Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor physics application for multiphysics simulations of advanced reactor designs jointly developed by Idaho National Laboratory and Argonne National Laboratory. This paper summarizes the motivation, significance, architecture, design, and features of Griffin. Griffin offers flexible and extensible features to address the challenges associated with advanced reactor designs. These features range from fundamental particle transport to specific reactor physics tasks. The features cover a wide range including on-the-fly and traditional two-step cross-section generation methods, steady-state and transient transport solvers suitable for both heterogeneous and homogeneous models, high-fidelity depletion where thousands of isotopes can be tracked and low-fidelity depletion characterized by burnup, etc. The most fundamental aspect that sets Griffin apart from other reactor analysis codes is that it is developed based on the MOOSE framework. A modular development approach is strongly enforced, with multiphysics being an essential element considered since the beginning of Griffin’s development. Griffin links various MOOSE physics modules and couples to other MOOSE-based applications and non-MOOSE-based applications for multiphyiscs simulations. Griffin includes three modules: ISOXML for preparing and managing multigroup cross sections, radiation transport for solving the neutron transport equation, and reactor analysis for user-oriented reactor physics analysis functionalities. Griffin uses various finite element methods for spatial discretization, multigroup approximation for energy discretization and discrete ordinates method, spherical harmonics expansion method, and diffusion approximation for streaming direction discretization to solve the neutron transport equation. Griffin’s flexibility is evidenced through Griffin’s various applications to fast reactor, high-temperature reactor, pebble bed reactor, molten salt reactor, and microreactor designs. Griffin development follows the software quality assurance procedure for MOOSE-based applications and with software requirements consistent with the ASME NQA-1 standard. Griffin has been adopted into the reactor analysis system for the U.S. NRC and is in use at U.S. companies, universities and national laboratories.

The research presented in this article describes progress in applying stochastic methods, uncertainty quantification, parametric studies, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated via the radiation transport code Griffin to simulate neutronics. Our goal is to develop a reduced-order (surrogate) model that can be rapidly sampled with perturbations to multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums (CDs), which is itself controlled by a hybrid proportional-integral-derivative (PID) controller actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time [Λ] and effective delayed neutron fraction [βeff] from a transient Griffin simulation executed via Griffin’s improved quasi-static solver to provide the kinetic parameters) as inputs to functions that control the CD rotation angle. By investigating numerous stochastic approaches, we developed a dual-purpose surrogate model of the NTP system, using polynomial regression in the Multiphysics Object-Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM). The trained model can be rapidly sampled while simultaneously perturbing various input parameters, such as coefficients on the PID control or temperature (directly affecting the neutron cross section). The surrogate model delivers accurate (within 5%) results at speeds orders of magnitude faster (minutes, not days of computational time) than the base model. Once the surrogate model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs as well as the effects of these inputs on the model output. For example, coefficients used in the PID control system may vary due to some type of physical interference, or uncertainty may exist in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters, and operational boundaries can be determined. The goal of this work is to support development of an advanced control system for operating CDs in a functioning NTP system. This work is a scoping study of the MOOSE STM.

Predicting thermal conductivity from the transport of electrons is a complex challenge which must be addressed for the design and production of nano- and microscale devices. In this work, we describe our progress in simulating thermal electron transport in silicon for the purposes of thermal conductivity prediction. We describe a new approach to solve the Boltzmann transport equation for electrons, using the self-adjoint angular flux formulation coupled with a novel approach in computing electron temperature and Fermi energy which does not require the combination of linear “inner” and nonlinear “outer” iterations. The electron Boltzmann transport equation is discretized in space by the continuous finite element method, and in angle by discrete ordinates, using the Multiphysics Object Oriented Simulation Environment, implemented in the radiation transport code Griffin. We rely on density functional theory calculations to provide material properties such as electron density of states, energy, wavevector, mean free path, and more. Our method couples the discrete electron groups through temperature and Fermi energy, to simulate thermal electron transport (in the absence of electric fields) for the prediction of thermal conductivity, thermal and electrical flux, and heat capacity. We show effective thermal conductivity and temperature results for different sized 2D slabs of Si at 300 K, which agree with other studies in the literature. Additionally, we report Fermi energy and efficiency of this method using the generalized minimal residual method.

Tristructural isotropic (TRISO) particles show great promise as a candidate fuel for use in several next generation high-temperature nuclear reactor designs due to their structural integrity and fuel performance at high temperatures and burnups. Computational codes exist that can simulate TRISO fuel performance characteristics and failure probabilities under extreme conditions which require knowledge of the TRISO coatings' thermophysical properties. The thermophysical descriptions of the TRISO particle's layers (i.e., buffer, pyrolytic carbon, and silicon carbide) currently used in fuel performance codes, however, assume that many of these properties are constant with respect to temperature or texture. In this paper, we obtain the full elastic stiffness tensors of the carbon and silicon carbide layers, which have transversely isotropic symmetry. The calculated elastic properties of each of the coating layers are in remarkable agreement with the current models at room temperature and correct orientations. Additionally, the textured 3C-SiC layer was found to exhibit novel auxetic behavior above 1500 degrees C. The anisotropic temperature-dependent thermal conductivities of the carbon layers were calculated using acoustical Gruneisen-Debye theory which are in excellent agreement with current models at room temperature and correct orientations. These texture-and temperature-dependent relationships can be incorporated into the thermophysical description of TRISO particles in order to more accurately model fuel performance and failure probabilities under extreme conditions in forthcoming high-fidelity computational simulations.

