Conference Agenda

This paper presents a summary of the results from phase 1 of the Critical Heat Flux (CHF) benchmark, organized by the OECD/NEA Task Force on Artificial Intelligence (AI) and Machine Learning (ML) for Scientific Computing in Nuclear Engineering. As the first in a series of AI/ML-focused initiatives led by the Task Force, this benchmark received 48 contributions from 31 institutions across 14 countries. Phase 1 focused on CHF regression in uniformly heated vertical tubes, utilizing a large public database of 24,579 CHF data points and a separate blind database containing 560 CHF points. Most submitted models employed either neural network architectures or gradient-boosting decision tree methods. Independent evaluations of the model predictions were conducted using standard statistical metrics applied to both databases. Model overfitting, generalization, and extrapolation performance were assessed using predictions for the blind database and various slice datasets. The results indicate that most ML models significantly outperform the 2006 Groeneveld CHF lookup table by at least a factor of 2, in part due to the explicit consideration of the heated length effects. For the considered databases, tree-based methods demonstrated superior performance, including in extrapolation scenarios to large tube diameters and high mass fluxes. While model accuracy generally improved with increasing model size (in terms of number of trainable parameters), a few promising models achieved high accuracy while maintaining a reasonable size.

Critical heat flux prediction models in water-cooled systems often rely on local equilibrium quality to avoid tracking upstream history effects. Historical critical heat flux experiments with uniformly heated vertical tubes suggest that, in sufficiently long tubes, outlet quality is an adequate parameter to substitute for the combined dependence on heated length and inlet temperature.

In this study, machine learning techniques were applied to the critical heat flux database of the United States Nuclear Regulatory Commission---the foundation for the 2006 critical heat flux look-up table of Groeneveld---to assess input parameter importance and redundancy using game-theoretic Shapley values. Supported by this analysis, three machine learning models were trained for critical heat flux prediction. Each model employed the same machine learning technique and four common input parameters: pressure, mass flow, tube diameter, and heated length. The fifth parameter varied between outlet quality, inlet temperature, and inlet subcooling.

The results confirmed previous findings that replacing parameters defining outlet conditions with those describing inlet conditions improves the statistical performance of critical heat flux prediction models. Additionally, using subcooling instead of temperature enhances predictive accuracy, particularly in cases where phase change is already occurring at the inlet.

Critical Heat Flux (CHF) plays a pivotal role in ensuring reliability and safety within boiling two-phase flow systems. Despite the development of numerous CHF prediction tools using conventional empirical correlations, machine learning, and deep learning methods, the complex mechanisms underlying CHF continue to challenge the development of a unified, accurate, and robust prediction model. The complexity is further exacerbated by varying experimental dataset developed over the decades of CHF research. In response to these challenges, the present study leverages state-of-the-art AI method, including ANN, CNN, Transformer model, and transfer learning techniques. The proposed AI-based CHF prediction model, particularly the Transformer model employing self-attention mechanisms, dynamically assigns importance to different parts of the input data. The approach significantly improves the model's capability for CHF prediction. The results indicate that the predictive performance of the Transformer-based AI model exceeds that of the Look-Up Table (LUT) method and a benchmark model from the OECD-NEA based on the database encompasses 24,579 CHF data point conducted in vertical, uniformly heated, water-cooled tubes from 59 distinct sources over the past 60 years. The five-input AI model achieved the best predictive performance: Mean P/M of 1.008, Std. P/M of 0.122, RMSPE of 12.3%, MAPE of 7.22%, NRMSE of 9.91%, and Q2 of 1.26%. Moreover, the AI-based CHF prediction model's prediction behaviors are examined and compared with the LUT method. This comparison confirms the model's resistance to overfitting. Finally, by utilizing transfer learning, the model's ability to predict CHF in tubes is extended to annulus and plate geometries.

The prediction of the Critical Heat Flux in a light-water nuclear reactor core is crucial for design, operation and safety. One of the most successful method to predict the CHF is to use the Groeneveld Look-up Table. It consists of the interpolation of more than 25000 CHF experimental data in tube geometry, recently collected in a dedicated NRC database. However, its accuracy is not completely satisfactory. To better understand and predict the CHF, the OECD/NEA Expert Group on Reactor Systems Multi-Physics (EGMUP) mandated a new task force for the development of an artificial intelligence strategy for CHF regression. In this context, the present article describes a series of machine-learning regressions applied to the NRC database to predict CHF. Trying with an increasing-complexity approach, the technics of SVR, Multilayer Perceptron, Physics-Informed Neural Network, Residual Network are applied. Almost each ML-technic gives better results than the Look-Up Table. The most performing one is the Residual Network 30x64 with a RMSPE of 11%. A sensitivity to feature selection, such as mass flow rate, pressure, diameter, length of the tube, inlet temperature, and enthalpy is performed. The length of the tube is decisive to have a good accuracy even if its physical role in the prediction is debatable.

Critical heat flux (CHF) is one of the most important parameters in the design and safety analysis of water-cooled reactors. In the past, extensive experimental studies were carried out by various researchers to understand the physical processes and to provide experimental data bases for the development of prediction models. Due to some practical reasons, such as privacy issue, experimental data obtained by one researcher cannot be made available for other researchers. This led to hundreds of prediction models with narrow valid parameter ranges.

Recently, machine learning (ML) method has attracted more and more interests in the CHF prediction. The necessary condition for a successful ML-model is a large data base for training and testing. The present study proposes a new method, called data-informed continuous machine learning (DI-CML), with the key feature to generate an artificial data base, which is almost similar to the data base of the previous researchers without knowing any original experimental data points.

This paper describes briefly the idea of the DI-CML approach, which is applied to the CHF prediction with the large CHF data base provided by the OECD-NEA benchmark working group. The results achieved so far confirm the feasibility of the DI-CML approach. At the same time, challenging issues and open tasks for the future research works are pointed out, to further develop and to improve the DI-CML approach.

The use of standard deep neural networks (DNNs) have been shown to have better predictive capability than the look-up table (LUT) method to predict Critical Heat Flux values based on input parameters. However, recent work has shown that the model produces unphysical dependence of CHF on the heated length parameter when the heated length parameter is large. We show that this undesired model behaviour is a result of having extremely few data points at high heated length values. One option to resolve this issue is to remove the heated length as an input parameter entirely, but the downside to this is that it removes the possible dependence of CHF on heated length at low heated length values. Consequently, we applied a physics informed neural network (PINN) which penalizes the dependence of CHF on heated length. We scaled this penalty so that it is proportionate to the heated length value. The resultant PINN model had a CHF dependence on heated length only at smaller heated length values and was practically independent of heated length at high heated length values. The PINN model has a lower accuracy on the training data compared to the reference DNN model, which shows that the provided training data strongly implies that there is at least some dependence of CHF on heated length. We studied variants of the penalty term of PINNs and finally obtained a model which had training data accuraries between the LUT method and the reference DNN method.

Despite the tremendous efforts to predict the critical heat flux (CHF), the existing models incorporate remarkable uncertainties due to challenging phenomenological nature and the limited regression feature. An approach applying the artificial intelligence technique for the CHF prediction is expected to overcome the limitations of the conventional methodologies. However, the prediction results by deterministic neural network algorithms, which consist of massive weight/bias matrix in a forms of point values, there are intrinsic concerns in terms of the black-box characteristics, generalization, and reliability for their practical applications. To resolve the concerns inhering in the deterministic approaches, probabilistic neural network frameworks facilitating the quantification of uncertainty and interpretation of their predictions in a wide range of the flow conditions were developed in this study. Three standalone probabilistic neural networks, i.e., Bayesian neural network (BNN), Monte-Carlo dropout (MCD), and Deep ensemble (DE), were constructed to demonstrate the feasibility quantifying the uncertainty information on their CHF prediction. In addition, a series of model-informed neural network architectures, in which the skeptical regression feature in the 2006 CHF look-up table primarily predicts the CHF and neural network models minimize the residual between the actual data and predictions, were developed to improve the generalization capability. The standalone and model-informed deep ensemble frameworks exhibit the best regression and generalization performances providing the aleatoric and epistemic uncertainties in their prediction. Furthermore, influences of the individual parameters and relationships among them are successfully analyzed by application of the interpretable AI technique.

Critical Heat Flux (CHF) is a key design parameter in water-cooled reactors, directly influencing operational safety margins and economic efficiency. However, accurately predicting CHF remains challenging due to its inherent complexity and uncertainty. This study evaluates the performance of two AI/ML models—XGBoost and Multi-Layer Perceptron (MLP—using the NRC CHF database containing approximately 25,000 data points under uniform heating conditions in round tubes.

A robust database splitting methodology was employed to create interpolation and extrapolation datasets for assessing model generalization. Results demonstrated that MLP outperformed XGBoost in interpolation and single-variable extrapolation scenarios. Notably, MLP achieved prediction accuracies comparable to LUT HBM even without explicit training on these data ranges, with improved extrapolation performance driven by feature engineering that transformed the output variable to log(δX). However, MLP exhibited limitations in multi-variable extrapolation regions, with errors approximately three times higher than LUT HBM.

In conclusion, this research demonstrates that AI/ML models, particularly MLPs with optimized input-output features can serve as robust alternatives to traditional LUT methods for CHF prediction in round tube geometries. Future work will address multi-variable extrapolation challenges and extend these methodologies to more complex geometries like rod bundles for broader applicability in reactor safety analysis.

