Pebble Bed Fluoride Salt-cooled High-temperature Reactor Research Articles

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.

Multiscale thermal-hydraulic modeling of the pebble bed fluoride-salt-cooled high-temperature reactor

The complex core geometry of Pebble Bed Reactors (PBRs) necessitates multiscale techniques for fast-turnaround design and analysis. This paper describes the multiscale model implemented in the Pronghorn PBR simulation tool and demonstrates application to steady-state analysis of the Mark-1 Pebble Bed Fluoride-Salt-Cooled High-Temperature Reactor (PB-FHR). Verification of the pebble model with fully-resolved heat conduction shows that material-wise pebble temperatures are predicted to within 10°C over a wide range in thermal conditions. Anisotropic drag models are correlated for the outer reflector blocks using COMSOL, providing closures for modeling of bypass flows. With a porous media model of the outer reflectors, the core bypass fraction and fuel, reflector, and structural material temperatures are predicted for a number of different inflow conditions. This work demonstrates the full-core analysis capabilities of the Pronghorn application and enables comprehensive reactor analysis with the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework.

Thorium utilization with pebble mixing system in fluoride salt-cooled High Temperature Reactor

Mixing system of uranium pebbles and thorium pebbles is compared with thorium blanket system to utilize thorium in Pebble Bed Fluoride Salt-cooled High Temperature Reactor (PB-FHR). A random modeling method is introduced to simulate the pebble mixing system. Cases with different volume fractions of uranium pebbles are researched to find the optimal utilization of uranium and the lower power nonuniformity. It indicates that using thorium in pebble mixing system with 80 vol% uranium pebbles can improve uranium utilization by 10%, while in thorium blanket system it can be increased by 20%. The radial power peak factor in pebble mixing system is about 1.48 while in thorium blanket system is about 1.83. In-pile residence time of thorium pebbles in pebble mixing system is only 4.7 year, while in thorium blanket system is 9 year. Thorium utilization with pebble mixing system in PB-FHR shows a little lower fuel utilization but higher safety and technical feasibility.

FHR, HTGR, and MSR Pebble-Bed Reactors with Multiple Pebble Sizes for Fuel Management and Coolant Cleanup

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.

Conceptual design of a freeze-tolerant Direct Reactor Auxiliary Cooling System for Fluoride-salt-cooled High-temperature Reactors

One of the key potential advantages of the Fluoride-salt-cooled High-temperature Reactor (FHR) is the use of passive safety systems that ensure the safe response of the reactor during anticipated operational occurrences, design basis events, and beyond design basis events. Typically, FHRs use a Direct Reactor Auxiliary Cooling System (DRACS) to remove the decay heat under a variety of accidents when the active reactor shutdown system is unavailable. Thus, it plays a key role in preventing the overheating/overcooling of the reactor in case of the failure of other primary means of heat removal. To enhance the operational reliability of DRACS, two DRACS designs are proposed in this study. The proposed DRACS designs are composed of two natural circulation salt loops and a water tank as the heat sink. This study focused on the transient behavior of DRACS of the FHRs during Loss of Heat Sink (LOHS) accident. Calculations were performed using RELAP5-3D to evaluate the design features of each concept, based on one design concept, the University of California, Berkeley’s Mark-1 pebble-bed FHR (PB-FHR). The calculation shows that the Mk-1 PB-FHR with DRACS proposed in this paper can operate for a relatively long time (about 90 h for design A and 430 h for design B) for a LOHS transient without operator involvement.

DEM–CFD simulation of modular PB-FHR core with two-grid method

For designing and optimizing the reactor core of modular pebble-bed fluoride salt-cooled high-temperature reactor (PB-FHR), it is of importance to simulate the coupled fluid and particle flow due to strong coolant–pebble interactions. Computational fluid dynamics and discrete element method (DEM) coupling approach can be used to track particles individually while it requires a fluid cell being greater than the pebble diameter. However, the large size of pebbles makes the fluid grid too coarse to capture the complicated flow pattern. To solve this problem, a two-grid approach is proposed to calculate interphase momentum transfer between pebbles and coolant without the constraint on the shape and size of fluid meshes. The solid velocity, fluid velocity, fluid pressure and void fraction are mapped between hexahedral coarse particle grid and fine fluid grid. Then the total interphase force can be calculated independently to speed up computation. To evaluate suitability of this two-grid approach, the pressure drop and minimum fluidization velocity of a fluidized bed were predicted, and movements of the pebbles in complex flow field were studied experimentally and numerically. The spouting fluid through a central inlet pipe of a scaled visible PB-FHR core facility was set up to provide the complex flow field. Water was chosen as liquid to simulate the molten salt coolant, and polypropylene balls were used to simulate the pebble fuels. Results show that the pebble flow pattern captured from experiment agrees well with the simulation from two-grid approach, hence the applicability of the two-grid approach for the later PB-FHR core design.

