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DOE OSTI2023

On Practical Aspects of Variational Consistency in Contact Dynamics

Usage of contact mechanics methodologies is a pervasive modeling requirement in dynamic simulations. While for some trivial problems, solutions taken from analytical geometry are available, use of a finite element framework is common to achieve formulation generality. This work explores two dynamic contact formulations: one based on the traditional node-to-segment (NTS) approach, and a variationally consistent segment-to-segment (STS) mortar formulation. The NTS formulation employed here enforces the constraints kinematically (i.e., the interpenetration is enforced to the solver tolerance), whereas the mortar approach uses Lagrange multipliers to enforce the contact constraints. Both approaches are implemented in the open-source finite element framework Multiphysics Object-Oriented Simulation Environment (MOOSE). The results highlight two relevant contact-interface-related dynamic phenomena in finite element simulations. First, stabilization of contact constraints is discussed, taking into account the evolution of the total energy in a benchmark problem. Second, the influence of finite element discretization on both of the aforementioned contact formulations is analyzed by exercising a large-deformation example with continuous relative sliding. Variationally consistent contact approaches such as the mortar formulation lead to improved energy preservation and avoid spurious excitation of the system's frequencies. This is especially relevant in settings where inertia and vibrations are of importance.

42 ENGINEERING↗

DOE OSTI2013

Point kinetics calculations with fully coupled thermal fluids reactivity feedback

The point kinetics model has been widely used in the analysis of the transient behavior of a nuclear reactor. In the traditional nuclear reactor system safety analysis codes such as RELAP5, the reactivity feedback effects are calculated in a loosely coupled fashion through operator splitting approach. This paper discusses the point kinetics calculations with the fully coupled thermal fluids and fuel temperature feedback implemented into the RELAP-7 code currently being developed with the MOOSE framework. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2013

A logical progression of steps for implementation and testing of the 7-equation, two-phase model into a computational framework

A seven-step progression is given for the implementation of the seven-equation model, employed in the new RELAP-7 thermal hydraulics system analysis code, within the MOOSE-compatible framework. The model is well-posed and treats both phases as compressible flow in a one-dimensional, variable cross-sectional area duct/pipe/component. Some appropriate tests are also outlined to benchmark the model/implementation for each step of the progression. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Entropy viscosity method applied to Euler equations

The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Nonlinear diffusion acceleration for the multigroup transport equation discretized with S{sub N} and continuous FEM with rattlesnake

Nonlinear diffusion acceleration (NDA) can improve the performance of a neutron transport solver significantly especially for the multigroup eigenvalue problems. The high-order transport equation and the transport-corrected low-order diffusion equation form a nonlinear system in NDA, which can be solved via a Picard iteration. The consistency of the correction of the low-order equation is important to ensure the stabilization and effectiveness of the iteration. It also makes the low-order equation preserve the scalar flux of the high-order equation. In this paper, the consistent correction for a particular discretization scheme, self-adjoint angular flux (SAAF) formulation with discrete ordinates method (S{sub N}) and continuous finite element method (CFEM) is proposed for the multigroup neutron transport equation. Equations with the anisotropic scatterings and a void treatment are included. The Picard iteration with this scheme has been implemented and tested with RattleS{sub N}ake, a MOOSE-based application at INL. Convergence results are presented. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Off-gas adsorption model and simulation - OSPREY

A capability of accurately simulating the dynamic behavior of advanced fuel cycle separation processes is expected to provide substantial cost savings and many technical benefits. To support this capability, a modeling effort focused on the off-gas treatment system of a used nuclear fuel recycling facility is in progress. The off-gas separation consists of a series of scrubbers and adsorption beds to capture constituents of interest. Dynamic models are being developed to simulate each unit operation involved so each unit operation can be used as a stand-alone model and in series with multiple others. Currently, an adsorption model has been developed within Multi-physics Object Oriented Simulation Environment (MOOSE) developed at the Idaho National Laboratory (INL). Off-gas Separation and Recovery (OSPREY) models the adsorption of offgas constituents for dispersed plug flow in a packed bed under non-isothermal and non-isobaric conditions. Inputs to the model include gas composition, sorbent and column properties, equilibrium and kinetic data, and inlet conditions. The simulation outputs component concentrations along the column length as a function of time from which breakthrough data can be obtained. The breakthrough data can be used to determine bed capacity, which in turn can be used to size columns. In addition to concentration data, the model predicts temperature along the column length as a function of time and pressure drop along the column length. A description of the OSPREY model, results from krypton adsorption modeling and plans for modeling the behavior of iodine, xenon, and tritium will be discussed. (author)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Multiphysics Analysis of the MSRE Experiment Using Griffin-SAM Coupled Code System

