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Uncertainty quantification and sensitivity analysis of a nuclear thermal propulsion reactor startup sequence

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 [ β eff ] 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.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

Sensitivity Analysis, Reduced-order Modeling, and Optimization of a Gas-Cooled Pebble Bed Reactor using Equilibrium-Core and DLOFC Performance

This work presents and applies a workflow for performing design optimization on gas-cooled pebble-bed reactors. Based on previous research, a representative equilibrium core of a pebble-bed reactor and a depressurized loss-of-forced-cooling model are created. These applications are built using the Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically utilizing Griffin, Pronghorn, and Bison. After defining design-related parameters and quantities of interest regarding reactor safety and efficiency, this multiphysics model is sampled using the MOOSE stochastic tools module. The result is a comprehensive dataset of configurations, enabling sensitivity analysis and the generation of reduced-order models. Subsequently, the dataset and reduced-order models are employed in an optimization study aimed at maximizing fuel utilization while adhering to safety and operational constraints. The optimization process leads to an improvement of fuel utilization by approximately 10\%, compared to engineering-judgment-based nominal conditions.

97 - MATHEMATICS AND COMPUTING↗

Thermal Hydraulics Analysis of a Divertor Monoblock Using SALAMANDER

Divertors are critical components in magnetic confinement fusion devices. One of the Divertor's crictial roles is absorbing the highest heat flux from the plasma. The Divertor accomplishes this through the use of divertor monoblocks and cooling channels. This work presents a thermal hydraulic analysis of a divertor monoblock using the Software for Advanced Large-scale Analysis of MAgnetic confinement for Numerical Design, Engineering and Research (SALAMANDER). SALAMANDER is an open source tool developed at Idaho National Laboratory for conducting multiphysics and multscale analysis of Plasma Facing Components (PFCs). For the monoblock, solid heat conduction is modeled in the block with a constant heat flux of 1E7 W/m^2 applied to the top of the block to represent peak heat flux from the plasma. The cooling channel (which is pressurized water at a Reynolds number of ~1,000,000) is modeled using a k-epsilon turbulence model with standard wall functions. The heat transfer between the solid and fluid domain is modeled using the Dittus-Boelter correlation for the convective heat transfer coefficient. This work aims to show the importance of a multiphysics modeling approach when performing simulations on PFCs.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Sockeye Heat Pipe Analysis Code Verification and Validation

Some of the most promising microreactor designs currently under development utilize heat pipe technology to transfer heat from the reactor core to the secondary side heat exchanger, due to the technology’s compactness, efficiency, passivity, and reliability. Sockeye is an engineering-scale heat pipe tool developed under the Nuclear Energy Advanced Modeling and Simulation Program to be used for the design and safety analysis of microreactors. Sockeye’s core capability lies in a 1D, two-phase, compressible flow model, used to simulate the working fluid inside the heat pipe. Sockeye is built on the Multiphysics Object-Oriented Simulation Environment framework, which allows for seamless multiphysics coupling with other Nuclear Energy Advanced Modeling and Simulation tools and can thus be used in a full-scale simulation of a microreactor assembly, which can include hundreds of heat pipes. This paper presents some initial verification and validation assessments performed for Sockeye. We demonstrate good agreement between Sockeye’s numerical results and steady-state analytic solutions for velocity and pressure drop, with differences attributable to the underlying assumptions made by the analytic solutions. We also show that Sockeye reproduces analytic predictions of key operational limits, such as the capillary limit and the sonic limit. Finally, we compare Sockeye results to experimental data for the SAFE-30 heat pipe module test.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Assessment of the MAMMOTH and PRONGHORN Pebble Bed Reactor Modeling Capabilities for the HTR-PM Design

