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SCALE Code System 6.2.1

The SCALE Code System is a widely-used modeling and simulation suite for nuclear safety analysis and design that is developed, maintained, tested, and managed by the Reactor and Nuclear Systems Division (RNSD) of Oak Ridge National Laboratory (ORNL). SCALE provides a comprehensive, verified and validated, user-friendly tool set for criticality safety, reactor and lattice physics, radiation shielding, spent fuel and radioactive source term characterization, and sensitivity and uncertainty analysis. Since 1980, regulators, licensees, and research institutions around the world have used SCALE for safety analysis and design. SCALE provides an integrated framework with dozens of computational modules including three deterministic and three Monte Carlo radiation transport solvers that are selected based on the desired solution strategy. SCALE includes current nuclear data libraries and problem-dependent processing tools for continuous-energy (CE) and multigroup (MG) neutronics and coupled neutron-gamma calculations, as well as activation, depletion, and decay calculations. SCALE includes unique capabilities for automated variance reduction for shielding calculations, as well as sensitivity and uncertainty analysis. SCALE’s graphical user interfaces assist with accurate system modeling, visualization of nuclear data, and convenient access to desired results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

MPACT Subgroup Self-Shielding Efficiency Improvements

Recent developments to improve the efficiency of the MOC solvers in MPACT have yielded effective kernels that loop over several energy groups at once, rather that looping over one group at a time. These kernels have produced roughly a 2x speedup on the MOC sweeping time during eigenvalue calculation. However, the self-shielding subgroup calculation had not been reevaluated to take advantage of these new kernels, which typically requires substantial solve time. The improvements covered in this report start by integrating the multigroup kernel concepts into the subgroup calculation, which are then used as the basis for further extensions. The next improvement that is covered is what is currently being termed as “Lumped Parameter MOC”. Because the subgroup calculation is a purely fixed source problem and multiple sweeps are performed only to update the boundary angular fluxes, the sweep procedure can be condensed to allow for the instantaneous propagation of the flux across a spatial domain, without the need to sweep along all segments in a ray. Once the boundary angular fluxes are considered to be converged, an additional sweep that will tally the scalar flux is completed. The last improvement that is investigated is the possible reduction of the number of azimuthal angles per octant in the shielding sweep. Typically 16 azimuthal angles per octant are used for self-shielding and eigenvalue calculations, but it is possible that the self-shielding sweeps are less sensitive to the number of angles than the full eigenvalue calculation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k eff , and α Using PARTISN

SENSMG is a tool for computing first-order sensitivities of neutron reaction rates, reaction-rate ratios, leakage, k eff , and α using the PARTISN multigroup discrete-ordinates code. SENSMG computes sensitivities to all of the transport cross sections and data (total, fission, nu, chi, and all scattering moments), two edit cross sections (absorption and capture), and the density for every isotope and energy group. It also computes sensitivities to the mass density for every material and derivatives with respect to all interface locations. The tool can be used for one-dimensional spherical (r) and two-dimensional cylindrical (r-z) geometries. The tool can be used for fixed-source and eigenvalue problems. The tool implements Generalized Perturbation Theory (GPT) as discussed by Williams and Stacey. Section II of this report describes the theory behind adjoint-based sensitivities, gives the equations that SENSMG solves, and defines the sensitivities that are output. Section III describes the user interface, including the input file and command line options. Section IV describes the output. Section V gives some notes about the coding that may be of interest. Section VI discusses verification, which is ongoing. Section VII lists needs and ideas for future work. Appendix A lists all of the input files whose results are presented in Sec. VI.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The NJOY Nuclear Data Processing System, Version 2016

The NJOY Nuclear Data Processing System, version 2016, is a comprehensive computer code package for producing pointwise and multigroup cross sections and related quantities from evaluated nuclear data in the ENDF-4 through ENDF-6 legacy card-image formats. NJOY works with evaluated files for incident neutrons, photons, and charged particles, producing libraries for a wide variety of particle transport and reactor analysis codes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Rattlesnake: User Manual

The drafted user manual for Rattlesnake, the multigroup radiation transport application based on MOOSE.

