Pebble Bed Core Research Articles

CFD modeling of natural convection in pebble bed geometry with finite volume method

Abstract In this study, we used the finite volume method to computationally model natural convective flow in packed bed geometry. Using the OpenFOAM® v2112 code, we performed the computational analysis. We successfully meshed the intricate packed bed flow geometry, which consists of several spheres positioned at random. The spheres have sizes of 0.006 and 0.01 m, and the associated Rayleigh numbers are 1.83 × 107 and 8.48 × 107 respectively. We used the packed bed heights of H/d = 5, 10, and 20 in the simulations. By comparing the results of the OpenFOAM® v2112 simulations of the natural convection flow for all self-heating sphere in a packed bed, we demonstrated that the velocity distributions and Nusselt values are in good agreement with the experimental data. Additionally, it was evident from the velocity and temperature distributions in a packed bed core that there was a major temperature rise at nearby low velocity fields and a minor velocity rise in the intermediate and upper elevations. We showed that increasing the height of the pebble-bed core and correspondingly increasing the quantity of spheres inside it makes the flow more difficult and also generates local hot spots. This study is notable for using the finite volume method to evaluate natural convection flow in all self-heating packed beds and for simulating packed bed flow using a significant number of spheres. These two factors contribute to the originality of this work.

Improvement of cylindrical nodal expansion method for treating HTGR void cavity

The cylindrical nodal expansion method (NEM) is promising for improving the efficiency of HTGR whole-core neutronics calculation. In HTGR, there generally exists large void cavity above the pebble-bed core. The traditional cylindrical NEM is formulated by the surface-partial-current (SPC) coupling form, which is unable to solve the problem containing void cavity. Aiming to overcome this problem, this paper proposes three types of improved calculation schemes for cylindrical NEMs to treat the void cavity. The first one is employing a modified SPC coupling form; the second one is employing the surface-net-current (SNC) coupling form combined with advanced matrix solvers; the third one is directly using the surface-flux (SF) coupling form. All of the three types of cylindrical NEM schemes have been developed in PANGU code. Numerical results demonstrate the capability and performance of the improved NEMs in calculating the HTGR containing void cavity.

Improved Methods for Calculating the Neutron Diffusion Coefficient of General Pebble Bed

There exists a neutron streaming effect in the high-temperature gas-cooled pebble-bed reactor (HTGR) pebble-bed core caused by the spatial heterogeneity of the neutron’s free path, which has a remarkable impact on neutron leakage. It is necessary to take into consideration the streaming effect in evaluating the homogenized diffusion coefficient of the pebble bed, prior to the whole-core diffusion calculation. In this paper, two methods are proposed for calculating the homogenized multigroup diffusion coefficient of the pebble bed based on migration area conservation theory and Benoist’s theory, respectively. Compared with existing methods, the newly proposed methods are adaptable to a general pebble bed consisting of multitype pebbles and nonvacuum atmosphere. Numerical results demonstrate the proposed methods’ effectiveness and consistency in evaluation of the pebble-bed homogenized diffusion coefficient.

Uncertainty analysis of keff due to the random packing of pebbles in the pebble bed HTR

There has been an increasing demand for the uncertainty analysis for the numerical results from complicated High Temperature Gas Cooled Reactors (HTGRs) system with the continued development of HTGR. In the pebble bed HTR, not only the fuel and moderator pebbles are randomly packed, but also the packing fraction of fuel pebbles has some uncertainty. A new grid-based Expanding System Method (ESM) is proposed to generate an explicit pebble bed core model with random packing of pebbles with different packing fractions. Even more important, the keff uncertainty due to the random packing and uncertainty of packing fraction are quantified based on this high-fidelity model. The numerical results indicate that the grid-based ESM can efficiently generate a realistic pebble bed core model and the uncertainty of keff due to the random packing of pebbles is relatively smaller than the contribution of nuclear data.

Numerical Study on the Thermal Field and Heat Transfer Characteristics of a Hexagonal-Close-Packed Pebble Bed

Fuel elements in a high-temperature gas-cooled reactor (HTGR) core may be stacked with a hexagonal close-packed (HCP) structure; therefore, analyzing the temperature distribution and heat transfer efficiency in the HCP pebble bed is of great significance to the design and safety of HTGR cores. In this study, the heat transfer characteristics of an HCP pebble bed are studied using CFD. The thermal fields and convective heat transfer coefficients under different coolant inlet velocities are obtained, and the velocity fields in the gap areas are also analyzed in different planes. It is found that the strongest heat transfer is shown near the right vertices of the top and bottom spheres, while the weakest heat transfer takes place in areas near the contact points where no fluid flows over; in addition, the correlation of the overall heat transfer coefficient with the Reynolds number is proposed as havg = 0.1545(k/L)Re0.8 (Pr = 0.712, 1.6 × 104 ≤ Re ≤ 4 × 104). It is also found that the heat transfer intensity of the HCP structure is weaker than that of the face-centered-cubic structure. These findings provide a reference for reactor designers and will contribute to the development of safer pebble-bed cores.

