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DOE OSTI2025

Fusion burn-propagation simulations using the collisional and radiative particle-in-cell code TRIFORCE

The ability to accurately model burn propagation in inertial confinement fusion plasmas is crucial for advancing fusion energy research. This work presents enhancements to the triforce hybrid fluid-kinetic multiphysics code, focusing on its kinetic half, which employs the particle-in-cell (PIC) method with Monte Carlo collisions (MCC). We use a moment-preserving collision model that mitigates numerical noise, particularly in spherical geometries where particle weights vary significantly. Additionally, we refine the treatment of inverse bremsstrahlung to account for electron–ion collision frequency reductions in degenerate plasmas and incorporate a blackbody radiation source to enable realistic photon injection. These improvements enable the simulation of 1-dimensional (1D) spherical fusion burn propagation in deuterium–tritium plasmas. Benchmark comparisons with the hydra radiation-hydrodynamics code confirm that triforce accurately captures the dynamics of hot-spot expansion and burn propagation, demonstrating sensitivity to ignition thresholds consistent with theoretical models. Findings show the ignition cliff to be less steep in our work compared to radiation-hydrodynamic modeling. These results highlight the role of kinetic effects in fusion ignition physics and underscore the necessity of hybrid fluid-kinetic models for advancing predictive capabilities in high-energy-density plasma systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Fluid modeling of low-temperature plasmas

Fluid models are essential for understanding and predicting low-temperature plasma (LTP) behavior in various scientific and industrial settings. This paper provides an introductory tutorial on fluid modeling of LTPs, covering model formulation, implementation, and computational simulations. The tutorial focuses on five main components of the formulation of LTP fluid models: fluid flow, energy, chemistry, electromagnetism, and material properties, as well as in essential aspects of model implementations, including multiscale phenomena, multiphysics coupling, and numerical convergence. Designed for students and early-career researchers, this work offers a practical foundation for developing and using fluid models, from in-house computational codes to commercial software, bridging fundamental theory with real-world applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Multifrequency eddy-current detection of fast transient thermal signatures for in situ monitoring applications

Eddy-current (EC) nondestructive evaluation has a long history of use in a variety of ex situ defect monitoring applications because of its exquisite sensitivity to local material variations. Due to the relationship between a material's conductivity and its temperature, EC methods have also been used to investigate quasistatic, long-range temperature variations in casting applications. However, these techniques remain underutilized for the measurement of rapidly varying, spatially nonuniform temperature distributions. In this work, we construct a model system capable of generating repeatable temperature transients in steel plates and measure real-time eddy-current signals with millisecond time resolution and spatial resolution of the order of 1 mm. Using a combination of Multiphysics simulations, fast thermal imaging, and time-resolved holographic interferometry, we tease apart contributions to the eddy-current signals arising from temperature variations and transient plate deformation. Finally, we perform a systematic study in which we vary the plate thickness and the eddy-current excitation frequency to demonstrate that eddy-current techniques can provide information about a three-dimensional, time-varying, subsurface thermal distribution, which is inaccessible to the traditional thermal imaging techniques.

Rosenberg, Ethan R. [Lawrence Livermore National L↗

DOE OSTI2026

Difference in neoclassical edge flows between strongly negative and positive triangularities in the XGC gyrokinetic simulation

The neoclassical baseline study of a strongly negative triangularity (NT) plasma and the corresponding positive triangularity (PT) plasma is performed using the edge-specialized, total-f gyrokinetic code (X-point Gyrokinetic Code, XGC). A DIII-D-like plasma is used, based on the negative triangularity discharge of DIII-D #193 793. An artificial positive triangularity (PT) equilibrium has been constructed to compare the edge rotation physics at the same triangularity strength but with opposite sign, while keeping the same elongation and other geometric parameters. Carbon(6+) ions are added to the deuterium plasma at an experimentally relevant level. By using the experimental profile of carbon toroidal rotation profile as an input, XGC finds that the deuteron rotation is significantly different from the carbon rotation at the inboard and outboard midplanes, mostly caused by the difference in the Pfirsch–Schlüter rotation. More importantly, a significant difference in the X-point orbit loss physics, thus the rotation source, is found between the positive and negative triangularity equilibrium models. However, it is also found that the agreement between the present neoclassical simulation and the experimental NT data is validated only within the middle of the pedestal slope, indicating the importance of edge turbulence. Finally, this study could establish a baseline for the multiphysics, multiscale studies that include turbulence of negative triangularity plasmas.

