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DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Neural-network based collision operators for the Boltzmann equation

Kinetic gas dynamics in rarefied and moderate-density regimes have complex behavior associated with collisional processes. These processes are generally defined by convolution integrals over a high-dimensional space (as in the Boltzmann operator), or require evaluating complex auxiliary variables (as in Rosenbluth potentials in Fokker-Planck operators) that are challenging to implement and computationally expensive to evaluate. In this work, we develop a data-driven neural network model that augments a simple and inexpensive BGK collision operator with a machine-learned correction term, which improves the fidelity of the simple operator with a small overhead to overall runtime. The composite collision operator has a tunable fidelity and, in this work, is trained using and tested against a direct-simulation Monte-Carlo (DSMC) collision operator.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

DOE OSTI2020

Characterization of flow and transport in a fracture network at the EGS Collab field experiment through stochastic modeling of tracer recovery

Energy extraction from subsurface reservoirs is important for addressing the increasing energy demand and environmental concerns such as global warming. However, the characterization of subsurface reservoirs, particularly reservoirs dominated by fracture networks remains a challenge due to the lack of means to directly observe subsurface processes. This study explores the feasibility and efficacy of characterizing fracture flow and transport processes in an enhanced geothermal system (EGS) testbed through stochastic tracer modeling. There are two enabling factors that allow application of stochastic modeling to characterize a subsurface reservoir. First, an abundance of geological and geophysical measurements enables the development of a high-fidelity and well-constrained fracture network model. Second, high-performance computing (HPC) allows running massive realizations efficiently. Six conservative tracer tests were stochastically modeled and produced satisfactory realizations that successfully reproduce field tracer recovery data from each tracer test. The evolution of flow and transport processes in the fracture network was then analyzed from these satisfactory realizations. This work demonstrates that stochastic tracer modeling on a high-fidelity fracture network model is feasible and can provide important insights regarding flow and transport characteristics in subsurface fractured reservoirs.

58 GEOSCIENCES↗

DOE OSTI2022

A robust deep learning workflow to predict multiphase flow behavior during geological C O 2 sequestration injection and Post-Injection periods

Simulation of multiphase flow in porous media is essential to manage the geologic CO 2 sequestration (GCS) process, and physics-based simulation approaches usually take prohibitively high computational cost due to the nonlinearity of the coupled physics. This paper contributes to the development and evaluation of a deep learning workflow that accurately and efficiently predicts the temporal-spatial evolution of pressure and CO 2 plumes during injection and post-injection periods of GCS operations. Based on a Fourier Neural Operator, the deep learning workflow takes input variables or features including rock properties, well operational controls and time steps, and predicts the state variables of pressure and CO 2 saturation. To further improve the predictive fidelity, separate deep learning models are trained for CO 2 injection and post-injection periods due to the difference in primary driving force of fluid flow and transport during these two phases. We also explore different combinations of features to predict the state variables. We use a realistic example of CO 2 injection and storage in a 3D heterogeneous saline aquifer, and apply the deep learning workflow that is trained from physics-based simulation data and emulate the physics process. Through this numerical experiment, we demonstrate that using two separate deep learning models to distinguish post-injection from injection period generates the most accurate prediction of pressure, and a single deep learning model of the whole GCS process including the cumulative injection volume of CO 2 as a deep learning feature, leads to the most accurate prediction of CO 2 saturation. For the post-injection period, it is key to use cumulative CO 2 injection volume to inform the deep learning models about the total carbon storage when predicting either pressure or saturation. The deep learning workflow not only provides high predictive fidelity across temporal and spatial scales, but also offers a speedup of 250 times compared to full physics reservoir simulation, and thus will be a significant predictive tool for engineers to manage the long-term process of GCS.

