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An extended hard particle method-discrete element method coupled model (EHPM-DEM) is proposed to simulate the drainage of square particle in 2D hoppers. The EHPM extends the hard sphere model to adapt for non-spherical shapes. A vertex-based extension of DEM is developed to solve collisions of square particles. A new coupled method is proposed, using the EHPM to simulate binary collisions and DEM to simulate multiple contacts. The collision between two triangles and the drainage of square particles in hoppers were simulated and compared to theoretical analysis and experiments, respectively, for validation. Moreover, the advantages of EHPM over DEM and the EHPM-DEM coupled solution over the pure soft DEM solution in computational efficiency have been demonstrated. In addition, the effects of restitution coefficient, friction coefficient, and the filled height on the discharge rates are analyzed, and a uniform discharge feature is discovered, which is especially useful for scaling studies. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1863-1876, 2016 [ABSTRACT FROM AUTHOR]

A thermal discrete element method (DEM) is used to simulate particle mixing and heat conduction inside wavy drums to explore the effects of wavy walls. Sinusoidal configurations with different waves on the walls are simulated. The Lacey mixing index is applied to analyze the mixing characteristics. The driven forces from the wavy wall, either positive/negative or effective driven forces, are analyzed to explain the mechanisms of mixing enhancement in the wavy drum. A new control parameter is proposed to explain the mechanism of mixing enhancement. It is found that a locally oscillating effect exists in wavy drums, which is imparted on the bulk rotating motions of particles and enhances the characteristics of particle mixing and heat conduction significantly. Except over large wave numbers and rotating speeds when the flow regime is deteriorated for mixing, the wavy drum is generally beneficial for mixing augmentation as well as conduction enhancement. [ABSTRACT FROM PUBLISHER]

The mixing characteristics of cubic particles in a cylinder mixer are analyzed by the SIPHPM simulation in comparison with spherical particles. The assembly of cubic and spherical particles of uniform size is pre-divided into two parts in the axial, circumferential or radial directions respectively. Then they are mixed when the cylinder is rotated at different rotational speeds of Ω d  = 15–60 rpm. The mixing degree is evaluated by either the Lacey mixing index or the mixing information entropy. A normalized mixing entropy is proposed here to compare the absolute degree of mixing with non-equivalent particle numbers. It is found that, for cubes, the radial mixing efficiency is higher than the circumferential, and the radial and circumferential mixing degrees are both larger than the axial. Compared with spheres, cubic shape may enhance the circumferential mixing whereas reduce the axial mixing levels at high rotating speeds. However, at low rotating speed, cubic shape always reduces the degree of mixing of all the three patterns. Moreover, the axial dispersion characteristics are also explored by the probability density functions and the axial paths. The spatial and temporal diffusion coefficients of concentration and kinetic energies are illustrated and used to explain the axial dispersion mechanism in analogy with diffusion equation. The mean diffusion coefficient of rotational energy is independent of rotating speed, which means the axial diffusion of rotational energy depends on the eccentric feature of cubic particle, i.e. rotational ability. In contrast, it is preferred to regard the axial dispersion mechanism of spheres as convection rather than diffusion. [ABSTRACT FROM AUTHOR]

In conventional CFD-DEM based on the cell-averaged-volume-fraction (CAVF), mesh size for gas phase is required to be larger than particle size. It is good for fine particles, whereas too coarse for large particles. A conservative virtual volume fraction method is proposed here for sub-particle LES-DEM coupled simulation of large particles. Although still based on CAVF, mesh size is smaller than particle size, and the LES-DEM coupled solution on finer grids incorporating the Smagorinsky sub-grid-scale stress tensor is proposed. The feedback force is redistributed onto the finer grids to perform the four-way coupling on fine scales. It is conservative for the inter-phase interactions between the super-particle (for drag force) and sub-particle (for feedback force) scales through the same distribution function. The 2D case and the 3D cases with or without LES are performed to demonstrate the capability of this model, and validated by an experiment of spouted bed. The important features on gas-phase are illustrated to demonstrate the application for capturing the gas-phase behavior on sub-particle scales. [ABSTRACT FROM AUTHOR]

The discharge of regular noncircular particles through a hopper orifice is simulated by discrete element method. A novel approach of incorporating distributed sub-spheres around the non-spherical particle borders is developed. The aim of this work is to explore the effect of roundness on the discharge behavior as well as relevant mechanisms of hopper discharge. Seven types of non-spherical particles, i.e. triangular, quadrilateral, pentagonal, hexagonal, heptagonal, octagonal and decagonal shaped particles, are chosen for comparative study. They are respectively discharged freely from the hopper beds of three different base angles, i.e. α = 65, 70 and 75 ° . The discharge process, fraction, flow rate, and voidages are analyzed to show the effect of particle roundness on discharge characteristics. [ABSTRACT FROM AUTHOR]