Deuterium↗

DOE OSTI2026

Calculating the space-charge-limited current density for nonplanar geometries by simulating the charge-free electric field

Calculating the space-charge-limited-current density (SCLCD) for a complicated diode geometry often requires computationally expensive particle-in-cell (PIC) codes. Here, this paper addresses this issue by using the charge-free electric field $E_0$ calculated using COMSOL Multiphysics to determine local and global SCLCD. The SCLCD obtained by using the surface average of $|E_0|^2$ on the cathode recovers theoretical results for one-dimensional (1D) planar, cylindrical, and tip-to-tip geometries in appropriate limits. We next compared tip-to-tip calculations with the SCLCD obtained using the PIC code Empire. The SCLCD calculated using COMSOL agreed well with Empire for flatter 1D tip-to-tip geometries and diverged with increasing sharpness. Physically, Empire predicts lower SCLCD than COMSOL because the electrons spread due to concentrated space-charge at the tip, whereas theory assumes that the electrons follow the charge-free electric field lines. We further assess the behavior of the SCLCD for tips protruding from the centers of flat, circular plates of various areas. Larger plate areas with constant tip size recover the 1D planar SCLCD globally and 1D tip-to-tip SCLCD locally, while reducing the difference between Empire and COMSOL calculations since larger plates capture more of the emitted electrons, reducing SCLCD suppression due to beam spreading. These results show that charge-free electric field simulations can be used to determine the SCLCD without needing to simulate particle dynamics in PIC.

Wright, Jack K. [Purdue Univ., West Lafayette, IN ↗

DOE OSTI2021

Continuous Integration, In-Code Documentation, and Automation for Nuclear Quality Assurance Conformance

The Multiphysics Object Oriented Simulation Environment (MOOSE) is an open-source, finite element framework for solving highly coupled sets of nonlinear equations. The development of the framework and applications occurs concurrently using an agile, continuous-integration software package. Included in the framework is an in-code, extensible documentation system. Using these two tools in union with the repository management tools GitHub and GitLab, a software quality plan was created and followed such that MOOSE and a MOOSE-based application (BISON) have been shown to meet the American Society of Mechanical Engineers’ Nuclear Quality Assurance-1 standard. The approach relies heavily on automation for both testing and documentation. The resulting effort demonstrates that a rigorous software quality plan may be implemented that incurs a minimal impact on day-to-day development of the software, satisfying the stringent guidelines necessary to operate the software in a safety function within a nuclear facility.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

BISON: A Flexible Code for Advanced Simulation of the Performance of Multiple Nuclear Fuel Forms

BISON is a nuclear fuel performance application built using the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element library. One of its major goals is to have a great amount of flexibility in how it is used, including in the types of fuel it can analyze, the geometry of the fuel being modeled, the modeling approach employed, and the dimensionality and size of the models. Fuel forms that can be modeled include standard light water reactor fuel, emerging light water reactor fuels, tri-structural isotropic fuel particles, and metallic fuels. BISON is a platform for research in nuclear fuel performance modeling while simultaneously serving as a tool for the analysis of nuclear fuel designs. Recent research in BISON includes techniques such as the extended finite element method for fuel cracking, exploration of high-burnup light water reactor fuel behavior, swelling behavior of metallic fuels, and central void formation in mixed-oxide fuel. BISON includes integrated documentation for each of its capabilities, follows rigorous software quality assurance procedures, and has a growing set of rigorous verification and validation tests.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Sockeye: A One-Dimensional, Two-Phase, Compressible Flow Heat Pipe Application

Sockeye is a heat pipe analysis application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element framework. The primary purpose of Sockeye is to provide a transient heat pipe simulation tool to be used in the analysis of nuclear microreactor designs. Sockeye provides the capability to perform one-dimensional, two-phase, compressible flow simulation of a heat pipe working fluid and two-dimensional, axisymmetric heat conduction for the heat pipe cladding and its surroundings. Sockeye is demonstrated against analytical solutions and experimental data from the SAFE-30 heat pipe module test.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Electron Target Cooling Analyses of the KIPT ADS Using MCNP and Ansys Fluent