58 GEOSCIENCES↗

DOE OSTI2024

A deep learning-based workflow for fast prediction of 3D state variables in geological carbon storage: A dimension reduction approach

Deep learning (DL) models are extensively used as surrogate models for high-fidelity simulations of multiphase fluid flow in porous media at large scales, enabling fast forecasts of the spatial–temporal evolution of three-dimensional (3D) state variables in geological carbon storage (GCS). However, training these models in high-dimensional space remains computationally demanding and prone to overfitting because of limited training data. This paper presents a novel workflow to address these challenges by integrating dimension reduction (DR) methods. Here, the proposed workflow employed pre-trained DR models to extract the latent variables of geological models and state variables and utilized the multi-layer perceptron (MLP) for constructing mapping functions between the input and output variables in latent spaces. Subsequently, the pre-trained reconstruction models converted the MLP-predicted latent state variables to their original high-dimensional form. Furthermore, we proposed a novel strategy for the DR and reconstruction of 3D saturation fields to account for the unique data characteristics of sparsity, nonuniformity, and discontinuity. The proposed strategy applied PCA and inverse PCA for 2D average saturation fields and developed a DL-based 3D reconstruction model, leveraging three 2D average saturation fields as input to produce a 3D saturation field as output. The pre-training of DR and reconstruction models and training of MLP models were conducted on 84 Gulf of Mexico (GoM) simulations and evaluated on 12 testing simulations. Each simulation contained 720 monthly time steps, with the first 360 months as the injection period and the rest as the post-injection period. The proposed workflow, incorporating DR and DL models, accurately predicts the normalized 3D pressure fields, achieving mean square error (MSE) of 2.92 × 10 -7 compared to the ground truth obtained from a full-physics simulator. Furthermore, the proposed strategy outperformed PCA and convolutional autoencoder (CAE) models on 3D saturation fields, resulting in minor workflow prediction errors with an MSE of 2.93 × 10 -5 . The results suggest the proposed workflow provides sufficient predictive fidelity across temporal and spatial scales, and enables a speedup of 160 times compared to the full-physics simulator, facilitating improved decision-making and risk assessment for large-scale GCS management in real-time scenarios.

3D reconstruction model↗

DOE OSTI2022

BISON validation of FeCrAl cladding mechanical failure during simulated reactivity-initiated accident conditions*

Here, a reactivity-initiated accident (RIA) is a postulated design basis accident in light water reactors (LWRs) in which a rapid reactivity insertion induces a fission rate increase and a fuel pellet temperature rise. During RIA, the fuel pellet thermally expands and may cause pellet-cladding mechanical interaction (PCMI). Separate effects PCMI tests were performed on C26M FeCrAl cladding tube samples, introducing biaxial stress via a well understood modified burst test (MBT) system. A high-speed camera in the MBT system captured the projections, covering a 360° view of the cladding deformation and enabling a digital image correlation (DIC) method to quantify the surface strains with high fidelity. Representative hot zero-power RIA mechanical loading conditions were applied to the sample, and the test duration ranged from 20 to 500 ms at an average temperature of 573 K. BISON finite element–based fuel performance code modeling was performed against the high-fidelity DIC data produced from the MBTs. Validation calculations were conducted with 2D models and systematically compared with test data of the burst time, burst pressure, burst hoop strains, and hoop strain rates. Based on the behaviors from the separate effects test, BISON calculations satisfactorily predicted the cladding deformation behaviors. Sensitivity analysis was conducted to identify highly influential mechanical properties responsible for the cladding failure behavior during the MBT experiments. The results highlight the significance of the cladding's mechanical strength in governing cladding strain, followed by the significance of the mechanical interactions between the pellet and the cladding.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Modelica-based system modeling for studying control-related faults in chiller plants and boiler plants serving large office buildings

System modeling is critical when studying operation faults in chiller plants and boiler plants. However, current fault models have difficulties faithfully representing the operation of chiller plants and boiler plants under the effects of those faults, especially the control-related ones. In this study, we present a systematic method to develop high-fidelity models for approximating the behaviors of chiller plants and boiler plants under faulty conditions. Compared to existing ones, the resulting fault models have two advantages: first, they better characterize the dynamic patterns in the system operation. In those models, control architecture and control logic are faithfully implemented. Thus, they can be used to study control-related faults, such as incorrect staging control due to sensor bias and mistuned feedback control. Second, they are readily extensible and can support large-scale investigations to explore different faulty conditions/scenarios. Those models are established in a hierarchical structure while modules in each layer can be redeclared and parameterized at upper layers. In such a case, modifications to the models can be realized through model modifiers and the process can be easily streamlined with scripts. We applied the proposed models in a comprehensive fault impact evaluation of the 13 control-related faults of chiller and boiler plants. In this evaluation, the proposed plant model is coupled with the EnergyPlus thermal load model to study the impact of various faulty scenarios. Based on the evaluation results, we identified the faults that have the most significant impacts on the operation of the chiller and boiler plants, respectively. We also found that the relationship between the impacts of the studied faults and the severity level of the faults are highly non-linear