Development of a GPU-accelerated 3D neutron dynamics code for PB-FHR

Pebble bed fluoride-salt cooled high temperature reactor (PB-FHR) is a kind of novel nuclear energy systems, combining advanced techniques such as coated particle fuel and molten-salt coolant to achieve better safety and economy performance. The compact core of a PB-FHR is geometrically complicated due to the randomly-packed pebble bed with fuel motion in a complex core chamber, which yields a highly detailed core-modeling for accurate neutron dynamics analysis. Three-dimensional fine mesh finite volume method is expected to achieve better accuracy because of its strong geometry adaptability in detailed core-modeling, but is much more time-consuming compared to other methods such as coarse mesh nodal method. A GPU-accelerated 3D fine mesh neutron dynamics code (GAND) is developed, using conjugate gradient method (CG) to solve the time-dependent multi-group neutron diffusion equations in r-z-θ coordinates. The GAND code is verified by a cylindrical reactor benchmark with good agreement, and is preliminarily applied to a PB-FHR core in both static and transient analysis. Speed-up ratio and other performance of GAND code using different equation preconditioners is studied, a best speed-up ratio of 21.65 has been achieved using Neumann polynomials-preconditioned CG.

The impacts of random effect and scattering effects on the neutronics analysis of the PB-FHR

The experimental thorium-based molten salt reactor with solid fuel will be constructed as an initial step to test and verify the technical feasibility of a large-scale thorium-based molten salt reactor in the next years. It is a type of pebble-bed fluoride-salt-cooled high-temperature reactor (PB-FHR). The pebble-bed reactors are composed of randomly distributed fuel pebbles which consist of fully randomly distributed TRistructural-ISOtropic (TRISO) coated-fuel particles. This special structure is known as the double random distribution. However, lacking of accurate modeling approach of random distribution, the regular lattice approximation was adopted in the previous Monte Carlo modeling of the 2-MW TMSR-SF0, which may introduce significant error. In order to explicitly model the random distribution of the PB-FHR, the random distribution of the TRISO coated-fuel particles within fuel pebbles are obtained by the random packing method (RPM) and the random distribution of the fuel pebbles within the reactor core are obtained by the discrete element method (DEM). In this work, regular lattice approximation approach and explicit modeling approach are applied to simulate the stochastic effect of the PB-FHR. The simulation results show that regular lattice approximation approach underestimates the keff by about 1000pcm. Besides, the thermal-neutron scattering effect of 2LiF-BeF2 and the resonance elastic scattering effect of uranium are studied in this work.

On the improvements in neutronics analysis of the unit cell for the pebble-bed fluoride-salt-cooled high-temperature reactor

The stochastic characteristics of the randomly distributed coated-fuel particles, the thermal-neutron scattering effect of the fluoride-salt and the resonance elastic scattering effect of heavy nuclides were neglected in early neutronics studies on the Pebble-Bed Fluoride-salt-cooled High-temperature Reactor (PB-FHR). In order to assess the impact of these effects on the neutronics calculation, the stochastic effect is analyzed by applying the explicit random modeling approach and Chord Length Sampling method, the thermal-neutron scattering effect of the fluoride-salt is quantified by evaluating and processing a new thermal-neutron scattering data library, and the resonance elastic scattering effect is covered by using the Doppler Broadening Rejection Correction (DBRC) method in this work. According to the critical calculations of the PB-FHR pebble unit cells with different TRISO Packing Factor (TPF), the different stochastic modeling methods lead to a difference of kinf by tens of pcm, the thermal scattering effect of 2LiF-BeF2 results in a decreasement of kinf by 104–290 pcm and the resonance elastic scattering effect leads to a decreasement of kinf by 107–437 pcm, respectively. In addition, the thermal-neutron scattering effect and resonance elastic scattering effect can be addible, the total impact of the thermal scattering effect of 2LiF-BeF2 and the resonance elastic scattering effect of heavy nuclide leads to a decreasement of kinf by 204–747 pcm.

