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SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool being developed at Argonne National Laboratory under the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM development aims for advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability for reactor transient analyses. To facilitate the code development, SAM utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage modern advanced software environments and numerical methods. SAM focuses on modeling advanced reactor concepts such as SFRs (sodium fast reactors), LFRs (lead-cooled fast reactors), and FHRs (fluoride-salt-cooled high temperature reactors) or MSRs (molten salt reactors). These advanced concepts are distinguished from light-water reactors in their use of single-phase, low-pressure, high-temperature, and low Prandtl number (sodium and lead) coolants. As a new code development, the initial effort has been focused on modeling and simulation capabilities of heat transfer and single-phase fluid dynamics responses in Sodium-cooled Fast Reactor (SFR) systems. The system-level simulation capabilities of fluid flow and heat transfer in general engineering systems and typical SFRs have been verified and validated. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As the code is still under ongoing development, this SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

File-Based One-Way BISON Coupling Through VERA: User's Manual

Activities to incorporate fuel performance capabilities into the Virtual Environment for Reactor Applications (VERA) are receiving increasing attention [1–6]. The multiphysics emphasis is expanding as the neutronics (MPACT) and thermal-hydraulics (CTF) packages are becoming more mature. Capturing the finer details of fuel phenomena (swelling, densification, relocation, gap closure, etc.) is the natural next step in the VERA development process since these phenomena are currently not directly taken into account. While several codes could be used to accomplish this, the BISON fuel performance code [8,9] being developed by the Idaho National Laboratory (INL) is the focus of ongoing work in the Consortium for Advanced Simulation of Light Water Reactors (CASL). Built on INL’s MOOSE framework [10], BISON uses the finite element method for geometric representation and a Jacobian-free Newton-Krylov (JFNK) scheme to solve systems of partial differential equations for various fuel characteristic relationships. There are several modes of operation in BISON, but, this work uses a 2D azimuthally symmetric (R-Z) smeared-pellet model. This manual is intended to cover (1) the procedure pertaining to the standalone BISON one-way coupling from VERA and (2) the procedure to generate BISON fuel temperature tables that VERA can use.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation

In this report, we present a new upwinding scheme for the multiscale capability in Rattlesnake, the MOOSE based radiation transport application. Comparing with the initial implementation of multiscale utilizing Lagrange multipliers to impose strong continuity of angular flux on interface of in-between subdomains, this scheme does not require the particular domain partitioning. This upwinding scheme introduces discontinuity of angular flux and resembles the classic upwinding technique developed for solving first order transport equation using discontinuous finite element method (DFEM) on the subdomain interfaces. Because this scheme restores the causality of radiation streaming on the interfaces, significant accuracy improvement can be observed with moderate increase of the degrees of freedom comparing with the continuous method over the entire solution domain. Hybrid SN-PN is implemented and tested with this upwinding scheme. Numerical results show that the angular smoothing required by Lagrange multiplier method is not necessary for the upwinding scheme.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

MARMOT update for oxide fuel modeling

This report summarizes the lower-length-scale research and development progresses in FY16 at Idaho National Laboratory in developing mechanistic materials models for oxide fuels, in parallel to the development of the MARMOT code which will be summarized in a separate report. This effort is a critical component of the microstructure based fuel performance modeling approach, supported by the Fuels Product Line in the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. The progresses can be classified into three categories: 1) development of materials models to be used in engineering scale fuel performance modeling regarding the effect of lattice defects on thermal conductivity, 2) development of modeling capabilities for mesoscale fuel behaviors including stage-3 gas release, grain growth, high burn-up structure, fracture and creep, and 3) improved understanding in material science by calculating the anisotropic grain boundary energies in UO$_2$ and obtaining thermodynamic data for solid fission products. Many of these topics are still under active development. They are updated in the report with proper amount of details. For some topics, separate reports are generated in parallel and so stated in the text. The accomplishments have led to better understanding of fuel behaviors and enhance capability of the MOOSE-BISON-MARMOT toolkit.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

BISON Theory Manual The Equations behind Nuclear Fuel Analysis

BISON is a finite element-based nuclear fuel performance code applicable to a variety of fuel forms including light water reactor fuel rods, TRISO particle fuel, and metallic rod and plate fuel. It solves the fully-coupled equations of thermomechanics and species diffusion, for either 2D axisymmetric or 3D geometries. Fuel models are included to describe temperature and burnup dependent thermal properties, fission product swelling, densification, thermal and irradiation creep, fracture, and fission gas production and release. Plasticity, irradiation growth, and thermal and irradiation creep models are implemented for clad materials. Models are also available to simulate gap heat transfer, mechanical contact, and the evolution of the gap/plenum pressure with plenum volume, gas temperature, and fission gas addition. BISON is based on the MOOSE framework and can therefore efficiently solve problems using standard workstations or very large high-performance computers. This document describes the theoretical and numerical foundations of BISON.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

