Predicting the capability of decay-heat removal for a pebble bed of the high-temperature gas-cooled reactor is a cutting-edge issue in the research of generation IV advanced reactors. In this ...research, numerical simulations of heat transfer in the pebble bed reactor have been conducted by developing two kinds of models, a particle-scale model and a porous media model. The aim is to estimate the effect thermal conductivity of the pebble bed and predict the internal temperature field. The former model relies on the pebble–pebble conduction and radiation at a scale as fine as every fuel pebble. The latter one is an overall model at the scale mainly on the whole feature and capability of the pebble bed reactor. These two models have generated consistent results in an intermediate case considering the effective thermal conductivity for radiation and conduction of the pebbles. Based on this consistency, the pebble bed’s overall features of the internal field of the temperature field in pressurized helium have been well predicted. The simulation results validate the pretty good capability of the pebble bed reactor on decay-heat removal. The maximum temperature of the reactor core is limited to about 350 °C at the 7 MPa pressurized helium. This means the safety of the HTR-PM reactor could be reasonably guaranteed.
•A new SPH kernel by combining a polynomial and a reciprocal term is proposed.•Validated by dam-break, the kernel is used for natural convection in reactor cores.•Comparing to existing kernels shows the differences and (dis)-advantages of them.•Various temperature differences, channel numbers/lengths are simulated.•A mapping method is used to transfer particles’ velocity/temperature to Eulerian.
A tritium breeder is a lithium-based material capable of producing tritium. Many researchers designing nuclear-fusion energy are studying tritium production using pebbles, which are solid-type ...breeders. The sphericity and size of the pebbles are critical in obtaining pebbles with good tritium-breeding efficiency. Furthermore, tritium-release efficiency can be increased by using pebbles with appropriate porosities. Promising raw materials for tritium-breeding materials include Li4SiO4 and Li2TiO3. Li4SiO4 has a higher lithium density than Li2TiO3 and exhibits excellent tritium-breeding efficiency. However, it has the disadvantage of being easily decomposed during the Li4SiO4-green-pebble sintering process because of its low structural stability at high temperatures and high lithium density. In this study, we attempted to determine the optimal conditions for manufacturing Li4SiO4 pebbles using the droplet–freeze-drying method. The optimal Li4SiO4 slurry conditions and sintering temperatures were determined. The optimal Li4SiO4 slurry-fabrication conditions were 3 wt% polyvinyl alcohol and 75 wt% Li4SiO4 based on the deionized-water weight content. The sintering temperature at which Li4SiO4 did not decompose and exhibited the optimum porosity of 10.8% was 900 °C.
Marine beaches worldwide are nowadays exposed to significant contamination by plastics. On the Baltic beaches, polyethylene, polypropylene, and polystyrene are most abundant. We investigate the ...generation of microplastics particles (MPs, characteristic size from 0.5 to 5 mm) from larger plastic items in the sea swash zone using a laboratory rotating mixer filled with water and natural coarse beach sediment (marine pebbles). Inclination of the axis of rotation and the volume of the material were adjusted in such a way that mixing resembled a breaking wave in the swash zone. Plastic samples used were of the types most commonly found on the sea beaches. Experimental 2cm×2cm-large plastic items made of low-density polyethylene (LDPE) were manufactured from common new garbage bags (thickness 5 μm); those made of polypropylene (PP) and polystyrene (PS) were produced from single-use tableware; samples of foamed plastics were presented by cubes (with 2-cm sides) cut out of standard building insulator sheets (foamed PS). Four sets of 24-h-long experiments were conducted (for each type of plastic separately), with step-wise (every 3 hours) examination of the generated MPs mass, number of particles and their qualitative characteristics such as shape, quality of the surface, general behaviour while mixing, etc. Statistically significant dependencies are obtained for the increase in mass and in number of MPs with time for all four used kinds of plastics. Brittle solid PS is shown to be the most productive in terms of both mass and number of MPs generated. Anisotropic springing PP is the most resistant. Tensile tearing of LDPE and fragmentation of foamed PS to compounding bubbles/spherules show the variety of mechanisms involved in fragmentation of plastics in the swash zone. Increase in MPs mass and the number of MPs particles with time, as well the link between them, are important for field monitoring and numerical modelling. Potentially shape-selective operation of sieves during sampling and sorting of MPs particles of various shapes is discussed.
