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Scale-up studies of fluidized beds are important for numerous fields. Fluidization in a multi-ring inclined nozzle spout-fluid bed (MRIN spout-fluid bed) is one of the most critical factors that affect the coating efficiency and uniformity of tri-structural isotropic (TRISO) nuclear particles in the fluidized bed chemical vapor deposition (FB-CVD) process. In this work, the flow pattern similarity principle was proposed to scale up a specially designed spout-fluid bed, which was aimed at maintaining the gas-solid contact efficiency, and was validated by electrical capacitance tomography (ECT) measurements. First, the traditional ECT method was developed for the specially designed MRIN spout-fluid bed according to the filling method. Then, the reconstruction algorithms were updated using the alternating direction multiplier method (ADMM) by introducing optimization constraints. The fluidization laws were investigated for different superficial gas velocities and distributor structures. We found that the gas distributor structure affected the merge point of the jets, which played an essential role in fluidization pattern changes. The statistically-based coefficient of variation (Cv) was proposed to distinguish the different flow patterns. Multi-ring spouting was then selected as a typical flow pattern for good fluidization and mixing, where the Cv ranged from 0.25 to 0.65. Then, the optimal design principles for the enlarged spout-fluid bed gas distributor were obtained. We determined that a smaller nozzle diameter (0.71d 0), larger nozzle spacing (1.12x 0), and slightly inclined angle (1.50θ 0) could improve fluidization, and that nozzle spacing was the most important factor. This study may be beneficial for the industrial design of the FB-CVD process and for the fabrication of high-density nuclear fuel particles. Additionally, it could be presented to a more general audience for scaling-up fluidized beds with a complex distributor, which would be beneficial for the fluidization research community.

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.

Using inclined vibrating plate (IVP) to gather spherical coated fuel particles is an important process in nuclear fuel particulate technology, especially in the manufacture of nuclear fuel elements for high-temperature gas-cooled reactor (HTGR). In order to get a satisfactory separation result, fuel particles are required to discharge uniformly and slowly into the IVP at a stable flow rate. To this end, the vibrating feeding system composed of a hopper and a new designed multi-layer multi-channel (MLMC) feeder is proposed in this paper to increase the discharge rate, optimize the uniformity of particle distribution and reduce the particle velocity near the outlet, which can produce a better separation of odd fuel particles. Subsequently, discrete element method (DEM) is used to investigate the motion of coated fuel particles in the feeding hopper. The accuracy of DEM is verified by comparing the experimental results with the simulation results. At the same time, the mass discharge rate (MDR) of particles in the hopper and the influence of geometry structure of hopper are studied. Finally, the motion of fuel particles in the new designed MLMC feeder is investigated, and the distribution characteristics of particles discharging out from the new feeder are analyzed. The simulation results demonstrate that the new designed feeding system can meet the optimal feeding requirements that the particles are discharged uniformly with the rather stable flow rate and the relatively lower particle velocity.

Particle coating process, one of the main methods to improve the particle properties, is widely used in industrial production and pharmaceutical industry. For the scale up and optimization of this process, a mechanistic and detailed study is needed or numerical simulation as an alternative way. Decomposition of substances usually involves multiple chemical reactions and produces multiple substances in the actual chemical reaction. In the study, a chemical reaction flow (CRF) model has been established based on kinetic mechanism of elementary reaction, the theory of molecular thermodynamics and the sweep theory. It was established with the comprehensive consideration of the decomposition of substances, deposition process, adhesion process, desorption process, hydrogen inhibition, and clearance effect. Then the CFD-DEM model was coupled with CRF model to simulate particle coating process by FB-CVD method, and the CFD-DEM-CRF coupling model was implemented in the software Fluent-EDEM with their user definition function (UDF) and application programming interface (API). The coating process in the spouted bed was analyzed in detail and the coating behavior under different conditions were compared at the aspects of CVD rate, coating efficiency, particle concentration distribution, particle mixing index and gas concentration distribution. It is found that the average CVD rate is 6.06 × 10−4 mg/s when the inlet gas velocity is 11 m/s and bed temperature is 1273 K, and simulation result agrees with the experimental result well. Average CVD rate and coating efficiency increase with temperature increasing, but decrease acutely with mass fraction of injected hydrogen increasing. The CFD-DEM-CRF coupling model can be developed as a basic model for investigating particle coating process in detail and depth and can provide some guidance for the operating conditions and parameters design of the spouted bed in the real coating process.