RELAP-7 Closure Correlations

The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL’s modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5’s and TRACE’s capabilities and extends their analysis capabilities for all reactor system simulation scenarios. The RELAP-7 code utilizes the well-posed 7-equation two-phase flow model for compressible two-phase flow. Closure models used in the TRACE code has been reviewed and selected to reflect the progress made during the past decades and provide a basis for the colure correlations implemented in the RELAP-7 code. This document provides a summary on the closure correlations that are currently implemented in the RELAP-7 code. The closure correlations include sub-grid models that describe interactions between the fluids and the flow channel, and interactions between the two phases.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Development of 3D Oxide Fuel Mechanics Models

This report documents recent work to improve the accuracy and robustness of the mechanical constitutive models used in the BISON fuel performance code. These developments include migration of the fuel mechanics models to be based on the MOOSE Tensor Mechanics module, improving the robustness of the smeared cracking model, implementing a capability to limit the time step size based on material model response, and improving the robustness of the return mapping iterations used in creep and plasticity models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Initial Testing of the Microscopic Depletion Implementation in the MAMMOTH Reactor Physics Application

Present and new nuclear fuels that will be tested at the Transient Reactor Test (TREAT) facility will be analyzed with the MAMMOTH reactor physics application, currently under development, at Idaho National Laboratory. MAMMOTH natively couples the BISON, RELAP-7, and Rattlesnake applications within the MOOSE framework. This system allows the irradiation of fuel from beginning of life in a nuclear reactor until it is placed in TREAT for fuel testing within the same analysis mesh and, thus, retaining a very high level of resolution and fidelity. The calculation of the isotopic distribution in fuel requires the solution to the decay and transmutation equations coupled to the neutron transport equation. The Chebyshev Rational Approximation Method (CRAM) is the current state-of-the-art in the field, as was chosen to be the solver for the decay and transmutation equations. This report shows that the implementation of the CRAM solver within MAMMOTH is correct with various analytic benchmarks for decay and transmutation of nuclides. The results indicate that the solutions with CRAM order 16 achieve the level of precision of the benchmark. The CRAM solutions show little sensitivity to the time step size and consistently produce a high level of accuracy for isotopic decay for time steps of 1x10^11 years. Comparisons to DRAGON5 with 297 isotopes yield comparable results, but some differences need to be further analyzed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

MARMOT Phase-Field Model for the U-Si System

A phase-field model for the U-Si system has been implemented in MARMOT. The free energies for the phases relevant to accident-tolerant fuel applications (U 3 Si 2 , USi, U 3 Si, and liquid) were implemented as free energy materials within MARMOT. A new three-phase phase-field model based on the concepts of the Kim-Kim-Suzuki two-phase model was developed and implemented in the MOOSE phase-field module. Key features of this model are that two-phase interfaces are stable with respect to formation of the third phase, and that arbitrary phase free energies can be used. The model was validated using a simplified three-phase system and the U-Si system. In the U-Si system, the model correctly reproduced three-phase coexistence in a U 3 Si 2 -liquid-USi system at the eutectic temperature, solidification of a three-phase mixture below the eutectic temperature, and complete melting of a three-phase mixture above the eutectic temperature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Initial 1.5D BISON Simulation Verification and Validation CASL FY17 Letter Report

This milestone report describes the current efforts to improve the usability of the recently developed 1.5 dimensional capability in BISON, the initial verification of this BISON capability, and initial validation of the 1.5 dimensional models against existing 2 dimensional axisymmetric full length light water reactor (LWR) fuel rods. The 1.5 dimensional (1.5D) capability in BISON was developed to enable the simulation of LWR fuel rods in a less computationally demanding simulation formulation while retaining key physics of interest. BISON was originally developed to solve 2D axisymmetric and 3D models, and this original development focus allows BISON to examine a wider range of fuel types and geometrically complexity than can be solved with lower dimensional frameworks. As the set of problems which BISON is used to solve expands, the software design requirements continue to evolve. Coupling physics in a higher dimensional geometry is not always required to resolve the physics of interest, such as the modeling of radial heat transfer and radial displacement. BISON, built on the dimension-agnostic MOOSE framework, is able to solve problems in 3D, 2D, and 1D with only minor modifications to the material definition code so that the appropriate geometrical representation can be applied in different problems of interest. The motivation for the development and validation of the BISON 1.5D capability is the CASL program's need for a simplified and computationally efficient version of BISON for use in the large multi-physics VERA simulations which include hundreds of individual fuel rods. The original development of the BISON 1.5D simulation capability is described in the CASL FY17 Letter Report from January 2017, and this report documents the continuing work identified in the previous report. The improvements to the usability of the 1.5D capability through input file simplifications, the results of the verification simulations, the results of the initial validation against the 2D assessment cases in BISON, and the future development needs are included within this report.