This assessment explores the current analysis methodologies of various external and MOOSE-based tools available at the Idaho National Laboratory to model pebble bed reactor multiphysics phenomena. The study involves three MOOSE-based, coupled codes: 1) MAMMOTH for reactor physics, 2) Rattlesnake for neutron transport and 3) Pronghorn for thermal fluids and strongly coupled conjugate heat transfer. These advanced tools are being developed under DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program (NEAMS). They currently contain a collection of advanced modeling capabilities that allow high-fidelity simulations of advanced reactor concepts including gas and fluoride-salt cooled pebble bed reactors. Software development of these tools follows NQA-1 standards ensuring software quality that many of the currently deployed legacy codes lack. In this work, the MAMMOTH Pronghorn tools are compared to the legacy codes PEBBED-THERMIX-KONVEK. The external codes in use are LAMMPS for pebble mechanics and Serpent for cross section preparation. The coupling under MOOSE enables significant flexibility for modern engineering tools since MOOSE applications can be seamlessly coupled with various levels of resolution. This report focuses on low-resolution (r-z) and midresolution (3-D) homogenized geometries. The high-resolution Pebble Tracking Transport solution is not pursued herein and is postponed to future work. The results from this assessment show that the new MOOSE-based tools compare well with the results from legacy tools (r-z) and produce reasonable accuracy limited by the methods in the legacy tools. In the 3-D studies, the PJFNK-SPH methodology available in MAMMOTH allows the reproduction of Monte Carlo results with a transport-corrected diffusion solution. This has implications for the coupled solutions since without the SPH correction the temperature coefficient of reactivity is under-predicted and leads to lower temperature feedback and a significantly higher eigenvalue showing a difference of 2000 pcm.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Performance of Coupled Physics Solvers for Multidisciplinary Hypersonic Flow Simulations on Several Classes of Computer Architectures

The application of hypersonic flow simulation tools to realistic flight scenarios will require the coupling of multiple physical effects to the baseline fluid dynamics. Such multiphysics effects can include the aerooelastic response of the airframe or engine components, dynamic transport of atmospheric particles, the deformation of solid-fluid interfaces that can ablate, pyrolyze, or erode, as well as a host of other processes, all of which are governed by unique sets of physical equations and models. Coupling multiple (and potentially disparate) physics solvers to a robust compressible flow solver poses additional challenges related to the stability, performance and scalability of the combined solver. The choices made during the software design process can therefore lead to a variation in simulation efficiency across different computer architectures. In this paper, we will consider two representative multiphysics hypersonic flow scenarios: the interaction of solid particulates with the flow field created by a hypersonic lifting body and the aerooelastic deformation of a model airframe under high-Mach-number flow conditions. For these simulations we explore the behavior of several hypersonic simulation tools, including Kestrel, FUN3D, US3D, and JENRE multiphysics framework, on several high performance computing systems containing various CPU and GPU architectures.

architecture↗

Prediction of PbLi fluid flow and temperature field in a thermal convection loop for qualification of fusion materials

Two modeling tools, a thermohydraulics code and a computational model in COMSOL Multiphysics, have been developed, tested and then applied to the analysis of fluid flow and heat transfer in a thermal convection loop (TCL). Such a device has recently been used to experimentally evaluate corrosion compatibility of APMT (Fe–21Cr–5Al–3Mo) steel with high-temperature molten eutectic lead-lithium (PbLi) alloy at Oak Ridge National Lab, TN, USA. Here, the 1-D thermohydraulics code allows for rapid calculations of the loop parameters as a function of the applied heat flux. The supplemental COMSOL finite-element computations provide detailed 3-D velocity and temperature field data but are much more time consuming. Both modelling tools demonstrate an excellent agreement in the computed circulation velocity as well as maximum and minimum temperatures. The performed TCL analysis focuses on flow development in the “hot” and “cold” legs, formation of Dean vortices in corner regions, blocking effect of the immersed samples, and radiative and convective cooling effects under the experiment-relevant conditions for Prandtl number Pr = 0.015, Grashof numbers Gr ~10 7 , and Reynolds numbers Re ~10 4 .

36 MATERIALS SCIENCE↗

Pronghorn: A Multidimensional Coarse Mesh Application for Advanced Reactor Thermal-Hydraulics

