Reactivity Feedback Modeling in SAM

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. The molten-salt-cooled pebble-bed reactor, or pebble-bed FHR (PB-FHR) is a promising candidate among advanced nuclear reactor concepts with its improved passive safety characteristics and high thermal efficiency. To support the development and utilization of the SAM code for PB-FHR safety analysis, activities on SAM code enhancements, reference plant model developments, and code validations have been performed in the past a few years to support near-term industry and NRC needs. This report summarizes recent progress under DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program in SAM code development and demonstration for transient safety analysis of Fluoride-salt-cooled High-temperature Reactors. SAM capabilities has been significantly enhanced over the years to add FHR specific modeling features, including salt freezing and thawing, spherical core channel and pebble bed core modeling, solid-fluid thermal radiation, tritium transport and general species transport in fluids and solids, and the general code enhancements on solver schemes of point kinetics module and reactivity feedback models. A reference PB-FHR model is developed, based on publicly available information from Kairos Power’s generic FHR design and the University of California, Berkeley (UCB) Mk1 design. A reference reactor model is foundational to the methodologies employed by NRC to verify the adequacy of computer codes and evaluation models. The reference FHR model was utilized for a number of selected FHR design basis accidents, including station blackout, loss of heat sink, loss of flow, transient overpower, and overcooling events.

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. This paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

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.

This report presents the modeling of the core of a generic pebble-bed reactor (PBR) at the system level using the System Analysis Module (SAM) code. This work is an extension of a previous work by the authors (Ooi et al. (2021)) that used the so-called 2-D ring model approach to model the PBMR-400. With the new approach, the pebble bed of the reactor is modeled with multiple PBCoreChannel components with spherical heat structures which allows the code to calculate thermal fluid parameters with built-in closure relations. The new core-channel approach is an improvement to the 2-D ring model approach as it does not introduce geometric distortions to the model and thus reduces the uncertainties of the predictions. In addition to thermal fluid simulations, point kinetics (PKE) are included to the model. Simulations are performed under a steady-state normal operation condition and a load-following transient scenario. This particular transient scenario is chosen as it tests both the thermal fluid and neutronics aspects of the model. The predicted results from both the steady-state and transient scenarios are compared with the results by Stew- art et al. (2021) who performed similar simulations with a Griffin-Pronghorn coupled tool. Despite the differences between the codes, with SAM being a system-analysis code and Pronghorn being a porous-medium code, both sets of results compare favorably. The over- all profiles and trends of the predicted temperatures and reactivities from the SAM and Griffin/Pronghorn simulations are similar, with some differences in their predicted values. The first part of the report covers the significance of a relatively fast-running approach that is capable of modeling the pebble bed reactor at the system-level while simultaneously capturing the radial thermal behavior of the core. Then, the modeling approach used in this work is discussed in details. Lastly, the results and comparisons with the Griffin/Pronghorn simulation are presented.

The DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program supports a full range of computational thermal fluids analysis capabilities and code developments for a broad range of advanced reactor concepts. The research and development approach under the thermal fluids technical area synergistically combines three length and time scales in a hierarchical multi-scale approach. To enable multi-scale thermal fluids capability using these codes, a key joint effort has been underway to develop an integrated system- and engineering-scale thermal fluids analysis capability, through integration of SAM and Pronghorn codes, both based on the MOOSE framework. This report summarizes recent advances in developing an integrated system- and engineering-scale modeling capability for the molten salt reactor (MSR) concept, which has gained significant interest in recent years. A consistent framework was established by coupling Pronghorn and SAM through the Saline interface, with thermophysical properties provided by the Molten Salt Thermal Properties Database-Thermophysical (MSTDB-TP). Further improvements were made to the coupling schemes and domain-overlapping strategies, enhancing the stability and robustness of multi-code simulations. Verification and validation efforts demonstrate the accuracy of this integration across a range of benchmark problems, including one-dimensional heated pipe flows, three-dimensional natural convection loops with evolving isotopic compositions, and molten salt reactor experiment (MSRE) demonstration cases. Within Pronghorn, new capabilities were introduced to model corrosion and noble-metal plating phenomena, supported by an extended thermal-hydraulics framework and refined turbulence treatments. To capture two-phase flow behavior, a multiphase Euler–Euler model was implemented in Pronghorn, including advanced closure relations, high-resolution advection techniques, and capillary force reconstruction. Preliminary verification cases confirm the fidelity of the approach, while planned validation efforts target canonical multiphase benchmarks and application to MSR components such as the MSRE pump bowl. Finally, updates to SAM’s MSR mass transfer modeling were extended to consider noble gas migration into porous structures like graphite. The point kinetics model was updated to include reactivity feedback contributions from any defined species, such as xenon. The gas transport model was expanded for applicability to gas mixtures, bubble efflux phenomena, and species transport between liquid and gas phases. A selection of multi-scale Sherwood number correlations from MOSCATO/NekRS and multi-phase correlations from literature have been added for improved accuracy in calculating mass transfer coefficients. A companion effort on developing system-level redox corrosion has also been incorporated into SAM. Collectively, these enhancements strengthen the predictive capability of SAM and Pronghorn for simulating MSR thermal-hydraulics, corrosion, multiphase behavior, and fission-product transport, providing a more complete toolset for design, safety analysis, and licensing support of next-generation MSRs.

