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DOE OSTI2022

Neutron elastic and inelastic scattering differential cross sections on carbon

Elastic and inelastic neutron scattering angular distributions were measured on natural carbon samples to confirm existing experimental data and evaluations in the fast neutron region and to guide improvements in resonance parameters, where needed. Sixty-four (n,n') differential cross section measurements were performed at 45 incident neutron energies between 0.5 and 8.0 MeV. Experimental angle-integrated elastic scattering cross sections are consistent with ENDF/B-VIII.0 values with the exception of the region from 3.2 to 4.0 MeV where our results are ~3% higher. In the 3.4 to 3.6 MeV region our differential cross sections are slightly lower at forward angles and somewhat higher at backward angles than the ENDF/B-VIII.0 calculations; however, our results are consistent with measured data from other research groups. The first- through fourth-order elastic scattering Legendre coefficients from fits to these experimental data are consistent with ENDF/B-VIII.0 values across this range of incident neutron energies. Inelastic scattering cross sections were measured at 12 incident neutron energies between 5.6 and 7.8 MeV. Angle-integrated cross sections agree well with the 1978 Perey and ENDF/B-VIII.0 values; however, the angular-distribution shapes deviate somewhat from the ENDF/B-VIII.0 calculations. These data will allow refinement of the resonance parameter description in this difficult energy region.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Evaluation and Validation of the n+ 63,65 Cu Cross Sections [Slides]

This presentation discusses the objective of the research which is to update n+ 63,65 Cu cross section evaluations with recently measured data to resolve discrepancies in benchmark performance. It also discusses the models used which are the R -matrix analysis and the analysis of angular distribution coefficients. Additionally, the validation methods that were used are discussed, including the Rez shielding benchmark and the ICSBEP criticality benchmarks. In conclusion, he n+ 63,65 Cu cross sections have been updated via R-matrix analysis up to 100 keV. An increased average capture cross section and the adoption of experimentally based Legendre coefficients lead to improved performance in reactivity benchmarks. In the fast region, the adoption of the JENDL-4.0 cross sections above 4.0 MeV improves the performance in shielding benchmarks. Ultimately, the n 63,65 Cu ENDF files will be submitted to ENDF/B-VIII.1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Updates to the n+ 63,65 Cu Angular Distributions [Slides]

The performance of the benchmark suite is very sensitive to changes in the angular distribution data. The quasi-differential measurements performed by Blain et al at RPI provide a valuable constraint. Furthermore, ENDF/B-VIII.0 disagrees with their measurements consistently at 300 keV (the transition between RRR and high energy). The next step is to conservatively adjust the Legendre coefficients near 300 keV, validating performance against both critical benchmarks and the RPI quasi-differential measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Updates and Validation for the n+ 63,65 Cu Cross Sections [Abstract]

The neutron induced total, elastic, and capture cross sections of 63,65 Cu isotopes were selected for evaluation in the resolved and unresolved resonance energy ranges by the National Criticality Safety Program to resolve discrepancies related to benchmark performance. This is especially evident for the series of ZEUS benchmarks in which copper is used as a reflector. Because copper is also used as structural material in both fission and fusion reactors, the need to address benchmark discrepancies linked to nuclear data deficiencies is a task of primary importance. The aim of this work is to describe the steps of evaluation work towards a consistent improvement of the benchmark performance. The R-matrix analysis with the SAMMY code focused on the 63 Cu(n,γ) reaction channel between 100-300 keV coupled to unresolved resonance region parameters up to 650 keV to fit average cross section data from a recent experiment. Due to the high sensitivity of many benchmarks to elastic scattering angular distribution data, especially for the 65 Cu isotope, the impact of these data was tested by generating Legendre coefficients from both resonance parameters and the Hauser-Feshbach model. Guided by the findings of Shaw et al., the performance of the current evaluation for 65 Cu was compared to that of ENDF/B-VII.1 and ENDF/B-VIII.0 by testing the reactivity coefficients corresponding to the validation suite of experimental criticality benchmarks for thermal, intermediate, and fast systems taken from the International Criticality Safety Benchmark Experiments Project Handbook. The benchmark performance is especially sensitive to 63 Cu(n,γ) and 65 Cu elastic scattering for neutron energies in the 100–500 keV region, whereas 100 keV is the upper limit of the resolved resonance region in the ENDF/B-VIII.0 evaluations for 63,65 Cu. The results highlight the need to handle the transition from the resolved resonance region to the high energy region carefully.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2023

A comparison of past and present computational methods for shape analysis of double-shell x-ray radiographs