The use of burnable absorbers integrated into TRISO/QUADRISO particles as a reactivity control method in a pebble-bed HTR reactor fuelled with (Th,233U)O2

High-temperature gas-cooled reactors (HTGRs) are one of the promising candidates for the next generation of nuclear reactors due to their inherently and passively safe in normal operation and even under accident conditions. There are two HTGR concepts, one based on a pebble-bed core, and the other is a prismatic core. One of the key differences between the pebble-bed core and the prismatic core is the complexity of applying the seed-blanket (SB) concept to the internal production of U-233 from Th-232 in order to extend the cycle length of the reactor. Actually, an enhancement of the operating cycle length in the pebble-bed reactors fuelled with (Th,233U)O2 can be reached by using high U-233 ratios, but these ratios could result in high excess reactivity at the beginning of life (BOL). In order to suppress the excess reactivity phenomenon at the early stage of the fuel cycle, to flatten the reactivity curve as a function of time, a new reactivity control method has been investigated by incorporating burnable absorbers into the fuel particles. This purpose is set up by introducing two varieties of BAs, including Gadolinia and Erbia, either as a homogeneous mixture with the fuel kernel in the TRISO particles or as an additional layer next to the fuel kernel producing the quadruple isotropic (QUADRISO) particles. The present work aims at characterizing the effect of these different loading patterns on some neutronic parameters that define the reactor core under BOL conditions as well as during burnup. In this attempt, the nominal UO2 (17 wt% U-235) fuelled core was used as a reference, while the other models adopt (Th,233U)O2 (17 wt% U-233) fuel with Gadolinia and/or Erbia with different loading patterns. The calculation results show that excess reactivity can be compensated during the early stages of core life and flattened during the cycle by adding Erbia doped with a few ppm of Gadolinia to the TRISO/QUADRISO particles. In these updated configurations, the new core life achieved is approximately 678 Effective Full Power Days (EFPDs), equivalent to 52.5 GWd/t on a single-batch discharge burnup. This means that from the core fuelled with UO2, which has a core life of 537 EFPDs (37 GWd/ton), an average period of 141 EFPDs is extended.

Impact of variable porosity models on the safety of high temperature pebble bed gas-cooled reactors

The Very High Temperature Reactor (VHTR) is one of the candidates of next generation of the nuclear reactors according to IAEA. Predicting the thermohydraulic behavior of High Temperature Reactors (HTR) is an important contribution to the development of this technology. Evaluation of thermohydraulic performance and a comparison with experimental data were proposed to the international research community. The impact of porosity of pebble beds in the thermohydraulic performance in normal operation and under accident condition is the goal of many kinds of research. In this sense, the three-dimensional CFD thermohydraulic simulation of a HTR using ANSYS CFX has been done. The full-scale approach is used to study the influence of different porosity scheme in the main structural materials of the HTR-10 reactor. The porous medium model was used to simulate the pebble bed core zone and the discharge system of pebbles. A comparison with experimental data was made. The steady-state thermohydraulic performance of the HTR-10 reactor at normal operation and anticipated transients without scram (ATWS) tests result, were used. In this work, was possible to estimate the effect of the porosity in the interior regions of the reactor and the impact on the temperature distribution. Finally, the study broadens the knowledge about the impact that the use of variable porosity has on safety analyses in pebble beds reactors.

Cardinal: A Lower-Length-Scale Multiphysics Simulator for Pebble-Bed Reactors

This paper demonstrates a multiphysics solver for pebble-bed reactors, in particular, for Berkeley’s pebble-bed -fluoride-salt-cooled high-temperature reactor (PB-FHR) (Mark I design). The FHR is a class of advanced nuclear reactors that combines the robust coated particle fuel form from high-temperature gas-cooled reactors, the direct reactor auxiliary cooling system passive decay removal of liquid-metal fast reactors, and the transparent, high-volumetric heat capacitance liquid-fluoride salt working fluids (e.g., FLiBe) from molten salt reactors. This fuel and coolant combination enables FHRs to operate in a high-temperature, low-pressure design space that has beneficial safety and economic implications. The PB-FHR relies on a pebble-bed approach, and pebble-bed reactors are, in a sense, the poster child for multiscale analysis. Relying heavily on the MultiApp capability of the Multiphysics Object-Oriented Simulation Environment (MOOSE), we have developed Cardinal, a new platform for lower-length-scale simulation of pebble-bed cores. The lower-length-scale simulator comprises three physics: neutronics (OpenMC), thermal fluids (Nek5000/NekRS), and fuel performance (BISON). Cardinal tightly couples all three physics and leverages advances in MOOSE, such as the MultiApp system and the concept of MOOSE-wrapped applications. Moreover, Cardinal can utilize graphics processing units for accelerating solutions. In this paper, we discuss the development of Cardinal and the verification and validation and demonstration simulations.