Huang, Sen↗

DOE OSTI2025

Establishing a process-structure-property-performance framework for SLS additive manufacturing through integrated multiscale modeling

This study presents a comprehensive suite of high-fidelity computational models that integrate multiscale and multiphysics simulations to capture the full Selective Laser Sintering (SLS) additive manufacturing process—from initial melting and solidification to mechanical response under external loads. Process simulations are linked with mechanical analysis through Representative Volume Elements (RVEs), establishing a process-structure–property-performance framework. The interaction between laser light and polyamide 12 (PA12) powder is modeled, accounting for laser characteristics and the optical, thermal, and geometrical properties of the powder. The heat source is incorporated into a heat transfer model, coupled with crystallization kinetics and densification models to predict material density and crystallinity. The porosity distribution from the densification model and crystallinity interpolated from experimental data are used to construct the RVEs. A multi-mechanism constitutive model is then calibrated using mechanical tests to predict the stress–strain response. Simulation results show good agreement with experimental data in terms of porosity, crystallinity, and mechanical performance when sufficient laser power (62 W or higher) is used. This research supports the inverse design of 3D-printed structures by introducing a high-fidelity framework that combines multiscale and multiphysics modeling with experimental calibration for predictive and performance-driven additive manufacturing.

SLS↗

DOE OSTI2023

Investigation of thermal hydraulic behavior of the High Temperature Test Facility's lower plenum via large eddy simulation

A high-fidelity computational fluid dynamics (CFD) analysis was performed using the Large Eddy Simulation (LES) model for the lower plenum of the High–Temperature Test Facility (HTTF), a ¼ scale test facility of the modular high temperature gas-cooled reactor (MHTGR) managed by Oregon State University. In most next–generation nuclear reactors, thermal stress due to thermal striping is one of the risks to be curiously considered. This is also true for HTGRs, especially since the exhaust helium gas temperature is high. In order to evaluate these risks and performance, organizations in the United States led by the OECD NEA are conducting a thermal hydraulic code benchmark for HTGR, and the test facility used for this benchmark is HTTF. HTTF can perform experiments in both normal and accident situations and provide high-quality experimental data. However, it is difficult to provide sufficient data for benchmarking through experiments, and there is a problem with the reliability of CFD analysis results based on Reynolds–averaged Navier–Stokes to analyze thermal hydraulic behavior without verification. To solve this problem, high-fidelity 3-D CFD analysis was performed using the LES model for HTTF. It was also verified that the LES model can properly simulate this jet mixing phenomenon via a unit cell test that provides experimental information. As a result of CFD analysis, the lower the dependency of the sub-grid scale model, the closer to the actual analysis result. In the case of unit cell test CFD analysis and HTTF CFD analysis, the volume-averaged sub-grid scale model dependency was calculated to be 13.0% and 9.16%, respectively. As a result of HTTF analysis, quantitative data of the fluid inside the HTTF lower plenum was provided in this paper. As a result of qualitative analysis, the temperature was highest at the center of the lower plenum, while the temperature fluctuation was highest near the edge of the lower plenum wall. The power spectral density of temperature was analyzed via fast Fourier transform (FFT) for specific points on the center and side of the lower plenum. FFT results did not reveal specific frequency-dominant temperature fluctuations in the center part. It was confirmed that the temperature power spectral density (PSD) at the top increased from the center to the wake. The vortex was visualized using the well-known scalar Q-criterion, and as a result, the closer to the outlet duct, the greater the influence of the mainstream, so that the inflow jet vortex was dissipated and mixed at the top of the lower plenum. Additionally, FFT analysis was performed on the support structure near the corner of the lower plenum with large temperature fluctuations, and as a result, it was confirmed that the temperature fluctuation of the flow did not have a significant effect near the corner wall. In addition, the vortices generated from the lower plenum to the outlet duct were identified in this paper. It is considered that the quantitative and qualitative results presented in this paper will serve as reference data for the benchmark.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Evaluation of light collection from highly scattering media using wavelength-shifting fibers