Implosion symmetry is a key requirement in achieving a robust burning plasma in inertial confinement fusion experiments. In double-shell capsule implosions, we are interested in the shape of the inner shell as it pushes on the fuel. Shape analysis is a popular technique for studying said symmetry during implosion. Combinations of filtering and contour-finding algorithms are studied for their promise in reliably recovering Legendre shape coefficients from synthetic radiographs of double-shell capsules with applied levels of noise. A radial lineout max(slope) method when used on an image pre-filtered with non-local means and a variant of the marching squares algorithm are able to recover p 0 , p 2 , and p 4 maxslope Legendre shape coefficients with mean pixel discrepancy errors of 2.81 and 3.06, respectively, for the noisy synthetic radiographs we consider. Here, this improves upon prior radial lineout methods paired with Gaussian filtering, which we show to be unreliable and whose performance is dependent on input parameters that are difficult to estimate.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

A Characteristics Approach to the Finite Element Method

Herein, we present a new method for solving the linear Boltzmann transport equation. Two commonly used and well-understood methods for solving partial differential equations are the method of characteristics (MOC) and the finite element method (FEM). We propose a new method that combines the fundamental concept of the FEM with the analytic solution from the MOC to obtain coefficients for the FEM basis function expansion. Traditionally, coefficients for the FEM basis function expansion are obtained via matrix inversion. Instead, we solve for the coefficients with the MOC and represent the underlying fields with the basis function expansion using these coefficients. We provide a convergence study for our method with results from two sets of FEM basis functions: Gauss-Legendre and Gauss-Lobatto sets. We also compare two different variations of our method categorized as short characteristics and intermediate characteristics.

42 ENGINEERING↗

DOE OSTI2026

Charge And Dynamic Current On Tubular Antennas For Various Drive Conditions

The mixed boundary value problem of a tubular conductor is solved using an approximate representation of its Fourier coefficients. A two term solution is derived, which represents the solution over an extremely broad range of aspect ratios. This representation is used to find the electrostatic solution and capacitance of a charged tube as well as the solution of a tube in a uniform field and its dipole moment. This second case is directly useful as a model for a monopole electric field probe. This approximation is a special case of a representation using a combination of Chebyshev and Legendre polynomials. Combining the charged tube and tube in a uniform field allows the solution of voltage driven tubular antennas. Comparisons are made with numerical solutions using piecewise sinusoidal representations of the current. The results are also generalized to the dynamic case and up to and beyond the first resonance. Simple corrections for finite gap and delta gap drives to magnetic frill drives are examined using infinite tube integral transform representations. Corrections between magnetic frill drives and coaxial drives are also given. Approximate drive corrections using conformal mapping and an effective radius are also discussed. Finally, this efficient current representation is applied to the magnetic problem involving simple tubular solenoids.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

High Fidelity CFD Simulations Supporting the KP-FHR

Kairos Power, LLC, is developing its version of the Fluoride-cooled High-temperature Reactor, the KP-FHR. The design uses a pebble bed core with fluoride salt as a coolant. The pebbles used in the KP-FHR have a diameter of 4 cm, with a shell fuel region where TRISO particles are embedded. A Pebble bed core design is adopted by several Gen IV reactors, They boast many benefits, such as fuel integrity, highly efficient heat transfer, and passive safety. However, it is challenging to accurately predict temperature and flow inside a pebble bed. Traditional approaches use the porous media model, which regards the pebble bed as a continuous medium, but with different temperature fields representing different levels, such as the fluid temperature, pebble surface temperature, and pebble center temperature. Empirical heat transfer correlations are adopted to calculate the heat transfer coefficient between different phases. However, empirical correlations are usually validated with experimental data, which usually lacks detail inside the pebble bed. The available experimental data is also generally at a high Reynolds number, which falls outside of the conditions of KP-FHR. Explicit computational fluid dynamics (CFD) simulations of randomly packed pebble beds have only become feasible recently. This is thanks to the rapid development of computational power and scalable algorithms. In this work, we used the Spectral Element Method (SEM) CFD code NekRS to simulate the randomly packed pebble bed in a cylindrical container. NekRS, which is the GPU variant of Nek5000, but refactored to utilize the computational power of GPUs using the OCCA library to run on hybrid architecture high performance computing systems. It was initially developed with the libParamunal library, but truncated and tuned for large-scale turbulence simulation. As a result, the SEM reaches higher precision with the same degrees of freedom by using a high-order Lagrange polynomial basis distributed on Gauss-Lobatto-Legendre quadrature inside each element, compared to lower-order methods, such the Finite Volume Method and Finite Element Method. The report is divided into five parts. We start with a general discussion of the pebble bed reactor, along with a specific investigation into the KP-FHR. The second part presents the numerical methodology. In the third part, we study a modular pebble bed with 1741 pebbles in a container of 7 pebble-diameter radius. Beyond LES simulations done by NekRS, we also leveraged the thermal radiation model in OpenFOAM to study heat transfer under no-forced-flow scenarios. Then, in the fourth part we simulated a pebble bed similar to the size of the Hermes Test Reactor. The total number of pebbles is in these simulations is 34,374. The container radius is 14 pebble-diameters. Finally, the report concludes in part five, with a discussion of future work.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