A DEM study of a rocking particle bed is performed to show the effects of rocking frequency and amplitude on particle discharge. Six rocking frequencies of f r = 0, 0.1, 0.2, 0.3, 0.4, 0.5 Hz with seven rocking amplitudes of θ r = 5°, 15°, 30°, 45°, 60°, 75° are simulated respectively. The particle distributions, discharged fractions, flow rates, particle trajectories and kinetic energies are compared and analyzed in detail to show and explain the features of particle discharging process under different rocking conditions. The rocking frequency is found to be the primary factor to determine the direction of influence on particle discharge, i.e. either beneficial or detrimental, whereas the rocking amplitude is the secondary factor to magnify the primary influence on particle discharge. In addition, the flare angle of the bed can determine the mode of influence on particle discharge, i.e. either a linearly varied discharge or an oscillated variation of discharge. The results are helpful to improve the process control and optimal design of the particle discharge beds in many engineering applications. [ABSTRACT FROM AUTHOR]

• For the solid-phase oxygen control LBE system, numerical simulations are performed for the 1:1 scale 3D UPBEAT loop. • Simulation results are in general agreement with experimental results at about 350℃ and empirical correlations at 500℃. • The mass transfer coefficient increases with the temperature and it reaches its maximum at about 475℃. The Venturi-type solid-phase oxygen control system with a bypass mass exchanger is widely regarded as an effective approach to keep the oxygen concentration in the LBE under reasonable ranges to reduce the corrosion. In this work, numerical simulations of the particle–fluid mass transfer of the oxygen concentration in LBE are performed for the 1:1 scale 3D UPBEAT loop under various conditions. The discrete element method is applied to generate the geometry of the packing of the PbO spheres. The velocity profile and oxygen concentration governing equations are solved by using the SST turbulence model. At the same temperature, the oxygen mass transfer coefficient increases monotonically with the flow rate. At the same mass flow rate, the mass transfer coefficient increases with the temperature, reaching a maximum at about 475 °C. It provides guidance for future research in the design and optimization of oxygen control systems under high temperature in lead–bismuth nuclear reactors. [ABSTRACT FROM AUTHOR]

• A force-heat transfer-analogy-based novel contact thermal resistance model is proposed. • Resembling Heat-flux by stress distribution makes free of singularity at the contact edge. • The model is validated in SC/FCC/BCC configurations and incorporated into thermal DEMs. • Appling to HTTU, temperature, ETC distributions and dynamic thermal responses are derived. • Increasing T out-wall from 200 to 1000 °C causes 20 % increase of effective thermal diffusivity. A novel particle-to-particle contact thermal resistance model is proposed in this study, based on the concept of analogy between force and heat transfer. The distribution of heat flux on the contact surface is assumed to resemble the distribution of stress, eliminating the issue of temperature singularity at the contact edge. The model is validated against existing theories and experiments, showing good agreement. The combined use of the model and the thermal discrete element method is applied to analyze temperature and effective thermal conductivity distributions in a pebble bed within a high-temperature test unit. The average effective thermal conductivity obtained from thermal conduction is found to be 2.99 and 2.61 W/(m·K) for power inputs of 20 kW and 82 kW, respectively. An increase in the outer wall temperature from 200 °C to 1000 °C results in an approximate 20 % increase in the effective thermal diffusivity. [ABSTRACT FROM AUTHOR]

Highlights: [•] We show a detailed analysis of void fraction (VF) in HTR-10 of China using DEM. [•] Radial distribution (RD) of VF is uniform in the core and oscillated near the wall. [•] Axial distribution (AD) is linearly varied along height due to effect of gravity. [•] Steady RD of VF in the conical base is Gaussian-like, larger than packing bed. [•] Joint linear and normal distribution of VF is analyzed and explained. [Copyright &y& Elsevier]