Opaque scintillators are designed to have a short scattering length such that scintillation photons are probabilistically confined to a small region of space about their origin. The benefit of this feature is that information on the interaction event topology can be recorded with greater fidelity than in traditional highly transparent media with sensors at large distances from the light production region. Opaque scintillator detectors rely on wavelength-shifting fibers to extract the scintillation light; however, the efficiency of light collection has not yet been directly measured in experiment. We measured the efficiency of light collection as a function of the optical parameters of an opaque liquid and the distance from the origin of the light to the fiber. We use the experimental data to validate a Monte Carlo model of light transport and collection and discuss a simple diffusion model that reproduces the results of Monte Carlo simulation with high fidelity. Furthermore, this combination of validated models has the potential for use in predictions of performance in various designs of future opaque scintillator detectors such as LiquidO.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Innovative approaches to neutron beam optimization: A case study of FP14 at LANSCE

This paper describes an experimental method to acquire high resolution energy- and spatially- resolved neutron beam spots using the time-gated neutron imaging system with Teledyne Pi-MAX4 camera. These experimental data offer a unique opportunity for benchmarking beam spot simulations. High-quality simulations depend significantly on a high-fidelity geometry model, which can be challenging for legacy facilities. We informed our MCNPX geometry model by latest metrology survey employing Leica laser tracker ATS600. It gave us a high fidelity description of our facility geometry. Such a robust integration of novel tools and methods yields a previously unattainable level of accuracy in both predicting and capturing neutron beam spots, marking a notable advancement over traditional methods reliant on static image plates. Here, to demonstrate the practical application of these tools, we are showing a non-uniform beam spot challenge at our Flight Path 14 (FP14) at the Los Alamos Neutron Science Center (LANSCE). Our precise MCNPX prediction of beam spot shifting as function of neutron energy was confirmed by experimental beam spot measured with extremely high level of detail. Results of this research demonstrate a significant leap in neutron beam optimization at LANSCE and set a new benchmark in beam spot characterization. The advanced methods presented here have potential for adoption at similar research facilities worldwide, aiming at substantial improvement in neutron beam delivery for experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

EVALUATION OF HOT CHANNEL FACTOR FOR SODIUM-COOLED FAST REACTORS WITH MULTI-PHYSICS TOOLKIT

The evaluation of hot channel factor (HCF) is of great significance to the quantification of safety margins for reactor designs. In this paper, HCFs for a sodium-cooled fast reactor (SFR) are evaluated with the Simulation-based High-efficiency Advanced Reactor Prototyping (SHARP) toolkit, which is developed under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Campaign of DOE for multi-physics reactor performance and safety simulations. The high-fidelity neutronics and thermal hydraulics solvers PROTEUS and Nek5000 in the SHARP toolkit are coupled to perform the multi-physics simulations for HCF evaluation. The HCFs induced by cladding manufacturing tolerance, fissile content mal-distribution, wire orientation and uncertainties on the cladding, coolant, and fuel properties are evaluated for a reference core SFR design (AFR-100). The HCFs calculated with the SHARP toolkit are compared to legacy HCFs for similar reactor types. The comparison demonstrates the reduction or elimination of modeling uncertainties in the calculation of HCFs using high fidelity advanced modeling and simulation tools without the need of expensive experiments. Moreover, the reduction of the uncertainties on HCFs evaluation allows an increase in nominal parameters and safety margin, which in turn improves the economic competitiveness of the SFR.

Hot channel factor (HCF)↗

DOE OSTI2023

An integrated coupling model for solving multiscale fluid-fluid coupling problems in SAM code

In this study, an integrated coupling method has been developed for solving multiscale fluid-fluid coupling problems in plant-scale safety analysis models in SAM (System Analysis Module) code. In this method, a higher-fidelity multi-dimensional (3D) flow module is used for reactor components of complex flow features (e.g., reactor core) and a lumped parameter one-dimensional (1D) flow module for plant-scale flow loops (e.g., primary loop pipe network), respectively. In this method, the 3D fluid equation/domain and 1D fluid equation/domain are tightly coupled at the residual level and solved simultaneously using the Newton’s method to overcome the convergence issues typically seen in existing approaches like separate domain approach, where the 3D fluid equation and 1D fluid equation are solved separately. Extensive and successful code verifications and demonstrations have been performed for this newly developed method. This new modeling approach significantly simplify the work flow in developing high-fidelity plant-scale safety analysis model, e.g. for pool-type reactors and pebble-bed reactors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Reactivity-initiated accidents in two pressurized water reactor high burnup core designs