High sintering temperatures and high pressures are often needed for the densification of SiC. The sintering of SiC can be facilitated by adding Al2O3–Y2O3 oxides as the sintering additives. In the present study, the SiC@Al2O3–Y2O3 composite nanoparticles with a core-shell structure were designed and prepared using a slow co-precipitation method in the presence of urea. It was found that by slowing down the hydrolysis rate of the metal ions, Al(OH)3 and Y(OH)3 could be co-precipitated and uniformly coated on the surface of the SiC nanoparticles by a heterogeneous nucleation mechanism. After subsequent heat treatment, SiC@Al2O3–Y2O3 nanoparticles with amorphous Al2O3–Y2O3 layers of 2–3 nm were obtained. SiC ceramics with different oxides aids were prepared by sintering the core-shell nanoparticles at 1800–1900 °C under a pressure of 30 MPa. For SiC with higher additives of 20 wt%, evident volatilization of the oxide aids occurred at high temperatures with the segregation of the oxides. For the sample sintered at 1800 °C, dense SiC ceramics with uniform sintering aids distribution were obtained with the Al2O3–Y2O3 content as low as 5 wt% and a surface Vickers hardness of 31.5 GPa was obtained.

Odd-shaped coated nuclear fuel particles are the main reason for the failure in the manufacture of fuel element, and the sphericity separation of fuel particles is one of the most significant process to improve the safety of high-temperature gas-cooled reactor (HTGR). The separation of particles by inclined vibrating plate (IVP) is based on the different friction force acted by the distinct shapes of particles. In this paper, Discrete element method (DEM), which is a numerical simulation method for analyzing and solving the dynamic properties of discrete systems, is used to investigate the separation process on the IVP. In view of the realistic fuel particles are all non-spherical particles with irregular shape, the super-ellipsoid model is utilized to describe the particles in the DEM simulation. A method to evaluate the separation efficiency is proposed in this paper to quantify the numerical simulation results of particle sphericity separation. The relationship among the operating parameters such as amplitude, frequency and inclination angle is combed, and the selection of the optimal value of these parameters are obtained. The effects of feeding-rate and height of feeder are investigated, and the particle collision is analyzed to explain the effect of feeding-rate. A set of optimized parameters are proposed, and it is identified that the DEM simulation results received by using these parameters meet the requirement of the fabrication process of coated fuel particles.

This study presents a new approach based on fiber Bragg grating (FBG) sensors toward measuring instantaneous and continuous changes of residual strain and stress in glass during glass-to-metal (GTM) sealing process. The GTM seal consists of three components which include stainless steel housing, borosilicate sealing glass and Kovar pin. The temperature cycle of sealing process was from room temperature (20 °C) to 880 °C, and then back to 20 °C. It was found that residual strain in glass increased rapidly at the glass transition region and gradually reached an asymptotic value with the decrease of temperature. The axial residual stress measured by the FBG sensor was 194.35 MPa at 20 °C. In addition, finite element modeling (FEM) was conducted to provide theoretical support. Stress modeling revealed that axial residual stress at the location of sensor was 145.47 MPa. The experimental determination of the residual stress is highly consistent with the theoretical calculation.

Owing to the difficulty for dense SiC sintering, high sintering temperatures and pressures are usually needed. Lowering the sintering temperature by adding Al2O3 as a sintering additive has previously been shown to be beneficial. However, traditional addition methods limit the effect of the Al2O3 owing to inhomogeneous mixing at the nanoscale. A SiC@Al2O3 composite nanoparticle with a core–shell structure is designed and prepared using the slow co-precipitation method. The differences between this method and the traditional mechanical ball milling method are interpreted by different experimental parameters, such as temperature, pressure, amount of additive, and mixing type. It is found that the method of slow co-precipitation enables homogeneous mixing of Al2O3 and SiC at a smaller scale, and makes the sintered SiC much denser and more homogeneous, when compared with the traditional method. The parameters of sintering at 1900 °C and 30 MPa for 30 min are recommended. The conclusions here are also beneficial for the sintering research of other ceramic materials.