Abstract Advanced reactor concepts span the spectrum from heat pipe–cooled microreactors, through thermal and fast molten-salt reactors, to gas- and salt-cooled pebble bed reactors. The modeling and simulation of each of these reactor types comes with their own geometrical complexities and multiphysics challenges. However, the common theme for all nuclear reactors is the necessity to be able to accurately predict neutron distribution in the presence of multiphysics feedback. We argue that the current standards of modeling and simulation, which couple single-physics, single-reactor-focused codes via ad hoc methods, are not sufficiently flexible to address the challenges of modeling and simulation for advanced reactors. In this work, we present the Multiphysics Object Oriented Simulation Environment (MOOSE)–based radiation transport application Rattlesnake. The use of Rattlesnake for the modeling and simulation of nuclear reactors represents a paradigm shift away from makeshift data exchange methods, as it is developed based on the MOOSE platform with its very natural form of shared data distribution. Rattlesnake is well equipped for addressing the geometric and multiphysics challenges of advanced reactor concepts because it is a flexible finite element tool that leverages the multiphysics capabilities inherent in MOOSE. This paper focuses on the concept and design of Rattlesnake. We also demonstrate the capabilities and performance of Rattlesnake with a set of problems including a microreactor, a molten-salt reactor, a pebble bed reactor, the Advanced Test Reactor at the Idaho National Laboratory, and two benchmarks: a multiphysics version of the C5G7 benchmark and the LRA benchmark.

We present a new method for predicting effective thermal conductivity ($\kappa_{\textrm{eff}}$) in materials, informed by ${ab\,initio}$ material property simulations. Using the Boltzmann transport equation in a Self-Adjoint Angular Flux formulation, we performed simulations in silicon at room temperatures over length scales varying from 10 nm to 10 $\mu$m and report temperature distributions, spectral heat flux and thermal conductivity. Our implementation utilizes a Richardson iteration on a modified version of the phonon scattering source. In this method, a closure term is introduced to the transport equation which acts as a redistribution kernel for the total energy bath of the system. This term is an effective indicator of the degree of disorder between the spectral phonon radiance and the angular phonon intensity of the transport system. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations.

We present a method for solving the Boltzmann transport equation (BTE) for phonons by modifying the neutron transport code Rattlesnake which provides a numerically efficient method for solving the BTE in its self-adjoint angular flux (SAAF) form. Using this approach, we have computed the reduction in thermal conductivity of uranium dioxide (UO2) due to the presence of a nanoscale xenon bubble across a range of temperatures. For these simulations, the values of group velocity and phonon mean free path in the UO2 were determined from a combination of experimental heat conduction data and first principles calculations. The same properties for the Xe under the high pressure conditions in the nanoscale bubble were computed using classical molecular dynamics (MD). We compare our approach to the other modern phonon transport calculations, and discuss the benefits of this multiscale approach for thermal conductivity in nuclear fuels under irradiation.

Thermal resistance across the interface between touching surfaces is critical for many industrial applications. We developed a network model to predict the macroscopic thermal resistance of mechanically contacting surfaces. Contacting interfaces are fractally rough, with small islands of locally intimate contact separated by regions with a wider gas filled boundary gap. Heat flow across the interface is therefore heterogeneous and thus the contact model is based on a network of thermal resistors representing boundary resistance at local contacts and the access resistance for lateral transport to contacts. Molecular dynamics simulations have been performed to characterize boundary resistance of Silicon Alumina interfaces for testing the sensitivity of thermal resistance to contact opening. Boltzmann transport simulations of access resistance in Si are conducted in the ballistic transport regime.

Measuring thermal conductivity in nuclear fuel is an important aspect of the safe operation of nuclear power plants or research reactors. In the past, knowledge of thermal conductivity in nuclear fuel has been obtained primarily through empirical studies and measurements. Studies are conducted with fuel in different stages of burnup. Measurements are taken with respect to the microstructure, determining a thermal conductivity for a specific concentration of fission products. However, to accurately determine thermal conductivity in nuclear fuel, other factors must be taken into consideration. A first principles, physics-based calculation of thermal conductivity must involve factors such as the microstructure of nuclear fuel, as this parameter constantly changes during the fission process through the formation of isotopic decay products. Oxide nuclear fuel is a ceramic, and heat transport in ceramics is dominated by phonon transport mechanics. Computational materials science has produced a body of work in phonon transport at the nanoscale [1, 2]. 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

Recent interest in fast reactor technology has led to renewed analysis of past reactor concepts such as Gas Fast Reactors and Sodium Fast Reactors. In an effort to make these reactors more economic, the fuel is required to stay in the reactor for extended periods of time; the longer the fuel stays within the core, the more fertile material is converted into usable fissile material. However, as burnup of the fuel-rod increases, so does the internal pressure buildup due to gaseous fission products. In order to reach the 30 year lifetime requirements of some reactor designs, the fuel pins must have a vented-type design to allow the buildup of fission products to escape. The present work aims to progress the understanding of the feasibility and safety issues related to gas reactors that incorporate vented fuel. The work was separated into three different work-scopes: 1. Quantitatively determine fission gas release from uranium carbide in a representative helium cooled fast reactor; 2. Model the fission gas behavior, transport, and collection in a Fission Product Vent System; and, 3. Perform a safety analysis of the Fission Product Vent System. Each task relied on results from the previous task, culminating in a limited scope Probabilistic Risk Assessment (PRA) of the Fission Product Vent System. Within each task, many key parameters lack the fidelity needed for comprehensive or accurate analysis. In the process of completing each task, the data or methods that were lacking were identified and compiled in a Gap Analysis included at the end of the report.