Figure 15 - uploaded by Martin Z. Bazant
Content may be subject to copyright.
Source publication
A series of one-to-ten-scale experiments were conducted at the Massachusetts Institute of Technology (MIT) to explore several key aspects of pebble flow in pebble-bed reactors. These experiments were done to assess not only the flow lines but also the relative velocities of the pebbles of various radii from the center line of the core. Half-model a...
Context in source publication
Similar publications
Jonathan Crary. Suspensions of Perception: Attention, Spectacle, and Modern Culture. An OCTOBER Book. The MIT Press, Cambridge, Massachusetts & London, England 1999. 397 pp, 107 ill. ISBN 0–262–03265–1.Hans‐olof BostrÖm (red.), Tolv begrepp inom de estetiska vetenskaperna Carlssons Bokförlag, Stockholm 2000. ISBN 91–7203–917–5
review of David Temperley's "Music and Probability". Cambridge, Massachusetts: MIT Press, 2007,
ISBN-13: 978-0-262-20166-7 (hardcover) $40.00.
O presente trabalho tem como objetivo apresentar uma prática docente
do ensino da Geometria em relação ao estudo de ângulos e polígonos. O trabalho
foi desenvolvido no segundo trimestre do ano de 2016, com 113 alunos de quatro
turmas de 6º ano do Ensino Fundamental, de uma escola privada da cidade de
São Paulo. Para tal nos valemos do uso do Scratc...
Citations
... Tertiary jet height Secondary jet height (28) Secondary damping factor follows the similar trend like primary damping factor as presented in Fig. 13(b). ...
... Values of the Coefficient of friction are taken from Frankowski et al. (2013) and Kadak et al. (2004) as presented in Table 1. Taking a cue from Lassaad, Mathieu, and Mohamed (2020) and Lee et al. (2013), Poisson's ratio for glass and plastic particles is decided to be 0.21 and 0.37, respectively. ...
Pulsating airflow-driven gas-solid fluidization is an effective method to segregate particles of different densities. The current article presents an elaborate computational study on the development of simulation methodology, and parametric trend identification of pulsating airflow-driven granular segregation for the first time using computational fluid dynamics (CFD), discrete element model-ing (DEM) coupled analysis. The rigorous validation of the computational prediction has been produced against the experimental result reported by Li et al. (2021) and an excellent agreement has been observed. Segregation behavior for different density ratios of particles, different patterns of pulsation, and different particle shapes is presented in the current article. The segregation index improves with the density ratio of the binary mixture of particles, but the rate of increment of the segregation index is highly dependent on the airflow rate. Near the optimal value of airflow rate, the rate of increment of the segregation index reduces with the density ratio. Keeping the bed height and material property constant, different patterns of pulsation namely-sinusoidal, triangular , and exponential have been adopted. The segregation index is higher for sinusoidal patterns, whereas it reduces when the pattern is changed to triangular and exponential. Particles of constant volume with different shapes are also considered to understand the effect of particle shape on segregation. The segregation index deteriorates with the increasing surface area of the particle at constant volume.
... The residence time of the fuel pebbles within the reactor core is mainly governed by their velocities and trajectories, which depend on the pebbles' initial insert points and core geometry, such as cone angle, outlet diameter, and discharge rate, and pebble properties (Choi et al., 2005;Rycroft et al., 2013;Gui et al., 2014;Gatt, 1970;. Studies have shown that the pebbles move in vertical streamlines with little or no crossing between them in the cylindrical section of the bed (Kadak and Bazant, 2004;Yang et al., 2009). The center-line pebbles follow the shortest path to exit the reactor core, while pebbles near the wall take the longest path. ...
... Due to the dense and opaque nature of PBRs, conventional optics-based velocimetry techniques have limited application in PBR, making it quite challenging to perform pebble flow studies in three-dimensional setups. Because of this, most of the earlier investigations Kadak and Bazant, 2004;Yang et al., 2009;Li, et al., 2013;Jia et al., 2016;Jia et al., 2017;Li et al., 2009;Jiang et al., 2012) were conducted in two-dimensional facilities (rectangular or semi-cylindrical models), whereby colored pebbles are visually tracked on an unrealistic flat transparent wall, and the flow behavior of the boundary pebbles is investigated. The pebble flow in 2-D experimental setups is not the same as the actual flow in a real reactor since pebble flow behavior is predominantly governed by core geometry. ...
... Yet, they all share a common shortcoming: the use of spheres of different sizes, densities, and surface friction from the actual pebbles utilized in PBRs. In the MIT investigation (Kadak and Bazant, 2004), for example, 6 mm plastic balls were utilized to simulate the fuel pebbles. Khan et al. studied pebble flow dynamics in a continuous pebble re-circulation experimental setup using glass marbles with a diameter of 0.5 in and a density of 2.5 g ). ...