1.5D Capability↗

Computational and Experimental Studies of Microstructure-Scale Porosity in Metallic Fuels for Improved Gas Swelling Behavior

This proposal will investigate the stability of bimodal pore size distributions in metallic uranium and uranium-zirconium alloys during sintering and re-sintering annealing treatments. The project will utilize both computational and experimental approaches. The computational approach includes both Molecular Dynamics simulations to determine the self-diffusion coefficients in pure U and U-Zr alloys in single crystals, grain boundaries, and free surfaces, as well as calculations of grain boundary and free surface interfacial energies. Phase-field simulations using MOOSE will be conducted to study pore and grain structure evolution in microstructures with bimodal pore size distributions. Experiments will also be performed to validate the simulations, and measure the time-dependent densification of bimodal porous compacts.

36 MATERIALS SCIENCE↗

RELAP-7 User's Guide

The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL’s modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5’s capability and extends the analysis capability for all reactor system simulation scenarios.This document is a user's guide on how to use the RELAP-7 code.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Advanced Seismic Probabilistic Risk Assessment Methodology: Development of Beta 1.0 MASTODON Toolset

Design of nuclear power plant (NPP) facilities to resist natural hazards has been a part of the regulatory process from the beginning of the NPP industry in the United States, but has evolved substantially over time. The original set of approaches and methods was entirely deterministic in nature and focused on a traditional engineering margins-based approach. However, over time probabilistic and risk-informed approaches were also developed and implemented in US Nuclear Regulatory Commission guidance and regulation. A defense-in-depth framework has also been incorporated into US regulatory guidance over time. As a result, today, the US regulatory framework incorporates deterministic and probabilistic approaches for a range of different applications and for a range of natural hazard considerations. Although the US regulatory framework has continued to evolve over time, the tools, methods and data available to the US nuclear industry to meet the changing requirements have not kept pace. Notably, there is room for improvement in the tools and methods available for external event probabilistic risk assessment (PRA), which is the principal assessment approach used in risk-informed regulations and risk-informed decision-making applied to natural hazard assessment and design. Development of a new set of tools and methods that incorporate current knowledge, modern best practice, and state-of-the-art computational resources would lead to more reliable assessment of facility risk and risk insights (e.g., the plant elements and accident sequences that are most risk-significant), with less uncertainty and reduced conservatisms. Development of the next generation tools and methods for external events PRA is ongoing under the Risk Informed Safety Margins Characterization (RISMC) technical pathway. The RISMC toolkit development centers on integration of the tools and methods under a common framework, MOOSE. These tools and methods make use of existing and newly developed tools and methods, coupled with the experience and data gained in the past decades, to define and analyze more realistic risk assessment models. Specific focus in this report is on the capability to model seismic risk using advanced SPRA methods. Over the last year, significant capability has been added to Mastodon to simulate 3-D wave passage effects through nonlinear soil. Verification has demonstrated the capability of Mastodon to model wave passage effects in 1-D, 2-D, and 3-D. Methods have been developed to incorporate probabilistic floor response capabilities. Additional capability will be added to Mastodon over the next year to implement a robust gapping and sliding element for cyclic shaking, web-based verification and user manuals, stochastic finite elements, and frequency independent damping. Verification of added capabilities has occured in parallel with code writing activities.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Multischeme transport with upwinding for Rattlesnake code

This report conclude our efforts at INL to make Rattlesnake, the MOOSE-based radiation multigroup transport application, fully support the multischeme transport capability. Specifically, it details all five types of interface condition with upwinding method for coupling eight available discretization schemes within Rattlesnake. These discretization schemes include SN (discrete ordinates method), PN (spherical harmonics expansion method) and diffusion for angular discretization, and continuous finite element method (CFEM) and discontinuous finite element method (DFEM) for spatial discretization. The other type of method based on Lagrange multipliers for coupling schemes based on CFEM has been studied in the past. Besides simple test problems, a more realistic application of multischeme transport for TREAT (transient reactor test facility) experiment modeling are presented. Several enhancements are reviewed at the end which could potentially be useful in the future.