97 MATHEMATICS AND COMPUTING↗

The coupling of the neutron transport application RATTLESNAKE to the nuclear fuels performance application BISON under the MOOSE framework

The MOOSE neutron transport application RATTLESNAKE was coupled to the fuels performance application BISON to provide a higher fidelity tool for fuel performance simulation. This project is motivated by the desire to couple a high fidelity core analysis program (based on the self-adjoint angular flux equations) to a high fidelity fuel performance program, both of which can simulate on unstructured meshes. RATTLESNAKE solves self-adjoint angular flux transport equation and provides a sub-pin level resolution of the multigroup neutron flux with resonance treatment during burnup or a fast transient. BISON solves the coupled thermomechanical equations for the fuel on a sub-millimeter scale. Both applications are able to solve their respective systems on aligned and unaligned unstructured finite element meshes. The power density and local burnup was transferred from RATTLESNAKE to BISON with the MOOSE Multiapp transfer system. Multiple depletion cases were run with one-way data transfer from RATTLESNAKE to BISON. The eigenvalues are shown to agree well with values obtained from the lattice physics code DRAGON. The one-way data transfer of power density is shown to agree with the power density obtained from an internal Lassman-style model in BISON.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Criticality safety enhancements for SCALE 6.2 and beyond

SCALE is a widely used suite of tools for nuclear systems modeling and simulation that provides comprehensive, verified and validated, user-friendly capabilities for criticality safety, reactor physics, radiation shielding, and sensitivity and uncertainty analysis. Since 1980, regulators, industry, and research institutions around the world have relied on SCALE for nuclear safety analysis and design. SCALE 6.2 provides several new capabilities and significant improvements in many existing features for criticality safety analysis. Enhancements are realized for nuclear data; multigroup resonance self-shielding; continuous-energy Monte Carlo analysis for sensitivity/uncertainty analysis, radiation shielding, and depletion; and graphical user interfaces. An overview of these capabilities is provided in this paper, and additional details are provided in several companion papers.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basis function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.

Cross sections↗

Simulate-HEX - The multi-group diffusion equation in hexagonal-z geometry

The multigroup diffusion equation is solved for the hexagonal-z geometry by dividing each hexagon into 6 triangles. In each triangle, the Fourier solution of the wave equation is approximated by 8 plane waves to describe the intra-nodal flux accurately. In the end an efficient Finite Difference like equation is obtained. The coefficients of this equation depend on the flux solution itself and they are updated once per power/void iteration. A numerical example demonstrates the high accuracy of the method. (authors)

97 MATHEMATICS AND COMPUTING↗

Transient MOC with frequency transform and DSA on unstructured mesh

We present an implementation of the transient method of characteristics (MOC) with isotropic time derivatives, accelerated by diffusion synthetic acceleration (DSA). The fully implicit frequency transform method is used to solve the transient problem with analytic precursor integration. The code works on meshes composed of almost any of the commonly used non-curvilinear finite element types, and can handle the deformation of geometry in time-dependent transport calculations. We present results of a continuous Fourier analysis for the transient multigroup DSA problem, and representative benchmarking results are presented for the C5G7-TD benchmark in 2D showing reasonable performance and agreement compared to other codes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Reactivity Runaway Reduction When Using Enriched Uranium in a Lead Fast Reactor

The possibilities for reactivity runaway reduction in a fast reactor when using enriched uranium are examined. Specifically, an approach supposing partial compensation of reactivity runaway by the addition of Np or Am, as consumable absorbers, into the starting load is analyzed. It is shown that from the standpoint of the development of large-scale nuclear power generation based on BREST-type reactors the use of a uranium starting load becomes inexpedient in implementing this approach. A starting load consisting of a mixture of enriched uranium and plutonium from spent RBMK fuel is studied. The results indicate that it is possible to develop a core with reactivity runaway not exceeding the effective delayed-neutron fraction during the entire period of operation. The neutronics characteristics were calculated using the Arktika multigroup diffusion code. The RISK code was used to determine the change in the nuclide composition.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Monte Carlo capabilities of the SCALE code system

