•Effects of spatial scale on modeling radiative heat transfer of packed particle beds are analyzed.•Long-range scale (LR) model is accurate for large conductivity ks≫kr or Λ>10.•Short-range scale ...(SR) model is inaccurate for ks≫kr but accurate for ks~O(kr) at low temperature.•Microscopic-scale (MS) model is the most accurate model used for correcting other models.•Over- and underestimation of radiative and conductive heat cause better prediction of SR at ks~O(kr).
Thermal radiation is important in high temperature packed pebble bed, which is still poorly understood. The present work is to analyze the effect of spatial scale in modeling thermal radiation of packed pebble beds. The long-range model (full integral scale), short-range model (partial integral scale) and microscopic models (sub-particle scale) are compared and analyzed with reference to existing correlations. In high temperature packed pebble beds, the long-range model takes into account all possible radiation between surrounding spheres, even those that are not direct Voronoi neighbors, whereas the short-range model considers only a portion nearby. It is found that when solid conductivity is much greater than the effective thermal conductivity of radiation (ks≫kr or Λ>10), the long-range model provides better results than the short-range model in predicting the radiative heat exchange. The short-range model overestimates solid conductivity at low temperatures (lower than 1215°C) when ks~O(kr) (or Λ<10) while underestimating radiative heat exchange. It therefore still provides predictions for total heat exchange that is in good agreement with experimental data in cases where the errors cancel out. Moreover, the short-range radiation model is more computationally efficient than the long-range model and microscopic model to compute view factor between particles of Voronoi neighbors.
•Eight 3-D structures (3DS) are designed and circulating pebble flows are studied.•Constructing two new indices to analyze the mixing of the upper and lower pebbles.•3DS impedes near wall pebble ...flow, increases cycling speed and mixing at the core.•Triangular/helicoidal 3DS are better in speeding up and enhancing mixing.•Saturation phenomenon for the number of structural grooves in 3DS is found.
The pebbles’ movement in the pebble beds of 10 MW high-temperature gas-cooled test reactor (HTR-10) presents as a kind of circulating quasi-static dense pebble flow. The mixing of the upper and the lower fuel pebbles is important because the fast and good mixing is beneficial to flattening the power distribution and lowering the maximum temperature in the lower part of the pebble bed, where the temperature is higher than other region because of the higher burn-up of fuel pebbles. To figure out the effect of different three-dimensional (3-D) wall structures on the flow and mixing of pebbles, eight 3-D wall structures are designed and mono sized pebbles with same density are adopted to simulate by discrete element method (DEM). With phenomenological methods and different mixing indices, qualitative and quantitative analysis are performed and presented hereinafter. All selected wall structures have different degrees of effect on impeding the pebble flow near the wall, accelerating the cycling speed of pebbles at the core region and strengthening the mixing of the upper and lower pebbles in the pebble bed. Compared with the designed trapezoidal and plane structures, triangular and helicoidal structures perform better in accelerating the cycling speed for pebbles at the core region and strengthening the mixing of pebbles by analyzing cycle index (CI), coordination-Lacey’s rule mixing index (CLMI) and coordination-concentration based mixing index (CCMI). In addition, a phenomenon of saturation for the number of structural grooves is reported in this literature. That is, the effect of accelerating the cycling speed of pebbles at core zones and strengthening the mixing gets closer to a certain degree if we make the different grooves denser. The optimal structure to accelerating cycling speed for pebbles in core zones and improving mixing is triangular structure among the four kinds of structures, while the optimum solution for the number of grooves requires deeper investigation.
The flow, stacking, and mixing of pebbles in the High-Temperature Gas-cooled Reactor (HTGR) will affect the power distribution of the core and thus affect the economy and safety of the nuclear ...reactor. Simulations of pebble loading and mixing in HTR-PM based on GPU-DEM have been studied with particle numbers ranging from 230,000 to 420,000. The effects of four loading methods on pebble mixing are compared and analyzed. Mean position, segregation index (SI), Lacey’s mixing index (PSMI), mixing entropy (ME), and porosity are used for quantitative analysis. In addition, an alternative approximate method is proposed to calculate the particle number fraction, which can help solve the problem that the particle number fraction is related to the mesh size. The final result shows that different physical parameters, such as mass and Young’s modulus, will induce slight stratification during pebble mixing. At the same time, the simulation results with different loading methods have different mixing degrees. The reduced model mixes better than the single-pebble-loading method, but the latter is closer to engineering practice.
