Bed Of Particles Research Articles

Impacts of packed bed polydispersity and deformation on fine particle transport

AbstractStatic granular packings play a central role in numerous industrial applications and natural settings. In these situations, fluid or fine particle flow through a bed of static particles is heavily influenced by the narrowest passage connecting the pores of the packing, commonly referred to as pore throats, or constrictions. Existing studies predominantly assume monodisperse rigid particles, but this is an oversimplification of the problem. In this work, we illustrate the connection between pore throat size, polydispersity, and particle deformation in a packed bed of spherical particles. Simple analytical expressions are provided to link these properties of the packing, followed by examples from Discrete Element Method (DEM) simulations of fine particle percolation demonstrating the impact of polydispersity and particle deformation. Our intent is to emphasize the substantial impact of polydispersity and particle deformation on constriction size, underscoring the importance of accounting for these effects in particle transport in granular packings.

Fundamental comminution efficiency gains with the CAHM platform technology

ABSTRACT The Conjugate Anvil Hammer Mill (CAHM) is a platform technology invented by Lawrence Nordell that embodies Dr Klaus Schönert’s guiding principles for highly efficient comminution into a series of commercial, production-scalable devices across multiple product size ranges. Schönert demonstrated that unconfined, compression breakage of single particles (or thin particle beds) between parallel plates produces the most energy efficient particle breakage. The CAHM Mark 1 Prototype and the MonoRoll are 2 new comminution devices that leverage these fundamental principles to produce comparable breakage at a fraction of the energy consumed by SAG mills, Ball mills or even High Pressure Grinding Rolls. The CAHM machine prototype has been tested at feed rates in excess of 60 t/h and is robust enough to be operated at a mine site for a pre-commercial demonstration. The MonoRoll is a 2 t/h retrofit of an existing pilot-scale ball mill. A mining industry consortium led by the Canada Mining Innovation Council and supported by Quebec and Federal government funding has designed, fabricated and tested both prototype machines over the last 4 years. Beyond the dramatic energy savings, implementing these technologies will generate additional benefits from simpler circuits and reduced scope 1, 2 and 3 carbon emissions. This paper reviews the design of these 2 prototypes in the context of Schönert’s fundamental principles for efficient breakage.

Influence of particle stacking modes on the fluidization characteristics of biomass particles in binary particle systems

Spouted bed is widely used in biomass combustion and other industrial production due to the advantages of good heat transfer performance and sufficient gas–solid mixing. In order to achieve higher heat and mass transfer performance and conversion efficiency, inert particles are often added to assist in the fluidization of biomass particles. However, the stacking patterns of different particles in a binary particle system can have some effects on particle flow, distribution, and bed stability. Therefore, in this study, the computational fluid dynamics–discrete element method was used to analyze the particle fluidization characteristics under four different particle stacking modes in a spouted bed. The results show that the average bed height of larger spherocylindrical particles is prioritized in binary particle systems. The void fraction of spherocylindrical particles tends to increase in the near-wall region, whereas spherical particles tend to decrease. When the binary particles are mixed at the initial moment, the change rule of vertical velocity of the two particles remains consistent. In addition, the vertical velocities of two kinds of particles when layered stacking is used are gradually close to each other only after a period of time. In addition, the orientation angle of the spherocylindrical particles in the spouted bed tends to be horizontal for both the single-component spherocylindrical particle system and the wall effect attenuates this phenomenon.

An experimental study on the impact of particle surface wettability on melt infiltration in particulate beds

Melt infiltration into porous media is an intriguing phenomenon that holds immense significance across various sciences and technologies. In this work, the problem of metallic melt infiltration in particulate beds is investigated for understanding and prediction of severe accident progression associated with a molten pool penetrating through an underlying debris bed which may form in the reactor core or in the lower head of a light water reactor.The present study aims to quantify the effect of particle surface’s wettability on melt infiltration kinetics. For this purpose, two categories of experiment are conceived and carried out to measure the wettability of different material surfaces by melt and to characterize melt infiltration kinetics in one-dimensional particulate beds, respectively. The melt material is tin–bismuth eutectic alloy with a melting point of 139 °C. Copper (Cu), stainless steel (SS), Tin (Sn) and tin-coated stainless steel (Sn-coated SS) are chosen as materials of substrates and particles in wettability measurement and melt infiltration study. The particulate beds, packed with 1.5 mm spheres, are preheated to 200 °C before the melt infiltration begins.The experimental data of wettability measurement shows that the contact angles of liquid Sn-Bi eutectic on the above-mentioned material surfaces range from 79° to 135°. The results of melt infiltration tests confirm the significant effect of wettability on melt penetration kinetics. The capillary force plays a significant role in the initial infiltration of particulate beds. Specifically, a wettable particulate bed enhances the initial melt infiltration, whereas non-wettable beds hinder it.