This study presents multiphysics analyses of the electron target cooling system of the accelerator-driven system (ADS) of the Kharkiv Institute of Physics and Technology (KIPT) using MCNP and Fluent computer programs. MCNP has been used to transport electrons, gammas, and neutrons, and to calculate the energy deposition in the target materials. The MCNP mesh-tally data have been imported into Fluent by a C subroutine that has been compiled and linked to Fluent as a user-defined function.The KIPT ADS is located in Ukraine and was in operation until February 2022. The Fluent model is based on the computer-aided design files from the manufacturing process of the target assembly. Here, the Fluent results for the reference case match very well the literature results obtained by STAR-CCM+ during the design phase. Other cases that differ from the reference one have been analyzed; in these cases, it is assumed a malfunction of the electron accelerator or of the water cooling system. The target cooling system operates normally for all the analyzed cases except when the inlet water mass flow rate is decreased. The transient analysis showed that the target cooling system can operate for 180 s with full power when the inlet water mass flow rate is decreased down by 75%.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Simulation of the NuScale SMR and Investigation of the Effect of Load-Following on Component Lifetimes

The NuScale SMR has been modelled using the Virtual Environment for Reactor Applications (VERA) multiphysics environment and the results compared with the publicly reported data in the Design Certification Application (DCA). The results show an excellent agreement for the compared axial and radial power distributions, temperature coefficients of reactivity, boron and control rod worths, and fast neutron flux. This NuScale model is then used to investigate the effect of different operational modes on reactor components to determine how flexible load-following operation may affect control rod and reactor pressure vessel (RPV) lifetimes. The control rod degradation is confirmed to primarily affect the silver-indium-cadmium (AIC) rod tip. The degradation rate is observed to follow a non-linear function of core power level where the increase in degradation decreases with insertion depth. For the variation in core power levels expected with current load-following schemes, the total control rod degradation is found to be mild, at 5-10% of usable life per cycle for a reactor operating at <80% power. Nonetheless, this enables load following strategies to be confirmed and/or modified to ensure that control rods do not need to be replaced during the 60+ year life of the reactor. The RPV degradation was found to be almost directly proportional to the core power level and was not overly sensitive to flux shape perturbations. Future work is planned using these damage functions to optimize operation over multiple NuScale SMR units and develop strategies for prognostics and health management.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Thermal Fluid Modeling Approaches in SAM for High Temperature Gas-Cooled Reactor Applications

This paper provides an overview of the unique modeling and simulation challenges and needs in the system and safety analysis of two common types of High Temperature Gas-cooled Reactor (HTGR) designs. The challenges are associated with the complex core geometry configurations and the change of the dominant heat removal mechanisms between normal operating conditions and decay heat removal transients. This requires that simulation tools utilize models with reasonable length scales and capture both the localized heat transfer and the core-scale heat transfer at the same time. To meet such analysis needs, different methodologies were developed. In conclusion, this includes adopting existing methods and further developing/improving them, as well as proposing innovative methods that leverage advanced computational frameworks such as the Multiphysics Object Oriented Simulation Environment (MOOSE).

HTGR↗

DOE OSTI2025

A MOOSE-Based Model for Fission Product Transport and Source Term Estimation for High-Temperature Gas-Cooled Reactors

Thanks to fuel elements containing tristructural isotropic (TRISO) particles combined with a low core power density and passive feedback mechanisms leading to modest temperature rises in the event of accidental events, high-temperature gas-cooled reactors (HTGRs) offer a high degree of reliability in terms of fission product retention. While the anticipated source term for HTGRs is expected to be very low, it is important to provide a quantitative estimate of radiological releases during nominal and accidental conditions. Here, we propose a computationally efficient mechanistic source term methodology relying on the Multiphysics Object Oriented Simulation Environment (MOOSE) for tracking fission product transport from TRISO particles up to the coolant pressure boundary, as well as modeling the transport and potential deposition of these nuclides inside the reactor coolant loop. The proposed computational scheme is applied to estimate source term inventories for a representative 10-MW(thermal) prismatic high-temperature microreactor and is qualitatively compared against known release fractions. In addition to providing an alternate analysis tool, this MOOSE model can help reactor designers quantify the influence of key design parameters relevant for studies of radiological dose consequences.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Modeling Flow in a Microreactor Core: From High-Fidelity CFD to Subchannel Analysis

