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A User Guide to PARET/ANL

PARET was originally created in 1969 at what is now Idaho National Laboratory (INL), to analyze reactivity insertion events in research and test reactor cores cooled by light or heavy water, with fuel composed of either plates or pins. The use of PARET is also appropriate for fuel assemblies with curved fuel plates when their radii of curvatures are large with respect to the fuel plate thickness. The PARET/ANL version of the code has been developed at Argonne National Laboratory (ANL) under the sponsorship of the U.S. Department of Energy/NNSA since the inception of the Reactor Conversion Program. Since Reduced Enrichment for Research and Test Reactors (RERTR) began in 1978, PARET/ANL has been benchmarked to experimental data including SPERT testing, and used to determine the expected transient behavior of a large number of reactors regardless of enrichment both inside and outside the Reactor Conversion Program. This document provides the pertinent information for the use of PARET/ANL Version 7.6. PARET/ANL models the various fueled regions of a reactor core as channels. Each of these channels consists of a single flat fuel plate/pin (including cladding and, optionally, a gap) with water coolant on each side. In slab geometry the coolant channels for a given fuel plate are of identical dimensions (mirror symmetry), but they can be of different thickness in each channel. There can be many channels, but each channel is independent and coupled only through reactivity feedback effects to the whole core. The time-dependent differential equations that represent the system are replaced by an equivalent set of finite-difference equations in space and time, which are integrated numerically. PARET/ANL uses fundamentally the same numerical scheme as RELAP5 for the time-integration of the point-kinetics equations. The one-dimensional thermal-hydraulic model includes temperature-dependent thermal properties of the solid materials, such as heat capacity and thermal conductivity, as well as the transient heat production and heat transfer from the fuel meat to the coolant. Temperature- and pressure-dependent thermal properties of the coolant such as enthalpy, density, thermal conductivity, and viscosity are also used in determining parameters such as friction factors and heat transfer coefficients. The code first determines the steady-state solution for the initial state. Then the solution of the transient is obtained by integration in time and space. Multiple heat transfer, DNB and flow instability correlations are available. The code was originally developed to model reactors cooled by an open loop, which was adequate for rapid transients in pool-type cores. An external loop model appropriate for Miniature Neutron Source Reactors (MNSR’s) was also added to PARET/ANL to model natural circulation within the vessel, heat transfer from the vessel to pool and heat loss by evaporation from the pool. PARET/ANL also contains models for decay heat after shutdown, control rod reactivity versus time or position, time-dependent pump flow, and loss-of-flow event with flow reversal as well as logic for trips on period, power, and flow. Feedback reactivity effects from coolant density changes and temperature changes are represented by tables. Feedback reactivity from fuel heat-up (Doppler Effect) is represented by a four-term polynomial in powers of fuel temperature. Photo-neutrons produced in beryllium or in heavy water may be included in the point-kinetics equations by using additional delayed neutron groups.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Sensitivity study of hydrogen Soret transport in yttrium Hydride-Based nuclear fuel

Yttrium hydride is an excellent solid neutron moderator material for high temperature nuclear reactor applications due to its high hydrogen density and exceptional hydride stability at high temperatures. Despite these attractive characteristics, the details of how hydrogen behaves within yttrium hydride while temperature gradients exist are still not well understood. The evolution of the hydrogen composition profile resulting from a temperature gradient requires knowledge of hydrogen’s heat of transport, a critical parameter that has not yet been measured for this material. In this work, we perform hydride redistribution, hydrogen dissociation, and hydrogen leakage calculations while varying the Soret heat of transport of hydrogen in yttrium hydride to elucidate the sensitivity of hydride stability under temperature gradients to this parameter. This study analyzes hydride stability of a hypothetical uranium-yttrium hydride nuclear fuel design during operation of a high temperature liquid metal-cooled nuclear reactor. Assuming U-YH x could be fabricated in a physically stabilized manner, this fuel system can likely maintain hydride stability while operating at very high power densities and temperatures. We find that even though the hydrogen dissociation pressure in the gas gap does vary by several percent as the heat of transport temperature parameter is varied, the hydrogen content in the U-YH x fuel meat is relatively insensitive to this parameter over the course of a high burnup fuel cycle; this is due to yttrium hydride’s excellent hydrogen retention under the high temperature conditions considered here. Here, this suggests that hydride stability analyses are insensitive to the value of the Soret heat of transport in U-YH x under steady state liquid metal-cooled reactor conditions. However, the susceptibility to internal gas overpressurization-induced stress-rupture of the cladding during a high temperature transient is more sensitive to this parameter due to the non-linear dependence of hydrogen gas dissociation pressure vs. composition and temperature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High-temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Modeling of Combined Lead Fast Reactor and Concentrating Solar Power Supercritical Carbon Dioxide Cycles to Demonstrate Feasibility, Efficiency Gains, and Cost Reductions

