Reactor Moderator Research Articles

Evaluating Hydrogen-based Moderators in High-Temperature Gas-cooled Reactors with 5 wt% Enriched Uranium Annular Fuel Rods

Abstract Small Modular Reactors (SMRs) based on high temperature gas-cooled reactor (HTGR) technology are being developed for providing high-temperature process heat and high-efficiency (>40%) electrical power generation. However, most of the HTGR-SMR concepts require high assay low enriched uranium (HALEU) fuel, with enrichments typically above 10 wt% 235U/U, to get sufficiently high burnup levels and fuel lifetime. The need for HALEU is primarily a consequence of the low volumetric density of fissionable material in tri-structural isotropic (TRISO) fuel particles, and also the use of graphite as a moderator/reflector. A previous study has shown that a modified prismatic HTGR fuel assembly with hydrogen-based moderator (7LiH) and cylindrical fuel elements of 5 wt% 235U/U enriched uranium can greatly reduce fuel consumption of a HTGR. However, such a design concept could lead to positive temperature reactivity coefficients (TRCs), making reactor control more challenging, with reduced passive safety. The purpose of this study is to evaluate variations of the hydrogen-based moderator in this alternative fuel assembly concept to identify configurations that achieve negative TRCs, thus improving passive safety characteristics. Calculation results demonstrate that negative TRCs can be achieved with reduced hydrogen mass such that natural uranium consumption is substantially less than that of the TRISO fuel concept, with comparable or higher core life. This study also explores the option of using 7LiOH and NaOH as hydrogen-based moderators, instead of 7LiH, thus allowing operation at higher temperatures, where hydrogen TRCs are lower.

Research on the calculation method of sensitivity coefficients of reactor power to material density based on Monte Carlo perturbation theory

The ability to calculate the material density sensitivity coefficients of power with respect to the material density has broad application prospects for accelerating Monte Carlo-Thermal Hydraulics iterations. The second-order material density sensitivity coefficients for the general Monte Carlo score have been derived based on the differential operator sampling method in this paper, and the calculation of the sensitivity coefficients of cell power scores with respect to the material density has been realized in continuous-energy Monte Carlo code RMC. Based on the power-density sensitivity coefficients, the sensitivity coefficients of power scores to some other physical quantities, such as power-boron concentration coefficients and power-temperature coefficients considering only the thermal expansion, were subsequently calculated. The effectiveness of the proposed method is demonstrated in the power-density coefficients problems of the pressurized water reactor (PWR) moderator and the heat pipe reactor (HPR) reflectors. The calculations were carried out using RMC and the ENDF/B-VII.1 neutron nuclear data. It is shown that the calculated sensitivity coefficients can be used to predict the power scores accurately over a wide range of boron concentration of the PWR moderator and a wide range of temperature of HPR reflectors.

Development and potential of composite moderators for elevated temperature nuclear applications

ABSTRACT Neutron moderators, such as nuclear-grade graphite, are essential components of high-temperature nuclear reactors. Their primary functions are to degrade the energy of fission-born neutrons into an energy range that promotes further fission and to serve as the central core structure. This paper will discuss historic reactor moderator materials, which are relatively simple monolithic materials each having intrinsic benefits and limitations. Additionally, a new class of engineered composite moderators is presented for which two examples are fabricated: magnesia-matrix composite systems with either beryllium-based or metal-hydride entrained phases. In additions to presenting their route to fabrication effectiveness as advanced moderators is discussed.

A density functional theory and neutron diffraction study of the ambient condition properties of sub-stoichiometric yttrium hydride

Several mechanical and thermophysical properties are required as a function of non-stoichiometry for the successful implementation of YH2-x for nuclear reactor moderator applications. Density functional theory calculations, in combination with neutron diffraction experiments, were used to study the structural and mechanical properties of YH2-x. Point defect analysis indicated H occupation primarily at the tetrahedral site within an fcc Y sub-lattice, confirming a fluorite YH2 structure. The small positive formation energy for H vacancies under Y-rich conditions predicted that hypo-stoichiometry is accommodated by Y+YH2 at ambient conditions and by H vacancies in the YH2-x single phase that is relevant to high temperatures. Neutron diffraction studies were used to confirm both the occupation of H on tetrahedral sites and the near-stoichiometric composition of the hydride phase in the two-phase Y+YH2 region of the phase diagram that dominates at room temperature. Energy minimized special-quasirandom-structures of H vacancies were used to calculate lattice parameters, elastic constants, and several other properties as a function of composition for the single phase YH2-x. The lattice parameter of YH2-x decreased by only 0.004 Å with increasing H/Y for the range 1.31≤H/Y≤2.0 indicating a negligible effect on lattice parameters due to vacancy formation. In the two-phase region, however, calculations predicted the density of zY+(1−z)YH2−x to increase with decreasing H/Y at lower temperatures due to the increased fraction of high-density Y metal. For the high temperature single phase, decreasing H/Y reduced the density as a consequence of the lattice expansion associated with vacancy formation. All elastic constants and moduli increased with increasing hydrogen content in single-phase YH2-x.