Investigation on the mechanism of enhancing heat transfer in a pebble bed by adding in the non-fixed number of smaller-sized spheres

Enhancing heat transfer in the pebble bed reactor could reduce the surface temperatures and lower the possibility of forming hot-spots. The effectiveness of inserting a smaller sphere into a structured pebble bed on optimizing the heat transfer has been confirmed, and yet, the mechanism of heat transfer enhancement is still not fully understood. The impact of the quantity and size of the small spheres on the heat transfer characteristics has been investigated in this study and the mechanism of enhancement was analyzed. It was found that: (1) When the volume or the surface area of the inserted sphere was kept the same, the overall heat transfer coefficients (HTC) of the pebble bed in case 2 or case 3 respectively demonstrated 1.4% or 2.8% higher than that of the bed in case 1; (2) the overall HTC showed an increasing trend with the decreasing ratio of the surface area to the volume; (3) the varying trends of local HTCs along the designated direction were similar among 3 cases and the strongest heat transfer positions were found near pebble-sphere contact points. Such findings will help to design a better pebble bed core.

Criticality Analysis of HTR-10 using an Open Source Monte Carlo code OpenMC

As one of advance nuclear reactor design, capability to model and analyze the pebble bed reactor is important. Availability and capability of an accurate open source and open access software for pebble bed reactor analysis is strategic. It can broaden the involvement of more student and researcher which finally may improve the research and development in this field. Current study aim to develop the pebble bed core model and perform a criticality study of HTR-10 core design. This study exploit the capability of openMC software to model a double heterogenety geometry using a TRISO Pack Model Building based on random sequential packing and closed random packing. Physical parametric surveys of the developed model show an expected results in which the model able to reflect the negative reactivity feedback of HTR-10 design. The critical height of HTR-10 model with helium from current model, VSOP, and MCNP are 125.881 cm, 125.804 cm, 126.116 cm, respectively. A code-to-code criticality analysis comparison of current model with VSOP and MCNP code reported by INET shows a good comparison and suggest that current method can be used for further pebble bed analysis.

Effect of pebble diameters on the heat transfer characteristics of a structured pebble bed in an HTGR

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.

The effects of fuel type on control rod reactivity of pebble-bed reactor

Abstract As a crucial core physics parameter, the control rod reactivity has to be predicted for the control and safety of the reactor. This paper studies the control rod reactivity calculation of the pebble-bed reactor with three scenarios of UO2, (Th,U)O2, and PuO2 fuel type without any modifications in the configuration of the reactor core. The reactor geometry of HTR-10 was selected for the reactor model. The entire calculation of control rod reactivity was done using the MCNP6 code with ENDF/B-VII library. The calculation results show that the total reactivity worth of control rods in UO2-, (U,Th)O2-, and PuO2-fueled cores is 15.87, 15.25, and 14.33%Δk/k, respectively. These results prove that the effectiveness of total control rod in thorium and uranium cores is almost similar to but higher than that in plutonium cores. The highest reactivity worth of individual control rod in uranium, thorium and plutonium cores is 1.64, 1.44, and 1.53%Δk/k corresponding to CR8, CR1, and CR5, respectively. The other results demonstrate that the reactor can be safely shutdown with the control rods combination of CR3+CR5+CR8+CR10, CR2+CR3+CR7+CR8, and CR1+CR3+CR6+CR8 in UO2-, (U,Th)O2-, and PuO2-fueled cores, respectively. It can be concluded that, even though the calculation results are not so much different, however, the selection of control rods should be considered in the pebble-bed core design with different scenarios of fuel type.

