Particle Packing Fraction Research Articles

Fuel Cycle Investigation for Wallpaper-Type HTR Fuel

As early as the 1970s, attempts have been made to reduce the peak fuel temperature in pebble bed-type high-temperature reactors (HTRs) by means of so-called “wallpaper fuel,” in which the fuel is arranged in a spherical shell within a pebble. By raising the particle packing fraction, fuel kernels are condensed to the outer diameter of the fuel zone, leaving a central part of the pebble free of fuel. This modification prevents power generation in this central fuel-free zone and decreases the temperature gradient across the pebble.Besides the reduction of maximum and average particle temperature, the wallpaper concept also enhances neutronic performance through improved neutron economy, resulting in reduced fissile material and/or enrichment needs or providing the potential to achieve higher burnup. To assess such improvements, calculations were performed using the PANTHERMIX code. Among other tests, investigations of fuel cycle under steady-state conditions and loss-of-coolant-accident calculations were conducted. Based on PANTHERMIX steady-state conditions, both particle failure fraction [with the CRYSTAL code (Code foR analYsis of STress in coAted particLes)] and fissile material cost can be determined.It is demonstrated that the wallpaper fuel type positively impacts the fuel cycle, reduces the production of minor actinides (MAs), and improves the safety-relevant parameters of the reactor. A comparison of these characteristics with those of Pebble Bed Modular Reactor (Pty) Limited (PBMR) type of fuel is presented: In comparison with PBMR fuel, the wallpaper design results in an increase of the effective neutron multiplication coefficient (by [approximately]925 pcm). This reactivity increase can lead to a burnup extension (from 96.4 to 101.3 MWd/kg), therefore improving the burnup of HTRs, or to an enrichment reduction (from 9.6 to 9.277 wt%). Both options decrease MA production [as defined in g/TW(thermal)·h, between 5.9% and 34.5%], making fuel reprocessing easier and reducing fuel cost (by 4.6% for the high-burnup option and by 3.7% for the low-enrichment option).Safety is also improved, with particle temperature being reduced during steady-state operations (by >55 K for the most exposed particles and by almost 10 K on average). This positively impacts particle failure fraction as calculated by the fuel performance code CRYSTAL, leading to a reduction of up to 85% of the particle failure fraction over its in-core lifetime. This reduces the in-core fission product release.While an increase of the graphite density in the central fuel-free zone increases thermal inertia, initiates a faster reactor shutdown, and delays recriticality, it also disturbs the thermal flux that raises pebble powers in the inner part of the core. This increases the highest kernel temperature during a depressurized loss-of-coolant accident from 1872 K for the PBMR case to 1876, 1917, and 1895 K, respectively, for the three wallpaper designs proposed.The fuel changes suggested in this paper offer more versatility to the HTR concept. The conversion ratio can be decreased, leading to lower MA buildup and fuel reprocessing cost, or raised, leading to lower fuel consumption and fuel cost.

Influence of the particle size on the microstructure and mechanical properties of grains containing mixtures of nanoparticles and microparticles: Levitator tests and pilot-scaled validation

Abstract The spray drying process is used in many industrial applications. However, different grain properties can be desirable depending on the later use of the powders produced. In this work the influence of the particle size on the particle packing fraction and the mechanical strength of grains containing silica nanoparticles, microparticles and their mixtures, was analyzed. Single droplet tests were carried out in an acoustic levitator at 120 °C. The shell thickness was calculated using the fluidity limits obtained from the modelling of the viscosity data. Results obtained showed good agreement with the experimentally measured ones. The addition of nanoparticles and high pH values produce an increase in the mechanical strength of the grains. Finally, different suspensions were dried in a pilot-scaled spray dryer. The results obtained for the mechanical strength of the spray died powders confirm the results obtained in the levitator test.

