Copper stable isotope geochemistry has the potential to constrain aspects of ore deposit formation once variations in the isotopic data can be related to the physiochemical conditions during metal ...deposition. This study presents Cu isotope ratios for samples from the Pebble porphyry Cu‐Au‐Mo deposit in Alaska. The δ65Cu values for hypogene copper sulfides range from −2.09‰ to 1.11‰ and show linear correlations with the δ18O isotope ratios calculated for the fluid in equilibrium with the hydrothermal alteration minerals in each sample. Samples with sodic‐potassic, potassic, and illite alteration display a negative linear correlation between the Cu and O isotope results. This suggests that fractionation of Cu isotopes between the fluid and precipitating chalcopyrite is positive as the hydrothermal fluid is evolving from magmatic to mixed magmatic‐meteoric compositions. Samples with advanced argillic alteration display a weak positive linear correlation between Cu and O isotope results consistent with small negative fluid‐chalcopyrite Cu isotope fractionation during fluid evolution. The hydrothermal fluids that formed sodic‐potassic, potassic, and illite alteration likely transported Cu as CuHS0. Hydrothermal fluids that resulted in advanced argillic alteration likely transport Cu as
CuCl2−. The pH conditions also control Cu isotope fractionation, consistent with previous experimental work. Larger fractionation factors were found between fluids and chalcopyrite precipitating under neutral conditions contrasting with small fractionation factors calculated between fluids and chalcopyrite precipitating under acidic conditions. Therefore, this study proposes that hydrothermal fluid compositions and pH conditions are related to Cu isotope variations in high temperature magmatic‐hydrothermal deposits.
Key Points
Copper isotope ratios are presented for 12 well characterized hypogene sulfide samples from the Pebble Cu‐Au‐Mo deposit, Alaska
The copper isotope results correlate with oxygen isotope results for hydrothermal alteration minerals in the same samples
The data suggest that fluid‐chalcopyrite fractionation factors are controlled by the Cu species in the fluid and the pH conditions
Display omitted
•A study of the PeLUIt-10 optimal dimension by adjusting the reactor's height-to-diameter ratio and volume reduction has been conducted to achieve targeted burnup, uniform power ...density distribution, and acceptable safety parameters.•Modifying the H/D ratio to 0.8 with a volume of 5 m3 significantly improves neutronic and thermal–hydraulic performance, maintaining safety thresholds during transient conditions.•The smaller core volume still meets minimum burnup targets of 60 MWD/kg-HM at a reactor volume of 4.4 m3 with acceptable safety characteristics.
This research investigates the impact of changes in reactor geometry to discover more optimal dimensional options for nuclear power plants with potential applications in remote areas of Indonesia. The reactor used is PeLUIt-10, a pebble bed High-Temperature Gas-cooled Reactor (HTGR) with a 10 MWt capacity and a “once-through-then-out” or OTTO fuel loading scheme. The neutronic and thermal–hydraulic performances of PeLUIt-10 were analyzed with its core size altered, first by modifying its height-to-diameter ratio (H/D ratio) and second by reducing its core volume. These analyses were performed using the Pebble Bed Reactor Neutron Diffusion (PEBBED) Code, a specialized tool to analyze HTGR reactor physics parameters, particularly Pebble Bed Reactors.. Neutronic parameters analyzed include total fuel flow, burnup, power peaking factor, and power density distribution. For thermal-hydraulics and safety, parameters include steady-state and transient fuel temperatures, especially in Depressurized Loss of Forced Cooling (DLOFC) accidents. Results show that the optimal design, maintaining a volume of 5 m3, is a reactor with a height of 159.57 cm and a diameter of 200 cm (H/D ratio of 0.8). The fuel can achieve a maximum burnup of 80.97 MWD/kg-HM at this size. Power density distribution at these dimension is better than another dimensions, with a relatively low power peaking value of 1.4. For safety parameters, the fuel temperature in transient conditions remains below the safety limit. Meanwhile, when the core volume is reduced, the minimum burnup target of 60 MWD/kg-HM at a reactor volume of 4.4 m3 with a diameter of 172 cm and height of 189.2 cm. Thus, for OTTO-cycle PeLUIt-10, altering H/D ratio is more beneficial.