SiC@Al2O3 composite nanoparticles with core-shell structure were prepared by a slow precipitation method, aimed at improving the sintering ability of SiC. SiC nanoparticles with average particle size of 100 nm were prepared by a fluidized bed-chemical vapor deposition (FB-CVD) method. The Al(OH)3 coating was formed by slow precipitation of aluminum nitrate in urea solution. The coating layer was then transformed to Al2O3 after further heat treatment. By controlling the rate of urea hydrolysis and the aluminum nitrate concentration in the solution, the thickness of the coating layer could be adjusted. The results of X-ray diffraction (XRD), Scanning electron microscope (SEM), Transmission electron microscope (TEM) and Energy Dispersive Spectrometer (EDS) indicated that Al2O3 was uniformly coated on the surface of SiC particles and the two phases were closely contacted. The improved sintering ability of SiC@Al2O3 composite nanoparticles were validated, and better mechanical properties were obtained compared with the sintering results using the conventional ball milling method.

Particle coating is a very important step in many industrial production processes as the particle coating layers may fix surfaces with unique advantages. Given the limitation and disadvantages of the existing simulation methods, a coupled CFD–DEM–CVD multi-physical field model for particle-coating simulations has been established taking into account the velocity field, temperature field, concentration field, and deposition model. In this model, gas behavior and chemical reactions are simulated in the CFD frame based on the conservation laws of mass, momentum, and energy. The particle behavior is simulated in the DEM frame based on the gas–solid interphase force model and contact force model. The deposition behavior is simulated in the CVD frame based on the particle movement–adhesion–deposition model. The coupled model can be implemented in Fluent-EDEM software with their user definition function and application programming interface. The particle coating process involving the pyrolysis of acetylene was investigated, and the effect of bed temperature and inlet gas velocity on deposition rate and coating efficiency were investigated based on the proposed model with adjustable deposition coefficients. Both the average deposition layer mass and the average deposition layer thickness were found to be proportional to the elapsed time and increased at the rate of about 1.05 × 10−2 mg/s and 3.45 × 10−4 mm/s, respectively, setting the inlet gas velocity to 11 m/s and bed temperature to 1680 K. A higher temperature and larger inlet gas velocity lead to a larger deposition rate, but the coating efficiency decreases because of limits imposed by the chemical reaction. At a bed temperature of 1280 K, the average deposition rate is 7.40 × 10−3 mg/s when the inlet gas velocity is set to 11 m/s, which is about double the deposition rate when the inlet gas velocity is set as 5 m/s. The proposed model can provide some guidance for the operating conditions and parameters design of the spouted bed in actual coating settings and can also be further developed as a basic model of mechanisms to integrate detailed information across multiple scales.

We presented an efficient semi-analytical model-based analysis of methane transport in shale reservoirs including multiple horizontal wells with nanopores and complex hydraulic fractures. Multiple important gas transport mechanisms in nanopores such as gas desorption, gas slippage and diffusion and pressure-dependent fracture conductivity are fully incorporated in the model. Both simple and complex fractures in multiple shale-gas wells can be easily and effectively dealt with in accordance with the discretization approach, which does not require detailed gridding like numerical model. The superposition principle is utilized to capture the interactions between all fracture segments in order to accurately simulate real gas transport from matrix to fractures and finally from fractures to wellbores. We verified the semi-analytical model against a numerical compositional reservoir model for two shale-gas wells with multiple simple planar hydraulic fractures considering the gas desorption effect. The semi-analytical model was used to analyze ultimate gas recovery of different complex hydraulic fracture patterns in a two-well scenario, which were generated from a complex fracture propagation model with and without considering natural fractures. In addition, it was applied to perform field-scale simulation with multiple wells and complex fracture geometries in accordance with microseismic data. The simulation results show that multiple gas transport mechanisms, pressure-dependent fracture conductivity and complex fracture geometries play an important role in controlling well productivity and gas recovery, which should be properly accounted for in the physical model in order to achieve more accurate long-term production forecasting of multiple-fractured shale-gas horizontal wells.

Particle mixing is a very important process in many industrial reactors. It is important to consider how to quantify the particle mixing behavior accurately under different conditions. In this paper, the drawbacks of traditional mixing indexes, such as Lacey index are discussed, and then a novel particle mixing index, without grid dependency and particle color dependency was proposed based on the neighbor distance method and coordination number concept. Its characteristics such as parameters selection, calculation method and multi-direction were discussed in details. The proposed mixing index was used for investigating particle mixing behavior in the multiple-spouted bed under conditions of different gas velocity ratios and different particle density ratios. The experimental results have been used to validate the simulation results at first. It is found that the improved mixing index is more superior and effective compared with the traditional mixing index methods, and suitable for the investigation of particle mixing behavior. It was indicated that the density ratio is a key factor to influence particle mixing process. The novel particle mixing index without grid dependency and particle color dependency is recommended to study particle mixing behavior in other particulate processes in the future.

