Fission Density Research Articles

Californium-252 production at the High Flux Isotope Reactor - II: Comparison between the highly enriched uranium and a proposed low-enriched uranium core

This is the second paper on a 252Cf production study performed in support of efforts to convert the High Flux Isotope Reactor (HFIR) from highly enriched uranium (HEU) to low-enriched uranium (LEU) fuel. The first paper primarily focuses on validating computational tools and nuclear data. This companion paper evaluates another critical aspect: the 252Cf production capability with a proposed LEU core. HFIR must maintain its world-class performance and missions following conversion and because 252Cf is a vital, multipurpose neutron-emitting radioisotope, the ability to efficiently produce 252Cf must be preserved. In this study, the HFIRCON transport and depletion tool, several nuclear data libraries, and Campaign 78 data were used to compute 252Cf production, sensitivity, and safety metrics. Results indicate the 252Cf production and production rates are slightly higher with a 95MWth LEU core compared with those obtained with the 85MWth HEU core. Additionally, the target peak fission rate densities, discharge cumulative fission densities, and heat deposition rates with the LEU core are within a few percent of those calculated with the HEU core. The findings suggest HFIR’s 252Cf production capability can be effectively maintained with an LEU core without adversely affecting the safety metrics.

Thermal conductivity of U-Mo alloy fuel

The thermal conductivity of U-Mo alloys for research reactor fuel was studied. Thermal conductivity is one of the most important properties concerning design, performance analysis, and safety evaluation of these alloys as research reactor fuel. Thermal conductivity data of unirradiated U-Mo alloy collected from literature were examined, analyzed, and used to develop a correlation as a function of Mo content and temperature. For irradiated U-10Mo alloy, a thermal conductivity correlation was developed as a function of fission density and temperature. This model considers the effects of porosity growth by fission gas bubbles, solid fission product accumulation, and buildup of grain boundaries due to recrystallization during irradiation.

Assessment of effective elastic constants of U-10Mo fuel: A multiscale modeling and homogenization study

The significant microstructural changes that U-Mo fuel undergoes during operation degrades its mechanical properties and structural integrity. Microstructural evolution entails the formation, evolution, and redistribution of porosity in conjunction with grain refinement. In the present paper, we employ numerical approaches to assess the impact of the various microstructural features—grains, nanoscale intragranular fission gas bubbles, and mesoscale intergranular voids—on the degradation of elastic constants. Phase-field microstructure models are combined with the asymptotic expansion homogenization technique in order to derive the effective elastic constants as a function of porosity and fission density. The results are verified and compared against theoretical bounds. Using this approach, elastic degradation in operating nuclear fuels can be quantified when the distributions of microstructural features are known.

Mechanical Properties of Irradiated U-10 wt. %Mo Alloy Degraded by Porosity Development

Abstract A plate-type nuclear fuel consisting of a solid monolithic foil of U-10 wt. %Mo is under development for use in the United States' high-performance research reactors. In support of developing this fuel, the fuel has been fabricated for the first time by a commercial fuel vendor and subsequently irradiated in a test reactor. This provides an opportunity to evaluate postirradiation mechanical properties of the commercially fabricated fuel. Four-point bend testing was conducted on the irradiated U-10Mo samples to generate the fuel material properties, including the modulus of elasticity and the bending strength. Although the material behaves in a brittle manner due to the accumulated porosity, a general trend of strength and modulus reduction was found as fission density increases. The data produced was evaluated using both Weibull statistics and a modulus degradation model with recommendations provided.

Atom probe tomography of segregation at grain boundaries and gas bubbles in neutron irradiated U-10 wt% Mo fuel

During neutron irradiation to fission densities > 5.2 × 1021 fiss/cm3, Xe agglomerates forming gas bubbles of varying size within the U-Mo fuel matrix. Herein, segregation of fission products to Xe bubbles and grain boundaries (GB) were studied using atom probe tomography (APT). Segregation behavior was found to vary among GBs, small bubbles (<10 nm), and larger bubbles (>10 nm). Solid fission products were enriched at GBs and larger bubbles, but not at small bubbles. A denuded zone was identified adjacent to a > 10 nm Xe gas bubble and a GB.

High Fidelity Whole Core Reactor Eigenvalue Calculation using the Hybrid Monte Carlo and Deterministic RAPID Code System

This paper examines the accuracy and performance of the RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system for whole core reactor simulation. The RAPID code is an implementation of the Multistage Response function Transport (MRT) methodology resulting in a hybrid Monte Carlo and deterministic technique. This paper utilizes the Watts Bar Unit 1 benchmark as the computational model to exam the accuracy and efficiency of RAPID compared to Serpent. The RAPID calculated eigenvalue and 3-D fission density distribution are compared to the results from Serpent. This paper shows that RAPID is able to obtain pin-wise, axially-dependent fission density in 7 minutes using one computer core, as opposed to assembly-wise, axially dependent fission density in 8 days on 40 computer cores.