•Pebble flow in two-region reactor is studied on effects of density & loading ratio.•Pebble has invariable central boundary & stable discharge ratio (=loading ratio).•L-H-L makes central region ...reduced, stagnant zone larger & total retention time longer.•H-L-H slows middle-pebble flow, enlarges central area & increases side-pebble density.•H-L-H leads to shorter total retention time and smaller stagnant zone.
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.
•A pebble bed test facility with internal heat source is setup for FHRs.•High-Pr Dowtherm A at low temperature simulates high-temperature FLiBe.•Flow regime transition criteria is setup.•Flow and ...convective heat transfer correlations are obtained for FLiBe in FHRs.
For Fluoride-salt-cooled High-temperature Reactors (FHRs), a pebble bed experimental facility with internal heat generation is set up, using the Dowtherm A as the simulant fluid. Dowtherm A can match the Prandtl number of FLiBe of 520–700 °C at a low temperature range of 45–105 °C. The effects of inlet temperatures, porosity and mass flow rate are investigated on the flow and convective heat transfer characteristics. A criterion is determined for the flow regime transition from the transitional to turbulent flow. The existing correlations are unable to predict the Blake-type friction factor in the transitional flow and show mixed performance in the turbulent flow. The present empirical correlations generally underestimate the convective heat transfer coefficients of the high-Prandtl-number fluid in the pebble bed. New correlations are proposed for predicting the flow and convective heat transfer coefficients with Prandtl number at 14–19 and Reynolds number at 90–2500.
Advances in the development of pebble bed reactors (PBRs) has created a desire for accurate and cost-effective simulation tools for design scoping studies and safety analysis. The current ...state-of-the-art for these simulations is the use of porous media models, although these models rely on correlations to capture the effects of flow features that are not explicitly modeled. One of the areas where correlation accuracy is currently lacking is in the near-wall region of the bed. In this region, the presence of the wall causes the pebbles to pack more orderly, drastically changing the geometry and flow behavior in this region.
This work presents a new generalized pressure drop correlation for PBRs based on the KTA equation. A high-to-low methodology is applied, where large eddy simulation (LES) is performed on two beds of 1568 and 1700 pebbles to generate a high-fidelity dataset. The flow fields are then averaged in time and separated into concentric rings of 0.05 Dpeb width. Average porosity, velocity, and pressure drop are extracted for each ring and the friction and form losses are calculated. The Reynolds number range for this study is 625–10,000, and thus the form losses are dominant over the friction losses. The form losses across the rings are investigated, and a correction term for the form loss calculation is determined and applied to the KTA equation to drastically improve the capability of modeling localized porosity effects in a porous media code. The improved correlation reduces near-wall velocity prediction error from over 50% with the KTA correlation to around 5%. Agreement in pressure drop prediction between LES and porous media simulations is also improved.
•4 Pebble beds are simulated with LES at Reynolds numbers from 625 to 10,000.•A correlation between the form constant and the region porosity is determined. (see Figure 10, Equations 20, 21)•The new correlation reduces the near wall velocity prediction error to ∼6%. (Section 3.2)•A blind test test points to the generality of the improved correlation. (Section 3.3.1)•Agreement of the pressure drop between NekRS and Pronghorn is improved for all beds. (Table 3)
The degree of coupling between dust particles and their surrounding gas in protoplanetary disks is quantified by the dimensionless Stokes number. The Stokes number (St) governs particle size and ...spatial distributions, in turn establishing the dominant mode of planetary accretion in different disk regions. In this paper, we model the characteristic St of particles across time in disks evolving under both turbulent viscosity and magnetohydrodynamic (MHD) disk winds. In both turbulence- and wind-dominated disks, we find that collisional fragmentation is the limiting mechanism of particle growth. The water-ice sublimation line constitutes a critical transition point in dust settling, drift, and size regimes. For a fiducial disk evolution parameter α̃≃10−3, silicate particles inteior to the ice-line are characterized by low St (≲10−2) and sizes in the sub-mm- to 1cm-scale. Icy particles/boulders beyond the ice-line are characterized by high St (≳10−2) and sizes in the cm to dm size range. Hence, icy particles settle into a thin layer at the outer disk midplane and drift inward at velocities exceeding the gaseous accretionary flow due to substantial headwind drag. Silicate particles in the inner disk remain relatively well dispersed and are to a large extent advected inward with their surrounding gas.
