Accurate prediction of liquid droplet entrainment during post-critical heat flux conditions is a high priority for enhancing the predictive capability of nuclear reactor thermal-hydraulic codes and enabling power uprates in existing light water reactors. However, the highly transient and complex nature of two-phase flow during reflood makes theoretical modeling of mass and heat transport processes extremely challenging. Consequently, most existing entrainment models rely on empirical correlations, which often tend to report predictions with large uncertainties. This paper presents the development of a physics-informed machine learning (PIML) model designed to improve the accuracy, reliability, and efficiency of entrainment predictions. Leveraging a comprehensive dataset from the U.S. Nuclear Regulatory Commission/Pennsylvania State University Rod Bundle Heat Transfer reflood experiments, both pure data-driven machine learning and PIML approaches were developed and systematically evaluated. Results show that both modeling strategies accurately capture overall entrainment behavior and significantly outperform conventional empirical models in terms of predictive accuracy. Furthermore, the impact of incorporating the newly developed PIML models into TRACE reflood transient simulations has been explored, demonstrating notable improvements in simulation fidelity.

Heat pipes are advanced passive thermal management devices that utilize phase change and capillary action to achieve efficient heat transfer. However, due to the complexity of the phenomena coupled in heat pipes, including capillary, phase change, turbulence, and compressibility effects, there are high uncertainties in the predictability of their operational regimes and performance. This PIRT exercise, conducted as a collaborative effort involving the Department of Energy (DOE) Microreactor Program (MRP), the Nuclear Regulatory Commission (NRC), and university partners systematically identifies, reviews, and prioritizes critical phenomena affecting the operation of heat pipes based on their importance and knowledge levels. Additional analyses and discussions are provided for phenomena with high importance and low knowledge, such as wick de-wetting, critical heat flux, contact angles, and pressure dynamics. The discussions include recognizing challenges and proposing future research directions for both modeling/simulation and experimental efforts. Additionally, the article addresses phenomena with medium importance and low knowledge that could impact heat pipe operation during non-normal or transient conditions, including frozen startup, laminar to turbulent transition, geyser boiling, wick priming, under-filling conditions, surface roughness of the wick, non-condensable gases trapped in the wick, and the timescales of startup and shutdown. This comprehensive evaluation serves as a valuable resource for guiding future research and development efforts, supporting the successful integration of heat pipes into nuclear reactors, and contributing to the advancement of heat pipe technologies in safety-critical industries.

This paper evaluates the performance of the U.S. Nuclear Regulatory Commission’s (NRC’s) thermal hydraulic code TRAC/RELAP Advanced Computational Engine (TRACE) against experimental reflood data from the NRC/Pennsylvania State University (NRC/PSU) Rod Bundle Heat Transfer (RBHT) test facility, as an integral step in verification of code accuracy. This paper is an extension of the NURETH-20 conference paper by the first author (Garrett et al., 2023) that has been recommended for consideration and submission to Nuclear Engineering and Design. An international study on reflood thermal-hydraulics, sponsored by the Nuclear Energy Agency (NEA) Working Group on Accident Management and Analysis (WGAMA), was conducted with data collected in the NRC/PSU RBHT test facility, located at the Pennsylvania State University. A series of 16 benchmark tests were conducted, with conditions covering a carefully selected range of oscillatory, variable stepped and constant rate reflood injection velocities. These unique conditions are useful for code validation and model improvement. These 16 tests were segmented into 11 open tests, followed by five blind tests. This paper covers the five blind tests as the 11 open tests were covered by Garrett et al. at the NURETH-19 conference (Garrett et al., 2021).For TRACE code benchmarking, a numerical model with the same dimensions as the RBHT facility was used. The initial and boundary conditions for this model were taken from experimental measurements. Many of the test conditions were chosen to examine sensitivities to important parameters, such as reflood liquid subcooling, reflood rate, and system pressure. The wide range of test conditions served to test the code and provide insight to its strengths and potential areas of improvement. These novel experiments were vital in this effort.Simulations were made for five reflood tests and comparisons between predicted and measured results were made for the transient cladding temperatures, vapor temperature, bundle liquid mass fraction, carryover fraction, and steam exhaust fraction. The comparison presented in this paper has provided useful insight into code improvements. Studies to more accurately model reflood phenomena are currently underway as a result of the work presented in this paper.