Assessment of possible cycle lengths for fully encapsulated microstructure fueled light water reactor concepts

The use of TRISO-particle-based dispersion fuel within SiC matrix and cladding materials has the potential to allow the design of extremely safe LWRs with failure-proof fuel. This paper examines the feasibility of LWR-like cycle length for such fuel with the imposed constraint of strictly retaining the original geometry of the fuel pins and assemblies. The motivation for retaining the original geometry is to provide the ability to incorporate the fuel “as-is” into existing LWRs while retaining their thermal–hydraulic characteristics. Another mandatory constraint is use of low enriched uranium (at or below 20 w/o).The feasibility of using this fuel is assessed by looking at two factors: cycle lengths and fuel material failure rates. Other considerations (e.g., safety parameters such as reactivity coefficients, feedback, etc.) were not considered at this stage of the study. The study includes the examination of increases in the TRISO kernel sizes without changing the thickness of any of the coating layers. In addition, cases where the buffer layer thickness is allowed to vary are also considered.The study shows that a naïve use of UO2 (even up to 20 w/o enrichment) results in cycle lengths too short to be practical for existing LWR designs and operational demands. Increasing fissile inventory within the fuel compacts shows that acceptable cycle lengths can be achieved. The increase of fissile inventory can be accomplished through multiple means, including higher particle packing fraction, higher enrichment, larger fuel kernel sizes, and the use of higher density fuels (that contain a higher number of U atoms per unit volume). In this study, starting with the recognized highest packing fraction practically achievable (44%), combinations of the other means have been evaluated. The models demonstrate cycle lengths comparable to those of ordinary LWRs.As expected, TRISO particles with extremely large kernels are shown to fail under all considered scenarios. In contrast, the designs that do not depart too drastically from those of the nominal NGNP HTR fuel TRISO particles are shown to perform satisfactorily and display a high rates of survival under all considered scenarios.

Effective interaction in asymmetric charged binary mixtures: The non-monotonic behaviour with the colloidal charge

In this work we study the effective force between charged spherical colloids induced by the presence of smaller charged spheres using Monte Carlo simulations. The analysis is performed for two size ratios, q = R(s)/R(b), two screened direct repulsions, κ, and two small particle packing fractions, Ø(s). We specially focus on the effect of the charge of the big colloids (Z(b)), and observe that the repulsion between big particles shows a non-monotonic behaviour: for sufficiently small charge, we find an anomalous regime where the total repulsion weakens by increasing the big colloid charge. For larger charges, the system recovers the usual behaviour and the big-big interaction becomes more repulsive increasing Z(b). This effect is linked to the existence of strong attractive depletion interactions caused by the small-big electrostatic repulsion. We have also calculated the effective force using the Ornstein-Zernike equation with the HNC closure. In general, this theory agrees with the simulation results, and is able to capture this non-monotonic behaviour.

Studi Sensitivitas Fraksi Packing Partikel TRISO dalam Desain Kritikalitas HTR Pebble Bed

HTR is a high temperature reactor used for electricity production and process heat applications such as hydrogen production, desalination of sea water, enhanced oil recovery and so on. HTR is designed based on the utilization of TRISO fuel particles that can prevent strongly the escape of fission products even at temperatures above 1600 o C. TRISO particles packing fraction is one of four key parameters that are essential in HTR design besides radius of the kernel, kernel density and fuel enrichment. This paper discusses the sensitivity of TRISO particles packing fraction that impacts to the loading of uranium in the fuel pebble, the long cycle of reactor operation and achievable maximum fuel burn-up. With the capability of Monte Carlo transport code MCNP5, all components of the reactor, starting from TRISO particles, were modeled in detail and explicit and calculated using the continuous energy nuclear data library ENDF/B-VI. The results show that the value of effective multiplication factor ( k eff) has a tendency to increase with decreasing particle TRISO packing fraction and to decrease with increasing fuel burn-up. K eff values decrease with increasing TRISO particle packing fraction both at the beginning of cycle (BOC) and at the end of cycle (EOC). Reactivity swing is also very sensitive on the TRISO particles packing fraction. From the analysis, it can be concluded that TRISO particles packing fraction greatly affects the neutronics performance of HTR pebble bed design. Packing fraction can change the effective multiplication factor ( k eff) and the swing reactivity with similar behavior.

Building microscopic soccer balls with evaporating colloidal fakir drops

Evaporation-driven particle self-assembly can be used to generate three-dimensional microstructures. We present a unique method to create colloidal microstructures in which we can control the amount of particles and their packing fraction. To this end, we evaporate colloidal dispersion droplets on a special type of superhydrophobic microstructured surface, on which the droplet remains in Cassie-Baxter state during the entire evaporative process. The remainders of the droplet consist of a massive spherical cluster of the microspheres, with diameters ranging from a few tens up to several hundreds of microns. We present scaling arguments to show how the final particle packing fraction of these balls depends on the dynamics of the droplet evaporation, particle size, and number of particles in the system.