97 MATHEMATICS AND COMPUTING↗

Benchmark Analysis of the HTR-10 with the MAMMOTH Reactor Physics Application

This report documents a set of benchmarks used to validate the Serpent and MAMMOTH neutron transport models of the HTR-10 reactor developed at Idaho National Laboratory. The high-fidelity Serpent Monte Carlo models of the HTR-10 critical and full core configurations include both random, discrete distributions of TRISO particles in the pebbles and random, discrete pebble distributions in the pebble bed core. The Serpent results agree very well with the critical and control rod worth measurements provided in the International Re- actor Physics Experiment Evaluation Project (IRPhEP) report if the ENDF/B-VII.r1 data- set is used. These Serpent models are subsequently used to prepare cross sections and flux tallies in a 10 coarse energy group structure for the MAMMOTH Reactor Physics MOOSE- based application. We find that MAMMOTH can reproduce the Monte Carlo solution for the HTR-10 reactor by using the PJFNK-SPH equivalence method. In all cases studied, the MAMMOTH results are within 120 pcm of the Monte Carlo reference calculation and the maximum errors in neutron absorption and generation rates are within 0.536% and 0.215% from the reference calculation, respectively. A set of benchmark exercises from the International Atomic Energy Agency (IAEA) HTR-10 benchmark in IAEA-TECDOC-1382 were conducted including parts B1 (critical), B2 (temperature coefficient) and B3 (control rod worth). The results we obtain for the critical core are in excellent agreement with the expected value and we confirm that with ENDF/B-VII.r1 data we match the critical eigen- value keff=1 to within 100 pcm. Our temperature coefficient calculation is consistent with the VSOP results generated by the German participants. The Chinese and South African VSOP models produce lower temperature coefficients, a fact that was noted in the original IAEA benchmark, but for which no explanation was provided. Both a full and single control rod worth calculations with Serpent and MAMMOTH agree well with the results from the IAEA benchmark. Finally, and most importantly, this work demonstrates that MAM- MOTH can recover the Monte Carlo high-fidelity solutions to an excellent accuracy using the PJFNK-SPH method. This sets the stage for the ultimate goal of using MAMMOTH in transient, multi-physics scenarios where correction of the cross sections is obtained for steady-state conditions and then used in the transient scenario for which no Monte-Carlo solution is available.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

FY17 CAES LDRD Annual Report

Metallic alloys are widely used or planned for use as structural and cladding materials in current and future reactors. Under irradiation, grain boundary (GB) cohesion strength decreases due to interaction with defects and impurities, leading to intergranular fracture and embrittlement of alloys. The objective of this project is to develop a technique for quantifying GB cohesion and its impact on fracture behavior in irradiated alloys, by utilizing transmission electron microscopic (TEM) in situ cantilever testing in concert with multi-scale modeling. The TEM in situ cantilever testing is a novel approach for studying the real-time mechanical response of materials. It will be used in this work for studying intergranular fracture behavior in several irradiated iron-based ferritic alloys and providing key information to link atomistic level events with mesoscale/macroscopic mechanical properties. The Multi-Physics Object-Oriented Simulation Environment (MOOSE)-based cohesive zone model (CZM) and extended finite element method (XFEM) for intergranular fracture of irradiated ferritic alloys will be developed in this work by utilizing atomistic results as inputs and experimental results for validation.

36 MATERIALS SCIENCE↗

Warthog: Coupling Nek5000 Thermal Hydraulics to BISON Fuel Performance through the Giraffe Interface

The Nuclear Energy Advanced Modeling and Simulation (NEAMS) program under the US Department of Energy (DOE) consists of three product lines. The Fuels Product Line (FPL), hosted at Idaho National Laboratory (INL), has produced a multiphysics framework with the name Multiphysics Object Oriented Simulation Environment (MOOSE) (Gaston et al. 2015). The FPL has also produced several high-fidelity physics codes including the fuel performance code Bison (Hales et al. 2016). The Reactors Product Line (RPL), hosted at Argonne National Laboratory (Argonne), has developed the high-order spectral-element Computational Fluid Dynamics (CFD) code Nek5000 (Fischer et al. 2015). The Integration Product Line (IPL), hosted at Oak Ridge National Laboratory (ORNL), is tasked with ensuring tools from the other product lines can be coupled together so that users may perform high-fidelity multiphysics simulations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Rattlesnake: User Manual

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

97 MATHEMATICS AND COMPUTING↗