During reflood conditions, spacer grids affect the complex flow dynamics inside the reactor core. They can breakup the dispersed droplets, thereby significantly reducing their diameters. This process enhances local heat and mass interfacial transfer, consequently reducing the peak cladding temperature (PCT). Therefore, accurately predicting droplet transport and size within a reactor core is very important for reactor safety analysis. Recently, the US. NRC TRACE code has been modified by extending its governing equations to incorporate a three-field approach that captures the dynamic behavior of droplet entrainment, transport, and their interactions with structures within the reactor core. The new TRACE (v5.0 patch 8) three-field framework incorporates droplet models accounting for entrainment from liquid pools, liquid films on vertical surfaces, and droplet breakup. This paper focuses on the influence of the spacer grid droplet breakup model on the behavior of reactor core during reflood transient. The selected droplet breakup model effectively captures the enhancement in interfacial heat transfer observed in experimental data. We evaluate the influence of the droplet breakup model on the three-field version of TRACE by comparing it to recent Rod Bundle Heat Transfer (RBHT) experiments. These experiments had previously indicated that TRACE tended to overpredict the PCT for various initial and boundary conditions. Subsequently, we conducted a detailed comparison between TRACE v5.0 patch 7 and the three-field TRACE (v5.0 patch 8) with and without the spacer grid droplet breakup model. Our findings demonstrate a significant improvement in predictive accuracy with the new breakup model compared to the base capability of TRACE v5.0 patch 7. This improvement results in more accurate predictions of PCTs and quenching times for the assessed conditions.

Reflood thermal hydraulics remains a difficult and complex subject, and understanding the physical phenomena that occur during a reflood transient is important to nuclear safety. The Organisation for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) Rod Bundle Heat Transfer (RBHT) project was designed to provide unique experimental data for code assessment and model development. Participants, which came from 21 international organizations, used analysis codes including APROS, ATHLET, CATHARE, CTF, MARS, RELAP5, TRACE, and SPACE to simulate the tests performed in the RBHT facility.The experimental campaign carried out within the OECD/NEA RBHT project produced data for a total of 16 reflood tests conducted in two test series. An "open" test series consisted of 11 experiments, and a "blind" test series consisted of 5 experiments. In the blind tests, only the initial and boundary conditions were provided to participants prior to simulation of those experiments. Reflood rates ranged from 0.5 to 15 cm/s, thus producing data applicable to dispersed flow film boiling and inverted annular flow film boiling. Inlet subcooling ranged from 2.8 to 80 K. Tests with variable reflood rates and oscillatory reflood rates were included in the test matrix. This paper describes the project and presents a summary of major experimental and analytical findings.

As part of the Organisation for Economic Co-operation and Development/Nuclear Energy Agency Rod Bundle Heat Transfer (RBHT) project, an experimental study was performed to investigate the entrained droplet sizes and velocities in a rod bundle under reflood conditions. Experimental results were obtained from the U.S. Nuclear Regulatory Commission/The Pennsylvania State University RBHT test facility using advanced dual laser measurement systems that allow for the simultaneous measurement of droplet behaviors at two axial locations during reflood transients. The RBHT facility is highly instrumented and contains a 7x7 electrically heated bundle with dimensions matching those in commercial pressurized water reactors. The combination of the measurement capabilities of the RBHT facility and the choice of appropriate experimental conditions allows for the measurement of unique droplet size and velocity distributions under different transient reflood conditions.

The accurate prediction of the fluid flow mass and the heat transfer process as well as the system response during reflood transients has long been a critical and challenging issue for reactor system safety analyses. Accurate characterization of the flow and energy transport can also significantly facilitate the various system/component design and optimization tasks. In the current study based on the U.S. Nuclear Regulatory Commission/Pennsylvania State University Rod Bundle Heat Transfer (RBHT) reflood experimental data, a comprehensive uncertainty analysis framework is developed using DAKOTA. The developed framework is used to perform an in-depth reflood model validation and verification for the subchannel analysis code COBRA-TF. In the meantime, the artificial intelligence (AI)-based machine learning (ML) model for rod cladding temperature prediction during reflood is also developed and evaluated using the current framework. Key input parametric effects for reflood thermal-hydraulic prediction include the system pressure, inlet liquid temperature/enthalpy, inlet mass flow rate, and average bundle power input. The figure of merit under consideration is the peak cladding temperature variations. It is found in the current study that, while further model improvement is needed, COBRA-TF can predict the correct parametric trends when compared with the RBHT data. On the other hand, it is challenging for the pure AI-based ML models to correctly reflect the parametric trends. Suggestions for future ML model development are provided in the end.

