Density Of Pebbles Research Articles

Thousands of planetesimals: Simulating the streaming instability in very large computational domains

The streaming instability is a mechanism whereby pebble-sized particles in protoplanetary discs spontaneously come together in dense filaments, which collapse gravitationally to form planetesimals upon reaching the Roche density. The extent of the filaments along the orbital direction is nevertheless poorly characterised, due to a focus in the literature on small simulation domains where the behaviour of the streaming instability on large scales cannot be determined. We present here computer simulations of the streaming instability in boxes with side lengths up to $6.4$ scale heights in the plane. This is $32$ times larger than typically considered simulation domains and nearly a factor $1,000$ times the volume. We show that the azimuthal extent of filaments in the non-linear state of the streaming instability is limited to approximately one gas scale height. The streaming instability will therefore not transform the pebble density field into axisymmetric rings; rather the non-linear state of the streaming instability appears as a complex structure of loosely connected filaments. Including the self-gravity of the pebbles, our simulations form up to $4,000$ planetesimals. This allows us to probe the high-mass end of the initial mass function of planetesimals with much higher statistical confidence than previously. We find that this end is well-described by a steep exponential tapering. Since the resolution of our simulations is moderate -- a necessary trade-off given the large domains -- the mass distribution is incomplete at the low-mass end. When putting comparatively less weight on the numbers at low masses, at intermediate masses we nevertheless reproduce the power-law shape of the distribution established in previous studies.

Pebble flow in the HTR-PM reactor core by GPU-DEM simulation: Effect of friction

The high-temperature gas-cooled reactor (HTGR) with spherical fuel elements contains complex pebble flow. The flow behavior of pebbles is influenced by various factors, such as pebble density, friction coefficient, wall structure, and discharge port size. Using a GPU-DEM numerical model, the effects of the friction coefficient on the cyclic loading and unloading of pebbles in the full-scale HTR-PM are studied. Numerical simulations with up to 420,000 spherical pebbles are conducted. Four sets of friction coefficient values are determined for comparative analysis based on experimental measurements. Discharging speed, residence time, stress, porosity, and velocity distribution are quantitatively analyzed. In addition, a comparison with the CT-PFD experiment is carried out to validate the numerical model. The results show that near-wall retention phenomena are observed in the reactor core only when using large friction coefficients. However, using friction coefficient values closer to the measured experimental values, the pebble bed in HTR-PM exhibited good flow characteristics. Furthermore, the friction coefficient also influences the porosity and velocity distribution of the pebble bed, with lower friction coefficients resulting in lower overall stress in the bed. The discharge outlet's influence varies with different friction coefficient values. In summary, this study demonstrates that the value of the friction coefficient has a complex influence on the pebble flow in HTR-PM, which provides important insights for future numerical and experimental studies in this field.

Li2TiO3 pebble fabrication by freeze granulation & freeze drying method

Lithium titanate (Li2TiO3) ceramic is one of the candidate tritium breeding material for fusion reactor. Li2TiO3 in the form of spherical pebbles are kept inside the canisters of the fusion blanket. Prior to pebble fabrication, Li2TiO3 powder was prepared by using Li2CO3 and TiO2 as precursor materials by solid-state reaction method. To make the powder-fine, they were mixed and milled together inside the high energy planetary ball mill followed by calcination at 1000 °C for 5 h. An experimental setup based on the freeze granulation and freeze-drying method was developed in-house, where the green pebbles of 1.5–2 mm were prepared by dropping Li2TiO3 slurry into liquid nitrogen through the 0.6 mm nozzle opening. The pebble drying was performed by the sublimation process at – 60 °C under vacuum followed by the sintering of green pebbles at 950 °C, 1050 °C, and 1150 °C. Various characterizations of the powder and pebbles were carried out to ascertain its phase purity, surface morphology, porosity, pore-size distribution, etc. The results of those characterizations confirm the single-stage reaction, phase purity, desired dimension of pebbles, and their physical and thermal properties. The details of those characterizations along with the dependence of sintering temperatures with the pore size distribution and bulk density of pebbles are discussed in this paper.