Deep generative models (DGMs) are powerful deep learning models for generating synthetic but realistic data by learning the underlying distribution of a training dataset. DGMs offer a potential solution to the challenges of data scarcity and data imbalance, which are very common in nuclear engineering as the measurement data is often obtained from costly experiments. Diffusion models (DMs), a relatively new family of DGMs, have demonstrated great potential in data augmentation especially for images and videos. In this work, we explored the effectiveness of DMs in generating scientific data for nuclear engineering applications. Our focus is on evaluating the performance of DMs in generating critical heat flux (CHF) data, using a training dataset that was originally used to develop the 2006 Groeneveld lookup table. The DM is assessed on its ability to capture the correlations between different parameters in the dataset and whether it generates physically meaningful values for each parameter. Additionally, we compared the full joint empirical cumulative distribution functions (ECDFs) of the real and synthetic datasets to evaluate the overall distributional similarity. The results show that DMs successfully generate CHF data by accurately learning the correlations between parameters without producing unphysical samples. The ECDF comparison further confirms that the synthetic data closely matches the measurement data, demonstrating the potential of DMs for data augmentation in nuclear engineering.

In this work, we compare human-developed and Artificial Intelligence (AI)-generated models for predicting Critical Heat Flux (CHF) in nuclear reactor safety analysis. This study harnesses AI and Machine Learning (ML) to develop predictive models that learn from experimental data, specifically using the extensive NRC CHF database. We compare human-developed models optimized via deep ensemble methods and Bayesian optimization with AI-agent-developed models using large language models (LLMs).

The human models use a Gaussian distribution approach for predictions, with uncertainty quantified through variance. Bayesian optimization refines hyperparameters such as learning rate and batch size, enhancing prediction accuracy measured by Root Mean Square Error (RMSE).

In contrast, an AI agent system, developed using a Large Language Model (LLM), autonomously created CHF predictive models with a neural network architecture. The LangChain suite facilitates system interactions, the execution of Python scripts, and task management through LangSmith and LangGraph, simulating a multi-agent system for an automated workflow that encompasses model development, training, and evaluation.

The performance comparison between the human and AI-developed models focuses on prediction accuracy, uncertainty quantification, and computational efficiency. The AI models demonstrated performance comparable to that of human-optimized models, showcasing their potential to automate nuclear safety analysis tasks.

This study highlights the promise of AI in enhancing nuclear reactor safety analysis. Future work should focus on integrating AI models with advanced simulation tools and expanding their application to broader safety analysis cases, including transients.

Accurate prediction of Critical Heat Flux (CHF) is crucial for the safe and efficient operation of nuclear reactors. Traditional CHF modeling methods often require extensive experimental data and are computationally expensive. In this work, we propose a novel approach to CHF prediction that combines active learning with Variational Inference (VI) in a Bayesian Feedforward Neural Network (BFNN) setting. By utilizing the uncertainty quantification inherent in Variational Inference, the most informative data points can be strategically chosen to incrementally train the model, thereby minimizing the computational cost as well as the data required for accurate predictions. VI is less expensive than other Bayesian inference methods, making it a feasible option for active learning with neural networks

BFNN begins with a small subset of training data and applies the reparameterization trick to approximate the posterior distribution of model weights. As new data is strategically selected based on uncertainty, the network updates its posterior distribution, improving accuracy while staying computationally efficient. This active learning framework prioritizes areas of high uncertainty, reducing data requirements and speeding up the learning process.

We evaluate our method on a CHF dataset, demonstrating substantial improvements in performance compared to traditional approaches. The framework is particularly suited for digital twins of nuclear reactors, where real-time updates and efficient learning from sparse data are essential. We aim to assess the performance using Mean Absolute Percentage Error (MAPE) and R² on a test set to show that our variational approach will achieve comparable accuracy and prediction quality at much lower data.

This study aims to enhance the prediction accuracy and expand the practical applicability of critical heat flux (CHF) calculations by integrating the thermal-hydraulic sub-channel analysis code COBRA-TF with machine learning techniques. A machine learning model was trained using the 2006 Groeneveld Lookup Tables released by the Nuclear Regulatory Commission (NRC), offering a comprehensive reference dataset for CHF prediction. Key input parameters required by the ML model include system pressure, mass flux of the working fluid, and critical quality, ensuring an accurate representation of thermal-hydraulic conditions. For COBRA-TF performance testing, 200 independent calculations were performed and assessed. The CHF values in these scenarios range from 400 to 4000 kW/m², providing a broad spectrum of conditions to validate the ML CHF model's performance. Comparative results show that, while all models demonstrated relatively good predictive performance, the machine learning-coupled COBRA-TF model significantly outperforms the standalone COBRA-TF predictions. This improvement is evidenced by a reduction in mean absolute error (MAE) from 161.64 to 117.58 (27% error reduction) and a decrease in root mean square error (RMSE) from 231.74 to 175.65 (24% error reduction). These findings highlight the ML-enhanced COBRA-TF model’s advanced predictive capability, presenting it as a reliable and versatile tool with potential for broader applications across diverse thermal-hydraulic environments.

In light water reactors, critical heat flux (CHF) is a thermal limit at which a boiling crisis occurs, marking the onset of departure from nucleate boiling (DNB) or dryout (DO). Several ML methods have been studied to predict CHF, but purely data-driven approaches struggle with interpretation, data limitations, and lack of physical context. This study builds on a hybrid approach that incorporates knowledge-based empirical correlations. Three ML techniques were evaluated in predicting correlation-measurement residuals and quantifying model uncertainties: deep neural network ensembles (DNNs), Bayesian neural networks (BNNs), and deep Gaussian processes (DGPs). These models were implemented using the public CHF dataset from the 2006 Groeneveld lookup table, focusing on cases of DO. Two training sizes were considered: a nominal case (80% of the original dataset) and a throttled case (0.1%). Hybrid DNN ensembles outperformed pure ML models and other methods, particularly in throttled cases, maintaining metrics below standalone correlations. They exhibited high confidence with low variability in predictions. BNNs showed similar results but with higher relative standard deviation and slightly elevated errors. Hybrid models resisted performance degradation with limited data, though errors were higher than bare correlations. DGPs had the least favorable metrics but small uncertainties in nominal cases. This methodology was then implemented in the thermal hydraulic code CTF as a first proof of implementation. Overall, these hybrid approaches were shown to offer a high degree of accuracy with low uncertainties, in addition to having a more interpretable basis compared to purely data-driven CHF modeling approaches.

The development of an accurate model to predict Critical Heat Flux (CHF) is essential for advancing nuclear power technology, where safety and efficiency are paramount. In this context, a Machine Learning (ML)-based model has been constructed based on the latest released NEA benchmark dataset on CHF. Comprehensive analyses have been conducted on feature selection, extraction, and features engineering to enhance model learning capacity. Additionally, a data augmentation process incorporating background noise was employed to increase robustness. Preliminary results indicate that this purely data-driven machine learning architecture, an 8-layer feedforward neural network with batch normalization and optimized dropout layers, outperforms traditional empirical models and lookup tables in regression tasks. The network leverages hidden data relationships for improved accuracy, suggesting that ML approaches could offer a more adaptable and precise tool for predicting the CHF, which is valuable in optimizing reactor cooling system design and operation. Future work could explore integrating physics-informed neural networks (PINNs) to blend data-driven insights with established physical laws, potentially enhancing model reliability and interpretability. Additionally, the inclusion of pretrained models could offer a powerful baseline, enabling the framework to leverage previously learned features and patterns, which may reduce computational costs and improve generalizability. Furthermore, applying explainability techniques like SHAP or LIME could provide critical insights into feature importance, helping refine feature engineering and model interpretability.

The growing demand for flexible power generation, particularly with small-scale advanced nuclear reactors integrated with other energy systems, requires load-following capabilities. These reactors must adjust to frequent power fluctuations, making advanced autonomous control systems essential for maintaining efficiency and safety. In this paper, we present a novel integrated hardware/software testbed designed to develop and evaluate advanced autonomous control strategies for small-scale advanced nuclear reactors. The testbed represents a shift from traditional nuclear power plant operations by incorporating machine learning-based digital twin technology. This allows nuclear systems to dynamically adjust their output, allowing load-following operation or integration with other renewable energy sources. The testbed comprises three main components. The first is a thermal-fluid facility with three loops and a control rod drive mechanism, simulating the operational characteristics of advanced nuclear reactors under various scenarios. The second component is the Control Process Automation (COPA) system based on the Open Process Automation Standard (O-PAS), providing a flexible control architecture using OPC-UA communications for seamless signal integration and access. The third component is a customizable control algorithm platform employing machine learning techniques such as Bayesian optimization and AI-Agent. This platform communicates with the thermal-fluid facility through the COPA system, enabling autonomous, real-time control adjustments based on varying power loads and operational conditions. Our results show that advanced autonomous control systems enhance load-following capabilities, improving adaptability and integration with renewable energy systems. This work paves the way for more resilient, efficient, and safer nuclear plant operations in an evolving energy landscape.

The eVinci™ Microreactor which is under development by Westinghouse Electric Company could bring a cost-competitive and reliable nuclear energy source to the world. The small size of the eVinci microreactor allows for transportability and rapid, on-site deployment.