•Loading & mixing of two kinds of pebbles in a real-scale bed are simulated•An in-house GPU-DEM program has been developed to simulate 420,000 particles•Mixing degrees are analyzed by mean position, SI, PSMI, ME, and porosity•Effect of mass and Young’s modulus on the mixing of pebbles is explored.•A new method is proposed to calculate number fractions to solve the mesh effects.
•Development Goal: Indonesia aims for net-zero emissions by 2060, driving nuclear microreactor development.•Design Focus: Incorporating thorium into the reactor design for improved efficiency and ...sustainability.•Analysis Scope: Neutronic analysis considers thorium-uranium utilization, emphasizing keff calculation.•Parameters Explored: Various thorium mass fractions (0 % to 90 %), core temperatures (900 K to 1200 K), and active core heights (125 cm to 197 cm).•Impact on Criticality: Thorium-uranium composition significantly influences reactor criticality.
Indonesia has committed to reducing greenhouse gas emissions in the framework of net zero emissions, and nuclear energy will be a part of the energy mix. Indonesia has been developing a 10 MWt micro reactor of high temperature gas-cooled reactor (HTGR) with pebble fuel containing 17 % enriched UO2 kernel with OTTO cycle scheme. For the government’s interest to use thorium, this paper assesses the possibility of replacing uranium with thorium. The assessment is performed by calculating the effective neutron multiplication factor (keff). Neutrons captured by 232Th lead to the formation of two intermediate isotopes, namely 233Th and 233Pa, the latter being a significant neutron absorption cross-section. Neutronics analysis is performed using parameters of thorium mass fraction, core temperature, and active core height. The thorium mass fractions varies from 0 % to 90 % Th. The core temperatures are in the range of the normal operating temperature at 900 K, assumed superheat temperature at 1200 K, and shutdown temperature at 300 K. The active core height varies at 197, 180, 150, 130, and 125 cm. This paper aims to determine the keff of the IMR at maximum thorium/uranium mass fraction composition, maximum active core height, core temperature, and fuel burn-up. The MCNP code is used for analysis. The results show that keff decreases with increasing thorium mass fraction and core temperature, and decreasing active core height. Calculations with thorium mass fraction of 15 %, core active height of 197 cm in 20 steps show that the reactor may be continuously operated for more than 920 days without refueling. The analysis results show that IMR design has negative temperature reactivity, inherent safety characteristics, and the ability to use thorium-based fuels.
A mobile agent, which is an autonomous device navigating in a graph, has to explore a given graph by visiting all of its nodes. We adopt the (arguably) weakest possible model of such a device: a ...deterministic memoryless automaton (DMA), i.e., a deterministic automaton with a single state. As expected, such a weak machine is incapable of exploring many graphs without marking nodes. Hence we allow the agent to use identical movable pebbles that can be dropped on nodes or picked from them. It turns out that this marking capability significantly enhances the exploration power of the agent. Our goal is to study how the availability of pebbles impacts the class of graphs that a DMA can explore.
We first concentrate on finite graphs and show that any finite tree can be explored by a DMA without pebbles but there exist (small) finite graphs that cannot be explored by a DMA without pebbles. Then we turn attention to infinite graphs and fully characterize the class of infinite trees that can be explored by a DMA without pebbles. We also define a large class of infinite trees that can be explored by a DMA with finitely many pebbles. It turns out that many of these trees cannot be explored by a DMA without pebbles. On the other hand, we show a large class of infinite trees that cannot be explored by a DMA with finitely many pebbles. Thus, availability of pebbles yields a strict hierarchy of difficulty of exploration of infinite graphs by a DMA, and this hierarchy is strict even for the class of infinite trees: some trees can be explored without pebbles, some trees can be explored with finitely many pebbles but not without pebbles, and some trees require infinitely many pebbles. Finally, we consider exploration by a DMA with infinitely many pebbles. It turns out that all infinite trees can be explored by a DMA with infinitely many pebbles. By contrast, we construct infinite graphs that cannot be explored by any DMA, even with infinitely many pebbles.