Molten salt reactors (MSRs) with flowing fuel have the unique feature of utilizing the fuel salt for heat generation and extraction at the same time since the fuel salt is circulating through the whole primary loop of the reactor. This movement of the fuel salt results in a partial decay of the delayed neutron precursors (DNPs) outside the core and corresponding redistribution in the active core region. To capture this phenomenon accurately, neutronics and thermal hydraulics computational tools need to be modified to handle the movement of the DNPs and their decay. Idaho and Argonne National Laboratories are actively working on developing neutronics and thermal hydraulics tools to model MSRs with flowing fuel. The neutronics code Griffin and the thermal hydraulics code SAM were extended to handle flowing fuel with the drift of the DNPs under the MOOSE framework. In this work, a simplified Multiphysics model of the Molten Salt Reactor Experiment (MSRE) is developed and utilized to perform steady-state and transient analyses. The MSRE experiments were designed to show the impact of the DNPs losses on core reactivity. The following section provides a description of the MSRE experiment with the core main parameters used to develop the model. Then, the developed Multiphysics model of the MSRE is presented. Finally, steady-state verification tests and unprotected loss of flow transient tests are discussed followed by a summary and conclusions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

The application of MAMMOTH for a detailed tightly coupled fuel pin simulation with a station blackout

The accurate calculation of desired quantities to predict fuel behavior in a nuclear reactor requires the solution of inter linked equations representing different physics phenomena. Traditional fuels performance codes often rely on internal empirical models for the pin power density and a simplified boundary condition on the cladding outer surface. These simplifications are performed because of the difficulty of coupling applications or codes on differing domains and mapping the required data. In this work the MAMMOTH application is employed in the demonstration of an approach that more consistent with first principles, in a simulation that couples the neutronics application Rattlesnake, the thermal fluids application RELAP-7 and the fuels performance application BISON. A single fuel pin was modeled based on the dimensions of a fuel rod from a Westinghouse 17*17 optimized PWR fuel assembly. The simulation consisted of a depletion period of 1343 days, representing three full operating cycles, followed by a station blackout (SBO) event. The fuel rod was depleted with a total pin power of 65.81 kW. After 1343 days the fission power was reduced to zero (simulating a reactor shutdown). Decay heat calculations provided the time-varying energy source after this time. For this problem, Rattlesnake, BISON, and RELAP-7 are coupled under MAMMOTH in a tightly coupled approach. Each system solves its physics on a separate mesh and, for RELAP-7 and BISON, on only a subset of the full problem domain. Rattlesnake solves the neutronics over the whole domain, which includes the fuel, cladding, gaps, water, and top and bottom rod holders. Here BISON is applied to the fuel and cladding with a 2-D axisymmetric domain, and RELAP-7 is applied to the flow of the circular outer water channel with a set of 1-D flow equations. For this work, the mesh on the Rattlesnake side is either be 3-D (for low order PN transport or diffusion) or 2-D axisymmetric (for diffusion). BISON has a matching ring structure mesh for the fuel so both the power density and local burnup are transferred accurately from Rattlesnake. At each depletion time step, Rattlesnake calculates a power density, fission density rate, burnup distribution and fast flux based on the current water density and fuel temperature. These are then mapped to the BISON mesh to perform a fuels performance solution. BISON calculates the fuel temperature and cladding surface temperature based upon the current power density and bulk fluid temperature. RELAP-7 then calculates the fluid temperature, water density fraction and water phase velocity based upon the cladding surface temperature. The fuel temperature and the fluid density are then passed back to Rattlesnake for another neutronics calculation. For this paper, sets of results from the detailed calculation are provided for both depletion and the SBO event. We demonstrate that a detailed simulation akin to first principles can be achieved using MAMMOTH and the various MOOSE application on differing domains. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Fuel performance analysis of FeCrAl cladding during LWR operation