DEVELOPMENT OF EXPERIMENTAL POWER REACTOR (EPR) MODEL FOR SAFETY ANALYSES USING RELAP5

Pebble bed reactor design, classified as the high temperature gas-cooled reactor (HTGR), is currently being part of BATAN main program to promote nuclear energy by starting the Experimental Power Reactor (EPR) program since 2015. Starting from 2018, the detail design document has to be submitted into nuclear regulatory body for further assessment. Therefore results of design analysis have to be supplemented by performing a design evaluation, which can be achieved by developing the model of the EPR. The development is performed using RELAP5/SCDAP/Mod.3.4 as the thermal-hydraulic analysis code validated for the light-water reactor having module for the pebble fuel element and non-condensable helium gas. Methodology of model development consists of defining the helium flow path inside the reactor pressure vessel, modelling of pebble bed core including its power distribution, and modelling of reflector components to be simulated under 100 % core power. The developed EPR model results in design parameters, which confirm the main thermal data of the EPR, including the pebble and reflector temperatures. The peak pebble temperature is calculated to be 1,375 °C, which requires further investigations in the model accuracy, since the reference values are around 1,015 °C, even it is below the pebble temperature limit. For safety analysis, the EPR model can be used under nominal core flow condition, which produces more conservative results by paying attention on the RELAP5 specific modules for the pebble bed-gas cooled system.Keywords: experimental power reactor, development, RELAP5, steady-state

Benchmarking of experimental setup for pressure drop calculation in a packed pebble bed using RELAP5

Pebble bed reactor (PBR) is one of High Temperature Gas Cooled Reactor (HTGR) having nuclear fuels formed by a number of pebbles containing uranium in the core. The PBR is the focus of this research since this type of HTGR is under development by BATAN in form of Experimental Power Reactor (EPR) since 2014. One of the challenges in designing the EPR as a PBR is to model the pebbles forming a bed in the core, since this pebble bed will determine the flow and heat transfer characteristics under certain core power and gas flow rate. One parameter under consideration is the pressure drop along the pebble bed as a function of gas velocity, which has been analyzed by building an experimental setup having different pebble diameters. The purposes of this work is to develop a model of the pebble bed experimental setup mentioned above using the RELAP5/SCDAP/Mod3.4 in order to study the RELAP5 capability in modelling the pebble bed core based on benchmarking of the simulation with the experimental results. The results show that values in determining the pressure drop coefficient (K) using RELAP5 can be estimated for the 1.25 cm, 2 cm, and 5 cm pebble diameter after comparing with experimental data. Those values, in particular for the 5 cm pebble diameter, which are related to the Reynolds number and different gas velocities, can be used in developing the model of EPR core having pebble diameter not far different from the experiment.

Study of heat transfer by using DEM–CFD method in a randomly packed pebble-bed reactor

The pebble-bed reactor is one of the most promising designs for the nuclear energy industry. In this paper, a discrete element method–computational fluid dynamics (DEM–CFD) approach that includes thermal conduction, radiation, and natural convection mechanisms was proposed to simulate the thermal-fluid phenomena after the failure of forced circulation cooling system in a pebble-bed core. The whole large-scale packed bed was created using the DEM technique, and the calculated radial porosity of the bed was validated with empirical correlations reported by researchers. To reduce computational costs, a segment of the bed was extracted, which served as a good representative of the large-scale packed bed for CFD calculation. The temperature distributions simulated with two different fluids in this DEM–CFD approach were in good agreement with SANA experimental data. The influence of the natural convection mechanism on heat transfer must be taken into account for coolants with strong convective capacity. The proposed DEM–CFD methodology offers a computationally efficient and widely applied method for understanding the heat transfer process in a pebble-bed core. The method can also be easily extended to assess the passive safety features of newly designed fluoride-salt-cooled pebble-bed reactors.

Experimental and numerical study on helium flow characteristics in randomly packed pebble bed

The high temperature gas cooled reactor (HTGR) with a packed pebble bed core has been one of the fourth generation reactors. The helium cooled pebble bed (HCPB) blanket packed spherical pebbles of lithium orthosilicate (Li4SiO4) has been recommended to Chinese Fusion Engineering Test Reactors (CFETR). Helium flow characteristics in spherical pebble bed are the key issues to design the pumping power. In this work, helium flow characteristics in a rectangular pebble bed channel filled with stainless steel particles whose diameters are 0.5 mm, 0.8 mm, 1.0 mm, 1.5 mm, and 2.0 mm, respectively, were investigated experimentally and numerically. The experimental results show that the compressibility cannot be neglected and it has an important influence on flow characteristics in the conditions with the enough large ratio of pressure drop to system pressure. Ergun correlation was compared with experimental values, and Ergun correlation modified with compressibility was deduced. The results show that Ergun correlation modified with compressibility can improve the ability to predict experimental values. The numerical results show that the particle friction factors modified with compressibility (fp*) in a rectangular pebble bed channel randomly filled with spherical particles can be predicted by using the models with SC-1, BCC-1, and FCC-1 arrangements. This work would provide some supports for the design of the helium supply system of the packed bed reactors.