This paper presents an overview of Pronghorn, a multiscale thermal-hydraulic (T/H) application developed by Idaho National Laboratory and the University of California, Berkeley. Pronghorn, built on the open-source finite element Multiphysics Object-Oriented Simulation Environment (MOOSE), leverages state-of-the-art physical models, numerical methods, and nonlinear solvers to deliver fast-running advanced reactor T/H simulation capabilities within a modern software engineering environment. This work summarizes the physical models, multiphysics and multiscale coupling, and numerical discretization in Pronghorn with emphasis on our initial target application to pebble bed reactors (PBRs). A diverse set of applications are shown to depressurized natural circulation in the SANA experiments, forced convection in the Pebble Bed Modular Reactor, three-dimensional (3-D)/one-dimensional coupling of Pronghorn and RELAP-7 systems T/H for loop analysis in the High Temperature Reactor Power Module, and forced convection in the Mark-1 Pebble Bed Fluoride-Salt-Cooled High-Temperature Reactor. A multiphysics coupling of Pronghorn, RELAP-7, and Griffin deterministic neutronics for a gas-cooled PBR demonstrates the capability of the MOOSE framework for reactor design calculations. These applications highlight the verification and validation underlying Pronghorn’s software development while emphasizing features that improve upon capabilities offered by legacy tools in areas such as 3-D unstructured meshing, physics modeling, and multiphysics coupling.

97 MATHEMATICS AND COMPUTING↗

Development of Critical Experiments to Provide Validation Data for Multiphysics Coupling Methods (Final Report)

Computational simulation has become one of the most important tools in the modern toolbox for nuclear reactor design. Reactor simulations, like the reactors themselves, involve multiple physical processes including neutronics, fluid flow and heat transfer (thermal-hydraulics), thermo-mechanics, fuel behavior, chemistry, and balance of plant. Each process can affect the behavior of the others, and advanced computational tools have been developed that couple separate physics models together to simulate the feedback effects. The objective of this work is to generate experimental data to support the validation of multi-physics reactor codes. It specifically targets the SHARP toolset from the NEAMS Reactor Product Line, but it is intended to be useful in any set of coded that couples thermal-hydraulics with neutronics simulations. The project takes advantage of the inherent flexibility of the RPI Reactor Critical Facility (RCF), a low power open-pool research reactor. The standard configuration of the RCF is used to explore the effects of moderator temperature on neutronic behavior and reactivity. Because the low power of the reactor generates no appreciable temperature change in the moderator, the moderator temperature is artificially changed with two 18 kW electric immersion heaters. The temperature feedback effects can be observed by recording the change in the reactor power as the reactor goes from a supercritical state, to critical, to a subcritical state. To expand the temperature range and temperature rate of change that can be investigated, an experimental apparatus consisting of a heated water loop was designed and installed in the RCF. In this setup, water from a heated reservoir tank is pumped through a pipe placed through the center of the reactor core. The water in the reservoir can be heated to around 70 °C and pumped through the system. The pump has a variable flow rate and electronic control, so a number of scenarios can be developed. A slug of water can be pushed through the system to generate a reasonably fast change in reactivity. The pump speed can be increased or decreased over the course of a measurement, or even oscillated at different periods, to observe the response of the reactor. To complement the experimental data generated by the RCF, a set of computational models have been developed. They are intended to illustrate the usefulness of the experimental data generated in validating coupled multi-physics simulations. A model previously constructed in MCNP has been used in conjunction with safety analysis at the RCF for many years and was modified to support the design of the heated water loop experiment. This model was translated into Serpent 2, a similar Monte Carlo code, which provided the added advantage of being able to produce collapsed cross-section data files for use in the deterministic neutron transport codes that are part of the SHARP toolset. A complete reconstruction of the RCF model, both with and without the heated fluid loop experiment, were necessary for use with the SHARP codes, PROTEUS (neutronics) and Nek5000 (thermal hydraulics), as these require an unstructured mesh format to operate. The computational requirements for fully coupled three dimensional simulations are significant, and challenges to full implementation and comparison with RCF experiments remain. A wide variety of experiments have been conducted for eventual benchmarking and validation of multi-physics reactor codes. A complete database of detailed time- and temperature-dependent measurements have been generated and stored. Several examples of the experimental results are presented here, with refinement and analysis of experiments ongoing. While these experiments still only address a finite range of operating conditions, in particular being limited to water in the sub-boiling regime, they represent a unique (to date) look at the feedback between temperature and neutronic behavior suited for validation of the coupling routines in multi-physics codes. It is hoped that these will be the foundation of future benchmarks that will provide confidence in the tools that will be used to develop the next generation of nuclear reactor systems.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Computational Fluid Dynamics Simulations to Support Efficiency Improvements in Aluminum Smelting Process