Accurately predicting post-critical heat flux (CHF) heat transfer is an important but challenging task in water-cooled reactor design and safety analysis. Although numerous heat transfer correlations have been developed to predict post-CHF heat transfer, these correlations are only applicable to relatively narrow ranges of flow conditions due to the complex physical nature of the post-CHF heat transfer regimes. In this paper, a large quantity of experimental data is collected and summarized from the literature for steady-state subcooled and low-quality film boiling regimes with water as the working fluid in vertical tubular test sections. A low-quality water film boiling (LWFB) database is consolidated with a total of 22,813 experimental data points, which cover a wide flow range of the system pressure from 0.1 to 9.0 MPa, mass flux from 25 to 2750 kg/m(2) s, and inlet subcooling from 1 to 70 degrees C. Two machine learning (ML) models, based on random forest (RF) and gradient boosted decision tree (GBDT), are trained and validated to predict wall temperatures in post-CHF flow regimes. The trained ML models demonstrate significantly improved accuracies compared to conventional empirical correlations. To further evaluate the performance of these two ML models from a statistical perspective, three criteria are investigated and three metrics are calculated to quantitatively assess the accuracy of these two ML models. For the full LWFB database, the root-mean-square errors between the measured and predicted wall temperatures by the GBDT and RF models are 5.7% and 6.2%, respectively, confirming the accuracy of the two ML models.

A correlation is developed for the liquid carryover fraction during both constant and oscillatory reflood with application to nuclear power accidents. The correlation, semi-empirical in nature, is based on extensive experiments in a 7 x 7 rod bundle array at the Nuclear Regulatory Commission/Pennsylvania State University Rod Bundle Heat Transfer (NRC/PSU RBHT) facility. Liquid carryover and entrainment can significantly impact quench behavior and maximum cladding temperatures during a postulated accident; therefore, accurate predictions of these phenomena are critical. The parameters associated with the stability at the liquid-vapor interface, and hence the liquid entrainment and subsequent carryover are established. These parameters provide the basic form of the correlation with experimental data from the NRC/PSU RBHT facility to determine the model coefficients. Using a weighted least-squares method that minimizes the error between modeled and experimental carryover fraction, we implemented a genetic algorithm to identify the parameters of this correlation. The proposed model is compared with experimental data and predictions from the NRC's TRACE code and lies within 20% error margin.

This work investigates the separate effects of liquid subcooling, substrate material, and surface micro-structure on the film boiling characteristics. A quenching facility was constructed to conduct vertical quenching experiments using rods with various substrate materials and surface morphologies. The surface morphology is characterized using field emission scanning electron microscopy (FESEM). Stainless steel, zirconium, and Inconel-600 rods are used with a diameter of 9.5 mm that simulates the size of fuel rods in commercial nuclear reactors. Other Inconel-600 rods with different porosity percentages are used to study the effect of fouling on the quenching behavior. The surface temperature and wall heat flux at the surface are deducted from the temperatures measured by the thermocouples embedded inside the rods using an inverse heat conduction code, from which the heat transfer coefficient and Nusselt number are calculated. The data are used to develop a generalized heat transfer correlations that includes the effects of liquid subcooling and substrate materials. It predicted the data within +/- 40% error band. The results also suggest that the heat transfer coefficient increases gradually as the sample cools down and in higher subcooled pools. Moreover, the variation in the substrate material shows a significant effect on the heat transfer characteristics. However, the surface micro-structure impact on the film boiling regime is negligible.

An experimental and numerical study was performed to investigate the effects of pressure and constant vs oscillatory flooding rates on the two-phase flow and heat transfer behavior of a rod bundle under reflood transient conditions. Experimental results were obtained from the NRC/PSU Rod Bundle Heat Transfer (RBHT) test facility from various test cases covering a range of system pressures with light water as the working coolant. For each pressure case, two experiments were performed, one for a constant flow rate, and one for an oscillating flow rate about the constant flow rate. The RBHT test facility, which contains 49 vertical, 3.66 m (12 ft) long test rods (four unheated corner rods and 45 heated rods) with Inconel 600 cladding in a 7 x 7 geometry, having the rod diameters, rod pitches and spacer grids comparable to those in commercial PWRs, was specifically designed to obtain fundamental flow and heat transfer data during reflood transients. The thermal-hydraulic code TRAC/RELAP Advanced Computational Engine (TRACE) was used in this study by performing simulations with the same geometry and operating conditions as the RBHT facility for each experiment. Results of the TRACE simulations were compared to the experimental data obtained in the RBHT tests. It was found that the trends on the pressure effects for constant and oscilatory flows on the thermal-hydraulic behavior of the rod bundle (i.e., the two-phase flow and heat transfer behavior of the rod bundle during reflood transients) predicted by the TRACE model agree well with the RBHT data. This comparison of results has also assisted in other studies to investigate numerical discrepancies currently underway.