Design and analysis of a computer experiment for the study of the distortion of an advanced gas-cooled reactor moderator brick

Engineering models, resolved using the finite element method, are used to model through-life changes in material properties and the resulting internal brick stresses in graphite moderator bricks within an advanced gas-cooled reactor (AGR). These models require inputs that describe the loading conditions of the moderator brick and coded relationships describing the behaviour of material properties as the brick ages. A highly multivariate spacio-temporal dataset of displacements, stresses and strains is returned as model output. In this work we describe a computer experiment conducted to study the variability in brick distortion resulting from parameter value uncertainty in the inputs to the model. We identify summary measures of brick shape and conduct global sensitivity analyses to identify the key uncertain parameters driving the variability in brick shape. Our results indicate that different measures of brick shape show sensitivities to different groups of model inputs and suggest that data obtained from core monitoring campaigns can be used to calibrate uncertain parameters in the model. Model calibration and the impact of calibration on predictions of internal brick stresses, which cannot be directly validated, are areas of current research.

Thermophysical properties of high-density, sintered monoliths of yttrium dihydride in the range 373–773 K

Yttrium dihydride is a promising nuclear reactor moderator for high-temperature, thermal micro-reactors due to its ability to retain hydrogen to high temperatures while having a relatively low impact on neutron economy. However, it is difficult to fabricate yttrium dihydride in high-density, near net-shape monoliths for moderator applications due to challenges associated with the hydrogen absorption process. In this study, high-density monoliths of yttrium dihydride were prepared by powder metallurgical methods. The lattice strain and thermal expansion coefficient were measured using neutron diffraction of powders of directly-hydrided yttrium, while the molar heat capacity and thermal diffusivity of sintered yttrium dihydride were measured using differential scanning calorimetry (DSC) and laser flash analysis (LFA), respectively. The molar heat capacity of yttrium dihydride was also calculated using density functional theory (DFT) for comparison. These parameters were used to then calculate the thermal conductivity and resistivity of yttrium dihydride as a function of temperature. The thermophysical properties of materials produced by both methods were observed to be consistent with the values from literature for yttrium dihydride. Due to the novelty of producing yttrium dihydride by powder metallurgical methods, this result indicated that the sintered monoliths were of high quality and that powder metallurgy is a viable method for large-scale production of yttrium dihydride monoliths for nuclear reactor moderator applications.

Effects of various types of reflectors on the 99Mo production in the VVER-Ts reactor targets

The effects from introducing various types of reflectors in the VVR-Ts reactor core on the 99Мо production were analyzed. Earlier the effects of only the beryllium reflector on the VVR-Ts reactor core characteristics, such as reactivity margin, neutron flux in experimental channels, and activity of the accumulated 99Мо, were calculated. The calculations are based on a generated precision model of the core which comprises one experimental channel where targets are irradiated for the 99Мо production. The model was built using the SCALE code. The code allows a fairly broad range of calculations to be performed, from criticality estimation to radiological assessment tasks. As the result of the computational analysis of the model, such characteristics were obtained as the effective multiplication factor, the power density in the 99Мо production targets, the neutron flux in the target raw material, and the quantity of the produced 99Мо after 120 hours of irradiation. The data was compared with the results of similar calculations of the VVR-Ts reactor core parameters. Further, the list of the materials used extensively as the reactor core reflector or moderator was formed based on reference literature. A number of models were obtained and analyzed on its basis, in which the water space on the core periphery was substituted for the investigated materials.