Bedload transport in rivers, size matters but so does shape

Bedload transport modelling in rivers takes into account the size and density of pebbles to estimate particle mobility, but does not formally consider particle shape. To address this issue and to compare the relative roles of the density and shape of particles, we performed original sediment transport experiments in an annular flume using molded artificial pebbles equipped with a radio frequency identification tracking system. The particles were designed with four distinct shapes and four different densities while having the same volume, and their speeds and distances traveled under constant hydraulic conditions were analyzed. The results show that particle shape has more influence than particle density on the resting time between particle displacement and the mean traveling distance. For all densities investigated, the particle shape systematically induced differences in travel distance that were strongly correlated (R2 = 0.94) with the Sneed and Folks shape index. Such shape influences, although often mentioned, are here quantified for the first time, demonstrating why and how they can be included in bedload transport models.

Effects of bed dimension, friction coefficient and pebble size distribution on the packing structures of the pebble bed for solid tritium breeder blanket

• Effects of bed width on the packing structures of pebble bed were investigated by DEM simulation. • Effects of pebble properties (friction coefficient between pebbles, pebble size distribution and pebble density) on the packing fraction of pebble bed were simulated and analyzed. • Packing structures of both the tritium breeder (Li 4 SiO 4 , Li 2 TiO 3 ) and the neutron multiplier (Be, Be 12 Ti) pebble beds were simulated and analyzed by DEM. In solid tritium breeder blanket, the packing structures of the tritium breeder pebble bed and the neutron multiplier pebble bed are very important to analyze the tritium breeder ratio and the heat and mass transfer process in the pebble bed. In this study, the numerous simulations were conducted to investigated the effects of bed dimension, friction coefficient between pebbles, pebble size distribution and pebble density on the packing structures of the ceramic tritium breeder (Li 4 SiO 4 , Li 2 TiO 3 ) pebble beds and the neutron multiplier (Be, Be 12 Ti) pebble bed by discrete element method (DEM), respectively. The simulation results reveal that the pebble bed dimension, friction coefficient and pebble size distribution have a significant impact on the pebble bed packing fraction. As the width of the pebble bed container increases, the average packing fraction of the pebble bed gradually increases, meanwhile the influence of volume fraction of the wall effect gradually decreases. In addition, a lower friction coefficient between pebbles (smoother surface of the tritium breeder and the neutron multiplier pebbles) and wider pebble size distribution will result in a higher packing fraction of the pebble bed. However, the material density of the ceramic tritium breeder (Li 4 SiO 4 , Li 2 TiO 3 ) pebbles and the neutron multiplier (Be, Be 12 Ti) pebble seems to have no obvious effect on the packing fraction of the wider pebble bed for the solid tritium breeder blanket.

Effects of density difference and loading ratio on pebble flow in a three-dimensional two-region-designed pebble bed

The pebble flow of a two-region-designed dynamic reactor core is simulated by discrete element method. The aims are to verify the feasibility of the two-region-designed reactor and explore the influence of loading ratio and pebble density on flow pattern. Results show that after a period of recirculation flow, the pebble bed can reach equilibrium states with invariable central boundary and stable discharging number ratio of pebbles in the middle to the side regions, which is consistent with the loading ratio of them. The mixing region at different heights and the dispersion of pebbles are analyzed. The mixing zone between the two regions is constrained within reasonable and acceptable ranges. The loading ratio has no influence on the retention rate. But it could significantly affect the two-region configuration, i.e. a larger loading ratio corresponds to a larger central region. Besides, both the shape of the central region and the stagnant zone could be affected by pebble density. Compared to the single-density condition, increasing the middle pebble density (the L-H-L condition) can accelerate the pebble flow and reduce the size of central region. Meanwhile the stagnant zone may be larger and the total retention time may be longer, which are not beneficial to the core safety. On the other hand, although the flow of middle pebbles may be much slower and the central area size may be larger by increasing the side pebble density (the H-L-H condition), all pebbles will flow out of the bed in shorter time, leading to smaller stagnant zone and shorter total retention time. Finally, the vertical flow can be greatly affected by pebble density distribution, and the axial velocity profiles show different patterns between the bottom and the upper part of the packed bed.