Based on the discrete element method (DEM) and GPU parallel computing, a particle heat transfer model is developed to simulate the heat transfer in a pebble bed of the high-temperature gas-cooled reactor (HTGR). The model is implemented based on a previously developed GPU-DEM program by our team and uses the mesh-based neighbor searching algorithm for the heat transfer calculation. This model couples the conduction and radiative heat transfer between the pebbles and incorporates neural networks and empirical fittings to calculate the radiation view factors, which can improve computational efficiency. The effective thermal conductivity of different models and experimental data are used to verify the accuracy of the model, and the influence of different radiation heat transfer models on the results is also compared. The results show that the effective thermal conductivity derived from the current model is comparable to the classical models at different temperatures, and the numerical simulation results based on the current model are in good agreement with the corresponding experimental data. Additionally, the model achieves a single-core speedup ratio of 126–395 times with GPU acceleration, significantly enhancing computational efficiency. In conclusion, the current model has been effectively verified for accuracy and computational efficiency, and it demonstrates great potential in dealing with large-scale pebble flow and heat transfer challenges in HTGRs. • A Voronoi-tessellation-free new heat transfer model is proposed for pebble beds. • View factors are calculated by neural networks to couple conduction and radiation. • GPU parallel computing is employed at a speedup ratio of 126–395 times of CPU. • An alternate-read-write method and unified Memory Access technology are used. • The model accuracy is validated and discussed by comparing it with experiments. [ABSTRACT FROM AUTHOR]

As an important class of particle flows in industrial applications, hopper flows, particularly those using pebbles (diameters d p ~ O (10-2) m), play a significant role in nuclear reactor engineering, e.g. HTGR and ADS reactors. However, the features and influencing factors of the binary mixture discharge have not yet been widely investigated. In this study, the discrete element method (DEM) simulation was adopted to analyze the discharge flow of binary mixtures consisting of ellipsoids and spheres in a hopper. After a model validation, the effects of particle aspect ratio (R a , the ratio of the major axis to the minor axis) of ellipsoids and component ratio (R n , the ratio of the ellipsoid number to the sphere number) of ellipsoids to spheres were analyzed. Flow patterns were visualized by colored pebble stripes according to pebbles' initial heights. Particle discharge flow rates were computed to examine their relations to particle aspect ratios and component ratios. The force structure and distributions of the binary mixtures were also explored. Results showed that pebble stripes followed quadratic function profiles. Adding ellipsoids was advantageous for particles discharging at lower particle aspect ratios (R a ≤2), while impedimental at large particle aspect ratios (R a ≥3). The discharge flow rate was inversely proportional to the particle aspect ratio at fixed component ratios, and linearly proportional to the 1/4th power of the component ratio at fixed particle aspect ratios. In addition, the discharge flow rate showed low sensitivity to the initial packing states of particles when the particle aspect ratio and component ratio were fixed. Unlabelled Image • Discharge of binary mixture of ellipsoid and sphere in a hopper is simulated by DEM. • Effects of ellipsoid on discharge is analyzed by aspect ratio and component ratio. • Flow pattern stripes are visualized and featured out by quadratic functions H ~ ar 2. • Relations between flowrate and aspect ratio and component ratio are analyzed. • Force structure and distributions of binary mixtures are demonstrated and analyzed. [ABSTRACT FROM AUTHOR]

• Effect of density difference on packing structure and flow pattern are studied. • Equivalent density and voidage are analyzed to describe spatial distribution. • Light particles tend to be pushed to side walls by heavy ones during circulation. • Higher density ratio may lead to more obvious squeezing phenomenon. • Different velocity patterns in lower and upper parts of the bed are observed. Based on the discrete element method, this work simulates the mixing flow of particles with different density in packed bed. The aim of this work is to explore the effect of density difference on the spatial distribution and flow characteristics of particles. After a premixed stacking, the particles start to discharge at fixed number rates being extracted from the bottom and then reinserted into the top of the bed to maintain the circulating flow. The results reveal that although different density can affect the local equivalent density, it has little influence on the uniformity and compactness of the whole bed with overall average voidage of about 0.39. The wall effects on particle distribution and voidage are observed near the wall. In addition, during the unloading time (time after the start of discharge), the proportion of light particles near the wall is always higher than 0.5 and keeps increasing. The increasing proportion and much higher number fraction of light particles compared with heavy one indicate that the heavy particles have the tendency to push the light particles to the side during the circulation process. Besides, the higher the ratio is, the more obvious this phenomenon is. Last but not least, both the axial and radial velocity profiles are analyzed, which show different patterns between the bottom and upper part of the packed bed. [ABSTRACT FROM AUTHOR]