... 6. A 1D streamline depletion is sufficient to capture the pebble flow since experiments show that the flow is axially dominated [20]. ...
... Khane [18] used the non-invasive radioactive particle tracking (RPT) technology and cobalt-60 tracer to complete the continuous pebble recycling experiment and obtain the particle movement information. Kadak [3] used two colors of particles in the semi 3D model to get the streamline of particles and the relative velocity of pebbles with different radius. ...
Particle movement in pebble bed has important applications in engineering. A fast region homogenization method based on experimental silo discharging process is proposed in this paper. It can obtain the particle information from the particle motion image, and quickly calculate the homogenization information of the region. Hough transform is applied to the image of silo unloading process in order to obtain the information of particle centroid and radius. The particle tracking velocimetry (PTV) algorithm processes two continuous images to realize particle matching. Based on the trajectories of the particle, a fast region homogenization method is developed to obtain the homogenization information of the region. By analyzing the possible relative geometric relationships between mesh elements and particles, the hash set is constructed in advance to quickly calculate the regional homogenization parameters. Compared with the traditional integral method, the calculation speed is greatly accelerated on the premise of ensuring the calculation accuracy. Finally, the particle area characteristics (average velocity and filling rate) of the near wall area and the central area of the pebble bed are compared.
... Even when the mixed-flow effect in the core is very strong, when the mixing proportion is set to 0.5 (50%), the variation in the peak power factor is only 0.0913%. In fact, according to the two-dimensional pebble flow experiment, the flow mixing proportions between the channels is only approximately 1% (Kadak, 2004). In this case, the uncertainty of the power peak calculation caused by the mixed-flow effect of the pebbles is approximately 0.0015%, and the influence on the Keff is even smaller. ...
There has been increasing demand for uncertainty quantification (UQ) in the nuclear engineering community. Thus far, most uncertainty analyses have focused on light water reactor (LWR). As an innovative reactor, the pebble-bed high-temperature gas-cooled reactor (PB-HTGR) features a continuous-fuel-cycling operation strategy and a movable core, which means the uncertainty analysis methods used for LWRs cannot be directly applied to the PB-HTGR. In this work, we summarize recent progress in the uncertainty analysis of the PB-HTGR at the Institute of Nuclear and New Energy Technology, Tsinghua University. We propose a framework for uncertainty analysis based on the well-developed, practical design of the PB-HTGR program system. In this framework, the uncertainty sources are divided into different components and steps, and the maximum fuel temperature in a depressurized loss of forced cooling accident is chosen as the final uncertainty output parameter. However, not all the issues are resolved as this system involves a complex combination of many physical and thermal factors. To date, within this framework, several milestones have been achieved in the PB-HTR uncertainty analysis. (1) We have developed the uncertainty analysis tool VSOP-UAM (very superior old program-uncertainty analysis in modeling), which uses a statistical sampling method. Using VSOP-UAM, we have achieved the uncertainty analysis of the equilibrium state, which is the typical state of the PB-HTGR, for the first time. (2) Using the VSOP-UAM analysis tool, we have determined the uncertainty propagation of the nuclear cross-section data, fission product yields, and key structural parameters. (3) To determine the UQ of the fission product yields, we developed an advanced sampling method that prevents the sampling of non-physical negative samples. (4) To facilitate a benchmark definition and UQ for the PB-HTGR, studies have also been conducted under the auspices of the Coordinated Research Project on High-Temperature Gas-Cooled Reactor Uncertainty Analysis in Modeling, launched by the International Atomic Energy Agency.
... There have been large-scale pebble-bed flow experiments that tracked pebble-bed flow. 5 More recently flow of pebbles has been measured using X-ray tomography where each pebble has a metallic pin. This allows for simultaneous following in three dimensions of the movement of each pebble, including rotation. ...
Three reactor types can be designed with pebbles (carbon spheres) as the reactor core: the pebble-bed high-temperature gas-cooled reactor (PB-HTGR), the pebble-bed fluoride-salt-cooled high-temperature reactor (PB-FHR), and the thermal-spectrum molten salt reactor (MSR) with fuel dissolved in coolant. In the HTGR and FHR, the pebbles are fuel (coated-particle fuel) and moderator (graphite). In a MSR the pebbles would be the moderator (no fuel). Recent advances enable prediction and modeling of pebble beds with two or more sizes of pebbles.