Solar power has innate issues with weather, grid demand and time of day, which can be mitigated through use of thermal energy storage for concentrating solar power (CSP). Nuclear reactors, including lead-cooled fast reactors (LFRs), can adjust power output according to demand; but with high fixed costs and low operating costs, there may not be sufficient economic incentive to make this worthwhile. We investigate potential synergies through coupling CSP and LFR together in a single supercritical CO 2 Brayton cycle and/or using the same thermal energy storage. Combining these cycles allows for the LFR to thermally charge the salt storage in the CSP cycle during low-demand periods to be dispatched when grid demand increases. The LFR/CSP coupling into one cycle is modeled to find the preferred location of the LFR heat exchanger, CSP heat exchanger, sCO 2 -to-salt heat exchanger (C2S), turbines, and recuperators within the supercritical CO 2 Brayton cycle. Three cycle configurations have been studied: two-cycle configuration, which uses CSP and LFR heat for dedicated turbocompressors, has the highest efficiencies but with less component synergies; a combined cycle with CSP and LFR heat sources in parallel is the simplest with the lowest efficiencies; and a combined cycle with separate high-temperature recuperators for both the CSP and LFR is a compromise between efficiency and component synergies. Additionally, four thermal energy storage charging techniques are studied: the turbine positioned before C2S, requiring a high LFR outlet temperature for viability; the turbine after the C2S, reducing turbine inlet temperature and therefore power; the turbine parallel to the C2S producing moderate efficiency; and a dedicated circulator loop. While all configurations have pros and cons, use of a single cycle offers component synergies with limited efficiency penalty. Using a turbine in parallel with the C2S heat exchanger is feasible but results in a low charging efficiency, while a dedicated circulator loop offers flexibility and near-perfect heat storage efficiency but increasing cost with additional cycle components.

14 SOLAR ENERGY↗

Dismantling of the Bohunice V1 Reactor Coolant System - 20011

About 2.5 kilometers from the village of Jaslovske Bohunice in the Trnava District in western Slovakia at the Bohunice V1 nuclear power plant, Westinghouse and VUJE are working on the dismantling of two VVER-440 units. The consortium was awarded this contract in October 2017 from Jadrova a vyradovacia spolocnost (JAVYS) and has begun onsite work to dismantle the reactor coolant systems of both units that operated at the plant. The Bohunice V1 plant is composed of two V-230 type VVER 440 units (440 MWe each). The first unit ceased operation on December 31, 2006, and the second on December 31, 2008, after 28 years of operation. The project strategy relies on the early release of some plant areas to allow the erection of new facilities to enable a fast and safe dismantling. These up-front activities play a crucial role within the whole project. Since schedule and ALARA are two key elements to be considered, it has been decided to separate the dry cutting activities from the ones occurring underwater. Two Wet Cutting Workshops will allow the segmentation and packaging of the high activity components. To take advantage of the large space available in the turbine building, a Dry Cutting Workshop has been built for segmenting the twelve steam generators of both units. Two more Dry Cutting Workshops (one per unit) have been installed in the reactor building for the fragmentation of the remaining large components and auxiliary systems components. This paper describes all current preparatory works as well as the on-going segmentation and packaging activities. Interesting lessons learned are also provided. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Experimental and Modeling Investigation of Overcooling Transients that Include Freezing, in Fluoride-Salt Cooled High-Temperature Reactors (FHRs). Final Report

The goal of this project was an experimental and modeling investigation of overcooling transients that include freezing in Fluoride-Salt Cooled High-Temperature Reactors (FHRs). The most impactful product of this research collaboration between Professor Scarlat’s group at UW Madison and subsequently at UC Berkeley, and Dr. Rui Hu’s group at Argonne National Laboratory was the initial demonstration of SAM application to FHR transients, and the generation of a freezing module for the SAM code. The national laboratory and industry graduate student internships enabled by this project were valuable for workforce development, and also for knowledge transfer between university, national lab, and industry.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Progress in Fast Modular Reactor Conceptual Design