Smelting is broadly described as the extraction of a metal from its ore. In the United States, aluminum is commonly produced by smelting alumina in bauxite using the Hall-Héroult process. Optimization of equipment and processes in conventional smelting is crucial to enhancing process efficiency and productivity, is necessary for improving the techno-economic feasibility, which directly manifests as the growth of the American economy. To achieve optima, insightful data on the multiphysics phenomena that are inherent to the process must be obtained through physical investigation or high-fidelity numerical simulations. The resolution of relevant scales in time and space for smelting operations requires intensive, high-performance computing (HPC) simulations. Hostile operating conditions limit physical data acquisition to specific techniques; therefore, these data do not describe the multiscale interaction of simultaneous effects. Fortunately, in recent decades, significant advancements in computing hardware and computational methods have made the numerical resolution of such a complex process possible. In this study, a high-fidelity simulation of aluminum smelting was performed using an open-source tool, OpenFOAM, which analyzed many parameters characteristic to underlying phenomena. A multiphysics model based on the Eulerian-Eulerian multifluid approach was adopted. This model can resolve critical issues in the electrolytic smelting of aluminum, such as bubbling of carbon dioxide from the anode(s), magnetohydrodynamics from electromagnetic effects, ionic dissolution of the alumina in the electrolyte, and the evolution of thermal profiles. This study provides valuable connectivity for characteristic data that can direct the future designs of efficient smelters. A basic framework to model and simulate the smelting process using OpenFOAM is presented for user modification in keeping with process development. Of relevance to the flow field, a detailed investigation of vortices produced by bubble motion and electromagnetics is discussed, along with their impact on the evolution of thermal profiles. The predictions show small-scale vortices in the clearance between the anode and cathode caused by magnetic forces. Predictions also indicate relatively large-scale vortices in the inter-anode space resulting from carbon dioxide rising through the electrolytic flow field. The formation of vortices at the edges of anodes was shown to direct alumina charged by the feeder to the bottom of the anodes, thus preventing the entrapment of gas bubbles in the periphery of the bottom of the anode. Symmetry was observed in the location of cold spots in the electrolytic mixture in the vicinity of the feeder. Cold spots were also observed in the clearance between the anode and cathode due to the flow’s transmission of unconverted alumina to this region.

36 MATERIALS SCIENCE↗

Development of Digital Twin Predictive Model for PWR Components: Updates on Multi Times Series Temperature Prediction Using Recurrent Neural Network, DMW Fatigue Tests, System Level Thermal-Mechanical-Stress Analysis