This work focuses on modeling the integral thermo-mechanical performance of FeCrAl cladded fuel during normal operation in light-water reactors. Preliminary analysis has been performed to assess FeCrAl alloys (namely Alkrothal 720 and APMT) as a suitable fuel cladding replacement for Zr-alloys, using the MOOSE-based, finite-element fuel performance code BISON. These simulations identify the effects of the mechanical-stress and irradiation responses of FeCrAl and provide a comparison with Zr-alloys. In comparing these clad materials, fuel rods have been simulated for normal reactor operation and simple steady-state operation. Normal reactor operating conditions target the cladding performance over the rod lifetime (∼4 cycles) for the highest-power rod in the highest-power fuel assembly under reactor power maneuvering. The power histories and axial temperature profiles input into BISON were generated from a neutronics study on full-core reactivity equivalence for FeCrAl using the 3D full core simulator NESTLE. Evolution of the FeCrAl cladding behavior over time is evaluated by using steady-state operating conditions such as a simple axial power profile, a constant cladding surface temperature, and a constant fuel power history. The fuel rod designs and operating conditions used are based off the Peach Bottom BWR and design consideration was given to minimize the neutronic penalty of the FeCrAl cladding by changing fuel enrichment and cladding thickness. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Multi-scale modeling of the evolution of structure and properties in materials for nuclear energy applications

Nuclear energy is an important component of an overall strategy to address climate change. Idaho National Laboratory (INL) is the U.S. Department of Energy’s primary facility for research and development in nuclear science and technology for energy generation, supporting the improvement and life extension of the existing reactor fleet and the development and licensing of new reactor designs. Computational modeling is an important component of these activities, particularly in the area of materials for nuclear applications, where experimental data can be very challenging and expensive to acquire, and where data is especially scarce for new reactor designs. INL has used multi-scale modeling – linking atomistic, mesoscale, and engineering scales – to improve the ability to predict the performance of materials for nuclear energy applications. These modeling efforts make extensive of MOOSE (Multiphysics Object-Oriented Simulation Environment), a general-purpose open source finite element framework developed at INL. In this talk, I will give an overview of the approach and tools used, and several examples of application, including performance of nuclear fuels, understanding radiation-driven formation of nanoscale void and gas bubble superlattices, and powder densification through electric field assisted sintering.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Structure and Process of Managing the UO2 Dry In-Pile Fracture Test Irradiation Experiment

The management and structure of a novel research and development (R&D) project can be hard to navigate. This is especially true when it involves nuclear fuel. Familiarity with institutional safety and procedural requirements, a well defined scope, and accurate cost estimates can all help ensure successful project management from start to finish. The Dry In-Pile Fracture Test (DRIFT) experiments performed at the Transient Test Reactor Facility are an excellent example of managing an R&D project within its scope and budget constraints. The objective of the DRIFT test was to develop fracture propagation data in a manner consistent with light-water reactors to validate and improve the fracture propagation models of uranium oxide fuels in the MOOSE (Multiphysics Object-Oriented Simulation Environment)-BISON-Marmot code framework [1].

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2023

Multi-scale modeling of the evolution of structure and properties in materials for nuclear energy applications

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

On the Degradation of the Effectiveness of Nonlinear Diffusion Acceleration with Parallel Block Jacobi Splitting