Instead of a fluid-based primary coolant system normally seen in nuclear power plants, eVinci Microreactor adopts heat pipes to transfer heat from the reactor to the Primary Heat Exchanger (PHX). The heat pipe design enables passive core heat removal which eliminates numerous components needed in active coolant systems and makes the eVinci microreactor a pseudo “solid-state” reactor with minimal moving parts.

The eVinci Nuclear Test Reactor (NTR) is a nuclear test facility dedicated for eVinci microreactor’s development. The NTR will provide critical engineering information for analysis code validation to support commercial licensing. The NTR is a highly integrated design involving strong interactions among various systems and components. It can test the multidisciplinary physics governing how the nuclear power is generated, controlled, and converted to thermal energy. To support the NTR development timeline, a first-of-its-kind thermal analysis has been performed which created a full scale and integrated CFD model of fully coupled, multiple NTR thermal systems.

The high-fidelity CFD analysis notably improves the inputs being used for design completion of the NTR and helps to expediate the design progression of various NTR systems and components.

In this paper the development of the NTR integrated CFD model is presented. Results of the analysis are introduced. The potential applications of the model will be also discussed.

In advanced U.S. molten salt reactor (MSR) designs, inert gas, such as helium, can be introduced to remove fission products, but can also induce reactivity fluctuations by increasing the core void fraction. This challenge was first identified in the Molten Salt Reactor Experiment (MSRE) at Oak Ridge National Laboratory, where gas entrainment affected reactor physics. Gas-induced fluctuations remain a concern for MSR operation, necessitating accurate predictive modeling. The drift-flux model has been used extensively in thermal-hydraulic codes to predict two-phase flow dynamics, including void fraction, but rely on constitutive terms that are typically estimated using empirical correlations. These correlations are generally developed for vertical upward pipe flows in water–air systems, limiting their applicability to alternative fluids and flow orientations. This paper presents a machine learning (ML) methodology using a supervised learning approach to predict constitutive terms in the drift-flux model. Two supervised ML models were trained on computational fluid dynamics (CFD) data to predict the distribution parameter and mean local drift velocity. These models were combined to compute the mean drift velocity. The methodology was applied to vertical pipe flow simulations under varying thermal conditions. The ML predictions showed good agreement with CFD data, with most results falling within the expected time-dependent fluctuation bounds. The largest errors were observed near the gas injection region. Overall, this study demonstrates the feasibility of ML-based modeling for constitutive terms in two-phase flow and highlights the need for broader datasets and experimental validation.

Small Modular Reactors (SMRs) are garnering global attention as a transformative solution for sustainable and clean energy production. Compared to traditional large-scale nuclear power plants, SMRs face challenges such as potentially higher generation costs and limited construction and operation experience. The virtual small modular reactor (VSMR) platform has emerged as a groundbreaking approach to innovating nuclear reactor design and optimizing safety through advanced simulation and analysis. Recognizing its significance, the Korean government designated the VSMR platform project as one of the Global Top Strategic Research Working Group in June 2024, A key enabler for VSMR implementation is the acceleration of computational fluid dynamics (CFD) simulations. While state-of-the-art machine learning (ML) models have shown promise in accelerating unsteady CFD, critical gaps remain, including (1) applicability to complex geometries, (2) suitability for long-term simulations, and (3) the lack of benchmark studies targeting nuclear reactor applications. This study aims to address these gaps by constructing CFD datasets for helical coil steam generators, developing state-of-the-art ML models fitted to CFD simulations, and benchmarking their performance under the same conditions. To ensure scalability to complex geometries, three base ML algorithms were selected: deep neural operator (DeepONet), graph neural networks (GNN), and implicit neural representations (INR). Preliminary results confirm the successful training of these models within their respective algorithms and provide a comprehensive performance comparison. These benchmark studies are expected to inform future ML model development strategies and significantly advance its application in VSMR.

One of the preliminary steps in the design and safety analysis of nuclear reactor systems is the formulation of the Phenomena Identification and Ranking Table (PIRT). PIRT was introduced by the United States Nuclear Regulatory Commission as part of the Code Scaling Applicability and Uncertainty methodology. PIRT depends on experts’ inputs and insight, and its formulation is based on the joint consensus and agreement of a panel of experts. The outcome of the PIRT is significantly affected by the domain knowledge of the participating experts. Moreover, oratory skills, thinking patterns, and biases (such as confirmation bias and psychological biases) can also affect the outcome of the PIRT process.

PIRT requires systematic strategy and knowledge abstraction at different levels. Counterfactual reasoning and knowledge transfer from different disciplines are also needed depending on the application. In this work, we aim to leverage the recent developments in the area of multimodal Large Language Models (LLMs) to build an AI-driven multi-agent framework for the implementation of PIRT. Foundation models based on frontier LLMs, customized and adapted by finetuning, retrieval augmented generation and prompt engineering, are used as proxy experts to support knowledge abstraction, reasoning and information retrieval for PIRT formulation. As PIRT results are impacted by the thinking patterns and inherent biases of the participating experts, theory of mind perspective in LLM under different configurations of multi-agent collaborations are also tested and explored. The demonstration of the framework is presented using a case study on an advanced reactor application.

Nuclear reactor system involves multiple physical processes which are coupled. In general, the traditional design process depends on the linear iteration and the manual trial calculations, which faces the challenge of the “combinatorial explosion” issue caused by vast and complex problem space. In recent years, the rapid development of Artificial Intelligence (AI) technology has brought new insight into the paradigm innovation of nuclear reactor system design, which includes the following four fields: model construction and knowledge discovery, reduced-order accelerated solution, design parameter optimization, and generative AI-assisted design. Moreover, the optimization-driven design method can be considered as the key of intelligent design, which can support the realization of intelligent design at three levels: characteristic parameter, shape variations, and topological relationship. Also,the relevant application has been conducted in the reactor thermal-hydraulic field. The AI-integrated optimization design technology is expected to shift the nuclear reactor design concept towards “function-led design”, which can be extended or inherited in many fields and finally support the realization of generative and heuristic reactor design.

Conventional analysis methods for nuclear reactors are inadequate for fulfilling high-fidelity computational demands, and many of them face challenges in achieving compatibility with a variety of distinct models. Furthermore, cross-platform computational approaches may encounter problems such as low computational efficiency, data transfer distortion, and incompatibility in analysis scales. In recent years, physics-informed neural networks (PINNs) and operator learning have emerged as an effective tool for solving partial differential equations (PDEs) governing physical fields. Their potential for application in multi-physics coupling computations within nuclear reactors is particularly noteworthy. This paper introduces deep reactor multi-physics network (DeepRMNet), a novel nuclear reactor multi-physics coupling computational framework combining operator learning and other deep learning methods. DeepRMNet decreases the computational deficiencies inherent in traditional numerical calculation programs, facilitating independent, coupled, and rapid predictions of physical fields such as material temperature field, neutron flux field and coolant flow field based on their physical constraints. The framework addresses challenges including variable material parameters, integral calculations, boundary conditions, eigenvalue functions and so on. In our test model, DeepRMNet has demonstrated favorable computational outcomes and coupling efficiency compared to conventional multi-physics coupling calculations. We argue that DeepRMNet offers a promising tool for reactor multi-physics coupling calculations and digital twin construction, with advantages over numerical calculation-based digital twins.

Introducing new parameters into neural networks often requires significant time, even when existing networks based on experimental data are available. This study proposes a novel approach for the reliability assessment of the Emergency Heat Removal System (EHRS), utilizing Physics-Informed Neural Networks (PINNs), which integrate new parameters into the neural network structure. By encoding new parameters directly into an existing network, this approach avoids the need to rebuild the network from scratch, significantly improving computational efficiency. As a result, PINNs deliver faster response times and enhanced accuracy, demonstrating superior performance compared to conventional neural networks. The method was validated through practical simulations under accident conditions, showing that PINNs outperform traditional models in terms of accuracy and computational efficiency.

The main coolant pump (MCP) is a critical component in transferring the liquid metal in the primary system and removing the decay heat of the core of lead-cooled fast reactors (LFRs), suffering a corrosion possibility from the liquid metal especially in the high-temperature and high-velocity working conditions. Accordingly, the flow field in MCP should be paid more attention in the optimal designing process besides the head and efficiency which are concerned by the traditional design approach. The present study addresses the complexities of multiple, interdependent design parameters for MCPs in LFRs, aiming to develop a surrogate model to obtain real-time solutions of the flow field in the MCPs under various structural and operation conditions. Firstly, numerical simulations were carried out to simulate the flow field structure of MCP under different design parameters, as well as provide some training data. Subsequently, a surrogate model was developed based on the physics-based modeling and the small-sample data from simulations, to enable real-time internal flow field obtaining under varying operating conditions. The model employs proper orthogonal decomposition to identify the primary modes of the flow field within MCP and utilizes a physics-informed neural network to compute the modal coefficients under specific parameters, thereby achieving order reduction and reconstruction of the flow field. Future work will primarily focus on the validation of the surrogate model using the experimental platform of the LFR main pump. Based on this model, a digital twin of the MCP will be constructed to facilitate rapid intelligent design and operational control.