Highlights • LB-IB-DEM simulation of pebble bed recirculation in HTGR is conducted. • Velocity, FFT and correlation analyses are used to explore gas-pebble two phase flows in HTGR. • Slow gas-pebble flows in HTGR have intermittent and periodic mass flow pattern. • Gas-pebble interaction follows a simultaneous and linearly-dependent two-phase flow pattern. • Helium-pebble flow in real HTGR is predicted to be dominated by pebble recirculation. Abstract The pebble bed is one type of the core of the high temperature gas-cooled reactor (HTGR), which is regarded as the candidate of the generation IV advanced reactor. It is important to explore the gas-pebble flow characteristics and the pebble recirculation under the helium atmosphere. In this work, we presented a lattice Boltzmann (LB) method – immersed boundary (IB) method – discrete element method (DEM) coupled approach to simulate a test facility of pebble bed under the recirculation mode of operation. After model validation by an experiment of sphere sedimentation, the process of pebble recirculated at five constant rates are simulated. The correlations of gas motion and pebble motion in the upper and lower half beds are analyzed to uncover the inter-phase relationships for such intermittent pebble flows. Based on the systematic analyses of the two-phase flows, including the mean field and r.m.s field, the historical variation, inter-correlation, and the spectrum and phase space representations, we found sufficient evidences for the characteristics of intermittency, simultaneity, periodicity, and linear dependence for the inter-phase interaction of gas-pebble flows. [ABSTRACT FROM AUTHOR]

The core of the high temperature gas-cooled reactor (HTGR) is a dense packed pebble bed with large-sized fuel spheres. In the CFD-DEM simulations of fluid-particle systems on sub-particle scale mesh, a smoothed void fraction method (SVFM) is developed to compute the void fraction field based on the particle position and volume. A diffusion function is obtained analytically as a spatial distribution function of particle volume in SVFM, which converges to the step-function-type distribution of particle volume in the sub-particle-scale divided finite volume method (DFVM) when the smoothing degree goes to 0. In validation by a spout fluidized bed when the cell size is less than the particle diameter, it is shown that SVFM is preferable to DFVM for the CFD-DEM simulation since it is in better agreement with the experimental measurements. Moreover, the CFD-DEM simulation using the SVFM on sub-particle scale meshes is performed for the benchmark problem of the HTR-10 reactor. The numerical results at the smoothing degree of η  = 0.5 are in good agreement with the empirical code of THERMIX – which is based on experimental measurements. In addition, the discussion indicates that the smoothing degree in SVFM is recommended to be 0.5–0.7 according to the void fraction distribution of Voronoi-tessellation. [ABSTRACT FROM AUTHOR]

To study the non-circular effect, the mixing of polygonal particles in a rotating drum is simulated by the soft-sphere imbedded pseudo-hard-particle model (SIPHPM method). Eight particle shapes ( N s = 3–10) are filled in the drum at rotating speeds ( ω = 0.5–3 π /s) respectively. The mixing process, quality, velocity and kinetic energy are analyzed by the mixing index and entropy. A cluster-like upcasting motion is found especially for square particles at the rapidest rotation. The mixing index and entropy show consistent variations of mixing degree. Two mechanisms can affect the mixing entropy, through either the static covering related to shapes or the concentration reduction in rolling/cascading/cataracting process related to the rolling capability. Only the first mechanism affects the mixing index. They are both used to explain the effects of particle shape on mixing from the points of view of overall dispersion uniformity and local concentration. The mixing index indicates higher mixing degree for the square, hexagonal and triangular shapes. Except the triangular and square shapes, other shapes play similar characteristics in the area fractions of the flowing core and static base, as well as the radial distributions of the mean and fluctuation velocities. Under the same rotating speed, the particle kinetic energy increases with N s , which is caused by the reduction of energy dissipation with a better roundness of particle shapes. [ABSTRACT FROM AUTHOR]

The effects of recirculation flow rates on the dense pebble flow (DPF) in a drained pebble bed are investigated through DEM simulation. After validation by experimental data, the velocity characteristics are analyzed and obvious intermittency characteristics are observed. The profile features and the shapes of the velocity distributions are estimated considering the flatness and symmetry for all flow rates. Fluctuation is estimated by the statistical parameter coefficient of variation and the newly proposed relative fluctuating kinetic energy (RFKE). Furthermore, the multi-fractal analysis of the velocity signals is carried out by the multiplicative cascade method (MCM). It has been found that the pebble flow follows the fractal phenomenon, and the intermittency of pebble flow has been measured quantitatively by the multi-fractal analysis. The increased flow rates always indicate smaller intermittency and higher frequency fluctuation, and vice versa. A new intermittency index C is proposed to quantitatively describe the intermittency of the DPF. The categorization of flow regimes of DPF has been discussed based on the analysis of combined parameters, i.e. the intermittency index C and relative fluctuating kinetic energy (RFKE). [ABSTRACT FROM AUTHOR]