This report details the progress of Idaho National Laboratory (INL) in creating a reference plant multiphysics model for the Advanced Burner Test Reactor (ABTR). This model was developed under Task 13 of the U.S. Nuclear Regulatory Commission project “Development and Modeling Support for Advanced Non-Light Water Reactors,” and is an extension of the reference plant model developed in Task 4b, which was improved upon in the following ways. (1) The discrete ordinates method was used in lieu of the super-homogenization (SPH)-corrected diffusion approximation in order to better capture the anisotropic scattering contribution and the neutron leakage change due to thermal expansion. (2) The novel neutronic spatial discretization approach, termed the ring-heterogeneous (RH) approximation, was conceptualized and introduced to capture the differential expansion of the materials in the core. This new technique proved capable of preserving fission rates and maintaining the eigenvalue within 2.5% and 266 pcm with 9 neutron energy groups, respectively. Separating the different materials in the core enables the differential expansion of materials to be explicitly accounted for, eliminating the need for problem-specific cross-section functionalization techniques. (3) The SAM model for the core and system thermal-hydraulics analysis was updated to include 61 channels instead of just four representative ones. This enables users to obtain improved spatial resolution for sodium temperature and density scalar fields. (4) All the mesh files were created via the Multiphysics Object-Oriented Simulation Environment (MOOSE) Reactor module, eliminating all reliance on external tools for mesh creation. (5) Finally, the fuel axial expansion now leverages the HT9 and UPuZr material properties that have been validated against experimental data. The reference plant model was used to perform a full-core unprotected loss of flow (ULOF) transient calculation, including neutronics, thermal and mechanical feedback mechanisms. Future work will be devoted to further enhancements of the model. Potential improvements to the model include the addition of the control rod driveline expansion feedback and the upgrading of the support plate model so as to explicitly include 3D effects. Additionally, a Nuclear Energy Advanced Modeling and Simulation funded parallel effort has completely automated the creation of the ring-heterogeneous (RH) mesh from the fully heterogeneous (FH) geometry, thus maximizing user friendliness for the sodium fast reactor sodium-cooled fast reactor (SFR) workflow and will be incorporated in future work.

In this paper, an Unprotected Loss of Flow (ULOF) assessment has been performed on the European Sodium Fast Reactor developed in the ESFR-SMART EU project. To conduct the analysis, a simplified 42 channel thermal–hydraulic model has been established in TRACE system code, using a point kinetics model accounting for various reactivity feedback effects. The assessment reveals the core behavior of a commercial size, 3600 MWth, sodium fast reactor using a state-of-the-art low void effect reactor core design. The study focuses on the sodium boiling phenomenon and sodium reactivity feedback effect evolution during the accident with the reference subassembly (SA) design. Following this analysis, a study has been performed with a modified SA design. The boiling progression and phenomenology within the reference and the modified core have been compared, and the impact of the SA modification was described.