Effect of inserted sphere size on heat transfer characteristics of FCC structured pebble bed in a HTGR

Hot spots appearing in an operating high temperature gas-cooled reactor (HTGR) core have been considered as the most possible reason leading to a severe accident like fission production releasing to the environment, therefore, investigation on their positions and thus seeking ways to reduce the possibility of their appearance have attracted scientists’ attention. In our previous studies, heat transfercharacteristics of a face–centered–cubic (FCC) structured pebble–bed have been discussed,and a correlation on heat transfer coefficient with Reynolds number was presented. In this study, a method, placing a small sphere in thegap area, which is able to enhance the convective heat transfer wasproposed and the effect verifiedas well. The influence of the sphere diameter on heat transfer performances wasinvestigated in details. It is concluded through results analysis that (1) inserted sphere lowered thelocal surface temperature of adjacent pebbles by varying surrounding flow field;(2) maximum velocity of the fluid and average heat transfer coefficientincreased with sphere diameter, particularly, comparing with no small sphere case, 12.95% enhancement was achieved. Such findings may provide dataand information for reactor designers, andhelp to develop a safer HTGR pebble–bedcore.

Experimental investigation of flow and convective heat transfer on a high-Prandtl-number fluid through the nuclear reactor pebble bed core

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.

Neutronics modeling and analysis of the TMSR-SF1 fuel lattice and full core with explicit fuel particle distribution and random pebble loadings

The first Solid Fueled Thorium Molten Salt Reactor (TMSR-SF1), a Fluoride-salt-cooled High Temperature Reactor (FHR) designed by the TMSR group of Chinese Academy of Science (CAS), is expected to be constructed in the near years. The combination of TRistructural-ISOtropic (TRISO) coated-fuel particles, pebble bed core, and Flibe coolant leads to various neutronics challenges, such as the double heterogeneity, distribution of TRISO particles, high density packed pebble bed, neutronics characteristics of Flibe salt, and etc. For the purpose of evaluating candidate neutronics codes, benchmark study will be conducted for the infinite fuel pebble lattice with explicitly described fuel particle distribution. For investigating key physics phenomena of the randomly packed pebble bed core, two coordinate generation methods will be explored in this study: Discrete Element Method (DEM) that accounts for inter-particle forces and a mathematical model (MM) that fills arbitrary domains through simple geometric rules on the addition of particles. While the former generates packing distributions closer to real-world scenarios, the latter is more computationally effective. The pebble loading effect on eigenvalues and fission power distribution will be studied. Emphasis is placed on the Flibe salt density reactivity effect -- the most unique feature of the FHR comparing to the conventional High Temperature Gas-cooled Reactors (HTGRs). Neutron balance based reactivity decomposition method will be employed for describing the underlying physics.

General nodal expansion method for multi-dimensional neutronics/thermal-hydraulic coupled problems in pebble-bed core systems

Motivated by the high efficiency and accuracy of nodal methods on the coarse meshes and the desire to solve the large-scale coupled problems in pebble-bed high temperature gas cooled reactor (HTR), a general nodal expansion method (GNEM) is successfully developed and extended to solve multi-dimensional neutronics/thermal-hydraulic(N/TH) coupled problems in pebble-bed reactor core systems. The developed GNEM combines the respective advantages of traditional nodal expansion methods (NEM) and modified nodal integral methods (MNIM). Specifically, the local analytical solutions of transverse integral equations in MNIM are obtained with the basis function expansion framework and nodal balance equation in NEM. The unified discrete formulation is also developed so that it’s convenient for GNEM to solve neutron diffusion equations, convention diffusion equations, pressure poisson equations, heat transfer equations and porous media flow models in the pebble bed core systems. Then all the governing equations of the N/TH coupled problems can be discretized by the GNEM on the coarse meshes so that the computational scale of coupled problems is greatly reduced for the desired precision. To achieve higher accuracy for the coupled problems on the coarse meshes, the high-order information is successfully transferred between the coupled terms by using GNEM. Finally, the coupled GNEM code is formally developed for N/TH coupled problems in pebble-bed reactor core systems. Numerical results show that the coupled GNEM code can track the reference solutions very well on the coarse meshes and show the high-accuracy advantage and the potential of GNEM for complicated multi-dimensional N/TH coupled problems. Further research is needed to add the coupled GNEM to the HTR analysis code-TINTE in order to simultaneously and effectively solve multi-dimensional coupled problems for realistic HTR reactor systems.