Effects of the physical and chemical properties of petroleum coke on its slurryability

In this study, the effects of particle size distribution (PSD), chemical composition and pore structure of petroleum coke on the slurryability of petroleum coke water slurry (PCWS) were investigated. Four petroleum cokes were studied, and they showed completely different slurryability. The solid concentration at fixed viscosity (i.e. apparent viscosity of 1000 mPa) (SCFV) of four PCWSs is different from each other, with the highest value of 70.9%, and lowest of 62.1%. The apparent viscosity of the four PCWSs all increased with an increase of the solid concentration. The results showed that the PSD, inherent moisture content, specific surface area and pore volume of petroleum coke were key factors to affect the slurryability. The slurryability was enhanced with increasing PSD range and particle packing fraction, and with decreasing inherent moisture content, specific surface area and pore volume.

One-dimensional hard rod fluid in a disordered porous medium: scaled particle theory

The scaled particle theory is applied to a description of thermodynamic properties of one-dimensional hard rod fluid in disordered porous media. To this end, we extended the SPT2 approach, which had been developed previously. Analytical expressions are obtained for the chemical potential and pressure of a hard-rod fluid in hard rod and overlapping hard rod matrices. A series of new approximations for SPT2 are proposed. It is shown that apart from two well known porosities such as geometrical porosity and specific probe particle porosity, a new type of porosity defined by the maximum value of packing fraction of fluid particles in porous medium should be taken into account. The grand canonical Monte-Carlo simulations are performed to verify the accuracy of the SPT2 approach in combination with the new approximations. It is observed that the theoretical description proposed in this study essentially improves the results up to the highest values of fluid densities.

Effect of packing fraction on ferromagnetic resonance in NiFe2O4 nanocomposites

Magnetic nanocomposites, composed of magnetic nanoparticles in an insulating matrix, can have properties not achievable in bulk, single-phase materials. This work reports on ferromagnetic resonance (FMR) measurements as a tool to investigate the internal magnetic field in nanocomposite samples of varying particle packing fractions. The ferromagnetic resonance frequency changes with particle packing fraction due to increased inter-particle interaction and demagnetizing field within the sample. Experimental results obtained on NiFe2O4 nanocomposite samples are compared to published theoretical models, and found to be consistent with the predicted trends. Extrapolation of the results to the limit of isolated particles indicates an average internal anisotropy field of 0.041 T for the NiFe2O4 nanoparticles.

A unified framework for non-Brownian suspension flows and soft amorphous solids

While the rheology of non-brownian suspensions in the dilute regime is well understood, their behavior in the dense limit remains mystifying. As the packing fraction of particles increases, particle motion becomes more collective, leading to a growing length scale and scaling properties in the rheology as the material approaches the jamming transition. There is no accepted microscopic description of this phenomenon. However, in recent years it has been understood that the elasticity of simple amorphous solids is governed by a critical point, the unjamming transition where the pressure vanishes, and where elastic properties display scaling and a diverging length scale. The correspondence between these two transitions is at present unclear. Here we show that for a simple model of dense flow, which we argue captures the essential physics near the jamming threshold, a formal analogy can be made between the rheology of the flow and the elasticity of simple networks. This analogy leads to a new conceptual framework to relate microscopic structure to rheology. It enables us to define and compute numerically normal modes and a density of states. We find striking similarities between the density of states in flow, and that of amorphous solids near unjamming: both display a plateau above some frequency scale ω(∗) ∼ |z(c) - z|, where z is the coordination of the network of particle in contact, z(c) = 2D where D is the spatial dimension. However, a spectacular difference appears: the density of states in flow displays a single mode at another frequency scale ω(min) ≪ ω(∗) governing the divergence of the viscosity.