Plug flow receives attention due to its advantages of low particle attrition, low pipeline wear and low energy consumption. A novel non-mechanical draft tube type feeder (DTF) for plug formation has been proposed in our previous study for vertical plug conveying of coarse particles. We further investigate the influence of key geometry parameter of the DTF on plug formation for different particle diameter. Furthermore, we attempt to extend the application of PIV technique to evaluate plug velocity in pneumatic plug conveying. Experiments for vertical plug formation are conducted with glass beads of three kinds of particle diameter (i.e. 6 mm, 4 mm and 2 mm). Plug formation characteristics are examined in terms of flow pattern in riser pipe, solids mass flowrate and pressure fluctuation. The experimental results show that four main features of plug flow pattern in the riser pipe are observed. Solids mass flowrate displays good linear relation to superficial gas velocity forthe same particle diameter in the plug flow regime, even with different relative entrainment height. Some interesting phenomena are observed for the pressure fluctuation. Plug velocity is successfully obtained by PIV technique with high temporal resolution. The present study provides a further understanding of the flow pattern and dynamic behavior of coarse particles in vertical plug formation with the draft tube type feeder.

Nano- and submicron particles typically exist in the form of agglomerates. The shear flow, a common local flow, plays an important role in the breakage and restructuring of agglomerates. In this work, the discrete element method (DEM) with a cohesive contact model is used to simulate the dynamic evolution of agglomerates under shear flow. The results show that the size and structure of agglomerates at a steady state are the results of competition among the shear gradient of the flow field, the surface energy and the initial structure of the agglomerates. Based on the variation of the radius of gyration (Rg) and fractal dimension (Df) of agglomerates with time, the following three stages can be distinguished: (a) a stage dominated by stretch and breakage, (b) a stage dominated by agglomeration and densification, and (c) a stage characterized by the steady size and structure of agglomerates. With increasing shear gradient, the agglomerate fragments at the steady stage become smaller, more compact and more uniform. When the shear gradient is high, increasing the surface energy can result in larger fragments with a more compact structure. However, when the shear gradient is low, increasing the surface energy does not lead to larger fragments. The effect of initial structure on the stable size and structure of fragments disappears gradually with the increase in shear gradient. The detailed simulation results can improve the understanding and control of the size and structure of agglomerates in practical devices.

Carbonaceous dust can bring some potential threats to the safe operation of the high temperature gas-cooled reactor. Predictive models based on physical generation mechanism have produced errors in regards of actual observations. Thus, the chemical generation mechanism is worth investigating. This paper mainly analyzes the formation of carbonaceous dust by chemical vapor deposition with carbon monoxide and hydrogen mixture as feed gas. The adopted substrate is made of Inconel 617 alloy. The effect of hydrogen content and reaction temperature on the generation of carbonaceous dust have been investigated. The morphology and microstructure of the deposited carbonaceous dust have been characterized by scanning electron microscope, energy dispersive spectrometer, and Raman spectrum. The experimental results show that the production of the carbonaceous dust is almost in parabolic relationship with H 2 flow rate, while for the influence of reaction temperature, the result is much closer to exponential relationship. In addition, two kinds of carbonaceous dust particles, larger agglomerate particles and small isolated particles, have been observed.

The present work focused on fundamentally modelling of the fluidized bed chemical vapor deposition (FB-CVD) process, which is the extensively used method to prepare TRISO particles and other types coated particles, aimed at optimizing and scaling up of the coated fuel particles fabrication technology using a mechanistic approach rather than empirical knowledge. Based on the experimental observation of the coating process, the population balance model (PBM) was used to describe the size distribution of nanoparticles in the FB-CVD process. The deposition rate model related to nanoparticle size distribution was developed based on the homogeneous and heterogeneous deposition coexistence mechanism. Furthermore, on a macroscopic scale, the computational fluid dynamics (CFD) and discrete element method (DEM) were coupled with the deposition rate model, establishing a multiscale simulation platform for simulating the FB-CVD particle coating process. In this proposed CFD-DEM-PBM model, the mass, momentum, and energy transfer, along with chemical reaction, nanoparticle formation, deposition along homogeneous and heterogeneous pathways were considered and simulated accordingly. The preliminary study has been conducted successfully and indicates that the proposed multiscale model has clear and important significance for investigating the particle coating process. However, it should be noted that the model parameters still need to be experimentally refined in the future.