Blockage has a significant impact on the flow and heat transfer characteristics of particles in discharging process and can affect the system security seriously. In this study, the discrete element method (DEM) was adopted to analyze the discharge flow of pebbles, ellipsoids, and cubes. The mechanism of blockage formation is the mechanical interaction between particles. With the increase of axial force, the frequency of the blockage increases. High probability of blockage formation arises when the local axial velocity difference d v z l is less than 0.075, while a large local difference in axial velocity (d v z l ≥ 0.075) can efficiently avoid blockage. With the increase of the bottom cone angle α of the geometric of the packed bed, blockage during particle flow can be avoided. When α increased to 60°, the particles of R d less than 0.248 can be discharged smoothly. In addition, the coefficient of friction μ between particles, the ratio of particle diameter to discharge orifice diameter R d and the aspect ratio R a of non-spherical particles are all factors influencing the formation of blockages. The critical conditions for particle blockage formation were proposed. For actual working condition of engineering, the application of R d less than 0.24 and μ less than 0.4 can effectively avoid blockage formation and ensure relatively safe operation for spherical particle systems. For ellipsoidal particles, low aspect ratio ( R a ≤ 4) can effectively avoid blockage. • Formation mechanism of blockages of particles in the hopper discharge is analyzed. • Shape parameters are proposed for optimizing the flow stabilities during discharge. • Local velocity difference is proposed as a decisive parameter of blockage formation. • Particle shape effect on the arch structure is analyzed after the blockage is formed. • Particles of R d ≤ 0. 248 can be discharged smoothly when bottom cone angle α ≥ 60 °. [ABSTRACT FROM AUTHOR]

Thermal radiation is important in high temperature packed pebble bed, which is still poorly understood. The present work is to analyze the effect of spatial scale in modeling thermal radiation of packed pebble beds. The long-range model (full integral scale), short-range model (partial integral scale) and microscopic models (sub-particle scale) are compared and analyzed with reference to existing correlations. In high temperature packed pebble beds, the long-range model takes into account all possible radiation between surrounding spheres, even those that are not direct Voronoi neighbors, whereas the short-range model considers only a portion nearby. It is found that when solid conductivity is much greater than the effective thermal conductivity of radiation ( k s ≫ k r or Λ > 10), the long-range model provides better results than the short-range model in predicting the radiative heat exchange. The short-range model overestimates solid conductivity at low temperatures (lower than 1215 °C) when k s ~ O ( k r ) (or Λ < 10) while underestimating radiative heat exchange. It therefore still provides predictions for total heat exchange that is in good agreement with experimental data in cases where the errors cancel out. Moreover, the short-range radiation model is more computationally efficient than the long-range model and microscopic model to compute view factor between particles of Voronoi neighbors. [ABSTRACT FROM AUTHOR]

A wide range of gravity-driven dense granular flows are studied numerically by using the discrete element method and statistical analysis. Intermittency and avalanche phenomenon of slow granular flows are illustrated clearly. Through analyzing time-energy data of flows with different velocities, the transformation of flow behavior from quasi-static to kinetic regimes is observed. More importantly, a general statistical rule on time-energy distribution of dense granular system under gravity is suggested. Based on this rule, the gravity-driven dense granular flows can be characterized quantitatively and categorized into three sub-regimes according to their primary features. [ABSTRACT FROM AUTHOR]

Friction affects pebble flow pattern in pebble-bed high temperature gas-cooled reactor (HTGR) significantly. Through a series of three dimensional DEM (discrete element method) simulations it is shown that reducing friction can be beneficial and create a uniform and consistent flow field required by nuclear engineering. Particle–wall friction poses a decisive impact on flow pattern, and particle–particle friction usually plays a secondary role; relation between particle–wall friction and flow pattern transition is also concluded. Moreover, new criteria are created to describe flow patterns quantitatively according to crucial issues in HTGR like stagnant zone, radial uniformity and flow sequence. Last but not least, it is proved that friction control of hopper part is more important than that of cylinder part in practical pebble beds, so reducing friction between pebbles and hopper surface is the engineering priority. [ABSTRACT FROM AUTHOR]

Crystallization of pebbles in pebble bed is a crucial problem in high temperature gas-cooled pebble-bed reactors. This phenomenon usually happens along the internal surface and leads to a large number of stagnated pebbles, which poses a threat to reactor safety. In real reactor engineering, wall structures have been utilized to avoid this problem. This article verifies the crystallization phenomenon through DEM (discrete element method) simulation, and explains how wall structures work in preventing crystallization. Moreover, several kinematic parameters have been adopted to evaluate wall structures with different shapes, sizes and intervals. Detailed information shows the impact of wall structure on flow field in pebble bed. Lastly, the preferred characteristics of an effective wall structure are suggested for reactor engineering. [ABSTRACT FROM AUTHOR]