Elastic moduli of high-density, sintered monoliths of yttrium dihydride

Yttrium dihydride has been considered as potential nuclear reactor moderator for micro-reactors operating in the thermal energy spectrum due to their ability to retain hydrogen to high temperatures while having a relatively low impact on neutron economy. Despite these advantages, it is difficult to prepare yttrium dihydride in high-density, near net-shape monoliths for moderator applications due to volume expansion upon hydriding and the pyrophoric nature of the material. In this work, high-density monoliths of yttrium dihydride were prepared by direct hydriding and using powder metallurgical methods. Resonant ultrasound spectroscopy was used to measure the elastic moduli of the sintered monoliths, while nanoindentation was used to determine the Young’s modulus and hardness of the directly-hydrided yttrium and the sintered monoliths. Single crystal elastic constants and related properties of yttrium dihydride were also determined using density functional theory (DFT) for comparison. Mechanical properties of materials produced by both methods were observed to be consistent with the values from literature for yttrium dihydride. Due to the novelty of producing yttrium dihydride by powder metallurgy, this result indicated that the monoliths produced by powder metallurgy were of high quality. To that end, powder metallurgy is believed to be a viable method for large-scale production of yttrium dihydride monoliths for nuclear reactor moderator applications.

Modeling and predicting total hydrogen adsorption in nanoporous carbon materials for advanced nuclear systems

The retention of hydrogen in a variety of disordered carbon materials including graphene nanoplatelets and amorphous carbon was measured by volumetric adsorption and modeled using thermodynamic methods. To date, high temperature hydrogen adsorption research in carbon has predominately focused on graphite used as plasma-facing materials in fusion systems, moderators in high temperature gas reactors, and fuel components in molten-salt cooled reactors. Tritium, a hydrogen isotope that is produced in these systems, adsorbs on carbon surfaces that could be used effectively as sinks to remove tritium. Since hydrogen has chemical similarity to tritium, it can be used as a surrogate to simplify experimental studies, greatly expediting materials exploration. Thus, an understanding and prediction of hydrogen behavior on carbon materials is essential for evaluation of performance and safety of present and future reactor designs. Chemisorption experiments were conducted on 9 different materials with a range of surface areas, pore volumes, and pore size distributions. The results showed that carbons with higher surface area and pore volume exhibit higher hydrogen adsorption, which is attributed to larger quantities of active sites. Further, hydrogen adsorption was found to increase in materials with greater micropore (<10 Å) surface area, which was interpreted as being a result of in-pore trapping. In contrast to previous studies that assumed a single isotherm, four isotherms were examined including two- and three-parameter methods and homo- and heterogeneous surface methods—the Langmuir, Temkin, Freundlich and Sips isotherms. Analyses of non-linear models by ordinary least squares and Marquardt's percent standard deviation minimization were performed. It was found that constant order homogeneous models that have been used in the past lack the ability to describe pathways and reactions steps that occur. Further, it was found that Sips isotherm consistently provided the best minimization of error and most accurate prediction.

3D-thermo-structural simulation of pressure tube–calandria tube behaviour under accident conditions in PHWR using ABAQUS

In-depth understanding of the thermo-structural behaviour of structure system and components (SSCs) of a nuclear power plant is necessary for both safety margin assessment, and for devising appropriate prevention and accident mitigation strategies. In a pressurised heavy water reactor (PHWR), the fuel in the form of fuel bundles resides inside pressure tube (PT). The pressure tube is surrounded by a co-axial calandria tube (CT). The heat generated by nuclear fission in fuel bundle is carried away by heavy water coolant, which flows inside pressure tube. The coolant is at high temperature and high pressure inside the pressure tube. The surrounding calandria tubes are at low temperature and low pressure under normal operating conditions. Under certain accident scenario, the fuel bundles cooling may be lost. This results in heating up of the fuel bundles which leads to increase in temperature of the pressure tube. The pressure tube starts deforming as its temperature increases. The deformed pressure tube may contact the calandria tube either by sagging or ballooning. This leads to increase in the calandria tube temperature. If the temperature on the outer surface of the calandria tube exceeds the critical heat flux, film boiling may occur on the surface of the calandria tube. If the area in dry-out is sufficiently large and the dry-out is prolonged, the pressure-tube/calandria-tube combination can continue to strain radially and may challenge fuel-channel integrity. The International Collaborative Standard Problem (ICSP) on Heavy Water Reactor (HWR) Moderator Sub-cooling Requirements is organized by the IAEA to facilitate the development and validation of computer codes for the analysis of fuel channel integrity. The objective was to assess the capability of safety analysis computer codes in predicting the associated phenomena namely; radiation heat transfer from fuel to the pressure tube (PT), from PT to calandria tube (CT) heat transfer, PT deformation or failure, CT to moderator heat transfer and CT deformation or failure. The current analysis is carried out as a part of international collaborative standard problem exercise. This work simulates the heat transfer phenomena along with resulting deformation of the pressure tube and calandria tubes in a finite element framework. The insights obtained from the detailed modelling of the structural aspects of the phenomena can be used to update the system safety analysis codes. In this paper, a coupled heat transfer and structural analysis of pressure tube -calandria tube assembly is carried out using the finite element code, ABAQUS. The heat transfer analysis implements radiation heat transfer from heater to PT and from PT to CT. Contact conductance between PT-CT is modeled based on contact pressure. Convection from outer surface of CT to water is also considered. Structural analysis included three cases elastic–creep, elasto-plastic and elasto-plastic with creep of the individual PT-CT assembly under thermal and mechanical loading. It is observed that the results matched well for the case where only elastic creep constitutive model was considered. The temperature variation of pressure tube and calandria tube along with resulting deformation is obtained. The simulation is able to capture and predict the progressive contact of PT with CT and the deformation of CT along with the PT using FEM model. It was observed during the experiment and captured in the simulation that the PT-CT assembly deformation lead to removal of heat to the moderator and channel integrity was maintained for the given moderator sub cooling margin.