Does size matter? Elasticity of compressed suspensions of colloidal- and granular-scale microgels

We investigate the mechanics of dense packing of very small, colloidal-scale, and larger, granular-scale microgel particles. At low particle concentration, thermally induced Brownian motion of the particles is important for the colloidal-scale systems; in contrast, such Brownian motion is irrelevant at particle packing fractions beyond jamming. As a consequence, colloidal and granular systems behave very similarly under these conditions. At sufficiently high compression of the microgel particles, their polymeric nature sets the scale of the osmotic pressure and shear modulus of the whole packing, in direct analogy with macroscopic, continuous polymer gels. This observation suggests that the particulate nature of microgels is inconsequential for their linear elasticity in a highly packed state. In contrast, the particulate nature of the microgels does become essential when the packed suspensions are forced to yield and flow; here, the differences between colloidal- and granular-scale particles are marked.

Short-time self-diffusion coefficient of a particle in a colloidal suspension bounded by a microchannel: Virial expansions and simulation

Self-diffusion of colloidal particles confined to a cylindrical microchannel is considered theoretically and numerically. Virial expansion of the self-diffusion coefficient is performed. Two-body and three-body hydrodynamic interactions are evaluated with high precision using the multipole method. The multipole expansion algorithm is also used to perform numerical simulations of the self-diffusion coefficient, valid for all possible particle packing fractions. Comparison with earlier results shows that the widely used method of reflections is insufficient for calculations of hydrodynamic interactions even for small packing fractions and small particles radii, contrary to the prevalent opinion.

Neutronic feasibility design of a small long-life HTR

Small high temperature gas-cooled reactors (HTRs) have the advantages of transportability, modular construction and flexible site selection. This paper presents the neutronic feasibility design of a 20 MWth U-Battery, which is a long-life block-type HTR. Key design parameters and possible reactor core configurations of the U-Battery were investigated by SCALE 5.1. The design parameters analyzed include fuel enrichment, the packing fraction of TRISO particles, the radii of fuel compacts and kernels, and the thicknesses of top and bottom reflectors. Possible reactor core configurations investigated include five cylindrical, two annular and four scatter reactor cores for the U-Battery. The neutronic design shows that the 20 MWth U-Battery with a 10-year lifetime is feasible using less than 20% enriched uranium, while the negative values of the temperature coefficients of reactivity partly ensure the inherent safety of the U-Battery. The higher the fuel enrichment and the packing fraction of TRISO particles are, the lower the reactivity swing during 10 years will be. There is an optimum radius of fuel kernels for each value of the fuel compact design parameter (i.e., radius) and a specific fuel lifetime. Moreover, the radius of fuel kernels has a small influence on the infinite multiplication factor of a typical fuel block in the range of 0.2–0.25 mm, when the radius of fuel compacts is 0.6225 cm and the lifetime of the fuel block is 10 years. The comparison of the cylindrical reactor cores with the non-cylindrical ones shows that neutron under-moderation is a basic neutronic characteristic of the reactor core of the U-Battery. Increasing neutron moderation by replacing fuel blocks with graphite blocks and dispersing the graphite blocks in the reactor core are two effective ways to increase the fuel burnup and lifetime of the U-Battery. Water or steam ingress may induce positive reactivity ranging from 0 to 0.16 Δk/k, which further demonstrates that the U-Battery is under-moderated.

Thermal-fluid characteristics of the transuranics fuel in a deep-burn HTR core

The Deep Burn Project is evaluating the feasibility of the DB-HTR (Deep Burn High Temperature Reactor) to achieve a very high utilization of transuranics (TRU) derived from the recycle of LWR spent fuel. This study intends to evaluate the thermal-fluid and safety characteristics of TRU fuel in a DB-HTR core using GAMMA+ code. The key design characteristics of the DB-HTR core are more fuel rings (five fuel-rings), less central reflectors (three rings) and decay power curves due to the TRU fuel compositions that are different from the UO 2 fuel. This study considered three types of TRU kernel compositions such as 100%(PuO 2 + NpO 2 + Am), 99.8%(PuO 1.8, NpO 2) + 0.2%UO 2 + 0.6 mole SiC getter, and 70%(PuO 1.8, NpO 2) + 30%UO 2 + 0.6 mole SiC getter. The first fuel type of TRU kernel produces higher decay power than the UO 2 kernel. For the second and the third fuel types, removing the initial Am isotopes and reducing the volumetric packing fraction of TRISO particles will reduce the decay power. The flow distribution, core temperature and TRISO temperature profiles at the steady state were examined. As a safety performance, this study mainly evaluated the peak fuel temperature during LPCC (low pressure conduction cooling) event with considering the impact of decay power, the annealing effect of the irradiated thermal conductivity of graphite, and the impact of the FB (fuel block) end-flux-peaking. For the 600 MW th DB-HTR core, the peak fuel temperature of 100%(PuO 2 + NpO 2 + Am) TRU was found to be much higher than the transient fuel design limit of 1600 °C due to the lack of heat absorber volume in the central reflector as well as to the increased decay power of the TRU fuel compositions. For a 0.2%UO 2 mixed or a 30%UO 2 mixed TRU, the peak fuel temperature was decreased due to the reduced decay power, however, it was still higher than 1600 °C due to the lack of heat absorber volume in the central reflector.