Heat and Mass Transfer Model for a Counter-Flow Moving Packed-Bed Oxidation Reactor/Heat Exchanger

Abstract Particle-based thermochemical energy storage (TCES) through metal oxide redox cycling is advantageous compared to traditional sensible and latent heat storage (SHS and LHS) due to its higher operating temperature and energy density, and the capability for long-duration storage. However, overall system performance also depends on the efficiency of the particle-to-working fluid heat exchangers (HXs). Moving packed-bed particle-to-supercritical CO2 (sCO2) HXs have been extensively studied in SHS systems. Integrating the oxidation reactor (OR) for discharging with a particle-to-sCO2 HX is a natural choice, for which detailed analysis is needed for OR/HX design and operation. In this work, a 2D continuum heat and mass transfer model coupling transport phenomena and reaction kinetics is developed for a shell-and-plate moving-bed OR/HX. For the baseline design, the model predicted ∼75% particle bed extent of oxidation at the channel exit, yielding a total heat transfer rate of 16.71 kW for 1.0 m2 heat transfer area per channel, while the same design with inert particles (SHS only) gives only 4.62 kW. A parametric study was also conducted to evaluate the effects of particle, air, and sCO2 flowrates, channel height and width, and average particle diameters. It is found that the respective heat transfer rate and sCO2 outlet temperature can approach ∼25 kW and >1000 °C for optimized designs for the OR/HX. The present model will be valuable for further OR/HX design, scale-up, and optimization of operating conditions.

Prediction of the sulfur driven autotrophic denitrification process via CFD-DEM approach

Sulfur driven autotrophic denitrification is an economic and efficient means to purify the nitrogenous wastewater. The long-term experimental study is quite time-consuming and expensive. In this work, a coupled computational fluid dynamics-discrete element method (CFD-DEM) is implemented to investigate the performance of long-term operating sulfur autotrophic denitrification process. The evolution of particle accumulation and nitrate removal efficiency in the packed bed reactors with different tube diameters and sulfur particle sizes are simulated. It is found that the NO-3-N removal rates for different tube diameters are close and a wider particle size distribution is shown in the slender reactor. The small particle bed shows a better NO-3-N removal efficiency.

CFD-DEM mixing of rod-like and spherical particles in fluidized beds

Understanding the behavior of particle mixing in fluidized beds is crucial for enhancing process design. This article focuses on investigating the effect of key parameters, such as volume fraction of spherical particles, length of rod-like particles, and aspect ratio of rod-like particles, on the mixing of binary mixtures containing spherical and rod-like particles. The study employs a computational approach which couples the computational fluid dynamics and discrete element method (CFD-DEM) to explore mixing behavior of particles. Non-spherical particles are modeled using the multi-sphere method. A combination of qualitative and quantitative approaches is employed to assess the mixing performance, including visual examination of the fluidized bed and calculation of the subdomain-based mixing index. It was shown that an increase in rod-like particle length, aspect ratio, and volume fraction of rod-like particles weaken the mixing. Furthermore, the quality of mixing is directly influenced by bubble size and particle granular temperature. This study offers valuable insights into the mixing behavior of rod-like and spherical particles, contributing to the design and optimization of binary fluidization processes.