Updating irradiated graphite disposal: Project ‘GRAPA’ and the international decommissioning network

Demonstrating competence in planning and executing the disposal of radioactive wastes is a key factor in the public perception of the nuclear power industry and must be demonstrated when making the case for new nuclear build. This work addresses the particular waste stream of irradiated graphite, mostly derived from reactor moderators and amounting to more than 250,000 tonnes world-wide. Use may be made of its unique chemical and physical properties to consider possible processing and disposal options outside the normal simple classifications and repository options for mixed low or intermediate-level wastes. The IAEA has an obvious involvement in radioactive waste disposal and has established a new project ‘GRAPA’ – Irradiated Graphite Processing Approaches – to encourage an international debate and collaborative work aimed at optimising and facilitating the treatment of irradiated graphite.

Thermal neutron scattering law calculations using ab initio molecular dynamics

In recent years, methods for the calculation of the thermal scattering law (i.e. S(α,β), where α and β are dimensionless momentum and energy transfer variables, respectively) were developed based on ab initio lattice dynamics (AILD) and/or classical molecular dynamics (CMD). While these methods are now mature and efficient, further advancement in the application of such atomistic techniques is possible using ab initio molecular dynamics (AIMD) methods. In this case, temperature effects are inherently included in the calculation, e.g. phonon density of states (DOS), while using ab initio force fields that eliminate the need for parameterized semi-empirical force fields. In this work, AIMD simulations were performed to predict the phonon spectra as a function of temperature for beryllium and graphite, which are representative nuclear reactor moderator and reflector materials. Subsequently, the calculated phonon spectra were utilized to predict S(α,β) using the LEAPR module of the NJOY code. The AIMD models of beryllium and graphite were 5 × 5 × 5 crystal unit cells (250 atoms and 500 atoms respectively). Electronic structure calculations for the prediction of Hellman-Feynman forces were performed using density functional theory with a GGA exchange correlation functional and corresponding core electron pseudopotentials. AIMD simulations of 1000–10,000 time-steps were performed with the canonical ensemble (NVT thermostat) for several temperatures between 300 K and 900 K. The phonon DOS were calculated as the power spectrum of the AIMD predicted velocity autocorrelation functions. The resulting AIMD phonon DOS and corresponding inelastic thermal neutron scattering cross sections at 300 K, where anharmonic effects are expected to be small, were found to be in reasonable agreement with the results generated using traditional AILD. This illustrated the validity of the AIMD approach. However, since the impact of the temperature on the phonon DOS (e.g. broadening of spectral peaks) was observed in AIMD analysis, this technique may be envisioned as the approach for deriving the needed atomistic data for thermal scattering law calculations under realistic temperature and structural conditions for a given material.

CFD model of a moderator tank for a pressure vessel PHWR nuclear power plant

The CFD thermal hydraulic simulation of a Pressurized Heavy Water Reactor (PHWR) moderator tank was performed. Heating was achieved by considering two heat sources, conduction/convection through the coolant channels and neutron thermalization. For the first method, a suitable 2D model for coupling the 3D with a 1D code to solve the in-channel coolant was implemented. For thermalization, a volumetric heat source was estimated. Due to the relevance of natural and forced convection in the heat transfer, the Boussinesq approach was assessed for high Rayleigh number flow before it was used to model the moderator tank. The results clarified the complex flow behavior and the temperature field. As expected from design, the thermal power transferred from coolant to moderator is not directly related to the fission power distribution but to the axial coolant temperature profile (nearly the same for all channels) and the non-homogeneous moderator temperature profile. The former was as expected for high-Rayleigh natural convection systems.