Harvesting the decay energy of 26Al to drive lightning discharge in protoplanetary discs

Chondrules in primitive meteorites likely formed by recrystallisation of dust aggregates that were flash-heated to nearly complete melting. Chondrules may represent the building blocks of rocky planetesimals and protoplanets in the inner regions of protoplanetary discs, but the source of ubiquitous thermal processing of their dust aggregate precursors remains elusive. Here we demonstrate that escape of positrons released in the decay of the short-lived radionuclide 26Al leads to a large-scale charging of dense pebble structures, resulting in neutralisation by lightning discharge and flash-heating of dust and pebbles. This charging mechanism is similar to a nuclear battery where a radioactive source charges a capacitor. We show that the nuclear battery effect operates in circumplanetesimal pebble discs. The extremely high pebble densities in such discs are consistent with conditions during chondrule heating inferred from the high abundance of sodium within chondrules. The sedimented mid-plane layer of the protoplanetary disc may also be prone to charging by the emission of positrons, if the mass density of small dust there is at least an order of magnitude above the gas density. Our results imply that the decay energy of 26Al can be harvested to drive intense lightning activity in protoplanetary discs. The total energy stored in positron emission is comparable to the energy needed to melt all solids in the protoplanetary disc. The efficiency of transferring the positron energy to the electric field nevertheless depends on the relatively unknown distribution and scale-dependence of pebble density gradients in circumplanetesimal pebble discs and in the protoplanetary disc mid-plane layer.

On the water delivery to terrestrial embryos by ice pebble accretion

Standard accretion disk models suggest that the snow line in the solar nebula migrated interior to the Earth's orbit in a late stage of nebula evolution. In this late stage, a significant amount of ice could have been delivered to 1 AU from outer regions in the form of mm to dm-sized pebbles. This raises the question why the present Earth is so depleted of water (with the ocean mass being as small as 0.023% of the Earth mass). Here we quantify the amount of icy pebbles accreted by terrestrial embryos after the migration of the snow line assuming that no mechanism halts the pebble flow in outer disk regions. We use a simplified version of the coagulation equation to calculate the formation and radial inward drift of icy pebbles in a protoplanetary disk. The pebble accretion cross section of an embryo is calculated using analytic expressions presented by recent studies. We find that the final mass and water content of terrestrial embryos strongly depends on the radial extent of the gas disk, the strength of disk turbulence, and the time at which the snow lines arrives at 1 AU. The disk's radial extent sets the lifetime of the pebble flow, while turbulence determines the density of pebbles at the midplane where the embryos reside. We find that the final water content of the embryos falls below 0.023 wt% only if the disk is compact (< 100 AU), turbulence is strong at 1 AU, and the snow line arrives at 1 AU later than 2-4 Myr after disk formation. If the solar nebula extended to 300 AU, initially rocky embryos would have evolved into icy planets of 1-10 Earth masses unless the snow-line migration was slow. If the proto-Earth contained water of ~ 1 wt% as might be suggested by the density deficit of the Earth's outer core, the formation of the proto-Earth was possible with weaker turbulence and with earlier (> 0.5-2 Myr) snow-line migration.