A tree-based automated machine learning approach of the obstructed view factor of thermal radiation in nuclear pebble beds

For the nuclear pebble bed of the high temperature gas-cooled reactor (HTGR), a tree-based automated machine learning approach is developed to discuss the complicated thermal radiation behaviors. The AutoML model for calculating the obstructed view factor between any two particles in the pebble bed includes the gradient boosting regression tree model with the fine-tuned hyperparameters and the analytical base model. Using the discrete packing of the HTR-PM nuclear reactor and the leaped Halton sequence, a large dataset of the view factor under different conditions is generated to train the AutoML model. On the same platform, numerical results show that AutoML model is approximately 5 × 105 times faster than the traditional approach. The Pareto front of the AutoML model indicates that the mean squared error decreases with the model complexity until it reaches the optimal solution. Then, the trained AutoML model is applied to the engineering pebble bed. It is shown that the average radiation exchange factor near the wall is lower than that in the bulk region. In addition, the packing height is also an important parameter for evaluating the radiative behaviors. In particular, when the height of the nuclear pebble bed is less than 20 times particle diameter, it is necessary to consider the contribution of the packing height to the radiation effective thermal conductivity.

STAR-CCM+ simulation of debris bed formation in the unheated DEFCON-S experiment

In a severe accident of light-water reactor, molten corium can be formed and discharged into the reactor cavity. If the resulting debris bed is not adequately cooled, it could threaten the containment integrity by causing a molten core-concrete interaction. This study analyzes a non-heating debris bed formation experiment of DEFCON-S using the STAR-CCM+ code. Relevant CFD models are established to reflect the interaction between particles and fluids to describe the particle behavior and flow of fluids. The shape and size of debris bed are predicted through the CFD calculation. The rolling resistance becomes an important parameter in this simulation. The prediction with the default values of STAR-CCM+ forms a spread shape of particle bed compared to the experimental result. The shape of debris bed obtained with modified rolling resistance coefficients gives consistency with the DEFCON-S experiment, having a deviation in diameter of 4.6 % and a deviation in height of 3.8 %.

Segregation of binary particles in gas-solid fluidized bed

Segregation of binary particles in gas-solid fluidized bed

Experimental investigation on shape segregation of 3D printed particles using an Freeman FT4 rheometer

This study examines how granular mixtures of differently shaped particles segregate in a Freeman (FT4) rheometer apparatus. The mixtures contained two sets of particles with varying shapes and relative sizes. While our focus was on the effect of particle shape on segregation, we recognized that even slight differences in size could lead to segregation. We specifically investigated when particles of different shapes have the same effective size, exploring three cases: 1) the largest sphere within a cubic particle (inscribed sphere), 2) the smallest sphere enclosing a cubic particle (circumscribed sphere), and 3) a sphere and cube with equal volume. Our key finding indicates that binary mixtures of cubical and spherical particles can significantly segregate either axially or radially in the particle bed with a circumscribed sphere configuration. We propose that the primary mechanism for this is percolation and additionally, in the case of radial segregation, ordering of cubes adjacent to the cylinder wall.

Determination of interparticle radiative heat transfer and radiation absorption for ellipsoidal particle beds using Monte Carlo ray tracing

The calculation of radiative heat transfer between particles in particle-based solar systems presents significant challenges in terms of computational cost and accuracy. This study addresses these challenges by employing the discrete element method to generate random particle packings and the Monte Carlo ray tracing method to investigate the influence of particle shape and volume fraction (ϕ) on interparticle radiation transfer and the absorption of incident radiation. The results reveal that, at low volume fractions, the shape and orientation of ellipsoidal particles have a pronounced impact on direct radiative transfer. Oblate particles exhibit the highest average radiation distribution factor (RDF), and the dispersion of RDF data is more prominent for oblate and elongated prolate particles compared to spheres. As ϕ increases to 0.35, the contribution of indirect transfer from neighboring particles becomes significant for oblate particles, resulting in a reduction in the dispersion of RDF data. Furthermore, when ϕ reaches 0.55, the decisive factor in determining RDF becomes the shielding effect of particles positioned between the emitting and receiving particles. The average RDF tends to converge among particles of different shapes, although oblate and elongated prolate particles still exhibit considerably larger RDF dispersion compared to spherical and near-spherical particles. Additionally, the effective absorptivity of the particle bed for incident radiation decreases as the aspect ratio of particles increases at all volume fractions. Moreover, the transmitted fraction demonstrates an exponential relationship with the depth, and beds composed of spherical particles exhibit better radiation transmittance compared to beds containing non-spherical particles.