MOOSE's radiation transport module Rattlesnake comprises a first order S N solver that can be accelerated with a flexible Nonlinear Diffusion Acceleration. At each NDA iteration, the streaming and collision operator of the S{sub N} equations are (approximately) inverted using a transport sweep. When executed on multiple processors parallel block Jacobi (PBJ) splitting is utilized lagging the processor sub-domain's incoming angular fluxes making the implemented method asynchronous, i.e. the convergence properties of NDA become dependent on the number of concurrent tasks and details of the partitioning. Within this work, we study the NDA convergence properties for the two-dimensional C5G7 benchmark problem PBJ with p = 1, 2, 4, 8, 12, 16, 24, 32, 48, 60, 72, 96 and 144 concurrent tasks. Rosa studied the convergence properties of PBJ splitting methods with and without transport synthetic acceleration (TSA) in slab geometry and two-dimensional Cartesian geometry, respectively. Rosa's iteration scheme lags both the incoming angular fluxes and the scattering source making it very similar to the method described here. Rosa found by means of Fourier analysis that convergence of unaccelerated PBJ can degrade for optically thin subdomains, i.e. for a large number of processors given a fixed domain size. Depending on the choice of parameters application of TSA can lead to an effective algorithm. In contrast to Rosa's work, this work focuses on PBJ splitting for NDA accelerated solution of the multigroup eigenvalue problem. Later, Zerr and Anistratov used their integral transport matrix method in conjunction with PBJ. This iteration scheme is different as it does not lag the scattering source. Nevertheless, Fourier analysis with Diamond Difference spatial discretization showed that the method degrades with increasing the overall size of the spatial domain while keeping the sub-domain size constant. In the case of an infinite medium, the observed spectral radius becomes unity. These references establish the iterative performance of PBJ for one-group fixed source problems discretized on rectangular cells, but for the Rattlesnake first order NDA method, an emphasis lies on multigroup eigenvalue problems. In this setting, the additional complication arises that the low order equations are not exactly inverted, but only to some iterative criterion. Further, as the low order problem is solved using Jacobian-Free Newton Krylov methods, a suitable preconditioner for the GMRES iterations is required. As the effectiveness of the preconditioners may decrease when more concurrent processes are used, we expect the low order solve to impact the overall effectiveness of the NDA method in parallel execution as well. Therefore, this work focuses on the question of how detrimental the asynchronicity of the high and low order iterative solutions is for the effectiveness of NDA solutions of realistic, unstructured grid, multigroup eigenvalue problems. The iterative convergence properties of Rattlesnake's NDA method for multigroup eigenvalue problems are studied for varying number of concurrent processes. Rattlesnake's NDA method is asynchronous because the high order transport sweep uses PBJ splitting and because the low order solve's preconditioners, algebraic multigrid and additive Schwarz, are asynchronous. We found that up to 144 processes the number of Picard iterations increases by a factor of 2-3 affecting but not destroying NDA's parallel performance for the C5G7 benchmark problem, a representative LWR (light water reactor) configuration. The solution of the NDA low order eigenvalue problem posed greater problems than expected for the solvers currently available in Rattlesnake mainly because of problems to effectively precondition the modified low-order problem. As a matter of fact, the low order problem becomes an advection-diffusion problem. Non-robustness was observed for the AMG preconditioned coarse mesh acceleration for more than 60 concurrent processes, which was fixed by increasing the number of permissible V-cycles per AMG call. For fine mesh acceleration AMG proved to be ineffective and we resorted to ASM. For both AMG and ASM, increasing number of linear iterations per nonlinear are observed when increasing the number of processes, but for ASM this problem appears to be worse. The results from this work also indicate that initial development efforts should be diverted from implementation of a high-order parallel sweeping algorithm to the effective and robust iterative solution of the low order NDA multigroup eigenvalue problem. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Grizzly: A Multi-scale and Multi-Physics Tool to Model Aging of Nuclear Power Plant Components

Grizzly is a multi-scale multi-physics tool being developed at Idaho National Laboratory (INL) as part of the US Department of Energy's Light Water Reactor Sustainability program to provide improved safety assessments of systems, components, and structures in nuclear power plants subjected to age-related degradation. Its goal is to provide an improved scientific basis for decisions surrounding license renewal, which would permit operation of commercial nuclear power plants beyond 60 years. Grizzly is based on INL's MOOSE framework, which enables multi-physics simulations in a massively parallel computing environment. The reactor pressure vessel (RPV) has been chosen as the initial application for Grizzly. The primary concern for the RPV is that it becomes increasingly susceptible to fracture initiation at the sites of pre-existing flaws over time. This is because exposure to irradiation and high temperatures embrittles the steel. Assessing the safety of an RPV under transient conditions involves simulations at multiple scales. At the engineering scale, strongly coupled equations of heat conduction and solid mechanics are solved to simulate the global response of the RPV to accident conditions. Sub-models are used to represent regions with pre-existing flaws and the stress intensity factors are evaluated from the domain integrals. Crack propagation is then determined using a model that provides the temperature and neutron fluence dependent fracture toughness of the RPV steel. The ability of Grizzly to provide accurate engineering scale estimates of RPV safety beyond 60 years of operation strongly relies on the predictability of the embrittlement model. Multiple models for embrittlement have been proposed, and the physically based empirical model is implemented in Grizzly. However, the formation of late blooming phases greatly reduces the confidence on the extrapolated values obtained from embrittlement model, which is further exacerbated by the absence of real field data for validation. Experimentally validated lower length scale models can significantly improve the predictability of the embrittlement model beyond the calibrated range and the development of such models is another ongoing effort in Grizzly. The modeling activity in Grizzly spans across different length scales, and can be divided into: (i) Irradiation induced microstructure evolution at the atomistic and single crystal length scale using molecular dynamics, atomistic kinetic Monte-Carlo, phase-field and rate theory; (ii) Effect of the irradiation induced defects on the flow stress and fracture processes at the polycrystalline scale using crystal plasticity. Subsequently, the prediction from these models can be used to obtain irradiation induced ductile-to-brittle transition temperature (DBTT) shifts from specimen-scale simulations; (iii) Global thermo-mechanical response of the RPV under normal and accident scenarios, and probabilistic risk analyses at the engineering scale using the DBTT shifts obtained from the lower length scale models. The item (i) has been discussed in a previous report. In this extended abstract an overview of items (ii) and (iii) is provided. The extended abstract summarizes the current status of the modeling effort under Grizzly. At the engineering scale, reduced order model development is underway using the statistical tool RAVEN. This will allow probabilistic analysis considering a wide range of flaw topologies in a computationally efficient manner. Coupling the irradiation induced defect growth predictions to crystal plasticity is also in progress. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