This study addresses the inverse problem of identifying a sharp, two-dimensional heat source within a conjugate forced convection system. The problem is formulated as a linear under-determined matrix equation, which requires a strong sparsity-promoting regularization. A deterministic-Bayesian hybrid solution framework was employed. The deterministic solution process utilized an iterative reweighted norm (IRN) algorithm to solve the Lp-Lq minimization problem. The enhanced sparsity-promoting capability is obtained through a small q value. An adaptive hyperparameter selection strategy is used to ensure solution convergence and minimize the user influence on the solution process. As a next step, Bayesian inference, with a discontinuity-adaptive Markov random field (DAMRF) prior, quantified solution uncertainty by providing a statistical distribution on the identified heat source magnitude. While the deterministic approach effectively reconstructed coarse geometries, resolving fine features was limited by sensor spacing and noise magnitude. The Bayesian method added uncertainty information on heat source strength but did not modify the (non-perfect) reconstruction shape. The combined features of automated hyperparameter tuning and uncertainty quantification enhance the robustness and reliability of the methodology, offering the potential for application in monitoring thermal-hydraulic systems.

The high-fidelity, high-order spectral element code NekRS developed at Argonne National Laboratory is designed to take full advantage of modern high-performance GPU computing architectures. It has been actively used during the past decade to perform low-to-high fidelity Computational Fluid Dynamics (CFD) simulations in both simple and complex geometries. However, due to its open-source nature and the focus on flexibility and performance over user-friendliness, the case set up in nekRS is not as intuitive or accessible as commercial CFD codes. This complexity often results in a steep learning curve for new users, and setting up cases can consume a significant amount of time. Users must manually define various simulation parameters, which can be error-prone and challenging. This work introduces a specialized chatbot designed to assist users in setting up and managing simulation cases in NekRS. By leveraging a curated database of sample cases, the chatbot guides users through problem domain definition, boundary condition setup, and solver parameter configuration. Leveraging machine learning and natural language processing techniques, the chatbot is designed to interpret user queries, deliver context-aware responses, and recommend relevant case examples customized to individual requirements. Additionally, it can troubleshoot common setup errors and recommend optimization strategies for high-performance computing platforms. The chatbot’s integration into the NekRS workflow aims to improve efficiency, reduce setup errors, and enhance accessibility, ultimately accelerating case preparation and enabling broader adoption of NekRS.

Developing a digital twin model for the reactor upper plenum and hot leg is critical for accurate and real-time monitoring of flow and temperature distributions. However, the complex internal structures and flow fields make traditional CFD methods unsuitable for real-time computation. Furthermore, the significant three-dimensional transient mixing effects cause the flow field to be highly sensitive to inlet boundary changes, while models based on limited CFD data fail to respond effectively to transient dynamics. This study proposes an efficient and high-fidelity transient digital twin modeling method combining non-intrusive model reduction with Fourier transform. CFD simulations generate full-order transient flow data under varing inlet temperature distributions. Fourier transform is used to extract mean flow fields, spatially averaged amplitudes and frequencies as key descriptors for the model. Proper orthogonal decomposition (POD) and artificial neural networks (ANNs) construct a rapid prediction model, and genetic algorithms enable inversion of inlet temperature distributions and high-fidelity reconstruction of spatial flow fields using measurement data. The results show that the digital twin model can rapidly predict the full mean flow field, average amplitude, and frequency under given inlet temperature distributions, capturing complex transient flow behaviors. It also enables inversion of inlet temperature distributions and high-fidelity reconstruction of full spatial flow fields, providing a novel pathway for reactor digitalization.

For safety studies of nuclear reactor cores, a Finite Volume thermal-hydraulic code with pourous media approach named THYC was developed by EDF to simulate steady-state flows of a two-phase mixture within the core of a nuclear reactor. The steady-state solution is obtained through a fictitious transient. Despite a relatively low individual computational time, many statepoints are considered in the safety studies, which can represent significant CPU time.

To speed up the computation, one possible objective is to reduce the number of iterations (i.e., the number of time steps) required to reach convergence. In the present work, the idea is to train a neural network to predict steady-state solutions and use this prediction to initialize the transient computation. This method allows to combine the advantages of neural network prediction, in terms of rapidity, with that of the THYC model, in terms of the physical validation of the solution.

To evaluate the potential of this method, a simplified 1D code was designed. It simulates a two-phase water-vapor flow in a heated channel. A neural network was trained to predict the solution fields from imposed boundary conditions. In this paper, we give a presentation of the methodology, the database selection process, the structure of the neural network and the optimization of the network's hyperparameters. The highlight of this work is that, by introducing spatial frequencies in the error for the optimization of the neural network, we significantly reduce the number of iterations by 50% to 80%.

To establish an efficient and high-precision model calibration method for enabling virtual entities (e.g., digital twins) to synchronously track performance variations of physical counterparts, this study focuses on the feedwater heater model. A weighted method and the artificial bee colony (ABC) optimization algorithm are integrated to develop an intelligent calibration method, along with a prediction-correction-based acceleration technique. The proposed methods are tested on feedwater heater models from typical Gen II, Gen III, and Gen IV reactors. Results demonstrate that the acceleration technique improves calibration efficiency by 60- fold. The intelligent calibration method outperforms traditional manual approaches in both efficiency and accuracy: for single-load-case calibration, it achieves 99% accuracy within 0.5 seconds; for multi-load-case calibration, 98% accuracy is attained within 1 second, and 99% accuracy within 10 minutes. Thus, the calibration method and acceleration technique developed in this study meet the requirements of high efficiency and precision for virtual entities such as digital twins.

Printed Circuit Heat Exchangers (PCHEs) are one of the promising heat exchanger candidates for advanced nuclear reactors and high-temperature applications. This study focuses on developing machine learning models to predict the friction factor (f_D) and Nusselt number (Nu) for semi-circular zigzag channels in PCHEs. A number of data samples were collected from published literature including the channel geometric characteristics and operating conditions. Various machine learning techniques were employed, involving the linear regression with non-linear transformations, kernel methods (Kernel Ridge Regression and Support Vector Regression), and Artificial Neural Networks (ANNs). The Kernel Ridge Regression (KRR) model with a polynomial kernel of degree 6 achieved good performance for Nu prediction, with an R² score above 0.99 and low percentage errors (MAPE < 4%, MPE < 20%). This developed model can contribute to optimize the heat transfer performance of PCHEs, but its application is limited to helium as the working fluid. However, the ANN model for fD prediction, while showing promising results (R² > 0.97, MAPE < 10%), exhibited high maximum percentage errors (MPE > 100%), indicating challenges in predicting the friction factors (fD) less than 0.1. This study highlights the potential of utilizing machine learning models to improve the PCHE design. However, the expanded datasets covering a wider range of geometric configurations, working fluids, and operating conditions, and a detailed analysis of the input feature distribution would be useful to improve model accuracy.

The main drawback of empirical correlations in thermal-hydraulics system codes is that the prediction capability heavily relies on the quality of the data and vastness of the experimental data employed in the study. Therefore, in a long-term research program to improve the accuracy and reliability of the safety analysis methods of nuclear reactors at Hanoi University of Science and Technology, we have developed a method of integrating data-driven and machine learning models with a computing program on the basis of the following two basic modules: (1) experimental data analysis and predictive model development based on experimental data; (2) code develoment module based on conservation equations using the finite volume element method. In this paper, we introduce preliminary results with some case studies.

Thermal stratification in large enclosures is an integral phenomenon to nuclear reactor system safety. Currently, the effective model for thermal stratification utilizes a multi-scale method that integrates 1-D system-level and 3-D CFD code, which offers thermal stratification details while supplying system-level data across various domains. Nonetheless, harmonizing two codes that operate on different spatial and temporal scales presents a significant challenge, with high-resolution CFD simulations requiring substantial computational resources. This study introduced a data-driven coarse-grid turbulence model based on local flow characteristics at a significantly coarser scale targeting improved efficiency and accuracy in reactor safety analysis concerning thermal stratification. A machine learning framework has been introduced to expedite the RANS-solving process by coupling of OpenFOAM and TensorFlow, which entails training a deep neural network with fine-grid CFD-generated data to predict turbulent eddy viscosity. The feasibility of the developed data-driven turbulence model was proven through the SUPERCAVNA experimental facility problem validation.

Flashing induced instabilities in vertical systems are one of the most common phenomena that can take place under low-pressure and low-power conditions. Typically, the vaporization process is trigged in the adiabatic riser due to the drop in the hydrostatic pressure. The physics of the flashing induced oscillations have been widely studied experimentally and numerically. However, most of the studied systems have been operated under natural circulation conditions which imposed restrictions in isolating the effect of the flow velocity in the process. Hence, the effect of the flow velocity during forced convection remains uncharted.

In this work, we study flashing induced instabilities under low pressure and low heat flux in a vertical pipe. The tests are conducted in a test loop consisting of a single horizontal heated channel followed a 5 m vertical inverted U-tube section. Sinusoidal flashing induced instabilities have been detected as the flow transitioned from stable single-phase to stable two-phase state. At low power, the oscillations are triggered by flashing and enhanced by subcooled boiling. As the power increases, boiling and flashing coexist. The oscillations amplitude and characteristics as a function of applied power are presented and explained physically.