•Local convective heat transfer coefficients (HTC) are higher in near-wall region.•Local HTC variation in the PBR is due to the variation of local gas velocities.•Local HTC are lower at center due to ...low void fractions and high flow resistance.•Variation of Local HTC at different diameter lines is higher at low Re number.
The aim of this study was to investigate the local heat transfer coefficients between the pebbles and the coolant gas in a PBR using an advanced measurement technique that consists of a heated pebble probe, a micro-foil heat flux sensor mounted flush on the surface of the heated pebble probe, and a thermocouple in the center of the bed void in front the sensor. In this work, the local heat transfer coefficients were derived at various axial levels, radial and angular locations and at different superficial inlet gas velocities that cover both transitional and turbulent flow conditions. The local heat transfer coefficients were found to be 22-32%, 34-39%, and 18-20% higher near the wall at superficial inlet gas velocities of 0.3,1.2, and 2m/s, respectively. This is due to higher volumetric flow at the wall where larger void in the pebble bed exists compared to the center region of the bed where the flow of the gas in the packed bed follows the least resistance path. Large deviations were obtained between the experimental overall heat transfer coefficients in the bed and the predictions of seven correlations that were selected from the literature. Furthermore, these correlations cannot predict the local heat transfer coefficients inside the PBR. This necessitates the development of new correlations for the prediction of the local heat transfer coefficients using the data obtained in this work. A pseudo-3D correlation was developed and was found to provide predictions that are in good agreement with the experimental values for the conditions used, with an averaged absolute relative error (AARE) of 3.33% at high Reynolds numbers for our operating and design conditions.
•Smoothed void fraction method (SVF) is proposed for a sub-particle CFD-DEM model.•Step function is replaced by diffusion function to improve simulation convergence.•SVF is validated, and virtual ...symmetric point method agrees with practical wall effect.•SVF used for HTR-10 benchmark problem on subparticle mesh agrees with THERMIX.•Effect of mesh size & smoothing degree are analyzed and optimum values are suggested.
The core of the high temperature gas-cooled reactor (HTGR) is a dense packed pebble bed with large-sized fuel spheres. In the CFD-DEM simulations of fluid-particle systems on sub-particle scale mesh, a smoothed void fraction method (SVFM) is developed to compute the void fraction field based on the particle position and volume. A diffusion function is obtained analytically as a spatial distribution function of particle volume in SVFM, which converges to the step-function-type distribution of particle volume in the sub-particle-scale divided finite volume method (DFVM) when the smoothing degree goes to 0. In validation by a spout fluidized bed when the cell size is less than the particle diameter, it is shown that SVFM is preferable to DFVM for the CFD-DEM simulation since it is in better agreement with the experimental measurements. Moreover, the CFD-DEM simulation using the SVFM on sub-particle scale meshes is performed for the benchmark problem of the HTR-10 reactor. The numerical results at the smoothing degree of η = 0.5 are in good agreement with the empirical code of THERMIX – which is based on experimental measurements. In addition, the discussion indicates that the smoothing degree in SVFM is recommended to be 0.5–0.7 according to the void fraction distribution of Voronoi-tessellation.
•A force-heat transfer-analogy-based novel contact thermal resistance model is proposed.•Resembling Heat-flux by stress distribution makes free of singularity at the contact edge.•The model is ...validated in SC/FCC/BCC configurations and incorporated into thermal DEMs.•Appling to HTTU, temperature, ETC distributions and dynamic thermal responses are derived.•Increasing Tout-wall from 200 to 1000 °C causes 20 % increase of effective thermal diffusivity.
A novel particle-to-particle contact thermal resistance model is proposed in this study, based on the concept of analogy between force and heat transfer. The distribution of heat flux on the contact surface is assumed to resemble the distribution of stress, eliminating the issue of temperature singularity at the contact edge. The model is validated against existing theories and experiments, showing good agreement. The combined use of the model and the thermal discrete element method is applied to analyze temperature and effective thermal conductivity distributions in a pebble bed within a high-temperature test unit. The average effective thermal conductivity obtained from thermal conduction is found to be 2.99 and 2.61 W/(m·K) for power inputs of 20 kW and 82 kW, respectively. An increase in the outer wall temperature from 200 °C to 1000 °C results in an approximate 20 % increase in the effective thermal diffusivity.