The St dichotomy across the ice-line translates to distinct planet formation pathways between the inner and outer disk. While pebble accretion proceeds slowly for rocky embryos within the ice-line (across most of parameter space), it does so rapidly for volatile-rich embryos beyond it, allowing for the growth of giant planet cores before disk dissipation. Through simulations of rocky planet growth, we evaluate the competition between pebble accretion and classical pairwise collisions between planetesimals. We conclude that the dominance of pebble accretion can only be realized in disks that are driven by MHD winds, slow-evolving (α̃≲10−3.5), and devoid of pressure maxima that may concentrate solids and give rise of planetesimal rings in which classical growth is enhanced. Such disks are extremely quiescent, with Shakura-Sunyaev turbulence parameters αν≲10−4. We conclude that for most of parameter space corresponding to values of αν reflected in observations of protoplanetary disks (≳10−4), pairwise planetesimal collisions constitute the dominant pathway of rocky planet accretion. Our results are discussed in the context of super-Earth origins, and lend support to the emerging view that they formed in planetesimal rings. Moreover, these results argue against a significant contribution (≳ 10%) of outer disk, carbonaceous material to the proto-Earth in the form of pebbles, in agreement with chemical and isotopic investigations of Earth’s accretion history.
•We model the Stokes number in disks evolving under turbulence and MHD winds.•Icy grains are larger, settle more readily, and drift faster than silicate grains.•Planetesimal collisions and pebble accretion compete in rocky planet formation.•Rocky embryos mainly grow by mutual collisions.•Pebble accretion can dominate in extremely quiescent inner disks.
Investigation on the positions of hot spots appearing in an operating pebble-bed of a high temperature gas-cooled reactor (HTGR) and seeking ways to reduce the possibility of their appearance have ...attracted scientists’ attention. Improving the convective heat transfer coefficient (HTC) of the bed could reinforce heat transferring and thus lower the temperature of the pebbles. In our previous studies, heat transfer characteristics of a face-centered-cubic (FCC) structured pebble-bed (pebble diameter of 12 cm) were discussed. In this study, 3 FCC beds were packed with pebbles of 3 different diameters (10 cm, 12 cm, and 14 cm) and the impact of pebble diameter on the heat transfer coefficient was firstly investigated; then, a small sphere was placed in the pebble-bed packed with 10 cm-diameter pebbles and how the sphere size affecting the heat transfer characteristics was studied. It was found that (1) reducing the pebble diameter improved the heat transfer performances, specifically, the bed with a pebble diameter of 10 cm demonstrated the best heat transfer ability and an enhancement ratio of 10.4% was obtained compared to the bed with 12 cm-pebbles; (2) the average HTC of the bed increased with the inserted sphere size, particularly, comparing to the pebble-bed without a small sphere, 27% enhancement was achieved for the bed packed with 10 cm-pebbles and a 4.14 cm-sphere; (3) A generic correlation of the Nusselt number was proposed as Nu = 0.1941Re0.8Pr0.4-0.3226(L/D-1.027)2Re0.8Pr0.4. Such findings provide references for reactor designers and will help to develop a safer pebble-bed core.
•Smaller pebble size enhances the heat transfer performances of a pebble-bed.•A 10.4% enhancement was achieved by reducing pebble diameter.•Heat transfer enhancement ratio as high as 27% was obtained.•A generic correlation on the Nusselt number of a pebble-bed was given.
•Single phase Be and Be12Ti pebbles were successfully fabricated by a combination method.•Surface analysis of Be and Be12Ti pebbles were carried out by using AFM and SEM.•Compression tests of Be and ...Be12Ti pebbles had been performed.•One method based on contact mechanics was introduced to evaluate the stiffness of Be and Be12Ti pebbles.