Here, this paper presents a safety analysis of two proposed core loadings for 24-month Pressurized Water Reactor (PWR) fuel cycles. This analysis focuses on reactivity-initiated accidents (RIAs) and evaluates core safety performance impacts of rod-averaged burnup limits up to 75 GWD/MTU and less than 7 % enriched UO 2 . The capabilities of Polaris, PARCS, and RELAP5-3D are leveraged to evaluate the core neutronic and thermal–hydraulic behavior for normal-operation, uncontrolled control rod withdrawal (CRW) transients, and control rod ejection (CRE) accidents. The two core designs are compared to identify features of realistic high burnup/extended enrichment core design approaches which have significant safety impact, identify experimental data needs for high-fidelity predictive modeling, and provide recommendations for future high burnup core designs. The first core design evaluated in this study was developed by Southern Nuclear Company and used an ZrB 2 Integral Fuel Burnable Absorber (IFBA) and B 4 C Wet-Annular Burnable Absorber (WABA)-based burnable poison strategy. The second core design assessed in this work used a Gd 2 O 3 -doped UO 2 burnable poison, similar to that used in boiling water reactors or French PWRs. Results indicate that fuel thermal limits are maintained for limiting CRW and hot full power (HFP) CRE transients. Cladding failure is predicted for the highest energy deposition rods in each core during limiting hot zero power (HZP) CRE accidents (where maximum radially averaged enthalpy exceeds 120 cal/g), though licensing may be permissible with a limited number of failed rods. While concerns exist regarding high critical boron concentration during steady state for the IFBA core and large plenum pressures for the gadolinia core design, the analysis demonstrates adequate safety performance during limiting RIA accident scenarios for two representative high burnup core designs. Design changes limiting plenum pressures and implementation of accident tolerant fuel (ATF) cladding features which minimize hydriding and susceptibility to pellet-cladding mechanical interaction (PCMI) are recommended for future high burnup fuel concepts. To support the technical basis for burnup limit increases, high-fidelity fuel performance models are needed to address physical effects not considered in this analysis, and high burnup irradiated fuel tests are required to extend applicability of the fuel failure limits and validate existing and future models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Improving the modeling of near-wall interphase heat transfer in porous media models of Pebble Bed Reactors

Here, this work aims to improve capabilities for modeling localized effects in porous media models of Pebble Bed Reactors. The wall-channeling effect is the primary local phenomenon of interest in a PBR, where the presence of the reflector wall disrupts the pebble packing, causing the pebbles near the wall to pack less efficiently and creating large void regions. Accurate modeling of the near-wall region is important as it will affect core bypass flow and temperature predictions. Porous media models are commonly used for design scoping and plant-level simulations of PBRs. Although these models have some capabilities to model the near-wall region, the correlations that are available in porous media codes are often inaccurate when a multi-region model is used to discretize the near-wall region. This work employs a high-to-low analysis to study the accuracy of available interphase heat transfer closures. NekRS, a spectral element computational fluid dynamics code, is used to perform Large Eddy Simulations. These LES simulation results are compared to porous media model results from the Pronghorn porous media code. The friction term of the KTA drag closure is first improved, reducing the error in the prediction of the near-wall velocity from over 50% to less than 5%. This is combined with improvements to the form term from previous works to produce a drag closure that is capable of accurately modeling the wall-channeling effect across a variety of flow conditions. The Nusselt number predictions of several heat transfer correlations are compared to the high-fidelity results where it is found that the KTA heat transfer correlation is capable of accurately predicting the local Nusselt numbers that were determined in the high-fidelity simulation. Comparison of the radial solid temperature profiles, however, reveal discrepancies between NekRS and Pronghorn. It is discovered that the implementation of the interphase heat transfer coefficient that exists in many current porous media codes is not valid when local porosities are modeled. Instead, it is suggested that the interphase heat transfer coefficient should be dependent on the local porosity, the Nusselt number, and the local solid surface-to-volume ratio. Implementation of this change produces improvement in the agreement between the results obtained by NekRS and Pronghorn while using the KTA heat transfer correlation.

interphase heat transfer↗

DOE OSTI2025

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↗