Reaction Cross Section Calculations in Neutron Induced Reactions and GEANT4 Simulation of Hadronic Interactions for the Reactor Moderator Material BeO

BeO is one of the most common moderator material for neutron moderation; due to its high density, neutron capture cross section and physical-chemical properties that provides usage at elevated temperatures. As it’s known, for various applications in the field of reactor design and neutron capture, reaction cross–section data are required. The cross–sections of (n,α), (n,2n), (n,t), (n,EL) and (n,TOT) reactions for 9 Be and 16 O nuclei have been calculated by using TALYS 1.6 Two Component Exciton model and EMPIRE 3.2 Exciton model in this study. Hadronic interactions of low energetic neutrons and generated isotopes–particles have been investigated for a situation in which BeO was used as a neutron moderator by using GEANT4, which is a powerful simulation software. In addition, energy deposition along BeO material has been obtained. Results from performed calculations were compared with the experimental nuclear reaction data exist in EXFOR.

Reaction Cross Section Calculations in Neutron Induced Reactions and GEANT4 Simulation of Hadronic Interactions for the Reactor Moderator Material BeO

Reaction Cross Section Calculations in Neutron Induced Reactions and GEANT4 Simulation of Hadronic Interactions for the Reactor Moderator Material BeO

Reaction Cross Section Calculations in Neutron Induced Reactions and GEANT4 Simulation of Hadronic Interactions for the Reactor Moderator Material BeO

Reaction Cross Section Calculations in Neutron Induced Reactions and GEANT4 Simulation of Hadronic Interactions for the Reactor Moderator Material BeO

Unsteady two-dimensional multiphysical simulation of a pressure tube model expanded to contact with the outer concentric tube

For the blind calculation of the International Collaborative Standard Problem (ICSP) experiment on heavy water reactor moderator subcooling requirements, the COMSOL Multiphysics code is used to simulate plastic deformation of a pressure tube (PT) as a result of the interaction of stress and temperature. It is shown that the thermal stress model of COMSOL is compatible to simulate the multiple heat transfers (including the radiation heat transfer and heat conduction) and stress strain in the simplified two-dimensional problem. The benchmark test result for radiation heat transfer is in good agreement with the analytical solution for the concentric configuration of PT and calandria tube (CT). Since the original strain model of COMSOL only considers an elastic deformation with thermal expansion coefficient, the PT/CT contact cannot be predicted in the ICSP. Therefore, the plastic deformation model by the Shewfelt and Godin, widely used in the fuel channel analysis of CANadian Deuterium Uranium (CANDU) reactor, is implemented to the strain equation of COMSOL. The heat-up of PT, the strain rate, and the contact time of the PT/CT are calculated with the boundary conditions (BCs) given for blind calculation of the ICSP experiment.The result shows a sudden expansion of the inner concentric PT within a few milliseconds. This unsteady simulation should be helpful for the conceptual design of experiment as well as for the understanding of multiphysics inside the fuel channels of the CANDU reactor.

Bulk graphite: materials and manufacturing process

Graphite can be classified into natural graphite from mines and artificial graphite. Due to its outstanding properties such as light weight, thermal resistance, electrical conductivity, thermal conductivity, chemical stability, and high-temperature strength, artificial graphite is used across various industries in powder form and bulk form. Artificial graphite of powder form is usually used as anode materials for secondary cells, while artificial graphite of bulk form is used in steelmaking electrode bars, nuclear reactor moderators, silicon ingots for semiconductors, and manufacturing equipment. This study defines artificial graphite as bulk graphite, and provides an overview of bulk graphite manufacturing, including isotropic and anisotropic materials, molding methods, and heat treatment.

ERRATUM: Simulation for Neutron Transport in PWR Reactor Moderator and Evaluation for Proper Thickness of Light Water Reflector

ERRATUM: Simulation for Neutron Transport in PWR Reactor Moderator and Evaluation for Proper Thickness of Light Water Reflector[Nguyen Tuan Khai and Phan Quoc Vuong, Comm. Phys. 25(1) (2015) 91--96]

Simulation for Neutron Transport in PWR Reactor Moderator and Evaluation for Proper Thickness of Light Water Reflector

Monte Carlo calculation method can be used for resolving particle transport in matter, and particularly the transport of neutrons in environment of reactor core. The method has become more efficiently because of high accuracy of updated nuclear data and fast development of advanced super-computing system. In this work, we would like to present calculations for kinematical characteristics of neutron transport in a typical configuration of the pressurized water reactor (PWR) fuel assembly based on the Monte-Carlo simulation method. We concentrate in two main results: (1) neutron energy spectrum at fuel rod and (2) optimal thickness of light water reflector.