Effect of particle size distribution and dynamics on the performance of two-dimensional packing

Extensive computer simulation is used to revisit and to generalize two classical problems: (i) the random car-parking dynamics of A. Rényi and (ii) the irreversible random sequential adsorption (RSA) of parallel squares of same size on a planar substrate of area L2. In this paper, differently from the classical RSA, the squares obey the size distribution n(a)=n(1)a−τ, where a=1,2,3,… is the area of the squares. Using this scaling distribution and three classes of packing dynamics we study the final packing fraction of particles, ⊖(τ,L), and in particular its thermodynamic limit L→∞. We show that the efficiency to attain a high/low packing density of particles on the substrate is strongly dependent on the value of the exponent τ and on the characteristics of the dynamics.

Validation of EMMS-based drag model using lattice Boltzmann simulations on GPUs

Interphase momentum transport in heterogeneous gas–solid systems with multi-scale structure is of great importance in process engineering. In this article, lattice Boltzmann simulations are performed on graphics processing units (GPUs), the computational power of which exceeds that of CPUs by more than one order of magnitude, to investigate incompressible Newtonian flow in idealized multi-scale particle–fluid systems. The structure consists of a periodic array of clusters, each constructed by a bundle of cylinders. Fixed pressure boundary condition is implemented by applying a constant body force to the flow through the medium. The bounce-back scheme is adopted on the fluid–solid interfaces, which ensures the no-slip boundary condition. The structure is studied under a wide range of particle diameters and packing fractions, and the drag coefficient of the structure is found to be a function of voidages and fractions of the clusters, besides the traditional Reynolds number and the solid volume fractions. Parameters reflecting multi-scale characters are, therefore, demonstrated to be necessary in quantifying the drag force of heterogeneous gas–solid system. The numerical results in the range 0.1 ≤ Re ≤ 10 and 0 < ϕ < 0.25 are compared with Wen and Yu's correlation, Gibilaro equation, EMMS-based drag model, the Beetstra correlation and the Benyahia correlation, and good agreement is found between the simulations and the EMMS-based drag model for heterogeneous systems.

Enhanced Electrocatalytic Oxygen Reduction through Electrostatic Assembly of Pt Nanoparticles onto Porous Carbon Supports from SnCl2-Stabilized Suspensions

Monodisperse Pt nanoparticles with atomic structures that span the cluster to crystal transition have recently been synthesized in electrostatically stabilized, aqueous-based suspensions. In the present study, the anionic charge from the stabilizing SnCl(2) sheath adsorbed on the surface of these particles is used for the first time to assemble Pt directly onto porous carbon supports via electrostatic assembly. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) reveals that these assemblies have substantially higher Pt-C dispersions than obtained from precipitation methods commonly used for commercial electrocatalyst systems. Energy dispersive spectroscopy (EDS) and inductively coupled plasma-mass spectrometry (ICP-MS) are used to determine that loadings of 10-30% by weight Pt (particle packing fractions from 0.05 to 0.25) are obtained through a single electrostatic application of these particles on Vulcan carbon, depending on particle size. The highest average oxygen reduction reaction (ORR) mass activity obtained using this approach is 90.4 A/g(Pt) at 0.9 V vs RHE in 0.1 M perchloric acid is with 1-2 nm particles that exhibit a transitional atomic structure. This activity compares to an average value of 74.0 A/g(Pt) obtained from densely packed electrostatic layer-by-layer (LbL) assemblies of unsupported particles and 36.7 A/g(Pt) commercial Vulcan electrocatalyst from Tanaka Kikinzoku Kogyo (TKK). Enhanced activity is observed with electrostatic assembly of any particle size on Vulcan relative to unsupported or commercial electrocatalyst with comparable durability. Such enhanced activity is attributed to improved reactant accessibility to the catalyst surface due to the increase in particle dispersion. An extinction coefficient of 7.41 m(2)/g at 352 nm is obtained across the entire cluster to crystal transition from 20 atom clusters to 2.9 nm single crystal nanoparticles, indicating that observed variation in ORR activity with particle size may be associated primarily with changes in atomic surface structure as opposed to the metallic character of the nanoparticles as assessed by UV-vis spectroscopy.