The Fast Modular Reactor (FMR) is a 100-MW(thermal) gas-cooled fast reactor being developed by General Atomics Electromagnetic System with the goal of developing a FMR for flexible and dispatchable power to the U.S. electricity market in the mid-2030s. The conceptual design aims to develop and verify simplified design features. These include an inert helium gas coolant, pellet-loaded fuel rods, installations with air cooling as ultimate heat sink, and small and passive heat removal systems. The goal is to ensure the development of a safe, maintainable, cost-effective, and distributed nuclear energy-generating station. The baseline technologies selected to achieve this goal are a helium coolant that is an inert gas with no chemical reaction with structural components, not activated, single phase, enabling high-temperature operation and a high thermal efficiency Brayton cycle; conventional uranium dioxide (UO 2 ) fuel, which is the most widely used and well-known fuel material, capable of high burnup (100 MWd/kg) and a long fuel life; and silicon carbide composite (SiGA®) cladding and internal structures that are chemically inert in the helium environment, exceptionally radiation tolerant, and being derisked by accident tolerant fuel technology development. Further, the reactor was specifically designed with passive safety features, including high-temperature in-core materials and a reactor vessel cooling system consisting of cooling panels of naturally circulating water. The passive safety of the core was confirmed for the depressurized loss-of–forced cooling accident, which showed the peak cladding temperature at ~1600°C during the transient, which is below the current design limit of 1800°C. The conceptual design of the FMR has been conducted for the reactor system, vessel system, generator and turbomachine, instrumentation and control, residual heat removal system, plant service system, and containment, as well as pre-application licensing documents.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

SCALE Analysis of a Fluoride Salt-Cooled High-Temperature Reactor in Support of Severe Accident Analysis

As part of a US Nuclear Regulatory Commission–sponsored project to assess the modeling and simulation capabilities for accident progression, source term, and consequence analysis for advanced reactor technologies with SCALE and MELCOR, SCALE was used for the modeling and simulation of a fluoride salt-cooled high-temperature reactor (FHR). Based on the preconceptual design for a small modular 236 MWth FHR developed by the University of California, Berkeley (PB-FHR-Mk1), a SCALE model of the PB-FHR-Mk1 reactor core was developed. The reactor was modeled at equilibrium state with different fuel compositions in different regions of the reactor. An iterative approach was used to interpolate and mix the burnup-dependent fuel compositions obtained through the depletion calculation of a core slice model. After demonstrating the applicability of SCALE’s multigroup (MG) approach for the simulation of the PB-FHR-Mk1, the resulting equilibrium core was studied in terms of the power profile, the flux profile, temperature reactivity coefficients, and the xenon reactivity. Furthermore, the tritium production rate in the salt coolant was determined, and the dependence of the one-group cross sections on the burnup and location in the reactor core was studied. The results obtained with SCALE were post-processed to provide the MELCOR team with the core inventory and decay heat of the equilibrium core, a zone-wise power profile, temperature feedback coefficients, the tritium production rate, and the xenon worth.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

SAM Code Development for Source Term Modeling in Fluoride-salt-cooled High-temperature Reactors

The SAM code is under development and supported by DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses. These advanced reactor concepts incorporate novel and improved approaches to achieve safety and economic feasibility. Many concepts leverage higher operating temperatures for improved efficiency with a variety of coolants and structural materials to support those needs. Such design choices may also pose unique radiological source term risks. There are continuous efforts to incorporate new physics and phenomena relevant to advanced reactor concepts, including capabilities to enable system-level source term modeling. The Pebble-Bed Fluoride-salt-cooled High-temperature Reactor (PB-FHR) is a promising candidate among advanced nuclear reactor concepts with its improved passive safety characteristics and high thermal efficiency. In addition to past efforts to support the development and utilization of SAM for PB-FHR safety analysis, the species transport modeling capabilities in SAM have been extended to simulate source term phenomena in concepts like the PB-FHR. The PB-FHR concept utilizes pebble-form TRISO fuel and FLiBe salt coolant to provide robust barriers to the release of almost all fission products and radiological source terms. However, tritium poses a unique radiological risk due to its significant production from neutron interactions with 6 Li and 9 Be in the FLiBe as well as its high mobility at elevated temperatures where it can permeate through structural metals. Secondly, the use of graphite at elevated temperatures poses the risk of oxidation damage to any structural components or fuel pebbles that are exposed to accidental air ingress. This report summarizes progress made in modeling these phenomena in SAM, which leverages the system-level multi-physics thermal hydraulic simulation to support an effective engineering-scale source term modeling capability. A tritium transport model is developed to simulate the various transport pathways in FHR and MSR concepts and is presented through verification and validation examples as well as demonstrations simulating experimental test loops and reference plant FHR models. A graphite oxidation model is also introduced to calculate local oxidation rates and is presented with initial validation results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The Virtual Test Bed (VTB) repository: a library of multiphysics reference reactor models using NEAMS tools