A Novel Fission-Matrix Based Radial Boundary Correction Methodology and its Implementation into the RAPID Code System

The RAPID code system utilizes a novel combined fission matrix methodology to rapidly solve the whole-core eigenvalue problem. To represent axial and radial reflector regions, the fission density distribution in the boundary assemblies, a fission density correction factor methodology was devised and demonstrated. Although, accurate results were achieved, because of the need for a full core Monte Carlo calculation, this technique requires significant computing resources. To address this issue, this paper introduces a novel FM based methodology, which achieves accurate results, however at very small computing expense. The methodology has been implemented into the RAPID code system, and successfully demonstrated for the Watts Bar whole core OECD/NEA

Contributions to the mechanistic understanding of the microstructural evolution in irradiated U-Mo dispersion fuel

Advanced microstructural characterization techniques, such as scanning electron microscopy (SEM) and scanning transmission electron microscopy - energy dispersive x-ray spectroscopy (STEM-EDS), were used to interpret the fuel microstructure evolution and fission products behavior in U-Mo dispersion fuel irradiated in the Advanced Test Reactor (ATR) as part of the European Mini-Plate Irradiation Experiment (EMPIrE) test. The larger as-fabricated fuel grain size achieved by heat-treating the U-Mo powder resulted in slower high burnup structure (HBS) development and reduced fission gas porosity. Slower HBS kinetics was observed at the fuel kernels’ periphery, which contained smaller and less fission gas bubbles at all fission densities (FDs) investigated and was attributed to a locally reduced damage density and fission products concentration, as corroborated with Monte Carlo simulations. The non-refined grains at the fuel kernel periphery hosted a perfectly ordered fission Gas Bubble Superlattice (GBS) up to 6.3 × 1021 fissions/cm3. Nano-scale STEM-EDS analysis presented in this study provided useful information on the GBS characteristic morphology and evolution in U-Mo fuel. The concentration of fission gas in the GBS progressively increased with FD, pointing to an evolution of the nanobubble pressure status with irradiation. A possible connection between the GBS collapse and HBS onset is proposed for which there exists a threshold in the misorientation of the refined sub-grains above which the GBS stability during irradiation is no longer preserved, resulting in the GBS collapse.

Underlying mathematical relations for efficient COMET response expansion coefficient and core calculations

The coarse mesh transport code COMET, a hybrid stochastic-deterministic neutronics solver with formidable computation speed, can provide high fidelity transport solutions to various reactor core problems. In this paper, to take advantage of local rotational and reflection symmetry existing in many reactor cores (e.g., fuel lattices and reflector blocks), the underlying mathematical relations among the response expansion coefficients of symmetric coarse meshes are developed to further improve the computational efficiency in both COMET response expansion coefficient generation and core calculation. This is done by a rigorous derivation of the transformation matrices for the angular and spatial expansion moments resulting from a rotation of a coarse mesh by an arbitrary angle or reflection of a coarse mesh. As a result, the relations for the response expansion coefficients of a coarse mesh with rotational symmetry can be then written as the Kronecker product of those transformation matrices. For coarse meshes with reflection symmetry, the sparse property, the outgoing surface symmetry property and the incident surface symmetry property of response expansion coefficients are rigorously derived. These underlying mathematical relations are implemented into COMET and evaluated on three stylized 3D PWR whole core benchmark problems. The COMET results using the response expansion coefficient library based on the underlying mathematical relations were compared to those using the library directly generated by Monte Carlo for all surfaces. It was found that the eigenvalues as well as the pin and assembly fission densities using the two libraries are in statistical agreement as expected. This indicates that the new COMET using the underlying mathematical relations maintains the high fidelity of the original COMET while improving computational efficiency by 10.7 and 3.7 times for COMET response expansion coefficient generation and core calculation, respectively. This also reduces the size of the library by 10.7 times.