This may enable the use of pebble beds with multiple size pebbles that create new options. A second smaller size of HTGR/FHR fuel pebble that fills some of the space between the regular pebbles can increase the power output for the same size reactor. For the FHR the second pebble size would reduce inventory of expensive coolant and may widen choices of salt coolants. In an HTGR or FHR, smaller pebbles with high actinide loadings and high heat transfer rates could be used to burn actinides while the larger pebbles are the driver fuel. Multiple pebble sizes in MSRs may enable varying the carbon-to-fuel ratio to optimize the neutron spectrum over time to more efficiently utilize the fuel and allow easy replacement of moderator. The smaller pebbles with no fuel and a high surface-to-volume ratio could be designed to remove (1) HTGR/FHR/MSR tritium from the coolant and (2) noble metal fission products and potentially other impurities in MSRs. We examine the potential incentives for pebble beds with multiple size pebbles. With the tools now available to quantify pebble-bed behavior with multiple size pebbles, the next step is to begin to quantify benefits and limitations for different applications of pebble-bed reactors with multiple sizes of pebbles.
... The version of the RPT technique that was used in this study has some inherent limitations: upper limit on tracking speed due to dynamically moving platform and lower counts were recorded due to collimated detectors (Shehata, 2005). Kadak and Bazant (2004) investigated a scaled-down pebble bed modular reactor (PBMR) for movement of fuel and graphite pebbles in a bi-disperse core concept to answer if they move in a streamlined manner or in a random haphazard fashion under different experimental models: 1.180 • half-model 2. 3-D opaque cylinder. In a 180 • half-model and continuous flow experimental set-up with dynamic central column, visual tracking of pebbles at the mid-plane transparent wall was carried out. ...
... A study in a full threedimensional opaque cylinder was also carried out to overcome this 'wall effect'. The effect of different bottom cone angles and exit opening diameters was studied as a part of the study carried out at M.I.T (Kadak and Bazant, 2004). The experimental set-up used in this study at M.I.T has some limitations: there was no continuous and automatic recirculation of exiting pebbles. ...
... Thousands of fuel pebbles, which are loaded from the top and discharged from the bottom, flow through the core under gravity at a very slow velocity (about 10 À4 -10 À3 m/h inside the bed), forming the so-called extremely slow granule flow. The mechanism of this special flow regime is poorly understood at present, and many investigations, including experimental Jiang et al., 2012;Kadak and Berte, 2001;Kadak and Bazant, 2004) and numerical (Choi et al., 2004(Choi et al., , 2005Li et al., 2009;Shams et al., 2012Shams et al., , 2013aFerng and Lin, 2013), have been carried out to reveal its features. The practical design of HTGRs is indebted to detail studies performed on different complications in pebble bed, like two-region arrangement (Yang et al., 2009), pebble dispersion (Gui et al., 2014a), stagnant region (Li et al., 2013) and optimization of bed configuration (Gui et al., 2014b). ...
... Pebble bed related experimental work has been recently done by Kadak and Bazant (2004) who performed scaled-down experiments on pebble flow for a PBR design with a dynamic central column formed of moderator pebbles. They used small plastic beads to represent the pebbles and studied the streamlines of the flow and the mixing of the moderator and fuel pebbles in a half model and a full three-dimensional model. ...
It is important to understand the packing characteristics and behaviour of the randomly packed pebble bed to further analyse the reactor physical and thermal-hydraulic behaviour and to design a safe and economically feasible pebble bed reactor. The objective of this work was to establish methods to model and analyse the pebble packing in detail to provide useful tools and data for further analyses. Discrete element method (DEM) is a well acknowledged method for analysing granular materials, such as the fuel pebbles in a pebble bed reactor. In this work, a DEM computer code was written specifically for pebble bed analyses. Analysis methods were established to extract data at various spatial scales from the pebble beds resulting from the DEM simulations. A comparison with available experimental data was performed to validate the DEM implementation. To test the code implementation in full-scale reactor calculations, DEM packing simulations were done in annular geometry with 450,000 pebbles. Effects of the initial packing configuration, friction and restitution coefficients and pebble size distribution to the resulting pebble bed were investigated. The packing simulations revealed that from the investigated parameters the restitution coefficient had the largest effect on the resulting average packing density while other parameters had smaller effects. Detailed local packing density analysis of pebble beds with different average densities revealed local variations especially strong in the regions near the walls. The implemented DEM code can be used for further analyses of pebble beds and can be customised for particular needs. The results of the packing simulations are useful when determining suitable values to obtain a pebble bed with the desired packing density for subsequent analyses. It is recommended to consider the local packing density variations especially in further coolant flow and heat transfer analyses.