Characterization of different darken sand particles and behavior under fluidized and irradiated conditions

The use of solid particles in a fluidized bed with concentrated solar irradiation from the top is a promising technology for the next generation of concentrated solar power (CSP) plants. Sand is an inexpensive and abundant material easy to fluidize, but it has a low absorptivity, which is around 0.5 according to different previous works. This optical property is a key parameter for CSP applications with solid particles. This work presents a novel methodology to induce darkening of the sand surface by inducing solid state diffusion of Mn in SiO2, rendering a stable material resistant to abrasion upon the fluidization process. For this study, two different samples considering different MnCO3:SiO2 weight ratios (1:30 and 1:50) were analyzed. The objective is to compare the two samples and optimize the concentration of MnCO3 to get the desired darkening of the sand and high absorptivity. First, the main properties of the particles were analyzed (particle size, morphology, color and absorptivity). Second, the samples were tested in a lab-scale fluidized bed directly irradiated from the top with a beam-down 4kW Xe lamp. Both samples were tested under three different fluidized velocities: 1.5, 2.0, and 2.5 times the minimum fluidization velocity (Umf). In both cases, there is a significant increase in the maximum temperature reached during the process, with temperatures exceeding 260 °C. This is clearly higher than the case of raw sand, which reaches 230 °C under the same conditions. Furthermore, these values exceed the highest temperature reached by SiC in the same facility, which is 250 °C, and it is considered as one of best tested materials for CSP applications.

Fully coupled discrete element method for graded particles transport in pipes

Hydraulic conveying of graded particles is much more complex than that of uniform particles but is not fully understood. A fully coupled computational fluid dynamics–discrete element method model is established for the hydraulic conveying of graded particles, which integrally considers the particle–fluid and particle–particle interactions and turbulence modulation from particles. The proposed model accounts for the stochastic motion of particles by the discrete random walk method and applies the diffusion averaging algorithm to obtain particle concentration in arbitrary cells for smooth and cell-independent data fields on unfavorable cells (fluid cell size ≤ particle size). The particle–fluid drag force is applied to slurry flows through densely packed particle beds due to the consideration of porosity modification. The proposed model well performs in simulating the hydraulic conveying of dense graded particles. Dynamics in slurry mixtures of bi-disperse particles are investigated regarding different particle size compositions. The results show obvious stratification between coarse and fine particles, e.g., fine particles settling at the pipe bottom elevate the coarse particles and form a “lubrication layer” with high velocity. The torque caused by particle–particle/wall contact is greater than the torque caused by the fluid. The pipe cross section is divided into four regions according to the particle angular velocity. The effect of particle concentration on liquid motion is small because the difference in local particle concentration is relatively small, but the maximum pressure drop corresponds to a critical particle size composition.

Dry Downhill Particle Motion on Mars

We recently flew a new setup on parabolic flights for the first time to study particle motion on Martian slopes under Martian gravity. Here, we describe the initial experiments. We used dust/sand beds at varying ambient pressure of a few hundred pascals. The inclination of the particle bed was varied from 0° to 45° and parts of the surface were illuminated under varying conditions. We could observe downhill motion of material related to the insolation at the lowest light flux used of 591 ± 11 W m−2 for JSC Martian simulant. Motion occurred at significantly lower inclinations under illumination than without illumination, i.e., down to about 10° compared to about 20°–30°, respectively. We attribute this reduction in slope to thermal creep gas flow in the subsoil. This induces a Knudsen compressor, which supports grains against gravity and leads to smaller angles of repose. This is applicable to recurring slope lineae and slopes on Mars in general.

Study of energy dissipation mechanisms and hotspot formation patterns during impact process in octogen explosives with circular cavities