In a solid-type ceramic breeding blanket, the functional materials, such as the breeder, multiplier, and reflector, are equipped in the form of pebble beds, while helium purge gas flows through ...pebble beds. The flow characteristics of purge gas need to be investigated in order to design and evaluate the performance of the blanket system, which depends on the configuration of pebble beds. In the current study, various pebble bed models were constructed according to the discrete uniform distribution and normal distribution of pebble sizes, and the packing fractions of the pebble beds were controlled using the discrete element method. Computational fluid dynamics simulations for the laminar flow of helium purge gas through pebble beds were then conducted. In particular, the effects of size distributions and packing fractions of pebble beds on the flow resistance were investigated in terms of pressure drop. Through a series of numerical analyses, it was found that the pressure drop increases not only, obviously, in proportion to the packing fraction of pebbles, but also in inverse proportion to the difference in pebble size. Since the pressure drop is related to the surface areas of pebbles, a smaller difference in the pebble size leads to a higher pressure drop due to a larger surface effect at the same volume of pebbles. The numerical results were also validated by comparing them to the semi-empirical formulae derived for the prediction of pressure drop in packed beds, such as the Ergun equation and the Kozeny-Carman equation. The current study will provide a basis for resolving the practical issues on blanket system design by extending it further to the purge gas flow and conjugate heat transfer that involve fragmentation and resettlement of pebbles.
This paper presents an overview of Pronghorn, a multiscale thermal-hydraulic (T/H) application developed by Idaho National Laboratory and the University of California, Berkeley. Pronghorn, built on ...the open-source finite element Multiphysics Object-Oriented Simulation Environment (MOOSE), leverages state-of-the-art physical models, numerical methods, and nonlinear solvers to deliver fast-running advanced reactor T/H simulation capabilities within a modern software engineering environment. This work summarizes the physical models, multiphysics and multiscale coupling, and numerical discretization in Pronghorn with emphasis on our initial target application to pebble bed reactors (PBRs). A diverse set of applications are shown to depressurized natural circulation in the SANA experiments, forced convection in the Pebble Bed Modular Reactor, three-dimensional (3-D)/one-dimensional coupling of Pronghorn and RELAP-7 systems T/H for loop analysis in the High Temperature Reactor Power Module, and forced convection in the Mark-1 Pebble Bed Fluoride-Salt-Cooled High-Temperature Reactor. A multiphysics coupling of Pronghorn, RELAP-7, and Griffin deterministic neutronics for a gas-cooled PBR demonstrates the capability of the MOOSE framework for reactor design calculations. These applications highlight the verification and validation underlying Pronghorn's software development while emphasizing features that improve upon capabilities offered by legacy tools in areas such as 3-D unstructured meshing, physics modeling, and multiphysics coupling.
The packing structures of a special “J” – cylinder-tours shape ceramic packed pebble beds, which might be used in the breeding zone of future fusion blanket and the other applications were ...numerically studied by the Discrete Element Method. The contact force and force chain distribution and the effect of the pebble diameter on the global packing factor have been investigated. Meanwhile, the analyses of radial and axial local packing factor distribution features and coordination number distribution were performed. The results showed that the global packing factor increased with decreasing pebble diameter and the cylindrical part of the packed pebble bed had a slightly higher global packing factor than the torus part. The contact force kept decreasing after a short period of rising and the force chain distribution showed a clear difference between two parts of the packed pebble bed. Both the radial and axial local packing factor exhibited oscillation behavior but a clear difference observed in two parts. The coordination number distribution was also analyzed to investigate the contact status in the packed pebble bed. The presented results of these investigations added to the understandings of the packing structure of irregular shape packed pebble beds, hence, could provide references for fusion facility design and other areas of industry such as chemical engineering research.
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•A special “J” shape ceramic packed pebble bed was simulated by DEM.•The main packing structures of the irregular packed bed were numerically studied.•The influence of the pebble diameter on the global packing factor was investigated.•Different local packing factor oscillation behavior in two parts was observed.•A slightly smaller average coordination number was observed and discussed.
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