously from the physics behind the secondary phenomena such as bed pressure drop and particle motion. Since Umf demarcates the transition from the fixed-bed to the fluidization flow regime, it could not be determined from the ΔPb–Ug↓ curve but could from the ΔPb–Ug↑ curve. Moreover, the initial fixed bed for measuring this curve must meet its definition. For the MFB with purely magnetizable particles, it could be obtained via decreasing Ug gradually from full fluidization to zero at H = 0 kA/m to minimize the wedging effect. For the MFB with magnetizable and nonmagnetizable particles, such a decrease of Ug should be quick to simultaneously minimize the wedging effect and segregation. The as-determined Umf remained invariant with H in both types of MFBs.

—Modeling the relative motion of large crustal blocks vitally depends on an adequate description of the forces acting between the blocks. To describe motion at high strain rates, it proved necessary to assume a dry friction to depend on the shear strain rate and, in some cases, on the amplitude of fault side displacement. The best known examples of large-scale motions with dynamically decreasing friction are long-runout rock avalanches and gravity-driven collapsing of the transitional cavities of large impact craters. In this work, the experience is discussed of using the model of acoustic fluidization as a factor of a temporary decrease in friction to quantitatively simulate impact crater shape on the Earth and other planetary bodies. Immediate promising ways to find more adequate models are outlined.

The minimum fluidization velocity of a supercritical water fluidization bed reactor (SCWFBR) is numerically nvestigated based on coupled Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations. The accuracy of the CFD-DEM model is firstly validated via previously published experimental data. Then, the model is adopted to study the effects of particle size distributions (PSD) on the minimum fluidization velocity in which four types of PSD including Gaussian-type, Mono-type, Flat-type and Binary-type are considered. Numerical results show that the minimum fluidization velocity for the Flat-type PSD is the smallest among the four while the one for the Mono-type PSD is the largest. The minimum fluidization velocities for the Mono-type and Gaussian-type PSD share quite similar values. However, it is conditionally valid when the largest amount of particle size in the Gaussian-type PSD is equal to its mean particle size which is used in the Mono-type PSD. The agreement of the minimum fluidization velocity between Mono-type and Gaussian-type PSD is also influenced by the number of small particles. The mechanism behind these phenomena is revealed by investigating the micro-structure of differently sized particles. Finally, predictive correlations for the minimum fluidization velocity of the SCWFBR are proposed based on the numerical results which demonstrates strong predictive capability for wide PSD.

The transfer of the dispersed layer into a fluidized state makes it possible to intensify the drying process. The small size of the particles leads to an increase in the surface of their contact with the coolant at a relatively low hydrodynamic resistance. Other positive qualities of fluidization are listed, which is very important when carrying out exothermic processes. We studied the behavior of the fluidized bed during the drying process. The curve of fluidization of beet chips is shown. The suspended state of the material began when the forces of the hydrodynamic layer were equal to the weight of all its particles per unit area of the cross-section of the working chamber. The region of existence of the fluidized bed is marked. In this area, the flow was relatively equilibrium (fluidized). On the surface of the layer, small waves were observed with different frequencies and amplitudes of oscillations, as well as with spontaneous fluctuations. This mode of operation was achieved as a result of the study of the structures of the support - gas distribution grid and the drying chamber. The flow velocity profile in the working chamber is investigated. An efficient equalization of velocities with the help of flat stamped grids has been established. The results were confirmed by the spectra of the flow in the drying chamber. Oscillations on the free surface of a fluidized bed are considered. The Euler equation was written, which made it possible, as a result of various transformations, to obtain a formula for calculating the oscillation frequency of the fluidized bed. The studies carried out made it possible to establish the regimes of pseudo-fluidization, to a certain extent minimizing the heterogeneity of the layer, which is of significant practical importance. However, the operating parameters need to be adjusted depending on the type of material to be dried and other indicators. The research results do not obscure the general provisions of nonequilibrium thermodynamics. The fluidized bed cannot be in an equilibrium state, since the transfer of substances is obvious: energy, mass and momentum. It is correct to regard the fluidized bed as unstable. Small and spontaneous fluctuations always exist in the layer. The absence of conditions for their decay becomes a condition for the instability of the process.

Acai berry residues have great potential for sustainable thermochemical conversion processes. Many of these systems, as well as drying technologies, use the fluidized bed technology, which requires the characterization of the minimum fluidization velocity. The experimental work consisted of obtaining pressure drop curves for different bed heights, inlet air temperature, and particles roughness. The theoretical and data simulation approaches encompassed the minimum fluidization velocity prediction by correlations found in literature and neural networks, respectively. The minimum fluidization velocities were determined in the range 0.67–1.56 m/s. The minimum fluidization velocity decreased exponentially with increasing air temperature in the range 50–80 °C, but increased with the increase of the bed height in the range 1.5–4.5 cm. This effect was only observed for particles with fibers, indicating a strong presence of interparticle cohesive forces. Correlations proposed by the literature were not adequate to predict the minimum conditions for fluidization since they are very specific for biomass type and fluidization conditions. Even performing parameter estimation from experimental data, it was observed a strong dependence on the particles properties and bed porosity at minimum conditions. The neural network developed in this work presented good accuracy in predicting the experimental results, and it can be considered a potential viable alternative to estimate the minimum fluidization velocity for different process conditions.