Vibration sorting is a common means in separating non-spherical particles from spherical particles. In this paper, the discrete element method (DEM) is applied to simulate the behavior of spherical particles and non-spherical particles motion on an inclined vibrating plate (IVP), and the influence of different operating parameters on the separation performance of the mixed particles is investigated. In the DEM simulations, both the spherical and non-spherical particles are modeled by super-ellipsoids. The simulation results show that the optimal vibration amplitude and frequency exist for the high separation efficiency of the mixed particles. The separation efficiency can also be enhanced by properly increasing the friction coefficient or decreasing the restitution coefficient between particles and plate. It is easier to separate the non-spherical particles from the spherical particles by diminishing the sphericity of particles. Besides, as long as the inclination angle of the plate is set at appropriate range and the feed rate of the mixed particles is moderate, the non-spherical particles can be separated effectively from the spherical particles. This research could be helpful for the understanding and optimal design of vibration sorting device.

Particle coating is an important method that can be used to expand particle-technology applications. Coated-particle design and preparation for nuclear fuel-element trajectory tracing were focused on in this paper. Particles that contain elemental cobalt were selected because of the characteristic gamma ray spectra of 60Co. A novel particle-structure design was proposed by coating particles that contain elemental cobalt with a high-density silicon-carbide (SiC) layer. During the coating process with the high-density SiC layer, cobalt metal was formed and diffused towards the coating, so an inner SiC–CoxSi layer was designed and obtained by fluidized-bed chemical vapor deposition coupled with in-situ chemical reaction. The coating layers were studied by X-ray diffractometry, scanning electron microscopy, and energy dispersive X-ray spectroscopy techniques. The chemical composition was also determined by inductively coupled plasma optical emission spectrometry. The novel particle design can reduce the formation of metallic cobalt and prevent cobalt diffusion in the coating process, which can maintain safety in a nuclear reactor for an extended period. The experimental results also validated that coated particles maintain their structural integrity at extremely high temperatures (∼1950 °C), which meets the requirements of next-generation nuclear reactors.

Absorber sphere pneumatic conveying is a special application of pneumatic conveying technique in the pebble bed High Temperature Gas-Cooled Reactor (HTGR or HTR). Granular discharge through a vertical pipe with a bend outlet is one of the control modes to determine solid mass flowrate which is an important parameter for the design of absorber sphere pneumatic conveying. Granular discharge rate through the vertical pipe with a bend outlet in the small absorber sphere system are investigated by discrete element method simulation. The effect of geometry parameters on discharge rate, the discharge rate fluctuation in the vertical pipe, and the effect of friction on steady discharge rate ( W s ) are analyzed and discussed. The phenomena of discharge rate fluctuation in the vertical pipe are observed, which are mainly resulted from the evolution of the average downward granular velocity. The steady discharge rate decreases rapidly with sliding friction coefficient increasing from 0.125 to 0.5, and gradually saturates with the friction coefficient further increasing from 0.5 to 1. It is interesting that the linear relation between W s 2/5 and pipe internal diameter D with zero intercept are found for the vertical pipe discharge with a bend outlet, which is different from the orifice discharge through a hopper or silo with none-zero intercept. A correlation similar to Beverloo’s correlation is developed to predict the steady discharge rate through the vertical pipe with a bend outlet. These results are helpful for the design of sphere discharge rate through the vertical pipe with a bend outlet in the small absorber sphere system of the pebble bed HTGR.

The gas-solid hydrodynamics of coarse particles in a two-dimensional spouted bed (2DSB) are measured using 6 mm glass beads to obtain quantitative experimental results. A one-dimensional mathematical model based on gas-solid mass and momentum balance is used to characterize the spout-annulus interaction and to further interpret the experimental results. The superficial velocity and static bed height are in the range of 2.58 to 4.39 m/s and 8.0 to 13.3 cm, respectively. Pressure fluctuation periodicity of the bed pressure drop is characterized by power spectral density (PSD) analysis. The whole-field particle velocity profiles in 2DSB are obtained by high speed CCD camera and PIV technique. The results show that particle motion in the spout in the present 2DSB experiments is dominated by the balance of drag force, solid stress and gravitation. The existence of obvious solid stress from particle impaction and friction leads to energy dissipation, which limits the increase of vertical particle velocity along the spout axis ( v yc ) in the spout and results in a flat stage of v yc with slight fluctuation near the bottom of the fountain. The solid stress also contributes to the nearly flat peak of lateral profile of downward particle velocity in the annulus. These detailed results are helpful for understanding the gas hydrodynamics and particle motion behavior of coarse particles in 2DSB, and for verification of the extended CFD-DEM coupling method for particle size approaching fluid cell size.