SCALE is a broadly used suite of tools for nuclear systems modeling and simulation that provides comprehensive, verified and validated, user-friendly capabilities for criticality safety, reactor physics, radiation shielding, and sensitivity and uncertainty analysis. For more than 30 years, regulators, licensees, and research institutions around the world have used SCALE for nuclear safety analysis and design. SCALE provides a “plug-and-play” framework that includes three deterministic and three Monte Carlo radiation transport solvers that can be selected based on the desired solution, including hybrid deterministic/Monte Carlo simulations. SCALE includes the latest nuclear data libraries for continuous-energy and multigroup radiation transport as well as activation, depletion, and decay calculations. SCALE’s graphical user interfaces assist with accurate system modeling, visualization, and convenient access to desired results. SCALE 6.2 will provide several new capabilities and significant improvements in many existing features, especially with expanded continuous-energy Monte Carlo capabilities for criticality safety, shielding, depletion, and sensitivity and uncertainty analysis. Finally, an overview of the Monte Carlo capabilities of SCALE is provided here, with emphasis on new features for SCALE 6.2.

97 MATHEMATICS AND COMPUTING↗

Advanced multiphysics coupling for LWR fuel performance analysis

Even the most basic nuclear fuel analysis is a multiphysics undertaking, as a credible simulation must consider at a minimum coupled heat conduction and mechanical deformation. The need for more realistic fuel modeling under a variety of conditions invariably leads to a desire to include coupling between a more complete set of the physical phenomena influencing fuel behavior, including neutronics, thermal hydraulics, and mechanisms occurring at lower length scales. This paper covers current efforts toward coupled multiphysics LWR fuel modeling in three main areas. The first area covered in this paper concerns thermomechanical coupling. The interaction of these two physics, particularly related to the feedback effect associated with heat transfer and mechanical contact at the fuel/clad gap, provides numerous computational challenges. An outline is provided of an effective approach used to manage the nonlinearities associated with an evolving gap in BISON, a nuclear fuel performance application. A second type of multiphysics coupling described here is that of coupling neutronics with thermomechanical LWR fuel performance. DeCART, a high-fidelity core analysis program based on the method of characteristics, has been coupled to BISON. DeCART provides sub-pin level resolution of the multigroup neutron flux, with resonance treatment, during a depletion or a fast transient simulation. Two-way coupling between these codes was achieved by mapping fission rate density and fast neutron flux fields from DeCART to BISON and the temperature field from BISON to DeCART while employing a Picard iterative algorithm. Finally, the need for multiscale coupling is considered. Fission gas production and evolution significantly impact fuel performance by causing swelling, a reduction in the thermal conductivity, and fission gas release. The mechanisms involved occur at the atomistic and grain scale and are therefore not the domain of a fuel performance code. However, it is possible to use lower length scale models such as those used in the mesoscale MARMOT code to compute average properties, e.g. swelling or thermal conductivity. These may then be used by an engineering-scale model. Examples of this type of multiscale, multiphysics modeling are shown.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Continuous-energy Monte Carlo neutron transport on GPUs in the Shift code

Here, a continuous-energy Monte Carlo neutron transport solver executing on GPUs has been developed within the Shift code. Several algorithmic approaches are considered, including both history-based and event-based implementations. Unlike in previous work involving multigroup Monte Carlo transport, it is demonstrated that event-based algorithms significantly outperform a history-based approach for continuous-energy transport as a result of increased device occupancy and reduced thread divergence. Numerical results are presented for detailed full-core models of a small modular reactor (SMR), including a model containing depleted fuel materials. These results demonstrate the substantial gains in performance that are possible with the latest-generation of GPUs. On the depleted SMR core configuration, an NVIDIA P100 GPU with 56 streaming multiprocessors provides performance equivalent to 90 CPU cores, and the latest V100 GPU with 80 multiprocessors offers the performance of more than 150 CPU cores.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Verification and Validation Tests of Gamma Library of MC2-3 for Coupled Neutron and Gamma Heating Calculation