One of the key areas of the development of Accelerator Driven Systems (ADS) are reactivity monitoring techniques. Since the measurement in the future industrial reactor have to be made in the real time applied methods should be accurate, simple and robust. Therefore methods based on point kinetic model are considered. Necessary experimental validation of selected methods was carried out within research project FP7 FREYA using VENUS-F reactor. This paper presents results obtained using the Sjostrand method and the source multiplication method. Since ADS core behaviour differs from the point kinetics obtained reactivity value depends on the detector position in the system. From the results it is clear that measurement results strongly depend on the position of the detector in the system. For the Sjostrand method these spatial effects can be successfully corrected using MCNP-calculated correction factors. Those correction factors do not change within the range of reactivity changes covered in the experiments. Spatial effects affecting source multiplication method are more complex and they depend also on neutron flux distribution in the core.

In this paper, the solution of the Neutron Point Kinetics model is presented, adding the effects of temperature and absorbers poisons within a historical and technical context to simulate the preliminary characteristics of the Chernobyl accident. The Point Kinetics model was able to extract physical information consistent with what was expected to predict the reactor situation until the accident. It was also possible to verify, given the results, that the Rosenbrock method was able to overcome the degree of stiffness of the ODE system, besides solving a non-linear problem. Thus, this study has contributed to highlighting the importance of temperature effects and especially absorbers poisons in the final power behavior, extremely relevant for decision making in the operation and safety of a nuclear power plant.

The Super System Code of the Korea Atomic Energy Research Institute (SSC-K) has been developed for the transient analysis of the Korea Advanced LIquid MEtal Reactor (KALIMER) system. Recently, a detailed three-dimensional (3-D) core thermal-hydraulic model was developed to describe nonuniformities of radial temperature and flow within a subassembly and to decrease the uncertainties in the reactor safety margins during accident situations. The Shutdown Heat Removal Test-17 (SHRT-17) performed in the Experimental Breeder Reactor-II (EBR-II) and the postulated unscrammed events for the KALIMER conceptual design have been analyzed using a code system that has coupled a detailed 3-D core thermal-hydraulic model with SSC-K. The coupled code predicted behaviors for the experimental trends for the protected loss-of-flow SHRT-17. The KALIMER-150 design was adopted for a plant application of the same code system. Three events, unprotected transient overpower (UTOP), unprotected loss of flow (ULOF), and unprotected loss of heat sink (ULOHS) were analyzed, and the simulation results were compared to those obtained using another code system that has coupled the Safety Analysis Section SYStem (SASSYS)-1 code with the same detailed 3-D core thermal-hydraulic model. The results, calculated with SSC-K coupled with the detailed 3-D core thermal-hydraulic model showed good agreement with the calculated results of the SASSYS-1 coupled code system for the UTOP and ULOF; however, some discrepancies were shown in the results for the ULOHS. These were found to have occurred because of a difference of the modeling for the decay heat removal system and primary coolant inventory. Through these analyses, the coupled code system was validated in order to be available for the safety analysis of a liquid-metal reactor (LMR) plant.

An implicit finite difference method for solving the corrected fractional neutron point kinetics equations

The Korea Atomic Energy Research Institute (KAERI) is developing KALIMER (Korea Advanced LIquid Metal Reactor), which is a sodium-cooled, metallic-fueled, pool-type reactor. The KALIMER-600 design concept (600 MWt) was selected as one of the reference GEN-IV sodium-cooled fast reactors (SFRs). The safety design philosophy of KALIMER-600 places maximum reliance on passive responses to abnormal and emergency conditions, and minimizes the need for active and engineered safety systems. KALIMER-600 utilizes the intrinsic negative reactivity feedback effect under design extended conditions where reactor scram failures are postulated. In order to assess the effectiveness of the inherent safety features, a scoping system analysis during unprotected overpower, loss of flow and under cooling events has been performed using the system-wide transient analysis code SSC-K. The present scoping analysis focuses on identification of enhanced safety design features that provide passive and self-regulating response to transient conditions and evaluation of safety margins. The results of the scoping analysis indicate an understanding of various inherent reactivity feedback mechanisms is very important in establishing design features. The analysis results show that the KALIMER-600 design concepts provide larger safety margins with respect to sodium boiling, fuel rod integrity, and structural integrity. The inherent safety can be enhanced by accounting for reactivity feedback mechanisms in the design process.

Best estimate calculation and uncertainty quantification of sodium-cooled fast reactor using MARS-LMR code

Power series solution method for solving point kinetics equations with lumped model temperature and feedback

FAST (floating absorber for safety at transient) for the improved safety of sodium-cooled burner fast reactors