Comparison of Zirconium Redistribution in BISON EBR-II Models Using FIPD and IMIS Databases with Experimental Post Irradiation Examination

Metallic fuels have seen increased interest for future sodium fast reactors due to their material properties: high thermal conductivities and advantageous neutronic properties allow for greater fission densities. One drawback to typical metallic fuels is zirconium redistribution, which impacts this advantageous material and its neutronic properties. Unfortunately, the processes behind zirconium migration behavior are understood using first principles, so before these fuels are implemented in future fast reactors, characterization and fuel qualification regimes must be completed. These activities can be supported through the use of robust modeling using the most accurate empirical models currently available to fuel researchers around the world. The tool that allows researchers to model this complex coupled thermo-mechanical behavior and nuclear properties is BISON. Additionally, BISON model parameters need to be compared against PIE measurements. The current work utilizes two fuel pins from EBR-II experiment X441 to optimize various model parameters, including porosity correction factor, thermal conductivity, phase transition temperature, and diffusion coefficient multipliers, before implementing the final model for seven fuel pins with differing characteristics. To properly evaluate the BISON simulations, the results are compared to PIE metallography data for each fuel pin, to ensure the zirconium redistribution is properly reflected in the simulation results. Six out of seven analyzed fuel pins demonstrate good agreement between the metallography images and BISON results, showing alignment of the Zr-rich, Zr-depleted, and moderately Zr-enriched zones at various axial heights along the fuel pins. Further work is needed to refine the model parameters for general pin use.

Evidence of Xe-incorporation in the bubble superlattice in irradiated U-Mo fuel

For years, researchers have reported competing ideas on the formation of fission gas bubble superlattices in metallic fuels, which was postulated to be comprised of elemental xenon (Xe) atoms. However, the chemical and physical arrangement of these elements within this gas bubble superlattice had not been verified. In this contribution, Xe was chemically profiled using atomic resolution scanning transmission electron microscopy (STEM) and atom probe tomography (APT) techniques in irradiated uranium-molybdenum (U-Mo) fuels. These complementary techniques provide conclusive evidence of Xe presence in the bubble superlattice up to fission densities of 4.5 × 1021 fissions/cm3 and give a quantitative assessment of Xe content within the bubble superlattice. Based on the results of simultaneous imaging and spectroscopy using STEM, the chemical composition of the Xe bubble superlattice was measured and found to be up to 8±1.3 atomic %. APT data complemented STEM findings on Xe distribution in irradiated U-Mo fuel sample. This study provides conclusive evidence that Xe is not only present within an atomically arranged bubble superlattice but provides fundamental insight into the physical state of Xe in low enriched U-Mo monolithic fuel.

Calculation of the effective thermal conductivity of porous polycrystalline U-10Mo alloy based on phase-field simulation

In the present work, the thermal conductivity of U-10Mo was calculated, considering the effects of different microstructures, including fission bubbles and recrystallization, through simulations using the phase-field method. The concept of effective thermal conductivity was used to describe thermal conductivity. Systematic calculation was conducted to determine the effect of fission bubble porosity on thermal conductivity. A shape factor was proposed to quantitatively represent the different shapes of bubbles, and the specific expression was also given. It was found that the shape factor had a significant impact on thermal conductivity. Additionally, the effects of grain refinement and coupled bubble evolution with different fission densities on thermal conductivity had been quantitatively studied. The calculated results were in good agreement with the experimental results. It was revealed that recrystallization had a significant impact on thermal conductivity, with higher irradiation density resulting in lower thermal conductivity due to the higher GB density and larger porosity. Based on the models presented in this paper, it is of great engineering significance to predict the thermal conductivity changes of U-10Mo fuel in service.

On the creep mechanisms and macroscopic creep rate modeling of high-uranium-density composite fuels

UN-U3Si2 composite fuel is a promising candidate of Accident Tolerant Fuels (ATFs). Its in-pile creep performance will have an important impact on the irradiation-induced thermo-mechanical coupling behavior and safety of fuel elements. Based on the existing mechanism-based creep models of UN and U3Si2, the finite element analysis was performed for the multi-scale creep behaviors of various UN-U3Si2 composite fuels, and the influences of the U3Si2 volume fraction, applied stress, temperature, fission rate, and grain size were investigated. The dominant creep mechanisms under different conditions were proposed, and the mechanism-based macroscopic creep rate model for the UN-U3Si2 composite fuels were correspondingly developed, quantitatively correlating with the macroscopic creep rate with the U3Si2 vol fraction, temperature, fission rate and equivalent stress. The creep rate predictions obtained by this model were in good agreement with the results of the finite element simulation. The research results indicate that: (1) the irradiation or thermal diffusion creep contributions from the UN and U3Si2 phases were dominated under various conditions; (2) the dislocation creep contributions from the dispersed-phase of U3Si2 were appreciable at the temperatures ranged from 500 K to 1300 K, while those of the matrix-phase of UN appeared only at an extremely high temperature of 1300 K; (3) different from the ordinary inert-matrix dispersion fuels, the macroscopic creep rates of UN-U3Si2 composite fuels were predicted to be almost independent of burnup, due to the slight difference in the irradiation swelling of UN and U3Si2; (4) the total creep contribution proportions of the U3Si2 or UN phase were almost equal to the initial volume fractions, while the creep contribution ratios within the UN or U3Si2 phase vary under different conditions. The evolutions of various creep contributions with the fission density were attributed to the fuel-swelling induced additional stresses.