For the accurate assessment of the heat generation rate in fast reactors, the gamma library of MC2 -3 and the MC2 -3 + GAMSOR procedure employing the coupled neutron and gamma heating calculation has been thoroughly verified against Monte Carlo results and validated using the ZPPR-15D gamma dose measurement data. NJOY outputs are post-processed in a consistent way with the NJOY procedure to avoid any missing data or double counting of data. Prompt heating for 379 out of 391 isotopes in the gamma library was verified against MCNP6.2 to within 1% relative error in total heating for most isotopes. For both a simple one-dimensional slab problem representing a sodium cooled fast reactor and the Experimental Breeder Reactor II (EBR-II) benchmark problem, the root-mean-square values of assembly power error were less than 0.5% for fuel assemblies, ~1% in blankets and ~1 to ~3% in reflectors compared to MCNP6.2 results. The most plausible cause for the 3% error in a reflector assembly is believed to be the error in the multigroup neutron cross sections for the reflector assembly. For validation, gamma doses measured with thermoluminiscent dosimeters (TLDs) in the ZPPR-15D experiment were calculated using GAMSOR. Due to the uncertainty in the TLD measurement with regards to the energy deposition of photons and neutrons, the validation data leads to a 12.7% uncertainty on the experimental measurement. With this uncertainty bound, the calculated doses all fell within one standard deviation of the measured value. Combined with the accurate calculation of reaction rate distributions and neutron spectrum measurements, these results indicate good agreement for the neutron and gamma heating calculations that were performed.

coupled neutron and gamma heating↗

SCALE capabilities for high temperature gas-cooled reactor analysis

The SCALE code system’s ability to address stochastic distributions of fuel particles within a graphite matrix has been revisited in both multigroup (MG) features and continuous-energy (CE) Monte Carlo methods. Furthermore, this paper describes current and emergent SCALE capabilities within the CSAS sequence to address double-heterogeneous systems and presents verification and validation studies of these methods and data. Good agreement was obtained for a high temperature gas-cooled reactor (HTGR) fuel pebble model between CSAS MG eigenvalue calculations and corresponding CE reference solutions. Code-to-code comparisons for this HTGR pebble model showed good agreement of CSAS-KENO and CSAS-Shift CE calculations and the Serpent and MCNP codes in terms of eigenvalues and reaction rate ratios. Validation studies based on two HTGR experiments resulted in good agreement between MG and CE results, as well as between experiment and calculation, although the level of agreement was significantly influenced by the applied ENDF/B nuclear data library.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Lattice physics calculations using the embedded self-shielding method in polaris, Part II: Benchmark assessment

Polaris is a 2D multigroup lattice physics capability in the SCALE code system used for the analysis of light water reactor fuel designs. In this work, verification and validation results of Polaris in SCALE 6.2 are presented. The SCALE/KENO continuous-energy Monte Carlo code is used as a reference to compare the results of more than 2,000 combinations of pressurized water reactor and boiling water reactor lattice designs and state points. Radiochemical assay measurements were also used to assess the accuracy of depletion calculations. Results show that Polaris, with ENDF/B-VII.1 cross section library, produces accurate lattice physics data for core simulators.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Data reduction in deterministic neutron transport calculations using machine learning

Neutron cross section matrices for fission and scattering data are required for each material, temperature, and enrichment level to calculate the neutron transport equation accurately. Here, this information can be a limiting factor when using the multigroup discrete ordinates (S N ) method when the number of energy groups is large. Machine Learning (ML) can be used to replace the need for the cross section matrices by reproducing the function that maps the scalar flux to the scattering and fission sources. Through the use of autoencoders and Deep Jointly-Informed Neural Networks (DJINN), the data storage requirements are reduced by 94% of the original data for a 618 group problem. This is accomplished while preserving the scalar flux, maintaining generality, and decreasing wall clock times.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