The accurate prediction of pressure drop in tightly packed, low–Reynolds number (Re) bare rod bundles is essential for the thermal-hydraulic design of the Microreactor Applications Research Validation and EvaLuation (MARVEL) reactor and other microreactor concepts. However, existing friction factor correlations, particularly the upgraded Cheng-Todreas (UCTD) correlation, have limited validation for the small pitch-to-diameter ratios (P/Ds) and transitional flow conditions characteristic of these systems. In this work, we perform high-fidelity large-eddy simulations (LESs) of both an infinite bare rod bundle and a finite bare 37-pin scalloped rod bundle across the range 1000≤ 𝑅𝑒 ≤5500. The simulations reveal strong gap vortex–driven transitional behavior and indicate that the UCTD may underpredict the friction factor by up to 28% at 𝑃/𝐷 = 1.05. Using the LES-calculated pressure drops, we formulate a new friction factor correlation that follows the Cheng-Todreas functional form but is calibrated for low-Re and tightly packed geometries representative of a MARVEL-like reactor. The correlation is implemented in the MOOSE (Multiphysics Object-Oriented Simulation Environment) subchannel module and compared against both the LES and UCTD predictions. Across all subchannel types, the proposed model reduces the streamwise velocity differences from as high as 44% (UCTD) to below 9%, and decreases the pressure gradient differences from 13% to 25% (UCTD) to 0.7% to 7% relative to the LES results. These results suggest that the new correlation has the potential to improve the pressure drop and flow field predictions for such geometries, highlighting the importance of high-fidelity simulations in supporting microreactor thermal-hydraulic model development and motivating future pressure drop experiments for compact rod bundles to further validate these findings.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

DOE OSTI2026

Depletion Benchmark Analysis on a Lead Fast Reactor Using PyARC/OpenMC

PyARC is a user-friendly fast reactor analysis tool that automates multiphysics workflows using the “extended suite” of Argonne Reactor Computation (ARC) codes by providing a single common input for model definition, code execution, and output post-processing. A lead fast reactor (LFR) benchmark model is used to perform depletion calculations using the newly integrated OpenMC depletion capability in PyARC, building on previous analysis using the ARC codes through PyARC and Serpent. Results for core lifetime k-effective, shutdown decay heat, and end-of-life heavy-metal inventory are compared to verify the PyARC/OpenMC integration against the PyARC/ARC workflow and Serpent for depletion analysis of LFR designs. The results show satisfactory agreement among all three methods, with remaining discrepancies largely attributable to differences in nuclear data libraries and decay-chain modeling detail rather than to fundamental modeling limitations.

Kiesling, Kalin R.↗

DOE OSTI2017

Transmutation approximations for the application of hybrid Monte Carlo/deterministic neutron transport to shutdown dose rate analysis

In fusion energy systems (FES) neutrons born from burning plasma activate system components. The photon dose rate after shutdown from resulting radionuclides must be quantified. This shutdown dose rate (SDR) is calculated by coupling neutron transport, activation analysis, and photon transport. The size, complexity, and attenuating configuration of FES motivate the use of hybrid Monte Carlo (MC)/deterministic neutron transport. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) method can be used to optimize MC neutron transport for coupled multiphysics problems, including SDR analysis, using deterministic estimates of adjoint flux distributions. When used for SDR analysis, MS-CADIS requires the formulation of an adjoint neutron source that approximates the transmutation process. In this work, transmutation approximations are used to derive a solution for this adjoint neutron source. It is shown that these approximations are reasonably met for typical FES neutron spectra and materials over a range of irradiation scenarios. When these approximations are met, the Groupwise Transmutation (GT)-CADIS method, proposed here, can be used effectively. GT-CADIS is an implementation of the MS-CADIS method for SDR analysis that uses a series of single-energy-group irradiations to calculate the adjoint neutron source. For a simple SDR problem, GT-CADIS provides speedups of 200 100 relative to global variance reduction with the Forward-Weighted (FW)-CADIS method and 9 ± 5 • 10 4 relative to analog. As a result, this work shows that GT-CADIS is broadly applicable to FES problems and will significantly reduce the computational resources necessary for SDR analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Predicting Large Deflections of Multiplate Fuel Elements Using a Monolithic FSI Approach