The pebble size is one of the factors affecting the flow characteristics of pebble-bed HTGRs. The binary-sized circulating pebble flow is investigated from the perspective of flow behaviors and packing structure. The discharge characteristics including discharge number and volume discharge rate, which are closely related to the equilibrium of the HTGR pebble bed, are explored. The results show that the proportion of each type of pebble maintains stability during circulation when the loading ratio is consistent with its number ratio (NR). From the qualitative and quantitative analysis of the retention, it is found that the size difference has no significant effect on the retention, and it takes nearly 1.7 ideal circulating periods for initially loaded pebbles to flow out in all cases. In addition, the actual retention period also shows no difference. Furthermore, the packing structure is investigated through arc-based analysis of porosity and packing fraction, number distribution, and coordination number. [Display omitted] [ABSTRACT FROM AUTHOR]

• Two ways of changing the outlet are compared to study the flow features in HTGRs. • Flow transition occurs earlier when reducing the outlet with fixed hopper height. • The flow pattern depends largely on the hopper angle rather than the hopper height. • Increasing the outlet improves the retention, sequence value and flow uniformity. • Changing the outlet by height does not affect pebbles within 1d from the wall. The effects of outlet size on the flow characteristics in the pebble bed are studied by means of Discrete Element Method (DEM). Two ways of changing the outlet are considered: fixed hopper angle ('D' cases) and fixed hopper height ('d' cases). The pebble flow inside pebble beds shows the characteristics of mass flow in the upper part and funnel flow in the lower part, therefore, the changes in the flow pattern are studied first to find out the special transition region by critical time and critical height. Results show that the transition of flow pattern will occur earlier when the opening is smaller, and the critical height of transition increases with the decrease of outlet size for 'd' cases. By contrast, there is almost no difference in the critical time and height in 'D' cases, indicating that the hopper angle is an important factor affecting the overall flow pattern rather than the hopper height. In the second part, from the perspective of core safety, the influences of outlet size on the retention, flow uniformity and velocity characteristics inside the core are analyzed. The increase of outlet size can improve both the retention and flow uniformity. Changing the outlet by adjusting the hopper angle has a more significant influence on the flow performance. From the analysis of pebbles in different radial positions, it can be found that although pebbles in the middle region flow out slower when the opening is larger, it is opposite in terms of pebbles near the wall, where less retention is observed. Overall, a larger proportion of pebbles are in motion with relatively small but similar speed, showing a more uniform movement. Interestingly, simply changing the hopper height to adjust the opening has no effect on the flow of pebbles within 1d range from the wall. [ABSTRACT FROM AUTHOR]

• Eight 3-D structures (3DS) are designed and circulating pebble flows are studied. • Constructing two new indices to analyze the mixing of the upper and lower pebbles. • 3DS impedes near wall pebble flow, increases cycling speed and mixing at the core. • Triangular/helicoidal 3DS are better in speeding up and enhancing mixing. • Saturation phenomenon for the number of structural grooves in 3DS is found. The pebbles' movement in the pebble beds of 10 MW high-temperature gas-cooled test reactor (HTR-10) presents as a kind of circulating quasi-static dense pebble flow. The mixing of the upper and the lower fuel pebbles is important because the fast and good mixing is beneficial to flattening the power distribution and lowering the maximum temperature in the lower part of the pebble bed, where the temperature is higher than other region because of the higher burn-up of fuel pebbles. To figure out the effect of different three-dimensional (3-D) wall structures on the flow and mixing of pebbles, eight 3-D wall structures are designed and mono sized pebbles with same density are adopted to simulate by discrete element method (DEM). With phenomenological methods and different mixing indices, qualitative and quantitative analysis are performed and presented hereinafter. All selected wall structures have different degrees of effect on impeding the pebble flow near the wall, accelerating the cycling speed of pebbles at the core region and strengthening the mixing of the upper and lower pebbles in the pebble bed. Compared with the designed trapezoidal and plane structures, triangular and helicoidal structures perform better in accelerating the cycling speed for pebbles at the core region and strengthening the mixing of pebbles by analyzing cycle index (CI), coordination-Lacey's rule mixing index (CLMI) and coordination-concentration based mixing index (CCMI). In addition, a phenomenon of saturation for the number of structural grooves is reported in this literature. That is, the effect of accelerating the cycling speed of pebbles at core zones and strengthening the mixing gets closer to a certain degree if we make the different grooves denser. The optimal structure to accelerating cycling speed for pebbles in core zones and improving mixing is triangular structure among the four kinds of structures, while the optimum solution for the number of grooves requires deeper investigation. [ABSTRACT FROM AUTHOR]