Orientation-Dependent Surface Faceting in UO{sub 2}

The surface behavior of UO{sub 2} plays an important role throughout the lifetime of this widely-used commercial nuclear fuel, from manufacturing to waste storage. UO{sub 2} surface properties affect fuel swelling behavior by determining the morphology, size and distribution of fission gas bubbles. Additionally, UO{sub 2} surface characteristics influence fracture behavior, which is controlled by the thermodynamics of fracture surfaces. Therefore, detailed understanding of the fundamental surface behavior will help advance prediction of the fuel performance of UO{sub 2}. Due to significant anisotropy in surface tension, faceting features form after annealing in both UO{sub 2} and many other crystalline materials. Knowledge of the correlation between crystallographic orientation and surface faceting features will expand the fundamental knowledge of UO{sub 2} surface characteristics, leading to a better understanding of fission gas swelling and fracture mechanisms. Inherent characterization technique limited previous studies on the crystallographic orientation of UO{sub 2} surface facets to low Miller index surfaces in single crystal specimens. In this study, synchrotron Laue microdiffraction was utilized to examine the crystallographic orientation of grains on the coarse surface of a polycrystalline UO{sub 2} specimen. The results were then compared with the surface morphology, obtained from scanning electron microscopy (SEM), so that a general correlation between the surface faceting features and crystallographic orientation in UO{sub 2} can be established. Both the fundamental surface characteristics and the crystallographic orientation measurements obtained in this study help advance the experiment validation of MARMOT, a mesoscale multi-physics code that predicts the coevolution of microstructure and properties within reactor fuel during its lifetime in the reactor. The MARMOT code is an indispensable component of the MOOSE-BISON-MARMOT (MBM) code suite that has been developed by Idaho National Laboratory to enable next generation fuel performance modeling capability as a part of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program Fuels Product Line (FPL). In this study, the surface-faceting features of UO{sub 2} were found to be dominated by the triple-plane structure and its variants. With this knowledge, by measuring the directions of the <110> edges, the crystallographic orientation of a surface UO{sub 2} grain can be precisely deduced in most regions of the standard stereogram triangle (SST) of the surface normal. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

Derivation of the Point-Kinetics Parameters for the Coupled Reactors

The design of coupled reactors, which provide two distinct spectral zones (fast and thermal), has recently drawn attention because it can provide configurations that could not be met in current thermal neutron test reactors and thus allows versatile irradiation tasks. A coupled reactor core is characterized by the neutron multiplicity of each zone as well as by the coupling between the two zones. It is desired to evaluate the integral point kinetics parameters that characterize the neutron physics of the coupled system. This summary provides a derivation of the equations for evaluating these point kinetics parameters. Following the strong and the weak form of the multigroup diffusion equation, the weak forms for the partial forward and adjoint solutions, each for a particular active region of the reactor core, are derived. These partial solutions are then used to collapse the weak form into the coupled-reactor point kinetics equations with the approximation of equilibrium. It is noted that these parameters are not meant for transient analysis because of the equilibrium approximation. They are rather used for characterizing the coupled system. The derived reactivity equations are then compared with those in Ref. 1. The equations are implemented in Rattlesnake, the INL MOOSE-based radiation transport application for multi-physics simulations. Numerical results are presented for a simple two-group problem. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Quantifying the Uncertainty in Deterministic Phonon Transport Calculations of Thermal Conductivity using Polynomial Chaos Expansions