Considerable focus has been given to hotspot generation and ignition phenomena in impact-induced explosives. Hotspot formation in explosives is typically attributed to internal dissipation and heat transfer occurring within them. This study refines the momentum and energy equations to illustrate the entire process of particle collision, temperature-rise evolution, and hotspot formation in octogen explosive bed under impact. By octogen, we mean the substance known as cyclotetramethylene tetranitramine, which is also commonly referred to as HMX. Dense particles are considered to have pseudo-fluid properties. During the impact of the explosive, we captured the propagation of the stress wave and compared its similarities and differences with the shock wave. The collision force model incorporates a combination of Hertz–Mindlin elastic and Thornton elastoplastic contact theories. The temperature-governing equation includes sliding friction, rolling resistance, and plastic dissipations as energy sources, taking into account the heat transfer processes between particles. Temperature evolution is a spatiotemporally correlated phenomenon divided into three processes: high-temperature bands formation, cavity collapse, and particle bed dispersion, all of which lead to hotspot formation near the cavity and near the wall. Plastic dissipation is the primary source for particle temperature-rise and hotspot formation. Furthermore, the effect of cavity size, impact velocity, and particle size on temperature evolution and hotspot formation patterns is analyzed. It was found that higher impact velocities and smaller cavity sizes are associated with increased hotspot temperatures near the wall, but the hotspot temperature near the cavity does not consistently vary with impact velocity and cavity size. This is attributed to the relationship between energy dissipation rate and void collapse time.

Multi-scale investigation of heat and momentum transfer in packed-bed TES systems up to 800 K

With the rising cost of energy and the advancement of corporate social responsibility, there is a growing interest in addressing the challenge of recovering and storing high-temperature waste heat. Sensible heat storage in packed beds stands out as a cost-effective and seemingly straightforward solution for high-temperature Thermal Energy Storage (TES). Engineering models developed to design low-temperature TES systems were tentatively used to design this new generation of high-temperature systems. Delving into the physics of coupled heat and mass transfer reveals a lack of validation of this approach. This study seeks to establish a comprehensive bottom-up methodology - from the particle scale up to the system level - to provide informed and validated engineering models for the design of high-temperature TES systems. To achieve this goal, we developed a multi-scale numerical model to explore the physics of heat and momentum transfer in packed-bed TES systems. At the microscopic scale (pore/particle), we consider the flow of a compressible high-temperature gas between the particles, coupled to transient heat conduction within the particles, with particular attention given to incorporating accurate temperature-dependent viscosity for the gas phase and thermal conductivity and density for both solid and gas phases. At the macroscopic scale (engineering), we propose a high-temperature extension of state-of-the-art two-equation TES models. The governing equations considered are the volume-average conservation laws for gas-mass, gas-momentum and energy of both phases. The multi-scale strategy is applied to a randomly packed bed of spherical particles generated with the discrete element method (DEM) software LIGGGHTS. Numerical models for both scales were implemented in the Porous material Analysis Toolbox based on OpenFoam (PATO), which is made available in Open Source by NASA. Microscopic scale simulations were used to infer the effective parameters needed to inform the macroscopic model, namely, permeability, Forchheimer coefficient, effective thermal conductivities, and the heat transfer coefficient. The informed macroscopic model reproduces with excellent accuracy the average temperature fields of the physics-based microscopic model. Pore-scale analysis shows highly three-dimensional flow characterized by reverse flow and strong cross-flow in the packed bed system. Moreover, it indicates the coupling between temperature and velocity fields, where a nonuniform velocity field results in uneven temperature distributions across the fluid and the solid spheres within the packed bed, subsequently affecting the macroscopic heat transfer coefficient. The overall strategy is validated by comparison to available experimental data. This bottom-up methodology contributes to the understanding and opens new perspectives for a more precise design and monitoring of high-temperature TES systems.

Study on the anisotropic flow characteristics of wet particles in liquid-solid fluidized beds

In liquid-solid fluidized beds, the presence of a liquid film around the surface of particles influences their collision behavior, leading in turn to the restitution coefficient no longer a constant. The present study introduces a dynamic restitution coefficient for wet particles to describe its dynamic variation during the process of particles colliding. The liquid-solid two-phase flow is simulated with Eulerian-Eulerian two-fluid method incorporating the anisotropic kinetic theory of granular flow based on second-order moment (SOM) model, in view of the anisotropy of particle fluctuations. This study aims to probe into the influence of liquid film and anisotropy of particle fluctuation on the particle-particle interactions and collision mechanisms. The predicted particle velocity and solid volume fraction are verified by the Limtrakul's et al. experiments. The simulated results show that the particle velocity fluctuations exhibit significant anisotropy, and the SOM model is superior to the KTGF model in capturing inhomogeneity and anisotropy of the flow field. The existence of a liquid film enhances energy dissipation during particle collisions and diminishes the anisotropy of particle velocity fluctuations. Also, the enhancement of particle density leads to a thicker liquid film and higher restitution coefficient, while the second-order moments are weakened and the anisotropy is remarkable. Furthermore, the effect of liquid viscosity on the liquid film thickness and restitution coefficient is more significant, where the particle fluctuations are reduced and the anisotropy is intensified by enhancing the liquid viscosity. In brief, both the liquid film and the anisotropy have impact on liquid-solid two-phase flow, by comparison, the effect of anisotropy is greater than liquid film.