With the next generation of nuclear reactors under development, modeling and simulation (MS) tools are being developed by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in order to support their design, licensing, and future operation. Mirroring the physical test beds currently under construction (i.e., EBR-II and ZPPR), the Virtual Test Bed (VTB) was launched by the National Reactor Innovation Center (NRIC) in collaboration with NEAMS to support the advanced reactor community. This collaborative effort, which involves multiple teams at both Idaho National Laboratory and Argonne National Laboratory aims to use NEAMS tools to model a wide range of reactor designs. Those models are automatically tested to ensure their continued functionality as the tools are further developed. Examples are extensively documented, each acting as a tutorial for applying the relevant NEAMS tools to that reactor design. Currently, five advanced reactor types (with a total of eight specific design variants) are simulated by a variety of different models. These models range from steady-state, core multiphysics simulations to integrated plant analysis during loss-of flow transients. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

LMFR design and optimization methodology

This paper presents and applies a methodology for designing and optimizing Liquid Metal-cooled Fast Reactors (LMFRs). The methodology, called the Design and Optimization Methodology (DOM), achieves its goals by the effective exploration of a search space. The paper presents two case studies to demonstrate DOM. Both studies were based on the WEC long-life core LFR design. In the first study, DOM was used to explore the search space in the vicinity of the WEC (Westinghouse Electric Company LLC) long-life core LFR design trying to find a more optimized design. The objective of this optimization attempt was to reduce the fuel cycle cost. The WEC long-life core LFR design uses uranium mononitride (UN) fuel with natural nitrogen enrichment. In the second study, DOM was used to design a competitive UN fueled Lead-cooled Fast Reactor (LFR) which uses {sup 15}N enriched UN fuel. Based on the results from the second study, an estimation of the {sup 15}N enrichment cost required to obtain an economic core was performed. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Deep Learning for Multigroup Cross-Section Representation in Two-Step Core Calculations

Here we investigate using deep learning, a type of machine-learning algorithm employing multiple layers of artificial neurons, for the mathematical representation of multigroup cross sections for use in the Griffin reactor multiphysics code for two-step deterministic neutronics calculations. A three-dimensional fuel element typical of a high-temperature gas reactor as well as a two-dimensional sodium-cooled fast reactor lattice are modeled using the Serpent Monte Carlo code, and multigroup macroscopic cross sections are generated for various state parameters to produce a training data set and a separate validation data set. A fully connected, feedforward neural network is trained using the open-source PyTorch machine-learning framework, and its accuracy is compared against the standard piecewise linear interpolation model. Additionally, we provide in this work a generic technique for propagating the cross-section model errors up to the k eff using sensitivity coefficients with the first-order uncertainty propagation rule. Quantifying the eigenvalue error due to the cross-section regression errors is especially practical for appropriately selecting the mathematical representation of the cross sections. We demonstrate that the artificial neural network model produces lower errors and therefore enables better accuracy relative to the piecewise linear model when the cross sections exhibit nonlinear dependencies; especially when a coarse grid is employed, where the errors can be halved by the artificial neural network. However, for linearly dependent multigroup cross sections as found for the sodium-cooled fast reactor case, a simpler linear regression outperforms deeper networks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Improvements to Passive Heat Removal Systems in SAS4A/SASSYS-1

Safe operation of a sodium cooled fast reactor (SFR) can be significantly aided by heat removal systems that do not rely on active power, but function using passive means. Passive heat removal from such reactors can employ systems that extract heat directly from sodium coolant by utilizing heat exchangers submerged in the coolant and natural circulation of a metal fluid sodium (or sodium potassium eutectic) to heat exchangers (generally air cooled) externally located. These types of systems are generally called Direct Reactor Auxiliary Cooling Systems (DRACS). Another type of passive heat removal system particularly suitable for pool-type SFRs relies on indirect extraction of heat by utilizing air flow in an annular region surrounding the reactor guard vessel which discharges the heat via the chimney effects to the atmosphere. These systems are generally called Reactor Vessel Auxiliary Cooling Systems (RVACS).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

SAM Code Enhancement, Validation, and Reference Model Development for Fluoride-salt-cooled High-temperature Reactors