Fabrication of Li2TiO3 pebbles by a selective laser sintering process

Lithium titanate, Li2TiO3, is an important tritium breeding material for deuterium (D)–tritium (T) fusion reactor. In test blanket module (TBM) design of China, Li2TiO3 is considered as one candidate material of tritium breeders. In this study, selective laser sintering (SLS) technology was introduced to fabricate Li2TiO3 ceramic pebbles. This fabrication process is computer assisted and has a high level of flexibility. Li2TiO3 powder with a particle size of 1–3μm was used as the raw material, whilst epoxy resin E06 was adopted as a binder. Green Li2TiO3 pebbles with certain strengths were successfully prepared via SLS. Density of the green pebbles was subsequently increased by cold isostatic pressing (CIP) process. Li2TiO3 pebbles with a diameter of about 2mm were obtained after high temperature sintering. Density of the pebbles reaches 80% of theoretical density (TD) with a comparable crush load of 43N. This computer assisted approach provides a new efficient route for the production of Li2TiO3 ceramic pebbles.

Fabrication of the Li2TiO3 tritium breeder pebbles by a capillary-based microfluidic wet process

Li2TiO3 is one of the most promising candidates among tritium breeders. In this work, Li2TiO3 pebbles with a narrow size distribution, high density, small grain size, and good sphericity are synthesized using the commercial Li2TiO3 powder as the raw material by a co-flow capillary-based microfluidic wet process. Highly uniform slurry droplets containing Li2TiO3 powder and polyvinyl alcohol were formed in the microfluidic device and then solidified with the cross-linking reaction between polyvinyl alcohol and borax. Li2TiO3 pebbles were finally obtained after sintering the green bodies. The size of sintered Li2TiO3 pebbles with a good sphericity (Dmax/Dmin < 1.05) can be controlled precisely in a size range of 400–1000 µm by adjusting the flow rate of disperse and continuous phases. The effects of the calcination method, sintering condition, solid content of slurry, and the particle size of Li2TiO3 powder on the relative density of Li2TiO3 pebbles prepared were studied in detail, and 97.16% T.D. (Theoretical Density) maximum relative density of the pebbles with 5 µm grain size were fabricated.

Giant planet formation with pebble accretion

In the core accretion model for giant planet formation, a solid core forms by coagulation of dust grains in a protoplanetary disk and then accretes gas from the disk when the core reaches a critical mass. Both stages must be completed in a few million years before the disk gas disperses. The slowest stage of this process may be oligarchic growth in which a giant-planet core grows by sweeping up smaller, asteroid-size planetesimals. Here, we describe new numerical simulations of oligarchic growth using a particle-in-a-box model. The simulations include several processes that can effect oligarchic growth: (i) planetesimal fragmentation due to mutual collisions, (ii) the modified capture rate of planetesimals due to a core’s atmosphere, (iii) drag with the disk gas during encounters with the core (so-called “pebble accretion”), (iv) modification of particle velocities by turbulence and drift caused by gas drag, (v) the presence of a population of mm-to-m size “pebbles” that represent the transition point between disruptive collisions between larger particles, and mergers between dust grains, and (vi) radial drift of small objects due to gas drag. Collisions between planetesimals rapidly generate a population of pebbles. The rate at which a core sweeps up pebbles is controlled by pebble accretion dynamics. Metre-size pebbles lose energy during an encounter with a core due to drag, and settle towards the core, greatly increasing the capture probability during a single encounter. Millimetre-size pebbles are tightly coupled to the gas and most are swept past the core during an encounter rather than being captured. Accretion efficiency per encounter increases with pebble size in this size range. However, radial drift rates also increase with size, so metre-size objects encounter a core on many fewer occasions than mm-size pebbles before they drift out of a region. The net result is that core growth rates vary weakly with pebble size, with the optimal diameter being about 10cm. The main effect of planetesimal size is to determine the rate of mutual collisions, fragment production and the formation of pebbles. 1-km-diameter planetesimals collide frequently and have low impact strengths, leading to a large surface density of pebbles and rapid core growth via pebble accretion. 100-km-diameter planetesimals produce fewer pebbles, and pebble accretion plays a minor role in this case. The strength of turbulence in the gas determines the scale height of pebbles in the disk, which affects the rate at which they are accreted. For an initial solid surface density of12g/cm2 at 5AU, with 10-cm diameter pebbles and a disk viscosity parameter α=10-4, a 10-Earth mass core can form in 3My for 1–10km diameter planetesimals. The growth of such a core requires longer than 3My if planetesimals are 100km in diameter.