• Discharge process of pebbles after liquids entering the reactor core is analyzed. • DEM with liquid bridge model are used to study discharge of wet pebbles. • Effect of liquids on discharge rate and velocity profile are analyzed. • Effects of liquid properties and contents on discharge process are compared. • Deep Neural Network (DNN) prediction model of residence time is proposed. The study of particle discharge flow is significant in industrial processes,especially wet cohesive particles. In this paper, the discrete element method (DEM), cohesion model and the viscous force model are used to study the influencing parameters of the discharge flow characteristics of cohesive system in three-dimensional packed bed. The cohesion between particles is described by liquid bridge model, the Bond number Bo and liquid content W are used to study the cohesive behaviour. The discharge efficiency decreases with the increase of particle viscosity. When Bo ⩽ 0.1 or W ⩽ 6 % , the uniformity of the particles in the hopper along the direction of gravity is basically the same of non-cohesive particle, but cohesive particles have a greater horizontal velocity fluctuations in the central area. The residence time t r of particles increases with the increase of cohesive force. The research results help to better understand the discharge characteristics of cohesive particle and provide a reference for the discharge behavior of the reactor core, especially under adverse damage conditions. Based on the simulation data, a Deep Neural Network (DNN) prediction model of residence time is proposed. The DNN prediction model was proposed to train the simulated data and predict the residence time of the particles in hopper based on the initial coordinates of each particle. After training and verification on more than 600,000 data, it has reached an accuracy rate of over 98% and meets the needs of engineering calculation. [ABSTRACT FROM AUTHOR]

• Embedded discrete element is proposed to compute force & heat transfer of particles • DEFEM realizes coupled simulation of deformation, movement & heat transfer of solids • DEFEM combines FEM and DEM, and avoids overlapping and penetration of meshes • DEFEM supports parallel computing and three times faster than a pure FEM solution • Particle deformation and heat transfer in packed layers are simulated and discussed. A new discrete element-embedded finite element method (DEFEM) scheme is proposed here, which solves the contact force and heat conduction of particles with embedded discrete elements (EDE), employs the finite element method (FEM) to get the deformation and internal temperature change of particles with heat and stress on the boundary and employs the discrete element method (DEM) to obtain the movement of particles. The DEFEM is characterized by coupling the deformation, motion and heat conduction of particles.Compared to either merely DEM or pure FEM, DEFEM combines the solution ideas of the FEM and DEM, and avoids the problem of overlapping and penetration of mesh elements in FEM. DEFEM also supports parallel computing, which is about three times faster than a pure FEM solution. As a demonstration, we developed an in-house code to perform DEFEM to simulate the extrusion and heat conduction of packed pebble bed, in comparison with a pure FEM solution for reference. Based on the numerical results, the characteristics of particle deformation and heat transfer in different extrusion speeds and layers are discussed. [ABSTRACT FROM AUTHOR]

• Discrete element method and super-ellipsoid model are used to study pebble flow. • Particle shape effect on discharging pebble flow in HTR-10 reactor core is analyzed. • Shape effects on discharge flow rates and velocity distribution are compared. • Shape effects on rotation of particles during discharging process are analyzed. • Proposed shape parameters for optimizing discharge flow performance are given. The discharge flow characteristics of particles are crucial in many industrial applications, and the shape of particle is an important influencing factor to the particle flow behavior. In this study, the discrete element method (DEM) was adopted to analyze the discharge flow of non-spherical particles in HTR-10 reactor core. After model validation, the shape effect on particle flow in hopper was analyzed. The super-ellipsoid model was used to the comparative study of particles with 5 different shapes which can represent a large number of shapes, including oblate ellipsoidal particles, prolate ellipsoidal particles, circular cylindrical particles, elliptical cylindrical particles, and cubical particles, respectively. The results showed that the more stable the packing structure, the higher the efficiency of the stacked volume. But the mobility of these particles was worse than particles with good flow properties. The increase in the blockness ( n 1 and n 2 ) will make the fluidity of the particles worse, and the particles with aspect ratio ( R a ) between 1.5–2 show better discharge behavior. Both the axial and radial velocity can be influenced by particle shape significantly, which will result in different discharge behavior. Rotation angle and direction angle distribution are introduced to analyze the rotation motion. Cylindrical particles showed the most obvious rotation, while the ellipsoidal particles rotated in a relatively small range. [ABSTRACT FROM AUTHOR]

After reexamining three mechanisms of thermal resistance in packed bed: particle-particle conduction through a finite contact area (PPA), conduction through a contact point (PPP), and through stagnant fluids near the contact point (PFP), a full mechanism model of contact thermal resistance (CTR) and the effective thermal conductivity (ETC) of particles with stagnant interstitial fluid is proposed here for thermal discrete particle simulations (TDEM). The current model agrees with experimental data of various conductivity ratios and void fractions, and can be applied for both dense and dilute gas-particle systems. It shows that the PPA mechanism is dominating when the conductivity ratio of particle-to-fluid κ is greater than 104. Moreover, when κ < 2000, the PPP mechanism becomes dominant and the PPA mechanism can be neglected. All these mechanisms incorporated in current model can be naturally imbedded in thermal discrete thermal method (TDEM). [ABSTRACT FROM AUTHOR]