Eulerian–Eulerian modeling is widely applied in simulations of multi-phase flows in fluidized beds. However, the validity of this model is questionable, especially with the limitation of gas–solid drag closures. In this study, CFD simulations were performed to investigate the validity of the numerical model for segregating fluidized bed. The numerical model was tested with experimental data from the literature to select the most appropriate gas–solid drag model. It was found that the Gidaspow drag model is generally better than the Syamlal–O’Brien, the BVK, and the Di Felice models. However, all the drag models showed poor agreement with experimental data of size segregating systems. Also, all the investigated gas–solid drag models mispredicted the minimum fluidization velocity of various fluidized bed systems. The Gidaspow and Di Felice models had an acceptable error, while the BVK and the SB always under-predicted the minimum fluidization velocity with high error. A new correlation was proposed to correct the computational superficial velocity to mitigate the effect of the error of fluidization velocity prediction by the Wen-Yu gas–solid drag model.

Comprehensive exploration on the pneumatic feeding characteristics of a fluidized bed can deepen the understanding of biomass pyrolysis. An Euler-Euler model coupled with KTGF is used to simulate the pneumatic feeding process of a two-dimensional cold-flow fluidized bed. The pneumatic feeding mechanism of fluidized bed is analyzed from three aspects: feed gas, feed biomass particles and pneumatic feeding. The feed gas exerts a radial drag force on the quartz sand particles, and merges with the fluidizing gas to promote local fluidization and reduce solid hold-up, which provides feeding space for biomass particles to enter. The radial collision between feed particles and bed materials promotes the diffusion and mixing of particles. And the interaction between feed gas and feed particles promotes them to enter the bed deeper. A dynamic model of pneumatic feeding into the fluidized bed reactor is established, including particle interaction, diffusion, mixing and fluidization together.

The simulation of particle fluidization behavior in a complex geometry with a large number of particles is challenging owing to the complexity of unstructured computational grids and high computational intensity. In this study, a virtual dual-grid model (VDGM) is proposed to calculate the solid volume fraction in unstructured grids and speed up the calculation. The VDGM is coupled with a computational fluid dynamics–discrete element method model to simulate particle fluidization behavior in a multi-ring inclined-hole spouted fluidized bed with 4.2 million particles under a high temperature of 1423 K. A computational fluid dynamics–discrete element method–virtual dual-grid model (CFD–DEM–VDGM) coupling model is implemented based on commercial software Fluent and EDEM. The time step settings in Fluent and EDEM and the pattern of particle data transfer in Fluent are improved to speed up the calculation. It is discovered that the VDGM can calculate the solid volume fraction in unstructured grids of complex geometry and speed up the calculation effectively. The calculation speed increased by more than 10 times compared with that of the segmentation sampling method. The new pattern of particle data transfer in Fluent can reduce data transfer time by more than 90%. The fluidization behavior of 4.2 million high-density particles in the multi-ring inclined-hole spouted fluidized bed is obtained and analyzed in detail. The CFD–DEM–VDGM coupling method is validated for the bed expansion height and spouting cycle time in a spouted fluidized bed via experimental results.

Mechanical agitation was usually applied to improve the fluidization quality of the fluidized bed. This study aimed to explore the effect of agitation on the fluidization characteristics and separation effect of a gas–solid separation fluidized bed. On the basis of the multiple reference frame model, the fluidized bed under mechanical agitation was simulated, where the symmetrical motion pattern of the bed particles was identified. Furthermore, when the agitation speed w was below 75 rpm, the fluidization quality was improved gradually with the lower density fluctuation variance of 0.06 g/cm3. Finally, under the appropriate operating conditions (fluidization number of 1.2, w = 75 rpm), raw coal was separated in a fluidized bed, and the yield of cleaned coal was 41.30% with an ash content of 14.27%. Moreover, the probable error was as low as 0.105 g/cm3, indicating the strong separation performance of the gas–solid separation fluidized bed with an agitator.

The cold flow hydrodynamics and segregation characteristics of a binary mixture of high-ash coal and sand have been investigated in a dual fluidized bed (DFB) gasifier. A short riser, maintained in the fast-fluidized bed regime by different combinations of primary and secondary aerations, is used. The influence of fluidization velocities, secondary-to-primary aeration ratio ( φ ), particle mixture properties has been examined on the full-loop pressure profile, solids circulation rate ( G s ), and segregation characteristics. A substantial influence on DFB pressure profiles is observed for the polydisperse binary mixture compared to unary sand particles having a narrow particle size distribution. Coarse particle fractions measured at loop-seal and pot-seal indicates significant segregation in the riser and the BFB, which reduces as fluidization velocities increase. Variations in G s and φ show a minimal impact on particle segregation. No reverse gas bypass is detected for the designed operating parameters through solids recycle valves, namely loop-seal and pot-seal. Except for some discrepancies observed at high superficial velocities and G s , the values of axial solids holdup in the riser yield a reasonable agreement between experiments and a hydrodynamic model based on empirical correlations.