High-Order Perturbation Method for Updating Response Functions for Time-Dependent Transport Calculations

The hybrid stochastic deterministic continuous-energy coarse mesh transport method (COMET) has been recently extended for high-fidelity efficient kinetics calculations in highly heterogeneous reactor cores. The method discretizes the time variable as a series of time grids and solves the resulting set of steady-state neutron transport equations. In this work, a high-order perturbation method is developed to update the COMET unperturbed response function library on the fly for changes in the discretized time step size Δ t h . The unperturbed response functions are precomputed with 1 / v Δ t h = 0 . The perturbation expansion coefficients are also generated during the unperturbed response function library precomputation. The adjoint solution needed by the perturbation method is calculated using the reciprocity relation without solving the corresponding adjoint problems. As a result, the method can be easily implemented into any stochastic code to generate the perturbation expansion coefficients together with the unperturbed response functions. The high-order perturbation method is benchmarked by comparing both the response functions and the time-dependent COMET core solution (fission density) with the corresponding reference solutions. It is found that the response functions generated by the perturbation method at second order are in excellent agreement with those directly computed by the Monte Carlo method. When Δ t h changes from 1.0E-4 s to infinity, the average and maximum relative differences in the various response functions were found to be in the range of 0.0000106% to 0.00116% and 0.000011% to 0.00121%, respectively. The fission density as a function of time calculated by COMET using the perturbation method is in excellent agreement with the reference solutions, with an average relative difference of 0.0065% to 0.075%. These comparisons indicate that the perturbation method at second order is highly accurate.

Integrated simulation of U-10Mo monolithic fuel swelling behavior

A separate computational branch has been implemented within the DART (Dispersion Analysis Research Tool) computational code to simulate the swelling behavior of U-10Mo monolithic fuel under the operating conditions of high-power research and test reactors (RTRs). The monolithic branch of the DART code implements a mechanistic rate-theory-based fission-gas-behavior model for the calculation of fission gas swelling, as well as a suite of thermal, physical, and mechanical models to consider various processes occurring in RTR fuels during irradiation. To accurately simulate and eventually predict U-10Mo monolithic fuel irradiation behavior, the code uses materials properties calculated with lower length-scale computational methods, such as gas atom diffusivity and U-Mo surface energy from atomic simulations and grain-morphology-specific recrystallization kinetics (recrystallized fuel volume fractions versus fission density) predicted using the phase-field method. The remainder of the fission gas behavior parameters used in the model were calibrated with measured intergranular bubble size distributions. With this integrated simulation approach, the swelling behavior of U-10Mo monolithic fuel was simulated for various initial grain sizes at different operating conditions and compared with measured data. Furthermore, because limited experimental data exist for parameter calibration, detailed sensitivity studies for the important parameters used in the fission gas behavior model were performed to examine their impact on both intergranular gas bubble morphology at low fission density, and on total porosity at high fission density.

A Consistent Low-Order Acceleration Technique for Coarse Mesh Transport (COMET) Methods

The COarse MEsh Transport (COMET) method, a hybrid continuous energy stochastic and deterministic transport method/tool based on the incident flux response expansion theory, is capable of providing highly accurate and efficient continuous energy whole-core neutron solutions to various heterogeneous reactor cores. In this work, a novel low-order (zeroth-order) acceleration technique is developed to significantly improve COMET’s computational efficiency for core calculations. This new method is based on consistent coupled low-order and high-order calculations to obtain the COMET core solution. In the low-order calculations, COMET is used to converge the total partial current escaping from each coarse mesh and the core eigenvalue. The resulting fixed-source problem in which the off-diagonal terms (equivalent to the scattering and fission neutron sources) are constructed by the zeroth-order solution are efficiently solved by the high-order COMET calculations. The resulting high-order angular flux on each coarse mesh bounding surface is then used to update (collapse) the low-order response coefficients. The coupled low-order and high-order calculations are repeated until both the eigenvalue and the low-order response coefficients are converged. The new acceleration method is implemented into COMET and tested in a set of stylized Advanced High Temperature Reactor (AHTR) benchmark problems. It is found that the core eigenvalues and the local fission density distributions predicted by COMET with the low-order acceleration agree very well with those computed by the original COMET. The eigenvalue discrepancy varies from 0 to 1 pcm, and the average relative differences in the stripewise and assembly-average fission density distributions are in the range of 0.021% to 0.032% and 0.004% to 0.01%, respectively. The comparisons have shown that the new low-order acceleration method can maintain COMET’s accuracy while improving its computational efficiency for core calculations by 12 to 16 times.