• 3D pebble flow in HTR-PM of different base shape, friction & loading mode is studied. • 3D pebble stripe, spindle & streamline by Lagrange & Euler description are analyzed. • Pebble flow is rather uniform with weak diffusion & dependence on base angle. • It has perfect mass flow is main body & funnel flow pattern within conical base. • Pebble streamline is tanh-like & not affected by friction, recirculation mode and rate. This work shows basic features of pebble flow in HTR-PM via DEM simulation, in accompany with pebbled beds of varied base angles, friction coefficients and recirculation modes. The effects of base angles, friction coefficients and recirculation modes on the characteristics of pebble flows are explored. Beside phenomenological observation by pebble stripes, the three-dimensional pebble spindles and pebble streamlines defined in the Lagrangian and Eulerian framework respectively are all computed and analyzed quantitatively to give full description of pebble flows. The probability density function of horizontal distribution is computed to quantify pebble diffusion in the pebble spindle. The pebble streamlines are also fitted with modeling functions well to give useful indications for reactor design, and the fitting coefficients under various conditions are provided. The simulation results will be useful for better understanding and predictions of the real pebble beds, as well as their influencing factors. [ABSTRACT FROM AUTHOR]

• Full integral scale gray-body radiation modellings of packed granules are discussed. • Black radiation model of black surface is proven to be valid strictly in packed bed. • P-P & P-W radiation is independent of emissivity in uniform radiation model. • Unreasonable to assume uniform radiation flux and radiosity on particle surface. • Particle scale radiation model is derived to predict radiation flux in DEM. • Effect of emissivity is proved a separable term in radiation heat transfer equation. Thermal radiation is an important part of heat transfer in granular systems, such as the packed pebble bed of high-temperature gas-cooled reactor (HTGR), bubbling fluidized bed, and other packed granular beds. In this paper, four models of multiple-body radiation within the packed granular bed were proposed and discussed in full integral scales, i.e. black radiation model, uniform radiation model, local radiation model and particle scale radiation model. For particle radiation with black surfaces, the black radiation model was proven to be valid strictly and it agreed with existing correlations and models. The radiative flux in the packed bed increased significantly with the particle emissivity. However, the existed Asakuma radiation model, two-flux model and the newly proposed local radiation model were almost independent of the particle emissivity since the uniform assumption was inappropriate for the gray radiation in the packed bed. The effect of emissivity was handled correctly in the local radiation model without the uniform assumption. Since the computation cost of local radiation model in large-scale granular systems was huge and not applicable in the CFD-DEM simulation, the particle scale radiation model was developed in this study to predict the radiation flux in discrete element method (DEM). It was shown that the effect of particle emissivity was a separable term in the radiative heat transfer equation. The particle scale radiation model provided a good approximation of the local radiation model and enabled efficient prediction of radiative heat transfer in a densely packed bed. [ABSTRACT FROM AUTHOR]

• New modeling of heat transfer in packed bed with continuum assumption is demonstrated. • A generic physical expression of radiation exchange factor for packed bed is given. • Approximation function model is proposed to solve radiation & conduction of particles. • Radiation in packed bed is proved equivalent to heat conduction at size ξ ≪ 1. • 2D application of radiation & conduction in packed bed is consistent with experiment. Radiative heat transfer is significant but rather complicated in the bed packed with lots of high temperature particles. Unfortunately, it cannot use traditional radiative transfer equation (RTE) to efficiently predict thermal radiation between particles in packed beds. With continuum assumption, an approximation function model (AFM) is proposed here. A generic physical equation of radiation exchange factor of packed bed is given, which is determined by surface emissivity and particle-scale packing structure. Compared with discrete element method (DEM) simulation, current radiation interaction function (RIF) gives a good estimation of the obstructed view factor of packed bed. The radiation in AFM is equivalent to that of heat conduction at size parameter ξ ≪ 1, and effective thermal conductivity (ETC) in central region of packed bed is higher than that of the whole bed. The AFM is also applicable for pebble bed with both radiative and conductive heat transfer, and it can predict consistent radial temperature distributions with that in experiments. The AFM works as a good replacement of traditional radiative transfer equation (RTE), and is also feasible to apply current equation to analyze other radiation models. [ABSTRACT FROM AUTHOR]