The long-term operation (LTO) of nuclear power plant (NPP) beyond their original design life of 40 years, can lead to more material damage associated with cyclic fatigue under thermal-mechanical loading cycles and associated long-term exposure of reactor material to the deleterious reactor-coolant environments. However, under this LTO condition the reactor components can still safely operate but may require more frequent Nondestructive Evaluation (NDE) of reactor components. Frequent NDE requirement may lead to frequent shutdown of the NPP. This in turn can lead to power outage and additional NDE-inspection-cost related economic loss. The economic loss can be minimized by reducing uncertainty in life estimation of safety-critical pressure boundary components and by implementing more digital approach such as by using upcoming digital-twin (DT) technology for predicting the structural states (e.g., time and location dependent inside/outside thickness temperature, stress, strain, plastic deformation, etc.) and associated fatigue life of a component in real time. Towards this goal Argonne National Laboratory (ANL) with the sponsorship of DOE Light Water Reactor Sustainability (LWRS) program is working on the development of a DT framework that can be used for real time environmental fatigue prediction of reactor components. The DT framework is based on limited experiment-data, Artificial-intelligence (AI) – Machine-Learning (ML) - Deep-Learning (DL) based techniques and Multiphysics-computational-mechanics such as finite element (FE) based modeling tools. Towards this overall goal, following are some of the major contributions made during the FY21: 1) Multiple 82/182 dissimilar metal weld (DMW) specimens (both solid-weld and joint-weld representing the actual reactor multi-metal nozzles) were fatigue tested. The resulting fatigue lives were compared to the NUREG-6909 based best-fit and design fatigue curves. Additionally, the results of 52/152 DMW fatigue specimens (which were recently tested at Republic of Korea under the sponsorship of International Nuclear Energy Research Initiative - INERI program) were compared to the NUREG-6909 based best-fit and design fatigue curves. From the comparison of 82/182 and 52/152 DMW test data with NUREG-6909 best-fit curve, most of the reported test data fall way away from the NUREG-6909 suggested best-fit or mean curve. The NUREG-6909 suggested best-fit curve is the best-fit curve of austenitic stainless steel and due to lack of enough data on Nickel-based welds, this is currently being used for predicting the life of Nickel-alloy-based welded components. However, the above observation may require higher scaling factor (e.g., ASME suggested factor of 20 on cycles rather than the current NUREG-6909 suggested factor of 12 on cycles) for scaling the austenitic-stainless-steel best-fit-curve for estimating the design or safe-life of a welded component. Accordingly, for example, if a DMW component experience a strain amplitude of 0.6% the PWR-water life of the component would be 52 cycles instead of 85 cycles. However, more DMW tests are required to further ascertain the above-mentioned observations. 2) A system level CAD and finite element model were developed which consists of reactor pressure vessel (RPV), part of steam generator (SG), part of pressurizer (PRZ), hot leg (HL), and surge line (SL). This is with detailed nozzle geometry and thermal-mechanical material properties of different metals to simulate realistic thermal-mechanical stress under connected system global thermal-mechanical boundary conditions. 3) Different system level heat transfer analyses were performed with estimation of relevant heat transfer coefficients. The resulting data were used in subsequent system level thermal-mechanical stress analysis and for generating spatial-temporal training and validation data for a system level digital-twin based temperature predictor. Transient heat transfer analyses were performed considering thermal boundary condition under design-basis (DB) loading and EDF (Électricité de France) data-based grid-load-following (EDF-GLF) loading cycles. 4) System level thermal-mechanical stress analysis was performed for identifying damage-prone hotspots and for future extension of the model for cyclic state prediction. From the system-level model simulation under DB loading cycle it is found that HL and the SL nozzle that connect to the HL can experience significant stress and strain and could be one of the weakest links in the overall reactor coolant system (RCS). 5) An AI/ML based DT model was developed for multi-time-series temperature prediction at any inside/outside thickness locations of PWR pressure boundary components. This is by using Recurrent-neural-network (RNN) and keras machine learning libraries. The RNN model was validated against two laboratory test-based data sets with one obtained through ANL’s in-air fatigue test system and other through PWR-water test loop. The experimentally validated DT model further validated against FE model results to predict thermal scarification related spatialtemporal temperatures at random locations of a component. The well validated DT model was then used for demonstrating spatial-temporal temperature prediction under 100+ years of reactor operation subjected to combined DB, EDF-GLF and randomized grid-load-following (RANDOMGLF) loading Cycles. The expert-elicitation DT model framework was developed assuming field/input/process measurements can be available from a few existing plant sensors and can readily be used by the NPP operators. The above temperature prediction model will feed to the next-step stress analysis model based on which the life of a component can be predicted in realtime, which is one of our future works.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Expanded verification and validation studies of hypersonic aerodynamics with multiple physics-fidelity models

Hypersonic aerothermodynamics is an important domain of modern multiphysics simulation. The Multi-Fidelity Toolkit is a simulation tool being developed at Sandia National Laboratories to predict aerodynamic properties for compressible flows from a range of physics fidelities and computational speeds. These models include the Reynolds-averaged Navier–Stokes (RANS) equations, the Euler equations with momentum-energy integral technique (MEIT), and modified Newtonian aerodynamics with flat-plate boundary layer (MNA+FPBL) equations, and they can be invoked independently or coupled with hierarchical Kriging to interpolate between high-fidelity simulations using lower-fidelity data. However, as with any new simulation capability, verification and validation are necessary to gather credibility evidence. This work describes formal code- and solution-verification activities, as well as model validation with uncertainty considerations. Code verification activities on the MNA+FPBL model build on previous work by focusing on the viscous portion of the model. Viscous quantities of interest are compared against those from an analytical solution for flat-plate, inclined-plate, and cone geometries. The code verification methodology for the MEIT model is also presented. Test setup and results of code verification tests on the laminar and turbulent models within MEIT are shown. Solution-verification activities include grid-refinement studies on simulations that model the HIFiRE-1 wind tunnel experiments. These experiments are used for validation of all model fidelities. A thorough validation comparison with prediction error and uncertainty is also presented. Three additional HIFiRE-1 experimental runs are simulated in this study, and the solution verification and validation work examines the effects of the associated parameter changes on model performance. Finally, a study is presented that compares the computational costs and fidelities from each of the different models.