Effects of applied load and particle size on the plastoelasticity and tablet strength of some directly compressible powders.

Correlations have been established between the particle size and packing fraction of microcrystalline cellulose, calcium phosphate dihydrate, corn starch and lactose, and the elastic recovery, stress relaxation, and tensile strengths of their tablets.

Revisiting the concept of HTR wallpaper fuel

As early as the 1970s, attempts were made to reduce the peak fuel temperature by means of so-called “wallpaper fuel”, in which the fuel is arranged in a spherical shell within a pebble: By raising particle packing fraction, fuel kernels are condensed to the outer diameter of the fuel zone, leaving a central part of the pebble free of fuel. This modification prevents power generation in this central fuel-free zone and decreases temperature gradient across the pebble. Besides particle temperature reduction, the wallpaper concept also enhances neutronic performance through improved neutron economy, resulting in reduced fissile material and/or enrichment needs or providing the potential to achieve higher burn-up. To assess such improvements, calculations were performed using Monte Carlo neutron transport and depletion codes MCNP/MCB. Among others, investigations of conversion ratio, temperature coefficient of reactivity, spent fuel composition and neutron multiplication (for which a method to determine the six-factor formula was developed), were conducted. It is demonstrated that this fuel type impacts positively on the fuel cycle, reduces production of minor actinides (MA) and improves the safety-relevant parameters of the reactor. A comparison of these characteristics with PBMR-type fuel is presented: By comparison with PBMR fuel, the “wallpaper design” results in an effective neutron multiplication coefficient increase (by about 1750 pcm), which is combined with a decrease of between 4.6 and 17.5% in MA production. An improved neutron economy of the heterogeneous design enables enrichment of the “wallpaper type” of fuel to be reduced by more than 6%. The fuel changes suggested in this paper offer more versatility to the HTR concept: Conversion ratio can be decreased (leading to lower MA build-up and fuel reprocessing cost) or raised (leading to lower fuel consumption and fuel cost). Variations around this concept also enable higher reactivity, thus higher achievable burn-up, improving sustainability of HTRs.

Rheology and Microstructure of Polymer Nanocomposite Melts: Variation of Polymer Segment−Surface Interaction

We have studied the effects of particle packing fraction, polymer molecular weight (MW), and polymer-segment-particle-surface affinity on the phase behavior of 44 nm silica dispersions in unentangled, low MW polyethylene oxide (PEO), polyethylene oxide dimethyl ether (PEODME), and polytetrahydrofuran (PTHF) through rheological measurement and small-angle X-ray scattering. Particles are shown to be stable in PEO nanocomposites up to high volume fractions due to an adsorbed layer of polymer segments that stabilizes particles in the melt. Comparison of the PEO nanocomposite to PEODME and PTHF nanocomposites reveals little evidence of an adsorbed layer in the spirit of the PEO nanocomposite. Measurement of the PTHF nanocomposite viscosity reveals evidence of segment slip at the particle surface by the particle intrinsic viscosity being less than Einstein's value. At higher particle volume fractions, the viscosity diverges, yielding an elastic response. The elastic response of the PEO nanocomposite has the signatures of a colloidal glass, while the PEODME and PTHF nanocomposites resemble a gel. Measurement of the particle structure factor reveals a change from overall repulsive particles in PEO to attractive particles in PTHF as the segment-surface interaction is changed.