The nature of computational simulations requires the inclusion of an uncertainty analysis, as we have limited knowledge of all physically determined input parameters for a computationally simulated problem. We rely on uncertainty quantification (UQ) to characterize our confidence in the outcomes. Quantifying uncertainty can provide a basis for certifications in high-consequence decisions, such as nuclear reactor design, and is a fundamental component of model validation. We employ a previously developed method of uncertainty quantification, polynomial chaos expansion with stochastic collocation (PCE-SC), applied to deterministic phonon transport simulations. In these simulations, we use the neutron transport code Rattlesnake, which solves the Self-Adjoint Angular Flux (SAAF) formulation of the transport equation with a continuous finite element (CFEM) spatial discretization and discrete ordinates, spherical harmonics angular discretizations. Rattlesnake was developed in the multi-physics object oriented simulation environment (MOOSE) framework. We have previously shown Rattlesnake to be effective in simulating phonon transport. We aim to provide a deterministic phonon transport framework for heterogeneous nuclear fuel with fission product defects to predict thermal conductivity (?). A first principles, physics-based calculation of thermal conductivity must involve factors such as the microstructure of nuclear fuel, which constantly changes during the fission process through the formation of isotopic decay products. Heat transport in oxide nuclear fuels is dominated by phonon transport. Impurities in the bulk material influence the transport of energy at the fundamental level, altering the scattering behavior of phonons and electrons. Conventionally, heat transport follows classical physics based on the heat equation derived from Fourier's law q = -k∇T, where q is heat flux, k is thermal conductivity and ∇T is a temperature gradient. However, Fourier's law is a macroscopic empirical law in which the thermal conductivity? does not have a mechanistic connection to the underpinning heat transport processes. Thermal conductivity of a material depends both on the material's intrinsic ability to transport heat and a variety of resistive effects caused by defects in the material. Thus ab initio prediction of the macroscopic conductivity - the property of interest for safe reactor operation - requires simulating detailed processes of heat transport, and then determining the effective thermal conductivity of the simulated material from the resulting heat flux under the imposed temperature difference. The thermal conductivity of a bulk, homogeneous, dielectric material can be well estimated by the mechanistically derived expression: k{sub bulk} = 1/3 C{sub ν}νgλ (2), where C{sub ν}, νg, and λ are the volumetric specific heat, phonon speed, and phonon mean free path, respectively. In these problems the relevant parameter is the material's acoustic thickness, its characteristic distance L relative to the phonon mean free path λ. In Eq. (2) the largest source of uncertainty is λ. While propagating uncertainty in λ to uncertainty in k through Eq. (2) is trivial, systems with extrinsic scattering require more sophisticated approaches. At the microscopic level, uncertainty in λ changes both a material's intrinsic thermal conductivity. Our goal is to propagate the uncertainty in λ through the deterministic transport computation of k. Because there are a small number of uncertain input quantities, we use the method of polynomial chaos expansion (PCE), which expresses solutions in the form of spectral expansions of an uncertain variable. This approach combines both intrusive and nonintrusive methods of uncertainty propagation techniques and results in a unique formulation which is very effective and efficient for problems with few uncertain parameters. Uncertainty Quantification and Sensitivity Analysis We use PCE-SC to measure propagation of uncertainty in a 3-D phonon transport problem of homogeneous silicon, to compute the mean and variance in temperature, heat flux and thermal conductivity. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Advancement of Functional Expansion Tallies Capabilities in Serpent 2

The need for accident tolerant fuels (ATFs) became self-evident after the series of unfortunate nuclear events at Fukushima Daiichi in 2011. Restarting the Transient Reactor Test Facility (TREAT) at INL is one component in this concerted effort to establish the ATF development and testing program under the United States Department of Energy. Prior to the closure of TREAT in 1994, each experiment required multiple low-power calibration tests before and after each run. Since then, computing advancements have set computer-based modeling and simulation (M and S) as the preferred calibration method. The anticipated savings are both temporal and monetary. MAMMOTH, a collection of M and S tools built from the finite element-based MOOSE Framework, has been established to support the designed experiments intended for TREAT. This collection of tools includes: 1) Rattlesnake, a striking diffusion-based neutronics code, 2) BISON, an advanced materials and fuels performance code, and 3) RELAP-7, a powerful thermal-hydraulics solver. Each is capable of independently performing its function accurately and effectively; unified, they create a powerful multiphysics reactor core M and S application. One unfortunate weakness in this configuration lies in the unique geometry and design of TREAT's core. Although simple to model, this poses a challenge to the diffusion solver in Rattlesnake. One alternative is to replace Rattlesnake with Serpent, a fully-fledged Monte Carlo (MC) neutronics code. Coincidentally, Rattlesnake calculations are frequently validated against Serpent simulations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