High-Temperature Gas-cooled Reactor (HTGR) has the advantages of inherent safety and supplying high-temperature process heat. Two-phase flow instability may occur within once-through steam generator (OTSG). Two-phase flow model plays a critical role in predicting the stability boundary. There are several two-phase flow models, including homogeneous equilibrium model (HEM), drift-flux model (DFM) and two fluid model (TFM), etc. DFM is much more precise than HEM when there is a significant velocity difference between the liquid and gas phases, while TFM is very complicated. Consequently, DFM is adopted to deal with the velocity of two-phase mixture region. According to the differences in friction factor and heat transfer factor, the convective heat transfer process in the secondary side of OTSG can be divided into three regions. These three regions are the subcooled water region, the two-phase mixture region and the superheated vapor region. A frequency-domain method is adopted for stability analysis. The essence of DFM is the derivation of void fraction from gas-phase mass conservation equations. The expression of void fraction subsequently leads to the formulation of expressions for mixture density, mixture mass flux and quality of two-phase mixture region and superheated boundary. The transfer function for pressure drop and inlet velocity is derived from momentum conservation equations of three regions using integral and small perturbation method. OTSG can operate stably at the designed power level. Compared to DFM, the stability boundary of superheated evaporation systems predicted by HEM is more conservative. The superheated evaporation systems become stable when distribution parameter or drift velocity increases.

Steam Generator Tube Rupture (SGTR) accident in lead-cooled fast reactor would result in high-pressure subcooled water jetting into the high-temperature melt pool in primary circuit. The intense phase change could trigger a steam explosion, seriously threatening the structural integrity within the reactor. However, there is still a lack of the theoretical study of key physical processes involved in the initial stage of the accident, limiting the development of the safety analysis programs. The study focuses on the three components which are water, steam, and liquid lead-bismuth and establishes theoretical models of jet breakup and phase change steam expansion. The characteristics of jet instability and the variation patterns of key parameters such as breakup time, breakup length and droplet diameter are analyzed. Additionally, the pressure impact on the melt pool generated by the phase change heat transfer and steam expansion is calculated. A comparison with existing research validates the model’s rationality. Results indicate that an increase in jet velocity reduces both the breakup length and droplet diameter, while jet radius has a limited effect on the characteristic parameters of jet. Further, the steam expansion causes the temperature drop and pressure summit in the melt pool. This research provides valuable guidance for assessments of the risk of steam explosion in SGTR accident and for the development of related safety analysis models.

This work describes a transient computational code for prediction of the heat transfer regimes and the channel wall temperature during a transient heating of the channel. The modelling includes the single phase and two-phase heat transfer regimes and post Critical Heat Flux film boiling calculations. The code is based on conservation equations and correlations from literature. A transient heating experiment of water flow inside a stainless-steel tube (1 m length and 8.3 mm in diameter) was used for validation of the model. The flow velocity inside the channel was about 3 m/s, the heating power was increased up to 38 kW and the exit pressure was almost atmospheric. During the experiment, the flow rate, the channel power and the local outer wall temperature of the channel were continuously measured. In the experiment, the channel was connected in parallel to a large bypass, and during the power increase, redistribution of the flow was obtained. Based on the continuously measured values, the model uses a suitable correlation for each regime to calculate the channel thermal parameters (coolant temperature and quality, and the wall temperature). In the single-phase regime, an over-prediction of the experimentally measured wall temperature was obtained, partially due to inaccurate temperature measurement. In the two-phase regime, a good agreement was obtained between the measured temperature values, the temperature trend in time and the model. A new correlation was proposed for the post-CHF regime, based on the calculated void fraction in that zone.

This article focuses on defining an axial void fraction from axial pressure profiles in two-phase critical flow discharges made with CriticAl Flow Test facility (CRAFTY), a novel separate-effect-test facility located in LUT University in Lappeenranta, Finland. Additionally, a method to approximate the flashing delay from the same axial pressure profiles is included. Axial temperature profile is used for detecting local superheat before flashing occurs along the axis of the discharge tube. The discharge tube in CRAFTY resembles the VVER-440 steam generator tube with inner diameter of 13 mm and has length-to-diameter (L/D) ratio of 350 for the used cases. A high subcooling case (ΔTsub~60 °C, pup ~ 8 MPa) and near saturation case (ΔTsub~5 °C, pup ~ 5 MPa) is used in the article. Both cases are rerun as well for increased certainty for analysis.

The axial pressure profiles can offer insights where the continuous liquid phase disperses into non-continous mist/droplet flow. At this transition zone lies the two-phase choke plane as the pressure information from downstream cannot travel into upstream anymore. In one-phase critical flow, the flow velocity reaches Mach 1 making the pressure signal stalled, unable to travel upstream. For two-phase critical flow this analogy is not correct. The two-phase sonic velocities are order of magnitude lower than either the liquid or gas phase.

The working fluid leakage accident in a supercritical carbon dioxide (SCO₂) Brayton cycle system of a reactor will result in the depressurization and discharge of SCO2 from the tube into the atmospheric environment, accompanied by critical flow phenomena of gas-liquid two-phase, which seriously threaten the heat transfer characteristics of the reactor core. The gas-liquid two-phase flow characteristics within the tube determine the size of the critical flow rate at the break. To accurately predict the critical flow rate, a testing technique must be developed to quantitatively measure the gas void fraction of the gas-liquid two-phase flow. In this paper, a phase state measurement method for gas-liquid two-phase flow during the depressurization and flash evaporation process of low conductivity SCO₂ is developed based on a wire mesh sensor assembly. Combined with the established SCO₂ depressurization and discharge experimental setup, the effects of factors such as temperature and pressure on the gas-liquid two-phase flow characteristics within the tube during the SCO₂ depressurization and flash evaporation process are explored. The distribution patterns of gas and liquid phases (bubble size, shape, and velocity, etc.) are analyzed to obtain typical flow patterns of the gas-liquid two-phase flow. Finally, based on the experimental results and key dimensionless numbers, a flow pattern map is plotted, and a prediction model for flow pattern transition boundaries is proposed. This lays the foundation for the study of critical flow phenomena.

The use of molten salt reactors (MSRs) presents a promising avenue for achieving energy independence and reducing reliance on fossil fuels. A key challenge in MSR development is enhancing heat exchanger efficiency while minimizing pressure drop and operational costs.
This study experimentally investigates the thermal-hydraulic performance of additively manufactured helically rifled tubing, a passive heat transfer enhancement (HTE) method that promotes flow mixing through centrifugal forces. The pressure drop characteristics of helically rifled tubes with different twist pitches (y = 3 and y= 6) were measured and compared to plain tubing, alongside computational fluid dynamics (CFD) simulations. Using Buckingham-Pi analysis, nine dimensionless groups were identified to characterize flow behavior and thermal performance. Preliminary experimental results indicate that existing helical rifling correlations significantly under predict frictional losses by 10%, highlighting the need for refined modeling approaches. A strong agreement was observed between simulations performed by Vulcanoff et al. and the experimental friction factor data for the helical rifling at the same geometric parameters (y=3). Geometric variation of the twist pitch from y=3 to y=6 suggests the dependence of the nondimensional parameter y/d_min diminishes at sufficiently high Reynolds numbers. Computational findings by Vulcanoff et al. suggest that helically rifled tubes improve heat transfer efficiency. Investigations are ongoing into the Nusselt number and thermal performance factor. This work provides a foundation for optimizing helical rifling geometries in MSRs, contributing to advancing advanced nuclear energy systems.

A new phenomenon, namely tangential oscillation of thermal stratification, can cause periodic temperature changes on the pipe wall and leads to material damage of thermal fatigue. At North China Electrical Power University, an experimental facility has been constructed and operated to investigate the initiation mechanism of the tangential oscillation of thermal stratification at pipeline elbows. In this study, experiments have been performed with variations of elbow-radiuses and inlet flow temperature. Results show temperature increase at the intrados side of the elbows, which indicates an angular shift of the thermal stratification at the elbow due to the centrifugal force. Thermocouples downstream of the elbow have captured temperature changes in the near-wall flow. The elbow-radius shows a clear influence on the locations of the high temperature region in the thermal stratification. In addition, temperature fluctuations have been calculated based on the measurement data. The location with the maximum temperature fluctuation can be found in the place, where the mean temperature reaches the maximum. Moreover, frequency spectra of the temperature data do not show any significant peak. Combined with the calculation results of Richardson-number, it can be understood that the thermal stratification is not stabile enough to keep the tangential oscillation downstream of the elbow. It leads back to the turbulent mixing enhancement at the elbow, which is clearly increased with decrease of elbow-radius. However, decrease of the elbow-radius leads to increase of the temperature fluctuation in the near-wall flow, which indicates a higher potential of thermal fatigue.

The Small Modular Reactors (SMRs), as an emerging nuclear energy technology, hold great promise for gradually replacing coal-fired power plants in the future due to its flexibility, high safety, and economic advantages, thereby contributing to the decarbonization of energy systems. In a domestically developed integrated SMR in China, the steam generator adopts a helical heat transfer tube design, with the outlet steam being saturated steam. Considering the compact size and high-level power density characteristics of SMRs, it is necessary to design an efficient and compact moisture separation component, to ensure that the quality of steam entering the turbine meets the required standards. This study conducted cold-state experiments and theoretical analyses on a designed swirl vane gas-liquid separator. Under conditions with different drainage step heights, the critical separation boundaries for both low-wetness and high-wetness scenarios were determined. For steady-state conditions, based on experimental data of the separation efficiency and pressure drop of guide vanes with different profile variation patterns, a predictive correlation was proposed. For unsteady conditions, a predictive model was developed to describe the transition from swirl annular flow to churn flow, and a flow regime map was constructed by integrating extensive experimental data with previous studies. These findings provide important theoretical support and experimental evidence for the optimization and performance enhancement of SMR steam-water separation systems.