The influence of complex natural fractures on multiple shale-gas well performance with varying well spacing is poorly understood. It is difficult to apply the traditional local grid refinement with structured or unstructured gridding techniques to accurately and efficiently handle complex natural fractures. In this study, we introduced a powerful non-intrusive embedded discrete fracture model (EDFM) technology to overcome the limitations of exiting methods. Through this unique technology, complex fracture configurations can be easily and explicitly embedded into structured matrix blocks. We set up a field-scale two-phase reservoir model to history match field production data and predict long-term recovery from Marcellus. The effective fracture properties were determined thorough history matching. In addition, we extended the single-well model to include two horizontal wells with and without including natural fractures. The effects of different numbers of natural fractures on two-well performance with varying well spacing of 200 m, 300 m, and 400 m were examined. The simulation results illustrate that gas productivity almost linearly increases with the number of two-set natural fractures. Furthermore, the difference of well performance between different well spacing increases with an increase in natural fracture density. A larger well spacing is preferred for economically developing the shale-gas reservoirs with a larger natural fracture density. The findings of this study provide key insights into understanding the effect of natural fractures on well performance and well spacing optimization.

In this work, a comparative study of Euler-Euler and Euler-Lagrange approaches for modeling gas-solid flows in the multiple-spouted bed has been carried out to investigate the hydrodynamics of gas-solid flows. The influence of inlet gas velocity on the hydrodynamics of gas-solid flows in the multiple-spouted bed is investigated as well. Hydrodynamic characteristics of gas-solid flows such as flow behaviors, solid volume fraction, particle velocity and particle trajectory are analyzed and discussed in detail, providing some basic mechanism analysis of the gas-solids in the multiple-spouted bed. It is found that the central spout gas jet is a little confined by the auxiliary gas jets, and the hole-to-hole synergy is quite obvious when the auxiliary spout gas velocity is higher than the central spout gas velocity. When central/auxiliary gas velocity is 10/20 m/s, the maximum vertical particle velocities predicted by Euler-Euler and Euler-Lagrange approaches are 452 mm/s and 721 mm/s at the height of 10 mm respectively. A typical cycle period of a single particle is about 1.25 s, and the residence time in the spout regions is about 0.14 s in one cycle period in auxiliary dominant pattern. The curves of bed expansion height versus time calculated by Euler-Lagrange approach rise and fall periodically, while the curves calculated by Euler-Euler approach keep steady with little change. It is much easier for particles to be blew in the multiple-spouted bed using the Euler-Lagrange approach. The simulation results obtained from two models can provide some guidance for modifying the multiple-spouted bed to optimize physical operations such as drying and coating in the multiple-spouted bed.

Electrical capacitance tomography (ECT) is widely used in research for different applications, e.g. in the petroleum, pharmaceutical and power industries, due to its nonintrusive and noninvasive features and low cost. So far, ECT has been successfully used with regular structures, such as circular and square shapes. However, in some cases, the measurement electrodes cannot be mounted directly on an irregular structure, high temperature objects or corrosive objects. In this work, a method is proposed for ECT to be used with an irregular structure, by filling the gap between the irregular structure and a regular ECT sensor wall. Accordingly, a split matrix method is proposed for image reconstruction. The characteristics of sensitivity maps with the filling method and different structures are investigated. To calculate sensitivity maps, two methods are used: the perturbation method and the potential method, and their effects on image quality are compared. The results show that there is no obvious difference between these two methods for imaging construction, but the potential method is more efficient than the perturbation method. Among different shapes, an image of a triangular object has a large deformation due to its sharp angle and hence the filling method is not suitable for imaging a triangular object. The split matrix method modified by relaxation factors is suitable for irregular structures in general and can generate satisfactory images. A hardware system based on an impedance analyser and a software package have been developed and used to validate the proposed methods. The experimental results show that the proposed method is promising for imaging two-phase flows in irregular structures.