The System Analysis Module (SAM) is under development at Argonne National Laboratory as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses. It utilizes the object-oriented application framework MOOSE to leverage the modern software environment and advanced numerical methods. The capabilities of SAM are being extended to enable the transient modeling, analysis, and design of various advanced nuclear reactor systems. This report summarizes recent progress under DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program in SAM code development, demonstration, and validation to support transient safety analysis of Fluoride-salt-cooled High-temperature Reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A hybrid surrogate modeling framework for the Digital Twin of a Fluoride-salt-cooled High-temperature Reactor (FHR)

While nuclear energy is a non-greenhouse-gas emitting energy source, expensive operational costs due to the high-level of safety requirements decreases their competitiveness in the sustainable energy market. Advanced reactor concepts paired with Digital Twins aim to increase the commercialization gains of nuclear energy by reducing operational costs, increasing reactor reliability and enhancing power generation. To support Digital Twin tasks such as real-time autonomous control, proactive maintenance monitoring or optimizing power demand operations, a fast and accurate virtual representation of the Nuclear Power Plant (NPP) is required. The computational cost of high-fidelity, physics-based models are unsuitable for real-time analysis or scalability. Here, in this work, a hybrid surrogate modeling framework is developed fora Fluoride-salt-cooled High-temperature Reactor (FHR) that leverages physics-inspired models for key reactor components and uses data-driven methods for rapid system state space prediction. The Xenon reactivity feedback model is integrated to inform the surrogate model about the reactor core and the homologous pump theory model is the basis for representing pump degradation. Using a detailed, two dimensional thermal hydraulics model to generate data on the FHR, we train a network of Vectorized Autoregressive Moving-Average with eXogenous input (VARMAX) models to predict the remaining state values. The result is a surrogate model that provides a detailed reactor state representation of 41 system states and a pump degradation analysis. The framework is applied to Load Follows profiles, yielding high accuracy and a speedup that is more than 4000x faster compared to the higher- fidelity thermal hydraulics model, enabling real-time operational intelligence and applications in long horizon predictions. While the surrogate model framework is demonstrated for the particular case of FHR, the hybrid physical/data-driven modeling approach including the network of surrogates and the underlying modularity has the potential to be applied to other physical asset systems.

Digital Twins↗

Nuclear reactor module with a cooling chamber for a drive motor of a control rod drive mechanism

In some embodiments, a nuclear reactor vessel comprises a containment vessel for a reactor pressure vessel (RPV); a control rod drive mechanism (CRDM) located in the containment vessel, the CRDM including drive motors configured to move control rods into and out of a nuclear reactor core located in the RPV; and a partition extending across a portion of the containment vessel configured to retain the drive motors in a separate fluid-tight barrier region within the containment vessel. Other embodiments may be disclosed and/or claimed.

Liszkai, Tamas↗

MOOSE Reactor Module: An Open-Source Capability for Meshing Nuclear Reactor Geometries

The U.S. Department of Energy (DOE) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has developed numerous physics solvers utilizing the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) framework for multiphysics reactor analysis. These solvers require input finite element meshes representing the discretized spatial domain. Typically, reactor analysts turn to licensed tools for the creation of reactor geometry meshes. Recently, open-source functionality has been added to the MOOSE framework to mesh common reactor geometries and improve MOOSE-based nuclear reactor application user workflows. The new functionality is primarily contained in the new Reactor module of MOOSE and includes support for hexagonal pins, assemblies, and cores, extended Cartesian geometry support, options for modeling static and rotating control drums within a hexagonal assembly, core periphery triangulation, and automatic tagging of pin, assembly, plane, and depletion regions for easier post processing of physics results. A set of reactor geometry mesh builder objects further streamlines the construction of hexagonal and Cartesian cores and allows mapping of materials to regions during mesh generation. The meshes produced with the MOOSE Reactor module may be used directly within MOOSE-based applications or exported as Exodus II files for use in other finite element solvers. The tools have been demonstrated and verified using a variety of NEAMS physics solvers on a range of reactor applications, including a sodium-cooled fast reactor core analysis using Griffin, a fast reactor assembly thermal deformation analysis using MOOSE Tensor Mechanics, and a heat pipe–cooled microreactor coupled analysis using Griffin, Bison, and Sockeye. MOOSE’s Reactor module provides significant advantages compared to the use of external meshing tools when analyzing Cartesian and hexagonal reactor lattices using MOOSE-based applications: immediate accessibility (open-source) to the end user, low barrier to entry for new users, speed of mesh generation, volume preservation of meshed fuel pins, and simplification of analysis workflow when used in conjunction with MOOSE-based applications.

99 GENERAL AND MISCELLANEOUS↗