42 ENGINEERING↗

BISON Fuel Fragmentation Relocation and Dispersal (FFRD) Assessment Database for Eventual Use in Bayesian Calibration

Existing light-water reactor (LWR) fuel vendors have been interested in seeking increased discharge burnups of nuclear fuel rods for improved economics for quite a few years. With increased burnups come additional challenges that must be addressed. It has been experimentally observed that average burnups higher than the current regulatory limit of 62 MWd/kgU may undergo fuel fragmentation, relocation, and dispersal (FFRD) during a loss-of-coolant accident (LOCA). Industry must demonstrate approaches to mitigate FFRD. In an effort to support industry, the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program within the U.S. Department of Energy (DOE) has for several years invested in developing multiscale models and creating a validation/assessment database for these models to study the mechanisms driving FFRD. This report provides an update on changes made to the assessment database and new models added to BISON to support the study of fuel rod behavior during FFRD. An effort has been initiated this year to begin adding dedicated inputs to the publicly available Virtual Test Bed (VTB) repository for industry use. A section of this report details the efforts made in this area. NEAMS has recently developed new capabilities in the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework’s stochastic tools module for calibration using Bayesian inference. The goal in the future is to use these capabilities to calibrate and identify weaknesses in the existing BISON models for FFRD. The report concludes with a discussion on the models most likely to benefit the most from such calibration.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO). PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Material Response↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗

MOOSE: A Modular Platform for Fission and Fusion Multiphysics

The Multiphysics Object-Oriented Simulation Environment (MOOSE) Framework, as well as MOOSE-based simulation tools, have accelerated the development of fission energy and advanced reactor technologies through the United States Department of Energy, Office of Nuclear Science, Nuclear Energy Advanced Modeling & Simulation (NEAMS) Program. MOOSE contains a complete platform of multiphysics simulation capabilities, capable of running on massively parallel systems, and is developed in an open-source manner with great attention paid to high-quality software quality assurance practices. This overall approach could greatly benefit the fusion energy community, which requires rapid design iteration and improvement in order to facilitate the successful development of fusion as an alternative energy source to fossil fuels. In the first half of this talk, applications of MOOSE and MOOSE-based tools for advanced reactor designs will be showcased, as well as MOOSE ecosystem infrastructure (such as the NEAMS Virtual Test Bed) that enables and accelerates fission reactor design. In the second half, a discussion of how the MOOSE approach to modeling and simulation is currently being applied internationally in fusion energy research and development at the United Kingdom Atomic Energy Authority will be discussed, and ongoing/future domestic research efforts will be highlighted.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

COUPLED GRIFFIN AND PRONGHORN SIMULATION OF THE MOLTEN SALT FAST REACTOR (MSFR) FOR THE VIRTUAL TEST BED

The Virtual Test Bed (VTB) repository hosts a wide range of challenge problems to showcase modeling and simulation capabilities to support advanced reactor demonstration. An overview of a coupled multiphysics model for Molten Salt Reactors (MSR) is presented here. The analysis leverages MOOSE-based tools (notably Griffin and Pronghorn) for neutronic and thermal hydraulic simulation. Neutron precursor drifting capability is showcased, along with some initial turbulence models. Both steady-state and transient coupled multiphysics results for an MSR concept are discussed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Detailed analyses of a TRISO-fueled microreactor: Modeling of a Micro-Reactor System using NEAMS Tools

Our analysis provides preliminary confirmation of the feasibility of applying the NEAMS codes for multiphysics simulations to model load following transients and accidental scenarios. Detailed demonstration was performed on a simple unit-cell model to perform transient simulations, while verifying accuracy of the multiphysics solution obtained with the NEAMS codes. Results on the full core focused on showcasing the multiphysics workflow rather than detailed verification of the results, at least for this report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