Summary
Pebble‐bed HTR utilizes the configuration of randomly distributed graphite and fuel pebbles which contain randomly dispersed TRISO particles, causing the double heterogeneity effect and ...making simulation get complicated. To establish a high‐fidelity whole core model of the annular core pebble‐bed HTR, this article proposes a two‐step whole core modelling scheme with flexibility. This scheme is verified by comparing the HTR‐10 initial critical benchmark results with the HTR‐10 experiment results. Based on the geometry modelling method and Monte Carlo simulation, this study investigates the effect of the central graphite column dimension and the pebble size upon the nuclear heating power density distribution in annular core pebble‐bed HTR. Results show that the annular core reactor has a more edgy distribution of neutron flux and nuclear heating power density and a higher peak value, compared with the cylindrical configuration core reactor. The annular core reactors with a higher thermal power could realize a higher helium outlet temperature with a precondition that the outlet helium flow is carefully separated and mixed. Accordingly, a higher thermoelectric conversion efficiency could be achieved. Reactors filled with smaller pebbles reach the criticality more quickly. However, the radius of the pebbles in the range from 2.5 to 3.5 cm does less effect than the size of the central graphite column does to the neutron flux and nuclear heating power density distribution. The running‐in phase of the annular configuration core reactor is investigated in the last section. The heating power density gradually flattens as the initial core pebbles fall and new fuel pebbles are loaded into the cavity. In this running‐in phase, we adopt a one‐to‐one mapping technique that sets the temperature of pebbles to their real value, varying from their locations. This enables us to do further work of the neutronics/thermal‐hydraulics analysis and the dynamic simulation which fit the realistic engineering practice, and to explore the fuel management scheme of the annular core high‐temperature gas‐cooled pebble‐bed reactor.
Abstract Monitoring bedload transport in rivers is a challenging research domain teeming with technical innovations and methodological developments aimed at improving our knowledge and models of ...bedload processes at different spatial–temporal scales. Radio frequency identification (RFID) technology has improved sediment tracking, allowing the characterisation of transport processes of individual particles at flood‐event scales. Meanwhile, geophone sensors have enabled the long‐term continuous monitoring of seismic signals that can provide surrogate measures of bedload fluxes at local scales, during flood events and at sediment‐pulses. The combination of these two techniques could allow sediment transport processes to be linked with both flood events and sediment pulses. In this study, we used a combination of active ultra‐high frequency RFID technology and geophone monitoring stations to link the virtual velocity of tracers with seismic activity, hydraulic forcing, and the properties of the tracked particles. Single and multiple regression models show that seismic activity best explained the observed variance (81%) of the virtual velocity of particles, in comparison with discharge (58%) and stream power (63%). Furthermore, when several control variables (seismic activity and particle properties) were combined in an empirical model, the model explained 89% of the variance and allowed quantification of the portions of the variance explained by hydraulic forcing, geophonic activity and tracked particles. These results show the high potential of these combined monitoring techniques for future in‐field experiments to investigate bedload processes at different spatiotemporal scales in rivers of different morphologies.
In the design process of a solid-type ceramic breeding blanket, it is important to identify the characteristics of functional materials in the form of pebble beds. In this study, the mechanical and ...thermal behaviors of lithium ceramic pebbles are numerically simulated using an in-house code developed for the discrete element analysis. First, the packing configurations of pebble beds under cyclic loadings are found and discussed in terms of the packing factor, average stress, and average coordination number. In particular, we investigate the effects of pebble size distributions and friction coefficients on the pebble packing. Subsequently, based on the resulting packing configurations, we analyze the heat conduction through the lithium ceramic pebble beds considering the elastic contact between the spherical pebbles. We then qualitatively evaluate the effective thermal conductivities of pebble beds, which also depend upon the pebble size distributions and friction coefficients. The results of the discrete element simulations reveal that a large size difference and low friction coefficient of pebbles lead to close packing and high thermal conductivity of the pebble beds.
We present a novel deterministic equilibrium core pebble-bed depletion algorithm. It differs from most other algorithms by distinguishing pebble age directly by burnup instead of using the number of ...completed passes through the core. Using burnup allows for a more physically realistic modeling of the pebble discharge process, especially for low pass cores. The major innovation of this algorithm is to define pebble fractions and number densities as a distribution over both space and burnup and then define an evolution operator for these quantities. The algorithm is implemented in the Multiphysics Object-Oriented Simulation Environment based reactor physics code Griffin. Numerical results show good agreement (eigenvalue to within 150 pcm, power peaking factor to within 0.2%) for the HTR-PM when compared to published Very Superior Old Programs (VSOP) results.
•A novel, numerically efficient pebble depletion algorithm was developed and implemented into the radiation transport code Griffin.•Pebbles are grouped by burnup allowing for a more accurate model of the pebble discharge process.•Numerical results agree well with published VSOP HTR-PM results.