Beryllium pebbles are planned to be used as a neutron multiplier in the Helium-cooled ceramic breeder (HCCB) tritium breeding blanket module (TBM) of ITER, which is also the primary option of the Chinese TBM program. Advanced neutron multipliers such as Be12Ti beryllide with high stability at elevated temperature are desired for demonstration power plant (DEMO) reactors. Prototypic pebbles 1 mm in diameter of single phase Be and 0.7 mm in diameter of binary Be12Ti beryllide were successfully fabricated by a combination method involving hot isostatic pressing and rotating electrode process. Surface microstructure of Be and Be12Ti pebbles were analyzed by using AFM and SEM. Compression properties of Be and Be12Ti pebbles were evaluated by mechanical compression. Beryllium pebbles displayed high ductility (50% deformation without fracture), which is better than that of beryllide pebbles. One method based on contact mechanics was introduced to evaluate the range of effective modulus and stiffness of Be and Be12Ti from compression load curves in the elastic regime.
Prediction of the time-related traits of pebble flow inside pebble-bed HTGRs is of great significance for reactor operation and design. In this work, an image-driven approach with the aid of a ...convolutional neural network (CNN) is proposed to predict the remaining time of initially loaded pebbles and the time interval of paired flow images of the pebble bed. Two types of strategies are put forward: one is adding FC layers to the classic classification CNN models and using regression training, and the other is CNN-based deep expectation (DEX) by regarding the time prediction as a deep classification task followed by softmax expected value refinements. The current dataset is obtained from the discrete element method (DEM) simulations. Results show that the CNN-aided models generally make satisfactory predictions on the remaining time with the determination coefficient larger than 0.99. Among these models, the VGG19+DEX performs the best and its CumScore (proportion of test set with prediction error within 0.5s) can reach 0.939. Besides, the remaining time of additional test sets and new cases can also be well predicted, indicating good generalization ability of the model. In the task of predicting the time interval of image pairs, the VGG19+DEX model has also generated satisfactory results. Particularly, the trained model, with promising generalization ability, has demonstrated great potential in accurately and instantaneously predicting the traits of interest, without the need for additional computational intensive DEM simulations. Nevertheless, the issues of data diversity and model optimization need to be improved to achieve the full potential of the CNN-aided prediction tool.
•An image-driven approach of CNN + DEM is proposed for pebble-flow in HTGRs.•CNN + DEX outperforms corresponding regression models on evaluation metrics.•VGG19+DEX model performs the best on test sets with the CumScore of 0.939.•Promising results prove the generalization ability of the VGG19+DEX.•As a potential real-time prediction tool, the trained model is more efficient than DEM.
•A reduced-order model was employed to reconstruct the pebble bed and pore flow.•Original snapshots were obtained through high-fidelity CFD-DEM methods.•The computation time is drastically reduced ...while the accuracy is guaranteed.•Rapid acquisition of pressure and flow characteristics of helium properties based on ROM results.•Based on ROM results, the influencing factors of the effective thermal conductivity of the pebble bed were analyzed.
In recent years, the pebble bed module has garnered increased attention due to its inherent safety and versatile applications, particularly in the form of High-Temperature Gas-Cooled reactors and fusion tritium breeding blankets. Understanding the thermal–hydraulic characteristics within the pebble bed is crucial for the safety evaluation and design of such reactors. To study pore flow in the pebble bed, discrete element coupling methods and computational fluid dynamics (DEM-CFD) are commonly employed. However, simulating thousands of pebbles can be computationally intensive and time-consuming. To address this, reduced order models (ROMs) have been developed to reduce the computational complexity by employing simplified systems instead of the original complex system, thereby significantly saving computational time while maintaining accuracy. In this work, ROMs have been established for body-centered cubic packing, face-centered cubic packing, and randomly packed beds of pebbles. Using the ROM results, subsequent analysis focused on two important thermal–hydraulic characteristics: pressure and effective thermal conductivity. A comparison was made between the results obtained from the full-order model (FOM) using CFD and the reconstructed ROM results. The case studies demonstrate the potential of the proposed approach in rapidly and accurately investigating significant flow and heat transfer features, such as pressure and temperature.
PDF