Demonstration of a multi-channel fluidized bed particle–supercritical carbon dioxide heat exchanger for concentrating solar applications

High-temperature thermal energy storage in oxide particles at temperatures above 600°C can couple concentrated solar energy with high-efficiency thermal power cycles to provide dispatchable solar-driven electricity. Challenges remain in developing cost-effective primary heat exchangers, which require expensive alloys, to extract the high-temperature thermal energy from the particles to power cycle fluids, such as supercritical CO2 (sCO2) in recuperated Brayton cycles. To explore one pathway for cost-effective, high-temperature particle heat exchangers, the current study demonstrates a shell-and-plate, particle–sCO2 heat exchanger with narrow-channel fluidized beds coupled with micro-channel sCO2 flows in the heat exchanger walls. This study evaluates the feasibility of multiple parallel, narrow-channel fluidized beds in shell-and-plate particle–sCO2 HXs, to achieve high bed-wall heat fluxes at elevated temperatures. A reduced-order model simulates the narrow-channel, fluidized-bed particle–sCO2 heat exchanger to design the fluidized bed geometry, in terms of depth, height, and number of channels,for a nominal 40-kWth heat exchanger at particle and sCO2 inlet temperatures up to 600°C and 400°C respectively. The resulting shell-and-plate heat exchanger design operates with bubbling fluidization of the downward-flowing oxide particles to enhance bed-wall heat transfer. The heat exchanger core is fabricated with etched sCO2 micro-channels in thin wall plates that are diffusion bonded to spacer frames to form the shell-and-plate structure with 12 parallel, fluidized bed channels, 10.4 mm deep. The heat exchanger is tested at the National Solar Thermal Test Facility at Sandia National Laboratories with CARBOBEAD HSP particles at design particle flow rates of 0.20 kg s−1 and inlet temperatures up to 525°C. Results show that fluidization across multiple parallel channel beds can maintain uniform particle inventory with a common freeboard zone above the heat exchanger core. Bubbling fluidization improves particle–wall heat transfer coefficients but also increases axial dispersion of particle thermal energy, which lowers the log-mean temperature difference such that total heat transfer remains relatively constant to within ±10% over a broad range of fluidization gas velocities. The axial dispersion required particle and sCO2 flow rates to be increased by 25% over model-designed conditions to achieve the targeted 40 kWth, which indicates the importance of incorporating axial dispersion into heat exchanger design models and of deploying bed structures to suppress it. This study demonstrates the feasibility and preferred fluidizing gas conditions for particle heat exchangers for releasing high-temperature thermal energy storage systems.

Spreading Behavior of Non-Spherical Particles with Reconstructed Shapes Using Discrete Element Method in Additive Manufacturing.

The spreading behavior of particles has a significant impact on the processing quality of additive manufacturing. Compared with spherical metal material, polymer particles are usually non-spherical in shape. However, the effects of particle shape and underlying mechanisms remain unclear. Here, the spreading process of particles with reconstructed shapes (non-spherical particles decomposed into several spherical shapes by stereo-lithography models) are simulated by integrating spherical particles with the discrete element method. The results show that more cavities form in the spreading beds of particles with reconstructed shapes than those of spheres with blade spreading. Correspondingly, particles with reconstructed shapes have lower packing densities, leading to more uniform packing patterns. Slow propagation speeds of velocity and angular velocity lead to "right-upwards" turning boundaries for particles with reconstructed shapes and "right-downwards" turning boundaries for spherical particles. Moreover, as the blade velocity increases, the packing density decreases. Our calculation results verify each other and are in good agreement with the experiment, providing more details of the behavior of non-spherical particles before additive manufacturing. The comprehensive comparison between polymer non-spherical particles and spherical particles helps develop a reasonable map for the appropriate choice of operating parameters in real processes.