The increase of liquid saturation badly affects the fluidization dynamics, even resulting in the failure of fluidization. Nevertheless, few researches focus on characterizing the flow pattern transition of wet particles. In this work, we discuss the effects of the liquid saturation, gas velocity and the particle size on the global fluidization dynamics of Geldart D particles by analyzing the pressure fluctuations in the fluidized bed. The results show that the bubble dynamics is intensified with the increasing liquid saturation and decreasing particle size. When the superficial gas velocity increases, the fluidization regimes change from expanding regime, to multi-bubbling regime and slugging. During the normal fluidization and slugging, the liquid bridge forces prevent the growth of large bubbles and promote the probability of bubble break-up. Thus, the average bubble size decreases and the number of bubbles increases, which lead to the intense bubble behavior. With the decreasing particle size, the effect of liquid bridge forces is enhanced, contributing to the intensified bubble dynamics, including fast rising, frequent coalescence and eruption of a large number of bubbles. Compared to dry particles, wet particles are easily to cause defluidization when the gas velocity is small. The PSD patterns have the sharp narrow peaks at frequency lower than 0.8 Hz. When the liquid saturation is increased to 30%, a gas channel forms in the bed, which resists the normal works of the fluidized bed. Basically, reducing the liquid saturation is a reasonable way to avoid defluidization.

A swirling gas-solid fluidized bed can effectively improve the fluidization quality and interphase heat transfer via the introduction of tangential gas flow. The Dense Discrete Phase Model (DDPM) is employed to investigate the gas-solid flow behaviors in a swirling gas-solid fluidized bed with the air plenum. In addition, the wall wear and particle mixing behaviors are also examined. The results demonstrate that various operation regimes appear with the increasing superficial velocity. The particles are prone to be centrifugally attached to the wall in the stable swirling regime and accompanied by strong elutriation. The decrease of central body height will reduce the bed pressure drop and swirling velocity. The increase of operation velocity is beneficial to particle mixing behaviors in a swirling bed with a lower central body.

The fluidized bed technique was applied to use with the Robusta coffee in this research. fluidization behavior and specific energy consumption were investigated under various coffee forms and distributor hole angles. Moreover, the minimum fluidization velocity (Vmf) was also determined. Experiments are carried out in a sample bed height of 5 cm with ambience air. In this study, two coffee forms (Ripe coffee cherries; RCC and parchment coffee; PC) and three distributor hole angles (45º, 60º and 90º) are examined. The experimental result shown that the fluidization behavior is influenced by coffee form and distributor hole angle. The RCC and distributor hole angle of 60º provided the low pressure drop throughout the superficial air velocity. The low values of Vmf and SEC were also achieved in the RCC and distributor hole angle of 60º.

Results from validation experiments on bubbling fluidization are presented. The tests were performed in three cylindrical columns having internal diameters of 2.5, 4, and 6 inches. The systems were designed to have considerably higher particle counts compared to the commonly used validation experiments found in published literature. Well-characterized glass particles having a Sauter mean diameter of 332 µm were used. The superficial velocity of air at the inlet was specified at five distinct settings in the range of 0.235–0.423 m/s corresponding to 2.97–5.35 Umf, where Umf = 0.079 m/s is the minimum fluidization velocity measured in the 2.5-inch unit. A systematic procedure was followed for each column involving five replicates of the selected inflow conditions in a randomized order. Uncertainty measures are provided for mean and standard deviation of differential pressure, while the statistics of interface height are reported with pixel threshold dependence. Overall, the findings from these experiments are consistent with the previous studies. The datasets generated are critical to assess coarse-grained modeling techniques developed for large-scale applications like Particle-In-Cell or Coarse-Grained Discrete Element Model, as well as elucidating the underlying physics.

The hydrodynamic behavior of cohesive TiO2 nanoparticle agglomerates was studied in a conical fluidized bed. The effects of size, particle polydispersity, and airflow velocity were analyzed in the transition regime from heterogeneous to homogeneous and turbulent fluidization. The simple-agglomerates size was ~25–75 μm with fractal dimensions of ~1.95–2.50. Adhesive CFD-DEM simulations were performed to study the interaction between the simple-agglomerates by combining Mindlin-Dersiewicz and Johnson-Kendall-Roberts (JKR) contact models. The effects of restitution and friction coefficients, probability density function, and coordination number of agglomerates were studied on the particle velocity profiles in the spout and annular zones. The error analysis results showed that bed dynamics is more sensitive to a change in the friction coefficient than in the restitution coefficient. A good agreement between the results was found for friction and restitution coefficients close to one, which is evidence of nearly elastic collisions between TiO2 agglomerates.