Globally, advanced reactors are adopting helical tube steam generators to reduce volume compared to traditional U-tube designs in large light water reactors. These steam generators feature a once-through operation and a shared header for multiple heat transfer tubes but often encounter issues associated with two-phase flow instabilities such as Density Wave Oscillations (DWO). Such instabilities are critical in boiling water reactor cores and pressurized water reactor steam generators, causing significant flow and pressure oscillations, which can potentially degrade the integrity of a system.

This study aims to address this gap by comparing experimental results on two-phase flow instabilities in helical tubes from previous research works with the predictions obtained from Korean nuclear safety codes MARS-KS and SPACE. The objective is to assess whether the current helical tube thermo-hydraulic models in these codes adequately reflect observed physical behaviors or if there are significant discrepancies that require model enhancements. This analysis intends to provide insights into the dynamics of two-phase flow in helical steam generators and help improve the predictive accuracy of safety codes, thereby enhancing the reliability and safety of advanced nuclear reactor.

In nuclear power systems, the insertion of a throttling device at the inlet of the heat exchange tubes in steam generators enhances the flow resistance within the single-phase flow region of the tubes, thereby mitigating the risk of flow instability within the steam generator. This study proposed a novel gear-type throttling device designed specifically for steam generators. Various gear-type throttling prototypes with differing gear heights were designed and fabricated for experiment and numerical analysis .Through a systematic experimental testing and numerical simulations, the resistance characteristics of the throttling device with different structural parameters were obtained in a wide range of flowing conditions, . The results reveal that the resistance coefficient of the innovative gear-type throttling device can fit for different operational requirements in steam generators. The resistance coefficient exhibits significant sensitivity in gear height and width. Additionally, the resistance coefficient for throttling devices with varying gear heights remains relatively stable across different Reynolds numbers.A mathematical relationship was established to correlate multiple structural parameters and the resistance coefficient. This work is valuable for the design optimization and validation of next-generation steam generators in the nuclear energy system.

The function of reactor core residual heat removal system is to extract heat from the core and reactor coolant systems during the shutdown of the power plant. According to the principle of simplified configuration, improving safety and economy, possible reactor core residual heat removal systems are studied, and the configuration of recommended optimization solution is fixed.The optimized configuration is based on two completely independent series; This configuration can be used for core residual heat removal function after connecting the primary circuit, and for containment spray function. the analysis of single failure and system capacity for this optimized configuration are performed. The analysis of single meets the safety requirements, except that the exemption criterion is used for the mode of residual heat removal, which can make sure the nuclear power plant is brought to the safe state.The capacity of key equipment including pumps and heat exchanger is analyzed,which is in making full use of the equipment of original some reactor, considering the equipment design, the shutdown time of plant, the design limit of containment and layout space comprehensively, the actual shutdown time and the pressure and temperature of containment are calculated, finally the capacity of equipment can meet the mode of residual heat removal and the mode of containment spray. The optimized reactor core residual heat removal scheme, not only improves the safety of the power plant, but also improves the economics, which has the great significance to the subsequent improvement of the market competitiveness of power plants.

Due in great part to the earthquake and ensuing tsunami, the Great East Japan Earthquake of 2011 seriously damaged the Fukushima Daiichi Nuclear Power Plant and resulted in a major accident. The malfunction of the cooling water level measuring system was one element causing this accident. Differential pressure gauge monitoring of the reactor pressure vessel (RPV) water level was used at the time. But the temperature of the reference side piping surged greatly during the severe accident, which caused the water on the reference surface to evaporate. It is not possible to precisely identify the real drop in water level since this evaporation lowered the differential pressure between the water level inside the reactor containment vessel and the reference piping.

In order to find a solution to this issue, we are working on a new water level meter that is capable of functioning even in severe accidents. Through the utilization of an ultrasonic transducer (TDX), this apparatus enables real-time measurements to be taken from outside the containment vessel of the reactor. The concept of measurement originates from the disparity in the reflection coefficients of ultrasonic waves that travel through metal that is in contact with water as opposed to air.

The results of experiments measuring the reflection coefficients of metal walls in contact with air and water using a small water level measuring device are reported in this work. Comparisons with hypothetical values computed with the ultrasonic wave propagation simulator SWAN21 verified the validity of the experimental results.

Digital twins are becoming essential in advanced nuclear reactor technology for real-time monitoring, predictive maintenance, and optimization. They help maximize uptime, predict failures, and enable cost-effective testing. However, most digital twins rely on deterministic models that fail to capture uncertainties in sensor data and modeling. While Bayesian models can quantify uncertainty, they require significant computational resources and do not scale well, making them impractical for real-time applications. This work presents the application of variational Bayesian last layer (VBLL) augmented recurrent neural networks (RNNs) to produce uncertainty-aware models while mitigating the issue of computational cost through variational inference. Variational inference allows the neural network to assign parameters to probability distributions rather than point values, and thus permits sampling of predictions to measure the uncertainty of the model. We apply both deterministic Long Short-Term Memory (LSTM) and VBLL LSTM to time-series sensor data collected from the High Temperature Test Facility (HTTF) at Oregon State University and train the models using data from a depressurized conduction cooldown (DCC) experiment. The deterministic LSTM and VBLL LSTM both achieve impressive predictive capabilities with ( R^2 >) 0.99 when forecasting solid and fluid temperature sensor profiles. Despite a small increase in computational cost, the VBLL LSTM is a promising direction for incorporating model uncertainty for real-time applications.

In recent years, image processing methods for gas-liquid two-phase flow, including computer vision techniques, bubble segmentation, and tracking algorithms, have seen significant development due to high efficiency and accuracy. Nevertheless, obtaining extensive, high-quality two-phase flow images continues to be a time-intensive and costly process. To address this issue, a generative AI architecture called bubbly flow generative adversarial networks (BF-GAN) is developed, designed to generate realistic and high-quality bubbly flow images through physically conditioned inputs, namely superficial gas and liquid velocities.

Initially, 105 sets of two-phase flow experiments under varying conditions are conducted to collect 278,000 bubbly flow images with physical labels of and as training data. A multi-scale loss function of GAN is then developed, incorporating mismatch loss and feature loss to further enhance the generative performance of BF-GAN. The BF-GAN’s results indicate that it has surpassed conventional GAN in generative AI indicators, establishing for the first time a quantitative benchmark in the bubbly flow domain. In terms of image correspondence, BF-GAN and the experimental images exhibit good agreement. Key physical parameters of bubbly flow images generated by the BF-GAN, including void fraction, aspect ratio, Sauter mean diameter, and interfacial area concentration, are extracted and compared with those from experimental images. This comparison validates the accuracy of BF-GAN's two-phase flow parameters with errors ranging between 2.3% and 16.6%. The comparative analysis demonstrates that the BF-GAN is capable of generating realistic and high-quality bubbly flow images for any given and within the research scope, and these images align with physical properties.

Boiling is a process in which heat from a submerged surface is removed through bubble vaporization. Consequently, the primary mode of thermal transport is governed by bubble dynamics. Therefore, one way to extract bubble data for estimating cooling performance is through the use of side-view shadowgraphs. However, linking bubble dynamics to other parameters remains challenging due to irregular bubble shapes and varied visualization setups. Even with neural networks, manual data annotation for initial model training demands significant time and effort, further complicated by instrumental differences such as varying lighting conditions. To overcome such facility limitations, this study utilizes an augmentation method to generate a synthetic bubble swarm dataset by assembling individual synthetic bubbles tailored to the experimental setup. This dataset is used to further train a Mask R-CNN for segmentation tasks to automate accurate bubble region predictions. After training, the model successfully identified bubble boundaries in high-speed camera images, extracted size distributions, and derived bubble trajectories under different heat fluxes. This demonstrates the feasibility of training models on augmented images to accurately segment bubble regions from experiments and to provide reasonable estimations of the sizes and trajectories of bubbles. This method serves as an alternative to traditional boiling heat transfer measurements, especially in setups where direct measurement of bubble statistics is limited or under conditions where conventional methods face material and instrumental constraints.

Heat transfer on boiling surfaces is a transient multi-dimensional process. Gaining an understanding of the dynamics of bubbles on such surfaces is a fundamental step toward an accurate heat partitioning models, which can be employed as best estimate models for LWR analysis. A number of traditional techniques have been developed for measuring and interpreting bubble dynamics, but they are time and computation demanding. Machine learning and computer vision have shown great potential to reduce this data interpretation burden in local feature detection such as bubble dry spot. However, a holistic segmentation of boiling features on heat transfer surfaces has not yet been demonstrated. In this study, we employed a U-NET based convolution neural network to conduct a global segmentation of a boiling surface, which allows for the classification of the dry areas, micro-sublayers, and single-phase areas from high-speed infrared images. For training the model, we obtained the ground truth partitioning from HSV phase detection images. After training, the U-NET model can predict the dry areas, micro-sublayers, and single-phase areas directly from the IR image. This successful demonstration paves the way for further research on predicting heat transfer performance based on IR images.