Pebble Flow and Coolant Flow Analysis Based on a Fully Coupled Multiphysics Model

In pebble bed reactors (PBRs), pebble flow and coolant flow are highly correlated, and the behavior of each flow is strongly influenced by pebble-coolant interactions. Simulation of both flows in PBRs presents a multiphysics computational challenge because of the strong interplay between the flows. In this paper, a fully coupled multiphysics model is developed and applied to analyze the pebble flow and coolant flow in helium gas-cooled and fluoride salt-cooled PBR designs. A discrete element method is used to simulate the pebble motion to obtain the distribution of pebble density and velocity and the maximum contact stress on each pebble. Computational fluid dynamics is employed to simulate coolant dynamics to obtain the distribution of coolant velocity and pressure. The two methods are fully coupled through the calculation and exchange of pebble-coolant interactions at each time step. Thus, a fully coupled multiphysics computational framework is formulated. A scaled experimental fluoride salt-cooled reactor facility and a full-core helium gas-cooled HTR-10 reactor are simulated. Noticeable changes, such as higher pebble density in the cylindrical core region and more uniform vertical fluid speed profile due to the coupling effect, are observed compared to previous single-phase simulations alone without coupling. These changes suggest that the developed computational framework has higher fidelity compared with previous uncoupled methodology in analyzing pebble flow in PBRs. For the scaled experimental fluorite salt-cooled reactor facility calculation, similar hydraulic loss can be obtained as measured in the University of California, Berkeley, Pebble Recirculation Experiment (PREX), demonstrating the potential of the developed method in thermal-hydraulic analysis for PBRs.

303 カーリング・ストーンの運動とカールのメカニズム(2) : カール比・スウィーピング・ペブル密度(カーリング・和弓)

303 カーリング・ストーンの運動とカールのメカニズム(2) : カール比・スウィーピング・ペブル密度(カーリング・和弓)

PARTICLE CLUMPING AND PLANETESIMAL FORMATION DEPEND STRONGLY ON METALLICITY

We present three-dimensional numerical simulations of particle clumping and planetesimal formation in protoplanetary disks with varying amounts of solid material. As centimeter-size pebbles settle to the mid-plane, turbulence develops through vertical shearing and streaming instabilities. We find that when the pebble-to-gas column density ratio is 0.01, corresponding roughly to solar metallicity, clumping is weak, so the pebble density rarely exceeds the gas density. Doubling the column density ratio leads to a dramatic increase in clumping, with characteristic particle densities more than ten times the gas density and maximum densities reaching several thousand times the gas density. This is consistent with unstratified simulations of the streaming instability that show strong clumping in particle dominated flows. The clumps readily contract gravitationally into interacting planetesimals of order 100 km in radius. Our results suggest that the correlation between host star metallicity and exoplanets may reflect the early stages of planet formation. We further speculate that initially low metallicity disks can be particle enriched during the gas dispersal phase, leading to a late burst of planetesimal formation.

Fabrication development of Li 2O pebbles by wet process

Lithium oxide (Li 2O) is one of the best tritium breeding materials. A small sphere of Li 2O is proposed in some designs of fusion blankets. Recently, reprocessing technology on irradiated ceramic tritium breeders was developed from the viewpoint of effective use of resources and reduction of radioactive wastes. The wet process is advantageous for fabricating small Li 2O pebbles from the reprocessed lithium-bearing solutions. Preliminary fabrication tests of Li 2O pebbles by the wet process were carried out. However, the density of the pebbles obtained was only 55%. Therefore, process improvement tests were performed in order to increase the density of Li 2O pebbles fabricated by this method. The improved process yielded Li 2O pebbles in the target range of 80–85% T.D.