Accurate simulation of reflood transients of a reactor core is one of the top priorities for nuclear reactor thermal–hydraulic and safety analysis. An in-depth understanding of the two-phase flow and heat transfer process during reflooding can provide extremely useful information on the design and analysis of the various safety systems as well as on the development of numerical analysis tools. In the current paper, the status of the reflood transients in the past several decades is overviewed and discussed in detail, in the hope to provide a roadmap for future relevant research. Following an introduction of the current topic, the phenomenological aspects related to reflood are discussed first. Then, studies on the two-phase flow thermal–hydraulic non-equilibrium are reviewed and evaluated critically. The flow channel pressure drop as well as the spacer grid effect constitute important parts of reflood thermal–hydraulic and safety analysis, and various studies on these topics are discussed. Another important consideration during reflood transients is the liquid droplet behavior since it affects the rod bundle thermal response. In addition, the current paper also identifies the several limitations and the need for future research work on reflood thermal hydraulics.

The year 2020 marks the 40th anniversary of the first International Topical Meeting on Nuclear Reactor Thermal-hydraulics (NURETH-1). Hosted by the thermal-hydraulics division (THD) of the American Nuclear Society, the NURETH series is the premier topical meeting exclusively dedicated to advances in nuclear reactor thermal-hydraulics. In this article, which opens a special issue dedicated to the 40th anniversary of NURETH-1, we provide a brief history of the NURETH series. We dedicate the bulk of the manuscript to a summary of the progress in thermal-hydraulics in the past 40 years, highlighting, key contributions presented in the NURETH series of conferences. We emphasize that, given the size and complexity of the field examined, this cannot be considered a comprehensive review. However, We hope the reader will find this article useful to reflect on the advances in the past 40 years and the current state of the art.

Accurate prediction of the reflood transients during LOCA has long been a challenging task. One reason for this is the substantial cost incurred to perform large-scale reflood tests, which are formidable in experimental expenditure and intensive in technology as well as program management. Another reason preventing a comprehensive understanding of reflood transients is the high-level complexity involved in the two-phase flow mass and heat transfer processes, which makes the measurement extremely difficult and inefficient. The situation has been significantly improved with the design and operation of the Nuclear Regulatory Commission (NRC)/Pennsylvania State University (PSU) Rod Bundle Heat Transfer (RBHT) test facility. A variety of advanced instrumentations were developed and used at this facility and very high-resolution data has been obtained, especially for the liquid droplet field. In the current study taking advantage of the unique NRC/PSU RBHT data, an extensive and comprehensive code evaluation and validation is carried out using the thermal-hydraulic sub-channel analysis code COBRA-TF. The system parametric effects investigated include: the system pressure, inlet liquid subcooling temperature, inlet flooding rate and rod bundle power. A variety of thermal-hydraulic quantities predicted by the numerical code are evaluated including: the quench front propagation, cladding, spacer grid and vapor temperature variations, two-phase pressure drop, liquid droplet velocity and coolant void fraction. In addition, the prediction errors are presented for each of the quantities in great detail in order to have a comprehensive understanding of the code performance. In general, COBRA-TF agrees relatively well with the experimental data in terms of the overall quench front propagation, only predicting slightly earlier quench. However, under low inlet subcooling and high flooding rate conditions, significant discrepancies are observed. The comparison with rod bundle thermal-hydraulic parameters indicates that COBRA-TF is able to predict the cladding temperature before quench well within a 15% range. The spacer grid and vapor temperature predictions are within 20% error. While the overall droplet velocity prediction is found to be within 30% error, COBRA-TF is able to capture the decreasing trend for droplet velocity during reflood. In addition, the prediction of the dispersed flow film boiling void fraction shows that the code always under-predicts the void fraction. While the most prediction discrepancy is found to be the two-phase flow pressure drop after quench, which involves more than 50% under-prediction for the bulk liquid boiling regime. The present study clarifies the effect of different system parameters on the various two-phase flow quantities during reflood. The results obtained provide answers for many existing code modeling issues and thus can be instructive and useful for future model development and code upgrading. (C) 2020 Elsevier Ltd. All rights reserved.