Thermal-hydraulic simulations of Once-Through Steam Generators (OTSGs) are crucial for operational optimization, real-time monitoring, and the development of digital twins. However, repeated and extensive simulations are computationally expensive. Model Order Reduction (MOR) techniques, such as Proper Orthogonal Decomposition (POD), offer an alternative approach to enhance computational efficiency while maintaining acceptable accuracy. Although POD is widely used for capturing dominant patterns in high-dimensional systems, its robustness within the parameter domain is limited due to its reliance on snapshots and potential inadequacy in representing highly nonlinear or complex systems. In this paper, we propose a novel framework for Parametric POD that integrates Long Short-Term Memory (LSTM) networks to enhance the accuracy and robustness of reduced-order models, and applied it to construct a Reduced-Order Model (ROM) of OTSGs. The framework leverages high-dimensional snapshots generated under varying reactor power levels, reducing them to a few dominant POD modes. Given the time-dependent nature of both the parameter (reactor power) and POD mode coefficients, LSTM is employed to approximate the mapping function between them. The resulting parametric ROM is verified for rapid estimation of primary and secondary side fluid temperatures in OTSGs using RELAP5 simulation results. The ROM achieves a maximum instantaneous fluid temperature deviation of less than 2.5 K (0.5% relative error) and reduces computation time to 1% of that required by RELAP5. This novel approach demonstrates significant potential to address computational challenges posed by numerous simulation inquiries, thereby enhancing the efficiency and applicability of OTSG modeling.

The demand for nuclear energy is rapidly increasing and, as such, the deployment of new reactors must be accelerated. Microreactors are being designed to provide electricity and heating for remote applications. Operating the microreactors in these applications will take advantage of remote and autonomous systems, which will be based on digital twin simulations. The development and validation of real-time digital twins is therefore a necessary component for microreactor deployment. The intended coupling of the digital twin control system to hardware provides opportunities to leverage methods that combine hardware and software. Hardware-in-the-Loop (HIL) testing can be integrated with a digital twin, in which an experimental subsystem will replace a region of the digital twin. As-built components can be tested directly, reducing time spent in intermediate modeling steps, and can be used for validation by providing real data for a portion of the reactor.

This paper will present the experimental setup, model development, and results of HIL testing combined with a digital twin of a microreactor cooled with heat pipes. The experimental subsystem will provide thermal hydraulic data of a hexagonal unit cell made up of a heat pipe and the surrounding region. The design of the experimental subsystem and the digital twin will be optimized to demonstrate the method and will not represent an existing microreactor. Validation of the digital twin will be performed by replacing subregions of the core with the experimental subsystem in the digital twin and comparing the results with those from the digital twin alone.

Heat pipes are passive two-phase heat transfer devices utilized in applications such as core cooling for nuclear microreactors, high-efficiency heat exchangers, and other advanced energy systems. The two-phase flow and heat transfer dynamics within heat pipes are often highly complex, particularly during transients and under vertical operating conditions. The present work develops a comprehensive heat pipe transient experimental database for a vertical heat pipe of approximately 2 meters in length using water as the working fluid, with the reported data including internal measurements of operating pressures, pressure drops, liquid film temperatures, evaporator wall temperatures, and vapor core temperatures. In particular, vapor core temperatures were obtained using a fiber optic distributed temperature sensor running along the entire heat pipe length. The database includes power input and condenser coolant flow rate transients to enable the evaluation of the heat pipe’s response to changes in both evaporator and condenser conditions. Experiments were conducted for two different wick types: annulus-screen and wrapped-screen. Important phenomena identified include vapor generation in the annulus and the presence of a subcooled liquid plug near the condenser endcap. The data obtained can be readily used for verification and validation of numerical modeling tools under development for heat pipe microreactor analysis.

Heat pipe cooled reactor (HPCR) is in the spotlight as one of the advanced reactor with the advantages of high inherent safety and compactness. HPCR was originally designed for application in space, low-efficiency power conversion systems were applied. Recently, the HPCR system for power generation has been actively studied with high efficiency power conversion system such as supercritical CO2 Brayton cycle. However, due to compact size of HPCR, there was a problem that the size of the intermediate heat exchanger that satisfies the core power increased. In this regard, we suggested new design of compact intermediate heat exchanger based on printed circuit heat exchanger (PCHE). The heat exchanger consisted of “heat pipe layers” in which heat pipes were inserted and “cooling channel layers” in which the cooling channels were machined. The structural integrity of each layer was evaluated based on ASME standard, and flow uniformity was evaluated through CFD. Based on the temperature distributions of the heater for heat pipe simulation and the heat exchanger body which were measure with fiber optic sensor (FOS), thermal contact resistance and overall thermal resistance of heat exchanger were measured. Through this study, the transportability of the designed heat exchanger was evaluated, and the possibility of comprehensive analysis through integration with the heat pipe and the reactor core model was confirmed.

Heat pipe-cooled microreactors (HPMRs) utilize alkali metal heat pipes for efficient and passive heat transfer. Simulating startup and shutdown of HPMRs require accurate modeling of transient heat pipe behavior. In this study, a 2-D transient heat pipe analysis code, SNUHTP, was developed with a melting/solidification model to simulate frozen startup and phase change effects. Transient verification against an analytical lumped model and steady-state validation using sodium heat pipe experiments showed good agreement in normal operation range of sodium heat pipe. The melting/solidification model was verified with a 1-D Stefan problem, and transient validation using the SAFE-30 heat pipe experiment showed delay in temperature rise due to latent heat effects. The results demonstrate that SNUHTP effectively predicts transient and steady-state heat pipe behavior, supporting its application to HPMR analysis.

The heat pipe-cooled reactor offers numerous advantages, including a compact design, high power density, exceptional reliability, and intrinsic safety features, making it a promising candidate for future mobile power generation systems. This reactor employs a solid-core design where high-temperature heat pipes establish a direct link between the reactor core and the energy conversion system, creating a compact and modular configuration. Despite its advantages, the intricate multiphysics interactions within the system pose considerable challenges for comprehensive analysis. To tackle this issue, this study proposes a multiphysics coupling analysis framework tailored for heat pipe-cooled reactors, developed within the OpenFOAM platform. The framework integrates neutron physics, core thermal transfer, heat pipe dynamics, and thermoelectric conversion models. Its accuracy is verified against experimental data from the KRUSTY space heat pipe reactor's ground-based nuclear testing. A complete system simulation of KRUSTY is then conducted, emphasizing the interplay of multiphysics phenomena under nuclear thermal power conditions.

The paper outlines ongoing research in a national funded joint project, applying machine learning methods to predict late-phase phenomena observed during severe accidents. The aim is to produce resource-efficient simulations that improve the understanding and predictive capabilities for these late-phase phenomena. Emphasis is on the long-term coolability of debris beds in the vessel, its remelting and possible relocation in the cavity as ex-vessel debris bed. For this purpose, a machine learning model is intended to be integrated to a PSS inhouse version of AC² program package, developed by Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) gGmbH, to make the complex calculation of heat transfer and dryout heat flux more efficient.
The aim is to develop an artificial neural network as a machine learning model. Several different network types are initially developed for this purpose, for example a physically informed neural network (PINN). As work progresses, these models should become more complex and be able to provide a fast and reliable prediction of the debris bed coolability for as many different boundary conditions as possible. According to the current status, the tested network types are already able to produce good preliminary results. They are able to predict the dryout heating power, selected as the output variable, to a good approximation. The training data are generated using the COCOMO-3D detail code from the Institute for Nuclear Energy and Energy Systems (IKE) at the University of Stuttgart.

The recent developments in data-driven methods have paved the way to new methodologies to provide accurate state reconstruction of engineering systems; nuclear reactors represent particularly challenging applications for this task due to the complexity of the strongly coupled physics involved and the extremely harsh and hostile environments, especially for new technologies such as Generation-IV reactors. Data-driven techniques can combine different sources of information, including computational proxy models and local noisy measurements on the system, to robustly estimate the state. This work leverages the novel Shallow Recurrent Decoder architecture to infer the entire state vector (including neutron fluxes, precursors concentrations, temperature, pressure and velocity) of a reactor from three out-of-core time-series neutron flux measurements alone. In particular, this work extends the standard architecture to treat parametric time-series data, ensuring the possibility of investigating different accidental scenarios and showing the capabilities of this approach to provide an accurate state estimation in various operating conditions. This paper considers as a test case the Molten Salt Fast Reactor, a Generation-IV reactor concept, characterised by strong coupling between the neutronics and the thermal hydraulics due to the liquid nature of the fuel. The promising results of this work are further strengthened by the possibility of quantifying the uncertainty associated with the state estimation, due to the considerably low training cost. The accurate reconstruction of every characteristic field in real-time makes this approach suitable for monitoring and control purposes in the framework of a reactor digital twin.

In the event of a severe accident in a nuclear power plant, accident prediction using artificial intelligence (AI) has gained attention as a promising Accident Management Support Tool (AMST). A notable approach is the development of surrogate models for accelerated accident prediction through deep learning-based supervised learning. Such models alleviate the computational complexity of severe accident analysis codes by training on data generated from the codes, significantly reducing the computational costs.