Continuous-Energy Time-Dependent Coarse Mesh Transport (COMET) Method for Kinetics Calculations

In this paper, the novel continuous-energy coarse mesh transport (COMET) method is extended to perform time-dependent neutronics calculations in highly heterogeneous reactor core problems. In this method, the time-dependent transport equation is converted into a series of steady-state transport equations by estimating the time derivative term using implicit finite differencing. The resulting steady-state transport equations, having additional terms that are imbedded in the total collision term and in the volumetric source terms, are then solved by the steady-state COMET method, in which all the phase-space variables, including energy, are treated continuously. Finally, the fission density distribution constructed by the steady-state COMET is used to solve a set of ordinary differential equations to obtain the delayed neutron precursor concentrations. The time-dependent COMET method is benchmarked against a direct continuous-energy Monte Carlo method (i.e., MCNP) in a set of infinite homogeneous problems and a set of single-assembly benchmark problems consisting of identical pin cells. It is found that the COMET results agree very well with the Monte Carlo reference solutions while maintaining its formidable computational speed (orders of magnitude faster than the Monte Carlo method).

The role of UC inclusions in the development of fission gas bubble superlattice neutron-irradiated monolithic U-10Mo fuels

Uranium Carbide (UC) inclusions are the most prevalent impurities in Uranium-Molybdenum (U-Mo) fuel and are considered undesirable because they could potentially affect fuel performance. This work revealed that, like grain boundaries, UC inclusions could help facilitate the formation of the fission gas bubble superlattice (GBS). The GBS is a highly organized complex defect structure that can effectively store fission gases, thereby inhibiting fuel swelling. Transmission electron microscopy (TEM) showed that GBS self-organization can initiate at the UC/U-Mo interfaces in U-10Mo fuel irradiated to low fission density. This study also revealed that the UC/U-Mo phase boundary in U-10Mo irradiated to low fission density is wavy and periodic in morphology and that GBS formation is semi-coherent with the UC boundary. Because the initiation of GBS preferentially occurs at grain boundaries and UC/U-Mo phase boundaries, it is expected that following GBS collapse at higher fission densities, high burnup structure development may initiate first at grain boundaries and UC/U-Mo interfaces.

Post-irradiation examination of low burnup U3Si5 and UN-U3Si5 composite fuels

This work presents post-irradiation examination data on UN-U3Si5 and U3Si5 fuels at low burnup (i.e., <10–15 GWd/tHM) with Kanthal AF® cladding. The results suggest good irradiation performance for both the silicide and nitride-silicide composite pellets. Optical microscopy revealed that the pellet-cladding gap is still open, and limited axial cracking was observed only in UN-U3Si5 pellets. Microcracking was isolated to the U3Si5 phase in all cases and was observed in pre-irradiation and depleted pellets, indicating that it was not irradiation induced. The fission gas release was minimal for the calculated fission density achieved (2.6 – 3.15 × 1020 fiss/cm3). No fission gas bubbles were observed in the optical metallography. These results suggest acceptable swelling and fission gas behavior for both the single phase and composite compositions.

Possible impacts of Mo chemical banding and second phase impurities on the irradiation behavior of monolithic U-10Mo fuels

This study investigated the microstructural behavior of both full-size and mini-size monolithic U-10Mo fuel plates irradiated to high burnup with a focus on the evolution of the second phase impurities in monolithic U-Mo using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and wavelength dispersive spectroscopy (WDS). Key indicators of possible mechanical and thermal compromise include cracks, large fission gas porosity, and interconnection of fission gas pores. For the fission densities evaluated in this work (3.5 × 1021 fissions/cm3 -5.1 × 1021 fissions/cm3), fine porosity can develop along the UC phase boundary; however, the size of the fission gas pores is no more than those observed in the U-Mo fuel phase. Other inclusions such as Si-rich second-phase impurities found in the as-fabricated microstructure were difficult to resolve post-irradiation because they can become overshadowed by porosity development in the fuel phase. Additionally, the presence of a Fe-rich sublayer formed in the Zr diffusion layer during fabrication remained enriched in the Zr layer in the irradiated U-10Mo microstructures near the U-Mo/Zr interface; however, based on the burnup assessed in this study the identified impurities did not appear to contribute to notable microstructural degradation.