As part of the Global Threat Reduction Initiative, the Oak Ridge National Laboratory is evaluating conversion of fuel for the High Flux Isotope Reactor (HFIR) from high-enriched uranium to low-enriched uranium. Currently, multiphysics simulations that model fluid-structure interaction phenomena are being performed to ensure the safety of the reactor with the new fuel type. A monolithic solver that fully couples fluid and structural dynamics is used to model deflections in the new design. A classical experiment is chosen to validate the capabilities of the current solver and the method. Here, a single-plate simulation with various boundary conditions as well as a five-plate simulation are presented. Finally, use of the monolithic solver provides stable solutions for the large deflections and the tight coupling of the fluid and structure and the maximum deflections are captured accurately.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2018

A Weighted Least-Squares Transport Equation Compatible with Source Iteration and Voids

We present that second-order forms of the transport equation allow the use of continuous finite elements (CFEMs). This can be desired in multiphysics calculations where other physics require CFEM discretizations. Second-order transport operators are generally self-adjoint, yielding symmetric positive-definite (SPD) matrices, which allow the use of efficient linear algebra solvers with an enormous advantage in memory usage. Least-squares (LS) forms of the transport equation can circumvent the void problems of other second-order forms but are almost always nonconservative. Additionally, the standard LS form is not compatible with discrete ordinates method (SN) iterative solution techniques such as source iteration. A new form of the LS transport equation has recently been developed that is compatible with voids and standard SN iterative solution techniques. Performing nonlinear diffusion acceleration (NDA) using an independently differenced low-order equation enforces conservation for the whole system and makes this equation suitable for reactor physics calculations. In this context, “independent” means that both the transport and low-order solutions converge to the same scalar flux and current as the spatial mesh is refined, but for a given mesh, the solutions are not necessarily equal. In this paper we show that introducing a weight function into this LS equation improves issues with causality and can render our equation equal to the self-adjoint angular flux (SAAF) equation. Causality is a principle of the transport equation that states that information travels only downstream along characteristics. This principle can be violated numerically. We show how to limit the weight function in voids and demonstrate the effect of this limit on accuracy. Using the C5G7 benchmark, we compare our method to the SAAF formulation with a void treatment (SAAFτ) that is not self-adjoint and has a nonsymmetric coefficient matrix. Finallyl, we show that the weighted LS equation with NDA gives acceptable accuracy relative to the SAAFτ equation while maintaining a SPD system matrix.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems

The Multilevel in Space and Energy Diffusion (MSED) method accelerates the iterative convergence of multigroup diffusion eigenvalue problems by performing work on lower-order equations with only one group and/or coarser spatial grids. It consists of two primary components: (1) a grey (one-group) diffusion eigenvalue problem that is solved via Wielandt-shifted power iteration (PI) and (2) a multigrid-in-space linear solver. In previous work, the efficiency of MSED was verified using Fourier analysis and numerical results from a one-dimensional multigroup diffusion code. Since that work, MSED has been implemented as a solver for the coarse-mesh finite difference (CMFD) system in the three-dimensional Michigan Parallel Characteristics Transport (MPACT) code. In this paper, the results from the implementation of MSED in MPACT are introduced, and the changes needed to make MSED more suitable for MPACT are described. For problems without feedback, the conclusions in this paper show that MSED can reduce the CMFD run time by an order of magnitude and the overall run time by a factor of 2 to 3 compared to the default CMFD solver in MPACT [PI with the generalized minimal residual (GMRES) method]. For problems with feedback, the convergence of the outer Picard iteration scheme is worsened by the well-converged CMFD solutions produced by the standard MSED method. To overcome this unintuitive deficiency, MSED may be run with looser convergence criteria (a modified version of the MSED method called MSED-L) to circumvent the issue until the multiphysics iteration in MPACT is improved. Results show that MSED-L can reduce the CMFD run time in MPACT by an order of magnitude, without negatively impacting the outer Picard iteration scheme.

3-D↗