However, surrogate models often present structural challenges, leading to low-resolution predictions and increased uncertainty, hindering effective decision-making for operators. This issue contradicts the essential requirements for AMST reliability. Structural issues arise from low temporal resolution and information loss during data preprocessing for training, limiting the model's accuracy due to cumulative computational errors in time series forecasting. Consequently, using surrogate models to predict thermal-hydraulic variables with refined time resolution during accident progression can yield unreliable results.

To address these challenges, this study aims to develop an auxiliary surrogate model to support accident prediction by identifying time varying patterns in the accident prediction data. This model is designed to predict the onset time and amplitude of physical variations, enhancing the accuracy and reliability of surrogate-based predictions during severe accidents.

This work is performed in the frame of the EU-funded project ASSAS (Artificial intelligence for Simulation of Severe AccidentS), which aims at developing a basic-principles severe accident simulator for a generic PWR-1300MW, by replacing models from ASTEC (severe accident code developed by IRSN) with machine-learning surrogate models. PSI’s tasks address essentially the CESAR module (thermal-hydraulic solver) in the primary and secondary circuits. This paper proposes a surrogate model able to reproduce the thermal-hydraulic behaviour of the reactor cooling system (RCS) during the early phase of a Station Blackout (SBO), i.e., until hydrogen generation, with a significant speed-up factor.

A suitable training dataset must be generated. A base case scenario is considered, involving a SBO without any safety measures until the onset of core oxidation. From this base case, various calculations are performed by depressurizing remotely the primary circuit at different times, followed by the recovery of emergency water injection, also at different times. From these ASTEC calculations only the variables needed for the surrogate model development are extracted. These include state variables for each control volume within the RCS domain, boundary conditions, and additional variables that provide information about the overall evolution of the accident and are useful for Machine Learning. The surrogate model is expected to compute each time-step, like ASTEC does, while also accounting for user decisions interactively during the accident simulation. The Machine Learning methods considered in this work are based on artificial neural networks, and more specifically recurrent neural networks, which are commonly used for time-series.

Small Modular Reactors (SMRs) are gaining increasing attention due to their enhanced safety features, flexibility, and scalability. Ensuring timely and accurate assessments of break sizes during break accidents is crucial for maintaining the safe and reliable operation of SMRs. However, current methods for evaluating break sizes mainly rely on the personal judgment of operators, which often fail to meet the speed and accuracy requirements in high-risk, time-sensitive situations. This limitation can hinder effective decision-making and risk management. Recent advancements in artificial intelligence (AI) have accelerated the development of data-driven methods for break size prediction, demonstrating significant potential for improving operational reliability. Machine learning models, particularly those with interpretability features, can provide real-time, data-driven predictions of break sizes, offering a faster and more accurate alternative to traditional methods. Furthermore, the interpretability of these models can foster greater trust in AI systems, particularly in safety-critical environments such as nuclear reactors. This study investigates Direct Vessel Injection (DVI) break accidents, utilizing explainable artificial intelligence (XAI) and hyperparameter optimization techniques to develop predictive models for break size. The results demonstrate that these models enable rapid and accurate prediction of DVI break sizes based on actual operational parameters. The findings of this research provide valuable insights for developing break size prediction models base on SMRs, contributing to improved safety and operational efficiency.

This research focuses on the safety evaluation of a design extension condition involving multiple steam generator tube rupture (MSGTR) scenarios. A series of operator actions are proposed to mitigate the accident, including depressurization, auxiliary spray operation, and steam generator blowdown. The efficacy of these actions is evaluated under various uncertainties using the best estimate plus uncertainty (BEPU) approach through RELAP5/DAKOTA coupling. The generated ensemble of system responses is used to develop an AI-based prediction model. Tools of explainable artificial intelligence, specifically a combination of attention mechanisms, gradient-based attribution, and parameter interaction analysis, are implemented to examine the model's decision-making process. This framework reveals phase-specific patterns and dynamic shifts in parameter relevance as the accident progresses through different stages–from initial break flow and pressure response, through various operator interventions, to final stabilization. The analysis quantifies the coupling between primary and secondary systems, particularly during critical phases of depressurization and cooldown, while demonstrating the model's adherence to established thermal-hydraulic principles. The result highlights the AI model's general alignment with established thermal-hydraulic principles, suggesting its potential for integration into nuclear safety management, provided its transparency and interpretability continue to be rigorously validated.

The cold trap of a liquid sodium purification system maintains concentration of impurities below an acceptable level to prevent deterioration of sodium fast reactor (SFR) components. A cold trap is typically monitored with multiple thermal hydraulic sensors. Timely detection of incipient anomalies in cold trap operation is important for efficient SFR operation and maintenance. Previous work developed a deep learning long short-term memory (LSTM) autoencoder for loss-of-coolant type anomaly detection in cold trap of the liquid sodium purification system at the Mechanisms Engineering Test Loop (METL) thermal hydraulic facility at Argonne National Laboratory. We found that relative delays in response time for multi-modal sensor monitoring systems affect anomaly detection time and certainty. We have developed a novel machine learning (ML) method to estimate sensor response delays in detection of signals related to anomaly events, and to use this information to augment the data to improve detection time. The anomaly signal is detected by establishing a threshold using the density distribution of the loss for the training data. Relative sensor delays were determined during testing by finding the times when the loss of each sensor rises above their respective threshold values. The time delays were then used for synchronization of the data. The augmented data was fed back to the LSTM autoencoder to detect the anomaly using sensor-averaged loss. A parametric study was conducted, in which the anomaly was gradually reduced until the signal-to-noise ratios (SNRs) approached unity. Results indicate that synchronization improves anomaly detection, especially for lower SNR anomalies.

The High Temperature Test Facility is an integral test facility located at Oregon State University, modeled after the Modular High Temperature Gas Reactor. It is designed to provide benchmark data for phenomena such as lower plenum mixing, depressurized conduction cooldown, pressurized conduction cooldown, and normal operational conditions. Numerous sensors are installed throughout the facility to measure variables like temperature, pressure, and mass flowrate, with data recorded at 2 Hz frequency. Several methods are under study for field reconstruction in online monitoring applications. One method that is promising with sequential data, but not well-studied in nuclear engineering is Recurrent Neural Networks (RNN). This study focuses on developing data-driven RNN models,specifically gated recurrent units (GRU) and long short-term memory (LSTM), to predict sensor outputs at various locations within HTTF. The models are trained on data from one subset of sensors and applied to predict the outputs of similar sensors - this was done 400 times, with 200 permutations of LSTM and GRU models each. Mean absolute error (MAE) was used as a performance metric to evaluate the predictions. It was found that 71 of the sensors can be used to train LSTM and GRU models, which can then predict the data of the other 71 sensors very well. The MAE of the predictions ranged from 0.28°C to 4.41°C for all models and permutations. Generally, the LSTM models have a higher accuracy relative to the GRU models with overall (average MAE value of 0.721°C for LSTM as opposed to 0.788°C for GRU).

The Shallow Recurrent Decoder networks are a novel paradigm recently introduced for state estimation, combining sparse observations with high-dimensional model data. This architecture features important advantages compared to standard data-driven methods including: the ability to use only three sensors (even randomly selected) for reconstructing the entire dynamics of a physical system; the ability to train on compressed data spanned by a reduced basis; the ability to measure a single field variable (easy to measure) and reconstruct coupled spatio-temporal fields that are not observable and minimal hyper-parameter tuning. This approach has been verified on different test cases within different fields including nuclear reactors, even though an application to a real experimental facility, adopting the employment of in-situ observed quantities, is missing. This work aims to fill this gap by applying the Shallow Recurrent Decoder architecture to the DYNASTY facility, built at Politecnico di Milano, which studies the natural circulation established by internally heated fluids for Generation IV applications, especially in the case of Circulating Fuel reactors. The RELAP5 code is used to generate the high-fidelity data, and temperature measurements extracted by the facility are used as input for the state estimation. The results of this work will provide a validation of the Shallow Recurrent Decoder architecture to engineering systems, showing the capabilities of this approach to provide and accurate state estimation.

Advanced reactor and fuel designs could be crucial in decarbonizing our energy portfolio. However, their development and implementation come with specific challenges, often related to the novelty of such designs, that must be addressed to ensure that such systems operate safely, reliably, and economically viable. Strategies like the preventive maintenance of such systems can support achieving these goals by potentially reducing the maintenance and operation costs while preserving the safety and reliability of such systems.

However, the preventive maintenance of nuclear reactors may rely on real-time monitoring of some physical properties of such systems, which can be challenging. Many probe designs cannot withstand the reactor's extreme conditions (e.g., temperature, radiation). In this context, physics-informed Convolutional Neural Networks (CNNs) offer a promising non-intrusive alternative for reconstructing physical fields, such as temperature and stress distributions, using minimal sensor data. This work presents the integration of machine-learning-aided tools with coupled thermomechanical and thermal-hydraulic simulations to assess the behavior of fuel rods during both steady-state and accident scenarios.

To train our CNN, we leveraged the capabilities of the MOOSE framework to build computational models representing the fuel rod thermomechanical behavior during steady-state operation and its response during a transient situation, such as an accident condition. These models were used to build the necessary datasets to train and test the prediction performed by the CNN architecture. These efforts provide a foundation for real-time monitoring and enhanced safety assessments of advanced reactor designs, addressing challenges in operational efficiency and accident management.