Dancoff factor analysis for pebble bed fluoride salt cooled high temperature reactor

In this work, an analytical expression based on a two-region spherical model for a High Temperature Gas cooled Reactor (HTGR), is applied to a Pebble Bed Fluoride salt cooled High temperature Reactor (PB-FHR) to calculate the average Dancoff factor for fuel kernel with various coated particle densities. The results are compared with those obtained by the Monte Carlo (MC) method. It is found that there is a good agreement between the analytical and MC, which implies that the two-region spherical model for the Dancoff factor calculation is applicable to PB-FHR. The Dancoff factors with and without FLiBe salt are both evaluated and compared to analyze the influence of FLiBe salt with different numbers of coated particles. The Dancoff factor with FLiBe salt is smaller than that without FLiBe salt from ∼ 11% to ∼ 3% when the number of coated particles in a fuel pebble increases from 5000 to 60,000. In addition, the effects of temperature and volume fraction of FLiBe salt on Dancoff factor are analyzed. Afterwards, the sensitivity of the infinite multiplication factor (k∞) to the Dancoff factor for a fuel cell of PB-FHR is further analyzed by the neutron transport calculation with a new developed routine. It is found that the infinite multiplication factor increases almost linearly with the increase of Dancoff factor, and a higher density of coated particles will lead to a sharper variation of k∞ with Dancoff factor.

Sustainability of thorium-uranium in pebble-bed fluoride salt-cooled high temperature reactor

Sustainability of thorium fuel in a Pebble-Bed Fluoride salt-cooled High temperature Reactor (PB-FHR) is investigated to find the feasible region of high discharge burnup and negative Flibe (2LiF-BeF2 ) salt Temperature Reactivity Coefficient (TRC). Dispersion fuel or pellet fuel with SiC cladding and SiC matrix is used to replace the tristructural-isotropic (TRISO) coated particle system for increasing fuel loading and decreasing excessive moderation. To analyze the neutronic characteristics, an equilibrium calculation method of thorium fuel self-sustainability is developed. We have compared two refueling schemes (mixing flow pattern and directional flow pattern) and two kinds of reflector materials (SiC and graphite). This method found that the feasible region of breeding and negative Flibe TRC is between 20 vol% and 62 vol% fuel loading in the fuel. A discharge burnup could be achieved up to about 200 MWd/kgHM. The case with directional flow pattern and SiC reflector showed superior burnup characteristics but the worst radial power peak factor, while the case with mixing flow pattern and SiC reflector, which was the best tradeoff between discharge burnup and radial power peak factor, could provide burnup of 140 MWd/kgHM and about 1.4 radial power peak factor with 50 vol% dispersion fuel. In addition, Flibe salt displays good neutron properties as a coolant of quasi-fast reactors due to the strong 9 Be(n,2n) reaction and low neutron absorption of 6 Li (even at 1000 ppm) in fast spectrum. Preliminary thermal hydraulic calculation shows good safety margin. The greatest challenge of this reactor may be the decades irradiation time of the pebble fuel.

Uranium utilization with thorium blanket in Pebble Bed Fluoride salt-cooled high temperature reactor

Thorium blanket fuel is investigated in Pebble Bed Fluoride salt-cooled High temperature Reactor (PB-FHR) with 19.9 at% 235U seed fuel to improve the utilization of uranium fuel. Uranium fuel utilization is optimized with lots of parameters, such as graphite-to-thorium atom ratio (C/Th), graphite-to-uranium atom ratio (C/U), discharge burnup of thorium and uranium, and the dimension of the seed/blanket region. It is found that the equivalent discharge burnup, defined as total released energy over the mass of uranium, could be improved to around 265 MWd/kgU, which is 20% higher than discharge burnup using pure uranium fuel. In equilibrium state, the temperature reactivity coefficients of fuel and coolant are both negative. Other properties such as radial power peak factor, life of reflector, in-pile residence time of thorium pebble and radioactive waste are analyzed. Finally, baseline design parameters are recommended for further thermal-hydraulic analysis and TRISO fuel performance.